The right format of the number is (45^8)(88^5).
Answer:
There are 8 zeros
Step-by-step explanation:
Using the unique factorization of integers theorem, we can break any integer down into the product of prime integers.
So breaking it down we have;
(45^8) = (3 x 3 x 5)^(8)
(88^5) = (2 x 2 x 2 x 11)^(5)
Now, if we put it back together as separate factors, we'll get;
(3^(16)) x (5^(8) ) x (2^(15)) x (11^(5))
Now let's find the number of zeroes by figuring out how many factors of 10 (which equals 2 x 5) we can make. Thus, we can make 8 factors of 10 so it looks like;
(3^(16)) x (2^(7)) x (11^(5)) x (10^(8))
Thus, we can see that there will be 8 zeros as the end is (10^(8))
The number of trailing zeros in the product of 457 and 885 is determined by the factors of 10 (2 and 5) in these numbers. In this specific case, there are no trailing zeros. This also applies in scientific notation - the number of significant figures after the decimal in scientific notation indicates the quantity of zeros at the end of the number.
Explanation:To determine the number of zeroes at the end of the number 457 · 885, consider the factors in the product. Each zero at the end of a number results from a factor of 10, which contains a factor of 2 and a factor of 5. Looking at the numbers 457 and 885, we notice that neither has a factor of 5, therefore there are no trailing zeroes in the product of 457 and 885.
This approach also applies to the scientific notation. The number of significant figures after the decimal in the scientific notation of a number corresponds to the quantity of zeros at the end of it. In such cases, leading zeros are not significant and only serve as placeholders to locate the decimal point. For instance, in the case of the number 1.300 × 10³, the scientific notation shows that there are three significant figures after the decimal and therefore, three zeros at the end of the number.
Overall, understanding how to find the number of trailing zeroes in a product, such as 457 · 885, without actual computation involves a knowledge of the factors of the numbers being multiplied and the principles of significant figures in scientific notation.
Learn more about Trailing Zeros here:https://brainly.com/question/31609866
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Is the sequence {an} bounded above by a number? If yes, what number? Enter a number or enter DNE. Is the sequence {an} bounded below by a number? If yes, what number? Enter a number or enter DNE. Select all that apply: The sequence {an} is A. unbounded. B. bounded above. C. bounded. D. bounded below.
Answer:
The sequence {an} is A. unbounded
Step-by-step explanation:
The sequence {an} is unbounded.
we say a sequence is bounded if and only it is bounded both above and it is also bounded below. clearly the sequence {an} is an unbounded sequence.
The sequence {an} is bounded if there is a number M>0 such that |an|≤M for every positive n.Every unbounded sequence is divergent
The sequence{an}. is an unbounded sequence, because it has no a finite upper bound
There is a 70 percent chance that an airline passenger will check bags. In the next 16 passengers that check in for their flight at Denver International Airport (a) Find the probability that all will check bags. (Round your answer to 4 decimal places.) P(X
Answer:
a) [tex]P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.00332[/tex]
b) [tex]P(X<10) = 1-P(X\geq 10) = 1- [P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)][/tex]
And we can find the individual probabilities like this:
[tex]P(X=10)=(16C10)(0.7)^{10} (1-0.7)^{16-10}=0.1649[/tex]
[tex]P(X=11)=(16C11)(0.7)^{11} (1-0.7)^{16-11}=0.2099[/tex]
[tex]P(X=12)=(16C12)(0.7)^{12} (1-0.7)^{16-12}=0.2040[/tex]
[tex]P(X=13)=(16C13)(0.7)^{13} (1-0.7)^{16-13}=0.1465[/tex]
[tex]P(X=14)=(16C14)(0.7)^{14} (1-0.7)^{16-14}=0.0732[/tex]
[tex]P(X=15)=(16C15)(0.7)^{15} (1-0.7)^{16-15}=0.0228[/tex]
[tex]P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.0033[/tex]
And replacing we got:
[tex]P(X<10) = 1-P(X\geq 10) = 1- [P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)] = 1-0.825=0.175 [/tex]
c) [tex] P(x \geq 10) = P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)[/tex]
And replacing we got 0.825
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=17, p=0.7)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
And we want to find this probability:
[tex]P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.00332[/tex]
Part b fewer than 10 will check bags
We want this probability:
[tex] P(X<10) [/tex]
We can use the complement rule and we have:
[tex]P(X<10) = 1-P(X\geq 10) = 1- [P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)][/tex]
And we can find the individual probabilities like this:
[tex]P(X=10)=(16C10)(0.7)^{10} (1-0.7)^{16-10}=0.1649[/tex]
[tex]P(X=11)=(16C11)(0.7)^{11} (1-0.7)^{16-11}=0.2099[/tex]
[tex]P(X=12)=(16C12)(0.7)^{12} (1-0.7)^{16-12}=0.2040[/tex]
[tex]P(X=13)=(16C13)(0.7)^{13} (1-0.7)^{16-13}=0.1465[/tex]
[tex]P(X=14)=(16C14)(0.7)^{14} (1-0.7)^{16-14}=0.0732[/tex]
[tex]P(X=15)=(16C15)(0.7)^{15} (1-0.7)^{16-15}=0.0228[/tex]
[tex]P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.0033[/tex]
And replacing we got:
[tex]P(X<10) = 1-P(X\geq 10) = 1- [P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)] = 1-0.825=0.175 [/tex]
Part c at least 10 bags
We can find this probability like this:
[tex] P(x \geq 10) = P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)[/tex]
And replacing we got 0.825
The probability that all 16 passengers will check their bags given a 70% chance for each passenger is found using a binomial distribution, resulting in a probability of 0.0047 when rounded to four decimal places.
Explanation:The question involves calculating the probability of passengers checking bags in a binomial distribution context. Since each passenger is an independent trial and has a 70 percent chance or probability (p=0.70) of checking bags, this indeed constitutes a binomial problem. Here, success is defined as a passenger checking their bags.
To find the probability that all 16 passengers will check their bags, we need to consider the binomial probability formula for exactly 'k' successes in 'n' trials: P(X = k) = (n choose k) * p^k * (1-p)^(n-k). For this case, every passenger checks their bags, meaning 'k' is 16 and 'n' is also 16.
