Answer:
At 7 hours from the visit telling the joke, everyone in town would have heard of it
Step-by-step explanation:
Exponential Grow
This is a good example of exponential growth, where the speed at which a rumor is spread out depends on the actual number of persons who already know it.
The visitor told the mayor a new joke at 10:00 am.
Total people who heard the joke=1
This person tells the joke to 3 people in one hour, so at 11:00 am, 1+3=4 persons heard the joke
Total people who heard the joke=4
Those persons take one hour to tell the joke to every 3 persons each. Thus at 11:00
4 + 4*3 = 16 persons heard the joke. This succession grows very quickly. At 12:00
16 + 16*3 = 64 persons heard the joke
We can note the number of persons hearing the joke is an even power of 2, that is
[tex]2^0=1[/tex]
[tex]2^2=4[/tex]
[tex]2^4=16[/tex]
[tex]2^6=64[/tex]
We can predict the result for each hour since the exponent is double the number of hours passed since the joke started to spread. The number of persons who have heard the joke after t hours is
[tex]N=2^{2t}[/tex]
We can iterate until we find the value of t so that
[tex]2^{2t}<9800[/tex]
Let's better find the limit value of t
[tex]2^{2t}=9800[/tex]
Taking logarithms
[tex]log(2^{2t})=log9800[/tex]
[tex]2tlog(2)=log(9800)[/tex]
Thus
[tex]\displaystyle t=\frac{log(9800)}{2log 2}[/tex]
[tex]t=6.6[/tex]
So at 7 hours from the visit telling the joke (between 16:00 and 17:00), everyone in town would know it
Note that
[tex]2^{12}=4096[/tex]
[tex]2^{14}=16384[/tex]
Murphy family has 4 members and they went to 7 games. Chen family has 5 members and they went to 4 games. In total, the two families spent $1200. If the seats cost the same for each person, how much did the Murphy family spend?
The Murphy family spend $ 700
Solution:
Given that,
Murphy family has 4 members and they went to 7 games
Let "x" be the cost of each game
Murphy family cost: [tex]4 \times 7 \times x = 28x[/tex]
Chen family has 5 members and they went to 4 games
Chen family cost: [tex]5 \times 4 \times x = 20x[/tex]
In total, the two families spent $1200
Therefore,
28x + 20x = 1200
48x = 1200
Divide both sides by 48
x = 25
How much did the Murphy family spend?
Murphy family cost = 28x = 28(25) = 700
Thus murphy family spend $ 700
A hypothesis test is to be conducted using LaTeX: \alphaα = 0.05. This means:_________.
a) there is a 5 percent chance that a Type II error has been committed.
b) there is a 5 percent chance that the alternative hypothesis is true.
c) there is a maximum 5 percent chance that a true null hypothesis will be rejected.
d) there is a 5 percent chance that the null hypothesis is true.
Answer:
c)
Step-by-step explanation:
α also known as type I error depicts the probability of rejecting the true null hypothesis. So, when α=0.05 then it means that there is 5% probability or chance of rejecting the true null hypothesis.
So, in hypothesis testing α=0.05 means that there is a maximum 5 percent chance that a true null hypothesis will be rejected.
Marisa wants to buy a quality phone for least $200.She has already saved $125 and plans to save an additional $10 each week.Write an inequality that represents this
The inequality representing Marisa's goal to buy a phone costing at least $200, with $125 already saved and a plan to save $10 each week, is 125 + 10w \\geq 200, where w is the number of weeks of additional savings.
Explanation:To write an inequality that represents Marisa's situation, we need to consider the amount she has already saved, the additional amount she plans to save weekly, and the minimum amount she needs for the phone. Marisa wants a phone that costs at least $200 and has saved $125. She plans to save $10 each week. We can use the variable w to represent the number of weeks she will save additional money.
Marisa's current savings plus the additional amount she plans to save for w weeks needs to be at least $200. This situation can be represented by the following inequality:
125 + 10w \\geq 200
Here, 125 represents the amount already saved, 10w represents the additional amount saved after w weeks, and the inequality symbol \\geq (greater than or equal to) establishes that Marisa's total savings must be at least $200.