The formula simplifies in this scenario to P(X = 16) = 0.70^16, as the combination of 16 choose 16 is 1. Following the calculation:
P(X = 16) = 0.70^16 = 0.0047 (rounded to four decimal places).
10) Thirty-seven percent of the American population has blood type O+. What is the probability that at least four of the next five Americans tested will have blood type O+?
Answer:
0.06597
Step-by-step explanation:
Given that thirty-seven percent of the American population has blood type O+
Five Americans are tested for blood group.
Assuming these five Americans are not related, we can say that each person is independent of the other to have O+ blood group.
Also probability of any one having this blood group = p = 0.37
So X no of Americans out of five who were having this blood group is binomial with p =0.37 and n =5
Required probability
=The probability that at least four of the next five Americans tested will have blood type O+
= [tex]P(X\geq 4)\\= P(X=4)+P(x=5)\\= 5C4 (0.37)^4 (1-0.37) + 5C5 (0.37)^5\\= 0.06597[/tex]
Answer:
Required probability = 0.066
Step-by-step explanation:
We are given that Thirty-seven percent of the American population has blood type O+.
Firstly, the binomial probability is given by;
[tex]P(X=r) =\binom{n}{r}p^{r}(1-p)^{n-r} for x = 0,1,2,3,....[/tex]
where, n = number of trails(samples) taken = 5 Americans
r = number of successes = at least four
p = probability of success and success in our question is % of
the American population having blood type O+ , i.e. 37%.
Let X = Number of people tested having blood type O+
So, X ~ [tex]Binom(n=5,p=0.37)[/tex]
So, probability that at least four of the next five Americans tested will have blood type O+ = P(X >= 4)
P(X >= 4) = P(X = 4) + P(X = 5)
= [tex]\binom{5}{4}0.37^{4}(1-0.37)^{5-4} + \binom{5}{5}0.37^{5}(1-0.37)^{5-5}[/tex]
= [tex]5*0.37^{4}*0.63^{1} +1*0.37^{5}*1[/tex] = 0.066.
4. Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admitted to this university
Answer:
Yes, Tom must be admitted to this university.
Step-by-step explanation:
We are given that the scores on national test are normally distributed with a mean of 500 and a standard deviation of 100.
Also, we are provided with the condition that Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test.
Let, X = score in national test, so X ~ N([tex]\mu=500 , \sigma^{2} = 100^{2}[/tex])
The standard normal z distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
Now, z score of probability that tom scores 585 is;
Z = [tex]\frac{585-500}{100}[/tex] = 0.85
Now, proportion of students scoring below 85% marks is given by;
P(Z < 0.85) = 0.80234
This shows that Tom scored 80.23% of the students who took test while he just have to score more than 70%.
So, it means that Tom must be admitted to this university.
Given the following: zA = 20 - 3x zB = 18 - 2y, where z is marginal utility per dollar spent, x is the amount spent on product A, and y is the amount spent on product B. Assume that the consumer has $14 to spend on A and B—that is: x + y = $14.
Instructions: Enter your answers as whole numbers.
a. How is the $14 best allocated between A and B?
$ on A.
$ on B.
b. How much utility will the marginal dollar yield? utils.
Answer:
a. x= $6, y= $8
b. z= $2
Step-by-step explanation:
at equilibrium, the marginal utility per dollar spent will be equal i.e
zA=zB
20-3x=18-2y
upon simplification, we arrive at
[tex]x=\frac{2}{3} (1+y)\\[/tex]......equation 1
since the total amount to spend is $14, then
x+y=14
x=14-y..............equation 2
if we solve equation 1 and equation 2 simultaneously
[tex]14-y=\frac{2}{3} (1+y)\\42-3y=2+2y\\5y=40\\y=8[/tex]
Hence for y=8
x=14-y=14-8
x=6
Hence the amount spent on Product A is $6 and the amount spent on product B is $8
b. to determine the amount of utility the marginal dollar will yield, we substitute the values of y and x into the the given equation,
zA=20-3x=20-3(6)
zA=20-18=2
zB=18-2y=18-2(8)
zB=18-16=2
hence the amount spent on the marginal utility is $2
Mary got 85% correct on her math test. Mary missed 6 questions. How many total questions were on her math final?
Answer: there were 40 questions on her math final.
Step-by-step explanation:
Let x represent the total number of questions in the math test.
Mary got 85% correct on her math test. This means that the number of questions that she got right is
85/100 × x = 0.85 × x = 0.85x
This also means that the number of questions that she missed would be
x - 0.85x = 0.15x
Therefore, if Mary missed 6 questions, it means that
0.15x = 6
Dividing both sides of the equation by 0.15, it becomes
0.15x/0.15 = 6/0.15
x = 40
According to some internet research, 85.2% of adult Americans have some form of medical insurance, and 75.9% of adult Americans have some form of dental insurance. If 89.4% of adult Americans have either medical or dental insurance, then what is the probability that a randomly selected adult American with have both medical and dental insurance
Answer:
0.717 or 71.7%
Step-by-step explanation:
P(M) = 0.852
P(D) = 0.759
P(M or D) = 0.894
The probability that a randomly selected American has both medical and dental insurance is given by the probability of having medical insurance, added to the probability of having dental insurance, minus the probability of having either insurance:
[tex]P(M\ and\ D) = P(M)+P(D)-P(M\ or\ D)\\P(M\ and\ D) =0.852+0.759-0.894\\P(M\ and\ D) =0.717=71.7\%[/tex]
The probability is 0.717 or 71.7%.
The result is a 71.7% probability of an adult American having both insurances.
The question revolves around finding the probability of a randomly selected adult American having both medical and dental insurance. To calculate this, we use the principle of inclusion-exclusion. According to the problem statement, the percentage of adults with medical insurance is 85.2%, with dental insurance is 75.9%, and with either of the two is 89.4%. The principle of inclusion-exclusion states that the probability of the union of two events (medical or dental insurance) is equal to the sum of the probabilities of each event minus the probability of their intersection (both insurances).
Let's denote the following:
P(Medical) = the probability of having medical insurance = 85.2%P(Dental) = the probability of having dental insurance = 75.9%P(Medical or Dental) = the probability of having either medical or dental insurance = 89.4%P(Medical and Dental) = the probability of having both medical and dental insuranceUsing the principle of inclusion-exclusion, we find P(Medical and Dental) as follows:
P(Medical and Dental) = P(Medical) + P(Dental) - P(Medical or Dental)
P(Medical and Dental) = 85.2% + 75.9% - 89.4%
P(Medical and Dental) = 160.1% - 89.4%
P(Medical and Dental) = 71.7%
Therefore, the probability that a randomly selected adult American will have both medical and dental insurance is 71.7%.
For example, the auctioneer has estimated that the likelihood that the second bidder will bid $2,000,000 is 90%. a) Use a decision tree to determine the optimal decision strategy for which bid to accept. b) Draw a risk profile for the optimal decision.
Answer:
See explanation to get answer.
Step-by-step explanation:
Solution
As per the data and information given in the question, there are three Bidders, one each on Monday, Tuesday and Wednesday.
Bidder 1 may bid on Monday either for $2,000,000 or $3,000,000 with probabilities 0.5 each
Therefore expected pay-off for Bidder 1 is $2,500,000 (2,000,000*.52 + 3,000,000*.5)
Bidder 2 may bid on Tuesday either for $2,000,000 with probability 0.9 or $4,000,000 with probability 0.1
Therefore expected pay-off for Bidder 2 is $2,200,000 (2,000,000*.9 + 4,000,000*.1)
Bidder 3 may bid on Wednesday either for $1,000,000 with probability 0.7 or for $4,000,000 with probability 0.3
Therefore expected pay-off for Bidder 3 is $1,900,000 (1,000,000*.7 + 4,000,000*.3)
Based on the comparison of the above mentioned calculations for the expected pay-off for the bidders, it is recommended that the optimal decision strategy among the bidders is to go for Bidder 1 with highest expected pay-off of $2,500,000 and accept the bid of Bidder 1.
Risk profile for the optimal solution is $2,000,000 with probability 0.5 and $3,000,000 with probability 0.5
Bid may be for $4,000,000 with probability of 0.1 by Bidder 2 or with probability 0.3 by Bidder 3
A rabbit population doubles every 6 weeks. There are currently 9 rabbits in a restricted area. If represents the time, in weeks, and () is the population of rabbits, about how many rabbits will there be in 112 days? Round to the nearest whole number.
The rabbit population doubles every 6 weeks. After converting 112 days to 16 weeks, we calculate the growth over 2.67 six-week periods to find that there will be approximately 61 rabbits after 112 days.
Explanation:The rabbits population grows exponentially and doubles every 6 weeks. To determine the population after a certain time, we would typically use a formula like P(t) = P0 (2^(t/T)), where P(t) is the population at time t, P0 is the initial population, 2 represents the doubling factor, and T is the time period for doubling in the same units as t. However, we need to convert days to weeks since the doubling time is given in weeks. There are 7 days in a week, so 112 days is equal to 112/7 = 16 weeks.
Following this, we calculate the number of periods in 16 weeks by dividing 16 weeks by 6 (the number of weeks it takes for the population to double). This gives us 16/6 = approximately 2.67. The population after 16 weeks would be P(16) = 9 (2^(2.67)). Simplifying with a calculator, we find the population to be about 61 rabbits, rounding to the nearest whole number.
The states of Ohio, Iowa, and Idaho are often confused, probably because the names sound so similar. Each year, the State Tourism Directors of these three states drive to a meeting in one of the state capitals to discuss strategies for attracting tourists to their states so that the states will become better known. The location of the meeting is selected at random from the three state capitals. The shortest highway distance from Boise, Idaho to Columbus, Ohio passes through Des Moines, Iowa. The highway distance from Boise to Des Moines is 1350 miles, and the distance from Des Moines to Columbus is 650 miles. Let d1 represent the driving distance from Columbus to the meeting, with d2 and d3 representing the distances from Des Moines and Boise, respectively
a. Find the probability distribution of d1 and display it in a table.
b. What is the expected value of d1?
c. What is the value of the standard deviation of d1?
d. Consider the probability distributions of d2 and d3. Is either probability distribution the same as the probability distribution of d1? Justify your answer.
e. Define a new random variable t = d1 + d2. Find the probability distribution of t.
Answer:
The driving distance for meeting at the three centres can be written as
d1=columbus
d2=Des moines
d3=Boise
The distance from des moines to columbus to 650 miles
from Boise to des moines is 1350
Therefore the distance from columbus to Boise
if the meeting is holding at columbus
0+650+1350=2000
Pr(columbus)=1/3
Pr(Des moines)=1/3
Pr(Boise)=1/3
a. Probability distribution is
capital c DM B
di 0 650 2000
Pr(di) 1/3 1/3 1/3
b. Expected value is multiplication of the probability of d1 and the outcome
E(x)=0*1/3=0
c. find the variance of d1 first
Var=(x-E(x))^2*Pr(d1)
Var=(0-0)^2*1/3
Var=0
the square root of var=standard deviation
S.D=0
d. probability distribution of d2 and d3 is equal to the probability distribution of d1 , because they all have a probability of 1/3(the likelihood that an event will occur is 1/3 for the meeting \location
e. d1=0
d2=650
d1+d2=650
pr(d1+d2)=1/3+1/3=2/3
Pr(d1+d2) will be on the vertical axis, while d1+d2 will be plotted on the horizontal axis of the probability distribution graph
Step-by-step explanation:
The driving distance for meeting at the three centres can be written as
d1=columbus
d2=Des moines
d3=Boise
The distance from des moines to columbus to 650 miles
from Boise to des moines is 1350
Therefore the distance from columbus to Boise
if the meeting is holding at columbus
0+650+1350=2000
Pr(columbus)=1/3
Pr(Des moines)=1/3
Pr(Boise)=1/3
a. Probability distribution is
capital c DM B
di 0 650 2000
Pr(di) 1/3 1/3 1/3
b. Expected value is multiplication of the probability of d1 and the outcome
E(x)=0*1/3=0
c. find the variance of d1 first
Var=(x-E(x))^2*Pr(d1)
Var=(0-0)^2*1/3
Var=0
the square root of var=standard deviation
S.D=0
d. probability distribution of d2 and d3 is equal to the probability distribution of d1 , because they all have a probability of 1/3(the likelihood that an event will occur is 1/3 for the meeting \location
e. d1=0
d2=650
d1+d2=650
pr(d1+d2)=1/3+1/3=2/3
Pr(d1+d2) will be on the vertical axis, while d1+d2 will be plotted on the horizontal axis of the probability distribution graph
In order to complete the service line information on claims when units of measure are involved insurance math is required. For example this is the HCPCS description for an injection of the drug Eloxatin: J9263 oxaliplatain, 0.5 mg if the physician provided 50 mg infusion of the drug instead of an injection the service line is j9263 x 100 to report a unit of 50(100x 0.5 mg=50). What is the unit reported for service line information if a 150 mg infusion is provided?