Taco Bell prepared 88 tacos for a meeting at Smith Elementry. If the tacos will be separaded equally among 4 trays, how many tacos will be on each tray?
Answer:
The answer is:
22 tacos per tray
Step-by-step explanation:
Number of trays:
Pretend 1,2,3, and 4 are the traysIf there's 4 traysand there's 88 tacosdivide 88 by 4Number of Tacos is 88:
88 ÷ 4 = 22Put 22 Taco's in each tray:
Tray 1. 22 Tacos
Tray 2. 22 Tacos
Tray 3. 22 Tacos
Tray 4. 22 Tacos
Dividing is Separating So your separating the tacos into 4 trays
Example of dividing:
John takes 5 cookies from the cookie jar, there are 20 cookies total. He goes out to his friends and wants to share his cookies, but his mom said "no more cookies after you take 5 cookies." He had 3 friends with him that day. John keeps 1 cookie for himself and gives 1 cookie to each friend his friends. Now they are left with 1 cookie, they divide the cookie into 4 pieces, splitting it into half, they now have 2 halves, they split those 2 into 2 pieces. This example is showing how John and his friends shared by dividing the cookies among each other.All 4 trays Add up to 88 tacos total
I hope this helped! <3
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠X.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠X = °
Answer:
Step-by-step explanation:
Triangle VWX is a right angle triangle.
From the given right angle triangle,
VX represents the hypotenuse of the right angle triangle.
With m∠X as the reference angle,
WX represents the adjacent side of the right angle triangle.
VW represents the opposite side of the right angle triangle.
To determine m∠X, we would apply
the tangent trigonometric ratio. It is expressed as
Tan θ = opposite side/adjacent side. Therefore,
Tan X = 2/1 = 1
m∠X = Tan^-1(1)
m∠X = 45°
Julia has 2 children who are 4 years apart in age. Julia is four times older than her youngest child. The sum of the ages of Julia and her 2 kids is 76 years
Answer: Julia is 48 years
The oldest child is 16 years
The youngest child is 12 years
Step-by-step explanation:
Let x represent the age of the youngest child.
Let y represent the age of the oldest child.
Let x represent Julia's age.
The sum of the ages of Julia and her 2 kids is 76 years. This means that
x + y + z = 76- - - - - - - - - - -1
Julia has 2 children who are 4 years apart in age. This means that
y = x + 4
Julia is four times older than her youngest child. This means that
z = 4x
Substituting z = 4x and y = x + 4 into equation 1, it becomes
x + x + 4 + 4x = 76
6x = 76 - 4 = 72
x = 72/6 = 12
y = x + 4 = 12 + 4
y = 16
z = 4x = 4 × 12
z = 48
Answer:
what?
Step-by-step explanation:
Consider two population distributions labeled X and Y. Distribution X is highly skewed while the distribution Y is slightly skewed. In order for the sampling distributions of X and Y to achieve the same degree of normality
A. Population Y will require a larger sample size
B. Population X will require a larger sample size
C. Population X and Y will require the same sample size
D. None of the above
Answer: B. Population X will require a larger sample size
Step-by-step explanation:
If a random variable say p has skewed distribution (whether right or left ) in a population then a bigger sample size is needed to make sure that the sampling distribution follows normal distribution.Given : Two population distributions labeled X and Y.
Distribution X → highly skewed
Distribution Y → slightly skewed.
Since Distribution X more skewed so , we will need a larger sample size of population X as compared to Y.
Hence, the correct answer is B. Population X will require a larger sample size
The correct option is B. Population X will require a larger sample size.
According to the Central Limit Theorem, the sampling distribution of the sample mean will tend to be normally distributed as the sample size becomes larger, regardless of the shape of the population distribution. However, the rate at which the sampling distribution approaches normality depends on the degree of skewness in the population distribution.
For a population distribution that is highly skewed (like Distribution X), a larger sample size is needed for the sampling distribution to approximate a normal distribution compared to a population distribution that is only slightly skewed (like Distribution Y). This is because the effects of skewness are more pronounced and take longer to "average out" in larger samples.
Therefore, to achieve the same degree of normality in their respective sampling distributions, Population X, with its high skewness, will require a larger sample size than Population Y, which is only slightly skewed.