Answer:
The service line is J9263 x 300 to report a unit of 150(300x 0.5 mg = 150).
Step-by-step explanation:
The drug J9263 Eloxatin contains 0.5 mg oxaliplatain.
For a infusion of 50 mg the unit reported for service line information is:
- Service line: J9263 x 100
- Unit reported for service line information: 50 = 100 x 0.5 mg
Hence, for a infusion of 150 mg, the unit reported for service line information is:
- Unit reported: 150(300 x 0.5 mg = 150)
- Service line information: J9263 x 300
Therefore, if the physician provided 150 mg infusion of the drug instead of an injection the service line is J9263 x 300 to report a unit of 150(300x 0.5 mg = 150).
I hope it helps you!
The unit reported for service line information for 150 mg infusion based on the injection description is :
150(300x 0.5mg = 150) j9263 × 300Given the injection description :
0.5 mg if physician provided 50 mg of infusion Service line = j9263 × 100For 150 mg infusion :
(150 mg ÷ 50 mg) = 3Unit reported would be:
[50(100x 0.5mg = 150)] × 3 = 150(300x 0.5mg=150)3(j9263 × 100) = j9263 × 300Therefore, the service line information and the unit reported would be:
150(300x 0.5mg = 150)j9263 × 300Learn more : https://brainly.com/question/11277823
Two computer specialists are completing work orders. The first specialist receives 60% of all orders. Each order takes her Exponential amount of time with parameter λ1 = 3 hrs−1. The second specialist receives the remaining 40% of orders. Each order takes him Exponential amount of time with parameter λ2 = 2 hrs−1. A certain order was submitted 30 minutes ago, and it is still not ready. What is the probability that the first specialist is working on it?
Answer:
0.6
Step-by-step explanation:
Data:
Let W be the event the order is not ready in 30 mins.
Then, let A be the event the first worker got the order. So, we want the probability, P(A/W). Using formula for conditional probability gives:
[tex]P (A/W) = \frac{P(AnW)}{P(W)}[/tex]
In this case, we need to calculate a couple of probabilities.
The event that W can happen can be like this:
1. the first worker got the order
2. the second worker got the order and it is not ready.
the probability for both events are disjoint, so:
for item (1) the probability will be 0.6 times the probability that the first worker takes 30 mins to do the job.
Calculating:
The probability that an exponential with parameter is 2 is given by:
[tex]P = \frac{1}{2}e^-{\frac{2}2} }[/tex]
so, the probability is [tex]0.6e^{-1}[/tex]
thus, the probability is > t is [tex]e^{-\lambda t }[/tex]
That's the same as 0.6
The probability that the first specialist is working on it is 0.4764.
How to calculate the probability?
P(not ready in 30 minutes(0.5 hrs) will be:
=P(specialist 1) × P(not ready in 30 minutes |specialist 1) + P(specialist 2) × P(not ready in 30 minutes specialist 2)
= 0.6 × (e-0.5*3) + 0.4 × (e-0.5*2)
= 0.6 × 0.2231 + 0.4 × 0.3679
= 0.2810
Therefore P(first specialist given not ready in 30 minutes(0.5 hrs))
=P(specialist 1) × P(not ready in 30 minutes |specialist 1)/P(not ready in 30 minutes(0.5 hrs))
=0.6 × (e-0.5*3)/0.2810
=0.6 × 0.2231/0.2810
= 0.4764
Learn more about probability on:
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Because all airline passengers do not show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. a. What is the probability that every passenger who shows up can take the flight?b. What is the probability that the flight departs with empty seats?
Answer:
a) 0.9961
b) 0.9886
Step-by-step explanation:
We are given the following information:
We treat passenger not showing up as a success.
P(passenger not showing up) = 0.10
Then the number of passengers follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 125
a) probability that every passenger who shows up can take the flight
[tex]P(x \geq 5) = 1- P(x = 0) - P(x = 1)-P(x = 2) - P(x = 3) - P(x = 4) \\= 1-\binom{125}{0}(0.10)^0(1-0.10)^{125} -...-\binom{125}{4}(0.10)^4(1-0.10)^{121}\\=0.9961[/tex]
b) probability that the flight departs with empty seats
[tex]P(x > 5) =P(x\geq 5) - P(x = 5) \\= 0.9961 -\binom{125}{5}(0.10)^5(1-0.10)^{120}\\=0.9961-0.0075\\ = 0.9886[/tex]
(1 point) Find the length L and width W (with W≤L) of the rectangle with perimeter 100 that has maximum area, and then find the maximum area.
Answer:
Width = 25
Length = 25
Area = 625
Step-by-step explanation:
The perimeter of a rectangle is given by the sum of its four sides (2L+2W) while the area is given by the product of the its length by its width (LW). It is possible to write the area as a function of width as follows:
[tex]100 = 2L+2W\\L = 50-W\\A=LW=W*(50-W)\\A=50W - W^2[/tex]
The value of W for which the derivate of the area function is zero is the width that yields the maximum area:
[tex]A=50W - W^2\\\frac{dA}{dW}=0=50 - 2W\\ W=25[/tex]
With the value of the width, the length (L) and the area (A) can be also be found:
[tex]L=50-25 = 25\\A=W*L=25*25\\A=625[/tex]
Since the values satisfy the condition W≤L, the answer is:
Width = 25
Length = 25
Area = 625
An aspiring venture capitalist is interested in studying early-stage companies. She claims that the proportion of new businesses that earn a profit within the first two years of operation is more than 18%. If the venture capitalist chooses a 10% significance level, what is/are the critical value(s) for the hypothesis test
Answer:
The critical value is 6.314
Step-by-step explanation:
Null hypothesis: The proportion of businesses that earn a profit within the first two years of operation is 80%
Alternate hypothesis: The proportion of businesses e earn a profit within the first two years of operation is greater than 18%
The hypothesis test has one critical value because it is a one-tailed test. It is a one-tailed test because the alternate hypothesis is expressed using the inequality, greater than.
n = 2
degree of freedom = n - 1 = 2 - 1 = 1
significance level = 10%
Using the t-distribution table, critical value corresponding to 1 degree of freedom and 10% significance level is 6.314.
Answer:
To determine the critical value or values for a one-proportion z-test at the 10% significance level when the hypothesis test is left- or right-tailed, we must use the look-up table for zz0.01. Since this is a right-tailed test, our critical value is positive 1.282.
Lucy is using a one-sample t ‑test based on a simple random sample of size n = 22 to test the null hypothesis H 0 : μ = 16.000 cm against the alternative H 1 : μ < 16.000 cm. The sample has mean ¯¯¯ x = 16.218 cm and standard deviation is s = 0.764 cm. Determine the value of the t ‑statistic for this test. Give your answer to three decimal places.
Answer:
The value of test statistic is 1.338
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 16.000
Sample mean, [tex]\bar{x}[/tex] = 16.218
Sample size, n = 22
Alpha, α = 0.05
Sample standard deviation, s = 0.764
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 16.000\text{ cm}\\H_A: \mu < 16.000\text{ cm}[/tex]
We use one-tailed t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{16.218 - 16.000}{\frac{0.764}{\sqrt{22}} } = 1.338[/tex]
Thus, the value of test statistic is 1.338
PLS HELP ASAP!!! WILL MARK BRAINLEST!!! Which statement best describes the relation (3, 4), (4, 3), (6, 3), (7, 8), (5, 4)? Question 2 options: The relation does not represent y as a function of x, because each value of x is associated with a single value of y. The relation does not represent y as a function of x, because each value of y is associated with two values of x. The relation represents y as a function of x, because one value of y is associated with two values of x. The relation represents y as a function of x, because each value of x is associated with a single value of y.
Answer:
The relation represents y as a function of x, because each value of x is associated with a single value of y.
Please help, I will give Brainliest!
After retiring, Mary wants to be able to take $1500 every quarter for a total of 20 years from her retirement account. The account earns 4% interest. How much will she need in her account when she retires?
If you could also give step by step, thank you!!!
Answer:
This isn't an answer but it might help
for exponential decay use a(1-r)^t
exponential growth uses a(1+r)^t
compound interest uses p(1+r/n)^(t x n)
and for interest compounded continuously use Pe^(rt)
a= initial amount, r= rate(%), t= time, P= principle (practically the same as a), and n= number of times compounded
for the different # of times compounded it goes like this: yearly n=1, daily n=365, monthly n=12, weekly n=52, quarterly n=4, semi-annually n=2, and bi-monthly (this is the tricky one) can be either n=6 or n= 24.
also as long as you have a calculator that can do semi-complex things like a Ti 30xs multiview or a ti 36x pro, I have both of those and they can do it as long as you input the formula, hope all this advice helps because I saw you post many of the same types of question. good luck.
Step-by-step explanation:
Answer: she would need $123775.5 in her account when she retires.
Step-by-step explanation:
We would apply the formula for determining future value involving constant deposits at constant intervals. It is expressed as
S = R[{(1 + r)^n - 1)}/r][1 + r]
Where
S represents the future value of the investment.
R represents the regular payments made(could be weekly, monthly)
r = represents interest rate/number of payment intervals
n represents the total number of payments made.
From the information given,
Since she would be taking $1500 four times in a year, then
R = 1500
r = 0.04/4 = 0.01
n = 3 × 20 = 60 times in 20 years
Therefore,
S = 1500[{(1 + 0.01)^60 - 1)}/0.01][1 + 0.01]
S = 1500[{(1.01)^60 - 1)}/0.01][1.01]
S = 1500[{(1.817 - 1)}/0.01][1.01]
S = 1500[0.817/0.01][1.01]
S = 1500[81.7][1.01]
S = 1500 × 82.517
S = 123775.5
In a completely randomized experimental design involving five treatments, a total of 65 observations were recorded for each of the five treatments. The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) 9. Refer to Exhibit 1. The sum of squares within treatments (SSE) is a. 1,000 b. 600 c. 200 d. 1,600 10. Refer to Exhibit 1. The number of degrees of freedom corresponding to between treatments is
a. 60
b. 59
c. 5
d. 4
Answer:
5
Step-by-step explanation:
numerator degrees of freedom=[tex]Treatments-1[/tex]
[tex]N_d_f=5-1=4[/tex]
Total degrees of freedom=[tex]Treatments\times \ Observations Recorded-1[/tex]
[tex]T_d_f=5\times13-1=64[/tex]
Denominator Degrees of freedom=[tex]T_d_f-N_d_f=64-4=60[/tex]
Therefore, to calculate the degrees of freedom corressponding to treatments:
[tex]F=\frac{MSR}{MSE}\\MSR=200\div4=50\\MSE=(800-200)\div 60=10\\F=50\div10=5[/tex]
In a data set with a minimum value of 54.5 and a maximum value of 98.6 with 300 observations, there are 186 points less than 81.2. Find the percentile for 81.2.
Answer:
81.2 is the 62th percentile
Step-by-step explanation:
What is the interpretation for a percentile?
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
300 observations, there are 186 points less than 81.2. Find the percentile for 81.2.
So
[tex]p = \frac{186}{300} = 0.62[/tex]
81.2 is the 62th percentile
Suppose that 76% of Americans prefer Coke to Pepsi. A sample of 80 was taken. What is the probability that at least seventy percent of the sample prefers Coke to Pepsi?