Using this equation for Wien’s Law (λ = 2898/T), the wavelength most emitted by the Sun (T = 6000K) is approximately: a. 48.3 µm b. 483 µm c. 0.48 µm
Step-by-step explanation:
By Wien’s Law we have
[tex]\lambda =\frac{2898}{T}[/tex]
where λ is in μm and T is in K
Given that
T = 6000 K
Substituting
[tex]\lambda =\frac{2898}{6000}=0.483\mu m[/tex]
Option C is the correct answer.
Final answer:
By using Wien's Law with the given temperature of the Sun (6000K), we calculate the peak emission wavelength as 0.483 micrometers, which corresponds to option c. 0.48 µm.
Explanation:
The student asked about the wavelength most emitted by the Sun as predicted by Wien's Law, given the temperature of 6000K using the equation λ = 2898/T, where λ is the wavelength in micrometers and T is the temperature in Kelvin. According to Wien's displacement law, the temperature and peak wavelength of emission of an object are inversely proportional.
Plugging in the given temperature (T = 6000K) into the equation λ = 2898/T, we calculate the peak emission wavelength to be 2898/6000 = 0.483 µm.
So, the correct answer is c. 0.48 µm.
PLZ HURRY IT'S URGENT!!
Which fraction represents the ratio 35:42 in simplest form?
7/5
6/5
6/7
5/6
Answer:
5/6
Step-by-step explanation:
The ratio 35:42 represents the fraction:
[tex]\dfrac{35}{42}[/tex]
Now we have to cancel this fraction - we will divide numerator and denominator by 7:
35/7 = 5
42/7 = 6
Therefore,
[tex]\dfrac{35}{42} = \dfrac{7\cdot 5}{7\cdot 6} =\dfrac{5}{6}[/tex]
NEED HELP!!!!
Use long division or synthetic division to find the quotient of (2x^3 + x^2 + 1)/(x + 1)
Answer: The quotient is 2x² - x + 1
Step-by-step explanation:
We would apply the long division method to find the quotient of
(2x^3 + x^2 + 1)/(x + 1)
The attached photo shows the step by step calculations
Omar begins training for a 5 km race by running 0.75 km the first day, 0.85 km the second day, and 0.95 km the third day. If he keeps increasing his distance each day according to the pace of his first three days, what is the first day in his training program that Omar will run greater than 5 km?
Final answer:
Omar will run greater than 5 km on the 44th day of his training program, as this is when the distance he runs each day according to the pattern in his training exceeds 5 km.
Explanation:
Omar increases his running distance each day by 0.10 km (from 0.75 km on the first day to 0.85 km on the second, then to 0.95 km on the third, and so on). To find the first day he will run greater than 5 km, we can create a sequence to represent the distances he runs each day. Since the difference between consecutive days is constant (0.10 km), this is an arithmetic sequence.
The first term (a1) of the sequence is 0.75 km, and the common difference (d) is 0.10 km. The nth term of an arithmetic sequence is given by an = a1 + (n - 1)d. We need to find the smallest n such that an > 5 km.
Setting up the inequality, we get:
0.75 + (n - 1)0.10 > 5
(n - 1)0.10 > 5 - 0.75
(n - 1)0.10 > 4.25
n - 1 > 42.5
n > 43.5
Since n must be a whole number, Omar will run greater than 5 km on day 44 of his training program.
A homes value increases at a average rate of 5.5% each yea. The current value is $120,000. What function can be used to find the value of the home after X years?
Answer: the function is
A = 120000(1.055)^x
Step-by-step explanation:
A homes value increases at an average rate of 5.5% each year. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r/n)^ nt
Where
A represents the value of the home after t years.
n represents the period of growth
t represents the number of years.
P represents the initial value of the home.
r represents rate of increase in value.
From the information given,
P = 120000
r = 5.5% = 5.5/100 = 0.055
n = 1
Therefore
A = 120000(1 + 0.055/1)^ x × 1
A = 120000(1.055)^x
A submarine dives 270 feet below the ocean's surface. It then rises 90 feet, rises another 40 feet, and finally dives 55 feet. What action is required by the submarine to get back to the surface?