A. 0.104
B. 0.142
C. 0.896
D. 0.858
E. Can not be determined.
Answer:
C. 0.896
Step-by-step explanation:
We use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 80, p = 0.76[/tex]
So
[tex]E(X) = np = 80*0.76 = 60.8[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{80*0.76*0.24} = 3.82[/tex]
What is the probability that at least seventy percent of the sample prefers Coke to Pepsi?
0.7*80 = 56.
This probability is 1 subtracted by the pvalue of Z when X = 56. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{56 - 60.8}{3.82}[/tex]
[tex]Z = -1.26[/tex]
[tex]Z = -1.26[/tex] has a pvalue of 0.1040.
1 - 0.1040 = 0.8960
So the correct answer is:
C. 0.896
State whether the data described below are discrete or continuous, and explain why. The volumes (in cubic feet) of dilferent rooms A. The data are discrete because the data can only take on specific values. B. The data are continuous because the data can only take on specific values. C. The data are discrete because the data can take on any value in an interval. D. The data are continuous because the data can take on any value in an interval
Answer:
Option D) The data are continuous because the data can take on any value in an interval
Step-by-step explanation:
Discrete Data:
The value of discrete data can be expressed in whole numbers.They cannot take all the values within an interval.Discrete variables are usually counted not measured.Continuous data:
The value of continuous data can be expressed in decimals.They can take all the values within an interval.Continuous variables are usually measured not counted.The volumes (in cubic feet) of different rooms
Since the volume can be expressed in decimals, it can take all the values within an interval. Also volume is measured not counted. Hence, it is a continuous variable.
Thus, the correct answer is:
Option D) The data are continuous because the data can take on any value in an interval
Final answer:
The correct answer is D: The data are continuous because the data can take on any value in an interval.
Explanation:
The volumes (in cubic feet) of different rooms would be considered continuous data because they can take on any value within an interval.
Unlike discrete data, which can only take on specific counting numbers, continuous data includes an infinite number of potential values.
For instance, a room can have a volume of 500.5 cubic feet, 500.55 cubic feet, 500.555 cubic feet, and so forth.
This level of precision is due to the fact that volume is a measurable attribute that does not have to be a whole number and can include fractions or decimals as well.
Therefore, the correct answer is D: The data are continuous because the data can take on any value in an interval.
Getting enough sleep. 400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct a hypothesis test to check whether this represents a statistically signi cant di erence from 50%, and use a signi cance level of 0.01.
Answer:
Yes, Hypothesis test represents a statistically significant difference from 50% .
Step-by-step explanation:
We are given that 400 students were randomly sampled from a large university, and 289 said they did not get enough sleep.
Let Null Hypothesis, [tex]H_0[/tex] : p = 0.50 {means from the students sampled from the university, proportion of them who did not get enough sleep is 50%}
Alternate Hypothesis, [tex]H_1[/tex] : p [tex]\neq[/tex] 0.50 {means from the students sampled from the university, proportion of them who did not get enough sleep is different from 50%}
The test statistics we will use here is;
T.S. = [tex]\frac{\hat p - p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion = 289/400 = 0.7225
n = sample of students = 400
So, test statistics = [tex]\frac{0.7225 - 0.50}{\sqrt{\frac{0.7225(1-0.7225)}{400} } }[/tex] = 3.143
Now, at 1% level of significance, z table gives critical value of 2.5758. Since our test statistics is more than the critical value which means test statistics will lie in the rejection region, so we have sufficient evidence to reject null hypothesis.
Therefore, we conclude that from the students sampled from the university, proportion of them who did not get enough sleep is different from 50%.
The question asks to perform a hypothesis test to determine if there is a significant difference between the proportion of university students who do not get enough sleep and the assumed 50%. The steps include stating hypotheses, calculating the test statistic, and comparing it with a critical value at a 0.01 significance level. A decision to reject or not reject the null hypothesis will be made based on this comparison.
Explanation:The student's question involves conducting a hypothesis test to determine if there is a statistically significant difference between the proportion of university students who do not get enough sleep and the assumed proportion of 50%. To perform this test at the given significance level of 0.01, the following steps need to be taken:
First, the null hypothesis (H0) is that the true proportion of students who do not get enough sleep is 0.5 (50%), and the alternative hypothesis (Ha) is that the true proportion is different from 0.5.Then, calculate the test statistic using the formula for a proportion hypothesis test: test statistic = (p-hat - p0)/sqrt(p0(1-p0)/n), where p-hat is the sample proportion and n is the sample size.The test statistic is compared to the critical value or p-value associated with the significance level of 0.01 to make a decision regarding the null hypothesis.For our example, with 289 out of 400 students not getting enough sleep, the sample proportion p-hat is 289/400 = 0.7225. Using the formula, the test statistic is then calculated and compared with the critical z-value for a 0.01 significance level. If the absolute value of the test statistic is greater than the critical z-value, the null hypothesis is rejected, suggesting that there is a statistically significant difference from 50%.
If the test statistic does not exceed the critical value, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest a significant deviation from 50%. Based on the results of the hypothesis test, conclusions about the sleep habits of university students can be drawn.
The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss, at various temperatures in degrees Celsius:
Temperature The toco toucan, the largest member of the toucan 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Percent heat loss from beak 33 34 33 36 36 47 52 51 41 50 49 50 55 60 60 62
The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is
The toco toucan, the largest member of the toucan + x
(Use decimal notation. Give your answer to four decimal places.)
Use the equation to predict The toco toucan, the largest member of the toucan beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 degrees Celsius.
%
What percent The toco toucan, the largest member of the toucan of the variation in beak heat loss is explained by the straight-line relationship with temperature?
%
Find the correlation The toco toucan, the largest member of the toucan (The toco toucan, the largest member of the toucan 0.001) between beak heat loss and temperature:
Answer:
Step-by-step explanation:
Hello!
The population of the study is the Toco Toucan, the largest member of the toucan family. It is believed that the length and size of the beak are due to its function of dissipating heat (a cooling mechanism).