Answer:
The action required by the submarine to get back to the surface is to rise 195 feet
Step-by-step explanation:
we know that
The ocean's surface or sea level is at an elevation of 0 feet.
we have
1) A submarine dives 270 feet below the ocean's surface
In this moment the position of the submarine is
-270 ft ---> is negative because is below the sea level
2) It then rises 90 feet
In this moment the position of the submarine is
-270+90=-180 feet
3) rises another 40 feet,
In this moment the position of the submarine is
-180+40=-140 feet
4) Finally dives 55 feet
In this moment the position of the submarine is
-140-55=-195 feet
therefore
The action required by the submarine to get back to the surface is to rise 195 feet
Final answer:
The submarine initially dives to 270 feet below the surface and undergoes a series of rises and dives. After all movements, it is at a depth of 195 feet. To return to the surface, it needs to rise 195 feet.
Explanation:
A student asked: A submarine dives 270 feet below the ocean's surface. It then rises 90 feet, rises another 40 feet, and finally dives 55 feet. What action is required by the submarine to get back to the surface?
To solve this problem, we will sum up the changes in the submarine's depth and find out how much more it needs to rise to reach the surface.
Initial dive: -270 feet (diving increases the depth, so it's represented as a negative number)First rise: +90 feetSecond rise: +40 feetFinal dive: -55 feetSumming up these changes: -270 + 90 + 40 - 55 = -195 feet.
The submarine is currently 195 feet below the surface. Therefore, to get back to the surface, the submarine needs to rise 195 feet.
Which set of ordered pairs has point symmetry with respect to the origin (0, 0)?
(-8, 3), (8, -3)
(-8, 3), (-3, 8)
(-8, 3), (-8, -3)
(-8, 3), (8, 3)
Answer:
(-8, 3), (8, -3)
Step-by-step explanation:
Point symmetry about origin means reflection of the given point about the origin.
The reflection of a point about the origin will cause the 'x' and 'y' value of the point to change its sign.
Therefore, the coordinate rule for point symmetry about the origin is given as:
[tex](x,y)\to (-x,-y)[/tex]
Now, let us check each of the given options.
Option 1:
(-8, 3), (8, -3)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3)
So, option 1 is correct.
Option 2:
(-8, 3), (-3, 8)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (-3, 8)
So, option 2 is not correct.
Option 3:
(-8, 3), (-8, -3)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (-8, -3)
So, option 3 is not correct.
Option 4:
(-8, 3), (8, 3)
Now, if (x, y) = (-8, 3), then its point symmetry is given as (-(-8), -3) = (8, -3) ≠ (8, 3)
So, option 4 is not correct.
Hence, only option 1 is correct.
Am I correct for the second part?
Answer:yes
Step-by-step explanation:
Answer:
should be the 3rd choice
Step-by-step explanation:
even though the 2nd choice is technically correct for a rhombus, but this property does not explain the first part of this 2 part question.
We are looking for an answer that supports pert 1 of the question.
by definition, a rhombus is a parallelogram with 4 sides of equal length, which means 2 adjacent sides will have the same length, which explains the answer in the first part because JK and KL are adjacent sides
In Sakura's garden, for every 5 red flowers, there are 10 yellow flowers. There are 75 total red and yellow flowers. How many red flowers are in Sakura's garden?
Answer: there are 25 red flowers in Sakura's garden.
Step-by-step explanation:
In Sakura's garden, for every 5 red flowers, there are 10 yellow flowers. This means that if there are 10 red flowers, there would be 20 yellow flowers. if there are 20 red flowers, there would be 40 yellow flowers. Therefore, the ratio of red flowers to yellow flowers in the garden is
5/10 = 10/20 £= 20/40 = 1/2 = 1:2
Total ratio = 2 + 1 = 3
If there are 75 total red and yellow flowers, then the total number of red flowers are in Sakura's garden would be
1/3 × 75 = 25
Answer:
25
Step-by-step explanation:
Step-by-step explanation: Understand it as a ratio. 5:10. Add both ratios together, 15. Make an expression, 15x=75. x=5, Then multiply 10 and 5 by 5 and that will give you the ratio of 25:50 red to yellow flowers.
Please help! I'm stuck on this question.
When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions? (Choose one)
A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.
B) We are interpolating. There are no concerns about interpolation.
C) We are interpolating. Interpolation is dangerous because the pattern of data may change inside the x range.
D) We are extrapolating. There are no concerns about extrapolation.
Answer:
A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.
Step-by-step explanation:
When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions? (Choose one)
A) We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.
B) We are interpolating. There are no concerns about interpolation.
C) We are interpolating. Interpolation is dangerous because the pattern of data may change inside the x range.
D) We are extrapolating. There are no concerns about extrapolation.
The answer is A
assuming we are looking for the value of y within the range of x, we are interpolating. Take for instance, the range of xi between 60 and 65, what is the value of y at point 62.5. This is interpolation.
But then we have the data sets of temperature of a particular place within 1 to 15 days in a month. if we are asked to look for its temperature on the 31st of that particular month, we are extrapolating, which might take a different pattern from the line of best bit
Using a least-squares line to predict y values for x values beyond the range of the data is called extrapolation. This process is risky because the pattern of data may change outside of the existing range, leading to inaccurate predictions.
Explanation:When using a least-squares line to predict y values for x values beyond the range of x values found in the data, we are extrapolating. This is because we are making predictions outside of the range of the existing data set. However, extrapolation comes with certain risks. The pattern of the data may not remain constant beyond the data we have, leading to inaccurate predictions.
Therefore, answer A is the most accurate: 'We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.'
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In how many ways can 3 apple trees, 4 peach trees, and 2 plum trees be arranged along a fence line if one does not distinguish between trees of the same kind?\
Answer:
24 ways
Step-by-step explanation:
4x3x2
12x2
24
A road crew must repave a road that is seven eights
miles long. They can repave one fifty six
miles each hour. How long will it take the crew to repave the road?
Write your answer in simplest form.
Answer:
seven eights mean; 8888888
they can repave one fifty six mile per hour; 156/hour
Step-by-step explanation:
To calculate total time to repave
8888888/156 = 56980.02 hours require
x4+x3+7x2-6x+8 / x2+2x+8
Answer:
The Final answer will be [tex]x^2-x+1[/tex] with remainder 0.
Step-by-step explanation:
We have attached the division for your reference.
Given:
Dividend = [tex]x^4+x^3+7x^2-6x+8[/tex]
Divisor = [tex]x^2+2x+8[/tex]
Explaining the division we get;
Step 1: First when we divide the Dividend [tex]x^4+x^3+7x^2-6x+8[/tex] with divisor [tex]x^2+2x+8[/tex] we will first multiply [tex]x^2[/tex] with the divisor then we get the Quotient as [tex]x^2[/tex] and Remainder as [tex]-x^3-x^2-6x+8[/tex]
Step 2: Now the Dividend is [tex]-x^3-x^2-6x+8[/tex] and Divisor [tex]x^2+2x+8[/tex] is we will now multiply [tex]-x[/tex] with the divisor then we get the Quotient as [tex]x^2-x[/tex] and Remainder as [tex]x^2+2x+8[/tex]
Step 3: Now the Dividend is [tex]x^2+2x+8[/tex] and Divisor is [tex]x^2+2x+8[/tex] we will now multiply 1 with the divisor then we get the Quotient as [tex]x^2-x+1[/tex] and Remainder as 0.
Hence The Final answer will be [tex]x^2-x+1[/tex] with remainder 0.
Suppose that the probability density function for the length x in feet of some type of fish caught by sport fishermen is given by p(x)=14 if 0≤x≤4, and is zero otherwise. What is the probability that a fish caught by a fisherman is between 0.25 and 2 feet long? 1/4 is less than 0.25 feet long?
For the described uniform distribution, the probability that a fish is between 0.25 and 2 feet long can be found by calculating the area under the probability density function graph, which gives a result of 43.75%.
Explanation:The given situation implies a uniform distribution as the probability density function is constant (equal to 1/4) for fish lengths between 0 and 4 feet, and zero otherwise. For such a distribution, the probability that the length x is in an interval can be found by calculating the area under the probability density function graph for that interval. As the graph is a rectangle, this is as simple as length times width.