You have two variables of interest.
X: Outdoor temperature.
Temperature (ºC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Y: Total beak heat loss, as a percent of the total body heat loss of a toucan.
Percent heat loss from beak 33 34 33 36 36 47 52 51 41 50 49 50 55 60 60 62
The objective is to construct a least-squares regression line to predict the body heat loss of the toucans given the outdoor temperature.
Using a statistical software I estimated the regression model:
^Yi= 2.71 + 1.96Xi
1. To predict what will be the value of the beak heat loss as a percent of the total body heat loss at a temperature of 25ºC you have to simply replace the value of X in the equation:
^Yi= 2.71 + 1.96 (25)= 51.71ºC
The expected beak heat loss given an outdoor temperature of 25ºC is 51.71ºC.
2. To know what percent of the variation of the beak heat loss is explained by the outdoor temperature you have to calculate the coefficient of determination.
R²= 0.85
This means that 85% of the variability of the beak heat loss as a percent of the total body heat loss of the Toco Toucans is explained by the outdoor Temperature under the estimated model ^Yi= 2.71 + 1.96Xi
3. The correlation coefficient between these two variables is r= 0.92, this means that there is a strong positive linear correlation between the beak heat loss and the outdoor temperature. This means that when the outdoor temperature rises, the beak heat loss increases.
I hope it helps!
The probability of a randomly selected adult in one country being infected with a certain virus is 0.0050.005. In tests for the virus, blood samples from 2626 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.
Answer:
0.1222 or 12.22%
Yes, it is unlikely.
Step-by-step explanation:
If the probability of someone being infected is 0.005, then the probability of someone not being infected is 0.995. In order for the combined sample to test negative (N), all of the 26 people must test negative. Thus, the probability that the combined sample tests positive is:
[tex]P(Sample = P) = 1 -P(N=26)\\P(Sample = P) = 1 -0.995^{26}\\P(Sample = P) = 0.1222=12.22\%[/tex]
There is a 0.1222 or 12.22% probability that the combined sample tests positive, which is unlikely to occur.
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the variance of the waiting time is 4.
Find the probability that a person will wait for more than 7 minutes. Round your answer to four decimal places.
Answer:
0.3075 = 30.75% probability that a person will wait for more than 7 minutes.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The standard deviation is the square root of the variance.
In this problem, we have that:
[tex]\mu = 6, \sigma = \sqrt{4} = 2[/tex]
Find the probability that a person will wait for more than 7 minutes.
This is 1 subtracted by the pvalue of Z when X = 7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7 - 6}{2}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a pvalue of 0.6915
1 - 0.6915 = 0.3075
0.3075 = 30.75% probability that a person will wait for more than 7 minutes.
The probability that a person will wait for more than 7 minutes is 30.85%.
What is z score?Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
Given; mean of 6 minutes and variance = 4 minutes, hence:
Standard deviation = √variance = √4 = 2 minutes
For > 7 minutes:
z = (7 - 6)/2 = 0.5
P(z > 0.5) = 1 - P(z < 0.5) = 1 - 0.6915 = 0.3085
The probability that a person will wait for more than 7 minutes is 30.85%.
Find out more on z score at: https://brainly.com/question/25638875
uppose that a car weighing 4000 pounds is supported by four shock adsorbers, each with a spring constant of 540 lbs/inch. Assume no damping and determine the period of oscillation TT of the vertical motion of the car.
Answer:
0.435 s
Step-by-step explanation:
Weight of car=m=4000 pounds
Spring constant for each shock absorber=k=540lbs/in
Effective spring constant=4k=4(540)=2160 lbs/in
We have to find the period of oscillation of the vertical motion by assuming no damping.
Time period, T=[tex]2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{w}{gk}[/tex]
Where g=[tex]386 in/s^2[/tex]
[tex]\pi=3.14[/tex]
Using the formula
[tex]T=2\times 3.14\sqrt{\frac{4000}{386\times 2160}}=0.435 s[/tex]
Hence,the period of oscillation of the vertical motion of the car=0.435 s
The US Census lists the population of the United States as 249 million in 1990, 281 million in 2000, and 309 million in 2010. Fit a second-degree polynomial P(t)=a_{2}t^{2}+a_{1}t+a_{0} passing through these points, where t represents years after 1990 (so t=0 corresponds to 1990) and P(t) represents population in millions (so P(0)=249). Sketch the parabola,P(t). Use the model to predict the population in the years 2020 and 2030. (Source: US Census Bureau). You may use technology to solve the system of 3 equations and 3 unknowns used to find your coefficients/constants for your model. The setup of your 3x3 linear system must be shown.
Answer: US predicted population in 2020 and 2030 will be 333 million and 353 million, respectively.
Step-by-step explanation:
Three different points are required to determine the coefficients of correspondent second-order polynomial. Three linear equations are form after substituting the variables associated with those points. [tex]t^{*}[/tex] is the year and [tex]p[/tex] is the population according to US census, measured in millions. That is to say:
[tex]a_{2}\cdot 1990^{2} + a_{1}\cdot 1990 + a_{0} = 249\\a_{2}\cdot 2000^{2} + a_{1}\cdot 2000 + a_{0} = 281\\a_{2}\cdot 2010^{2} + a_{1}\cdot 2010 + a_{0} = 309[/tex]
There are different approaches to solve linear equation systems. In this problem, a matrix-based approach will be used and a solver will be applied in order to minimize the effort and time required to make the need operations. The solution of the 3 x 3 linear system is shown as following:
[tex]a_{2} = -\frac{1}{50},a_{1}=83,a_o=-85719[/tex]
Now, the second-order polynomial is:
[tex]p(t)=-\frac{1}{50}\cdot (t+1990)^{2}+83\cdot(t+1990)-85719[/tex], where [tex]p(t) = 249[/tex] when [tex]t=0[/tex].
The predicted populations are:
[tex]p(30) = 333, p(40) = 353[/tex]
US predicted population in 2020 and 2030 will be 333 million and 353 million, respectively.
2. Give the euclidean norm, sum norm, and max norm of the. fallowing vectors. (a) (1, 1, l] (b) [3,0,0] (c) [-1, 1,4] (d) ( - 1.4, 3] (e) [4, 4, 4, 4]
Answer:
See below
Step-by-step explanation:
Recall first:
Given a vector
[tex](x_1,x_2,...,x_n)[/tex]
Euclidean norm
[tex]\sqrt{x_1^2+x_2^2+...+x_n^2}[/tex]
Sum norm
[tex]|x_1|+|x_2|+...+|x_n|[/tex]
Max norm
[tex]Max\{|x_1|,|x_2|,...|x_n|\}[/tex]
Now let us apply these definitions to our vectors
Vector (1,1,1)
Euclidean norm
[tex]\sqrt{1^2+1^2+1^2}=\sqrt{3}[/tex]
Sum norm
|1|+|1|+|1| = 3
Max norm
Max{|1|, |1|, |1|} = |1| = 1
Vector (3,0,0)
Euclidean norm
[tex]\sqrt{3^2+0^2+0^2}=\sqrt{3^2}=3[/tex]
Sum norm
|3|+|0|+|0| = 3
Max norm
Max{|3|, |0|, |0|} = |3| = 3
Vector (-1,1,4)
Euclidean norm
[tex]\sqrt{(-1)^2+1^2+4^2}=\sqrt{18}[/tex]
Sum norm
|-1|+|1|+|4| = 1+1+4 =6
Max norm
Max{|-1|, |1|, |4|} = |4| = 4
Vector (-1.4, 3)
Euclidean norm
[tex]\sqrt{(-1.4)^2+3^2}=\sqrt{10.96}[/tex]
Sum norm
|-1.4|+|3| = 1.4+3 = 4.4
Max norm
Max{|-1.4|, |3|} = |3| = 3
Vector (4,4,4,4)
Euclidean norm
[tex]\sqrt{4^2+4^2+4^2+4^2}=\sqrt{4*4^2}=8[/tex]
Sum norm
|4|+|4|+|4|+|4| = 16
Max norm
Max{|4|, |4|, |4|, |4|} = |4| = 4
Final Answer:
- Vector (a) has a Euclidean norm of approximately 1.732, a sum norm of 3, and a max norm of 1.
- Vector (b) has a Euclidean norm of 3, a sum norm of 3, and a max norm of 3.
- Vector (c) has a Euclidean norm of approximately 4.243, a sum norm of 6, and a max norm of 4.
- Vector (d) has a Euclidean norm of approximately 4.123, a sum norm of 5, and a max norm of 4.
- Vector (e) has a Euclidean norm of 8, a sum norm of 16, and a max norm of 4.
Explanation:
Sure, let's calculate the norms for each of the given vectors:
(a) For the vector (1, 1, 1):
- The Euclidean norm (also known as the L2 norm) is the square root of the sum of the squares of the components. For this vector, it's [tex]\(\sqrt{1^2 + 1^2 + 1^2} = \sqrt{3} \approx 1.732\)[/tex].
- The sum norm (or L1 norm) is the sum of the absolute values of the components. For this vector, it's |1| + |1| + |1| = 3.
- The max norm (also known as the infinity norm) is the maximum absolute value component of the vector. For this vector, it's [tex]\(\max(|1|, |1|, |1|) = 1\)[/tex].
(b) For the vector (3, 0, 0):
- The Euclidean norm of this vector is [tex]\(\sqrt{3^2 + 0^2 + 0^2} = \sqrt{9} = 3\)[/tex].
- The sum norm of this vector is |3| + |0| + |0| = 3.
- The max norm of this vector is max(|3|, |0|, |0|) = 3.
(c) For the vector (-1, 1, 4):
- The Euclidean norm of this vector is [tex]\(\sqrt{(-1)^2 + 1^2 + 4^2} = \sqrt{1 + 1 + 16} = \sqrt{18} \approx 4.243\)[/tex].
- The sum norm is (|-1| + |1| + |4| = 1 + 1 + 4 = 6).
- The max norm is max(|-1|, |1|, |4|) = 4.
(d) For the vector (-1, 4):
- The Euclidean norm is [tex]\(\sqrt{(-1)^2 + 4^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.123\)[/tex].
- The sum norm is |-1| + |4| = 1 + 4 = 5.
- The max norm is max(|-1|, |4|) = 4.
(e) For the vector (4, 4, 4, 4):
- The Euclidean norm is [tex]\(\sqrt{4^2 + 4^2 + 4^2 + 4^2} = \sqrt{16 + 16 + 16 + 16} = \sqrt{64} = 8\)[/tex].
- The sum norm is |4| + |4| + |4| + |4| = 4 + 4 + 4 + 4 = 16.
- The max norm is max(|4|, |4|, |4|, |4|) = 4.
Now we have calculated the three types of norms for each of the vectors:
- Vector (a) has a Euclidean norm of approximately 1.732, a sum norm of 3, and a max norm of 1.
- Vector (b) has a Euclidean norm of 3, a sum norm of 3, and a max norm of 3.
- Vector (c) has a Euclidean norm of approximately 4.243, a sum norm of 6, and a max norm of 4.
- Vector (d) has a Euclidean norm of approximately 4.123, a sum norm of 5, and a max norm of 4.
- Vector (e) has a Euclidean norm of 8, a sum norm of 16, and a max norm of 4.
On any given day, there is a 52% chance of there being an auto-related accident on a certain stretch of highway. The occurrence of an accident from one day to the next is independent. (Use Statdisk to compute the values and write the answers below) (a). What is the probability that there will be 4 accidents in the next 9 days
Answer:
See the explanation.Step-by-step explanation:
We need to observe total 9 days.First we need to choose any 4 days from the 9 days. From these total 9 days, 4 days can be chosen in [tex]^9C_4 = \frac{9!}{4!\times5!} = \frac{6\times7\times8\times9}{4!} = 126[/tex] ways.
The probability of occurring an auto related accident is [tex]\frac{52}{100}[/tex].
Similarly, the probability of not occurring an accident is [tex]\frac{100 - 52}{100} = \frac{48}{100}[/tex].
Hence, the required probability is [tex]126\times(\frac{52}{100} )^4(\frac{48}{100} )^5[/tex].