Here, the interval is from 0.25 to 2 feet. The length of this interval is (2 - 0.25)= 1.75 feet. The width of the rectangle is the constant probability density function value of 1/4. Hence, the probability that a fish caught by the sports fishermen is between 0.25 and 2 feet long is 1.75 * 1/4 = 0.4375 or 43.75%.
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Helen, Francesca, and Olivia each took a test that had 25 questions. Helen got 20 questions correct, Francesca answered 3 questions incorrectly, and Olivia got 84% of the questions correct. The three unlabeled marks on the double number line below represent the percent and number of the questions each of the three friends answered correctly. Use the double number line to order Helen, Francesca, and Olivia from least to greatest according to the percentage of questions correct.
Answer:
the order is Helen Olivia Francessca
Step-by-step explanation:
ik im late but i hop this helps C:
The order of percentage of correct questions from least to greatest.
80% < 84% < 88%
Helen < Olivia < Francesca.
What is a percentage?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of questions in the test = 25.
Helen:
Percentage of the number of questions correct.
= 20/25 x 100
= 80%
Francesca:
Percentage of the number of questions correct.
= 22/25 x 100
= 88%
Olivia:
Percentage of the number of questions correct.
= 84%
Thus,
Arranging the percentage in increasing order.
80% < 84% < 88%
Helen < Olivia < Francesca.
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Let f(x) = -2x + 4 and g(x) = -6.0 – 7. Find f(x) – g(x).
Please show your work and explain steps! GIVING BRAINLIEST!!
Answer:
-2x + 3
Step-by-step explanation:
f(x) - g(x)
(-2x + 4) - (-6.0 - 7)
-2x + 4 - (-6.0) - 7
-2x + 4 + 6.0 - 7
-2x + 10 - 7
-2x + 3
A researcher uses an anonymous survey to investigate the television-viewing habits of American adolescents. Based on the set of 356 surveys that were completed and returned, the researcher finds that these students spend an average of 3.1 hours each day watching television. For this study, the set of 356 students who returned the surveys is an example of a _______.a. parameter b. statistic c. population d. sample
Answer:
Option b) Sample
Step-by-step explanation:
We are given the following in the question:
Survey:
356 surveys on television-viewing habits of American adolescents.
Result:
Average of 3.1 hours per day.
Population and sample:
Population is a collection of all the possible observation of individuals or variable of interest.A sample is always a part of the population.It is a subset of population.For the given survey, those who responded to the survey forms a a sample as it is a part of 356 surveys that is a subset of population.
The correct answer is
Option b) Sample
Suppose that a basketball player different from the
ones in Example 2.5-2 and in Exercise 2.5-1 can make a
free throw 60% of the time. Let X equal the minimum
number of free throws that this player must attempt to
make a total of 10 shots.
(a) Give the mean, variance, and standard deviation of X.
(b) Find P(X = 16).
Answer:
a. Mean = 6
Variance = 2.4
Standard Deviation = 1.55
b. P(X=16) = 0.124
Step-by-step explanation:
Given
n = Total shots = 10
p = Probability of success = 60%
p = 60/100
p= 0.6
q = Probability of failure
q = 1-p
q = 1 - 0.6
q = 0.4
a.
Mean = np
Mean = 10 * 0.6
Mean = 6
Variance = npq
Variance = 10 * 0.6 * 0.4
Variance = 2.4
Standard Deviation = √Variance
Standard Deviation = √2.4
Standard Deviation = 1.549193338482966
Standard Deviation = 1.55 --------- approximated
b.
We have X = 16
x = 10
Assume that the events "success" on the various throws are independent.
The 10th success came on the 16th attempt
So, the player had exactly 10 successes and 6 failures on 16th trial
So Probability = nCr 0.6^10 * 0.4^6
Where n = 15 and r = 9 (number of attempts and success before the 16th trial)
15C9 * 0.6^10 * 0.4^6
= 5005 * 0.0060466176 * 0.004096
= 0.123958563176448
= 0.124 ------ Approximated
A. The mean, variance, and standard deviation of x are: Mean: 16.67, Variance: 11.11 and Standard deviation: 3.33. B. The probability that the player will need exactly 16 attempts to make 10 successful shots is approximately 0.123
Given that a basketball player can make a free throw 60% of the time, we are to determine the minimum number of free throws that this player must attempt to make a total of 10 shots.
Since each shot is independent and has a 60% chance of being successful, this scenario follows a negative binomial distribution.
(a) Calculating the mean, variance, and standard deviation:
Mean:
[tex]\[ \mathbb{E}[X] = \frac{r}{p} = \frac{10}{0.60} = \frac{10}{0.6} = 16.67 \][/tex]
Variance:
[tex]\[ \text{Var}(X) = \frac{r(1-p)}{p^2} = \frac{10(1-0.60)}{0.60^2} = \frac{10 \cdot 0.40}{0.36} = \frac{4}{0.36} = 11.11 \][/tex]
Standard deviation:
[tex]\[ \sigma = \sqrt{\text{Var}(X)} = \sqrt{11.11} \approx 3.33 \][/tex]
So, the mean, variance, and standard deviation of x are: Mean: 16.67, Variance: 11.11 and Standard deviation: 3.33
(b) Finding P(X = 16)
The probability mass function of a negative binomial random variable \is given by:
[tex]\[ P(X = k) = \binom{k-1}{r-1} p^r (1-p)^{k-r} \][/tex]
[tex]\[ P(X = 16) = \binom{15}{9} (0.60)^{10} (0.40)^{6} \][/tex]
Calculating the binomial coefficient:
[tex]\[ \binom{15}{9} = \frac{15!}{9!(15-9)!} = \frac{15!}{9!6!} \][/tex]
This can be computed as follows:
[tex]\[ \binom{15}{9} = \frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 5005 \][/tex]
Combining these:
[tex]\[ P(X = 16) = 5005 \cdot 0.0060466 \cdot 0.004096 \approx 0.123 \][/tex]
Therefore:
[tex]\[ P(X = 16) \approx 0.123 \][/tex]
So, the probability that the player will need exactly 16 attempts to make 10 successful shots is approximately 0.123
Can someone please answer this I don’t understand!
Point P is located at (2, 2) and point T is located at (7, 17). What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?
Use the section formula and show values for: m: n, Point 1, Point 2, and ALL work to find coordinates of partitioning point.
The coordinates of X are (5, 11).
Solution:
Given points of the line segment are P(2, 2) and T(7, 17)
Let X be the point that partitions the directed line segment PT in the ratio 3 : 2
Using section formula, we can find the coordinate of the point that partitions the line segment.
Section formula:
[tex]$X(x, y)=\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)[/tex]
Here, [tex]x_{1}=2, y_{1}=2, x_{2}=7, y_{2}=17[/tex] and m = 3, n =2
Substitute these in the section formula,
[tex]$X(x, y)=\left(\frac{3 \times 7+2 \times 2}{3+2}, \frac{3 \times 17+2 \times 2}{3+2}\right)[/tex]
[tex]$=\left(\frac{21+4}{5}, \frac{51+4}{5}\right)[/tex]
[tex]$=\left(\frac{25}{5}, \frac{55}{5}\right)[/tex]
[tex]=(5, 11)[/tex]
X(x, y) = (5, 11)
The coordinates of X are (5, 11).
for box A find the constant proportionality
Answer:
Are there like any images or opinions for your question
ten people are in a room wearing badges marked 1 through 10. three persons are selected at random and their badge numbers are recorded. what is the probability that the smallest of these badge number is 6?
Answer:
P=1/12
Step-by-step explanation:
From Exercise we have ten people are in a room wearing badges marked 1 through 10.
For first man we conlude that the probability that is 5/10, that his number at least 6.
For second man we conlude that the probability that is 4/9, that his number at least 6.
For third man we conlude that the probability that is 3/8, that his number at least 6.
Therefore, the probability is
P=5/10 · 4/9 · 3/8 = 1/12
P=1/12
Ethan decides to type up some documents while waiting for the meeting to start he can type two pages every 1/8 hour if the meeting starts 3/4 hour later than the scheduled time how many pages can he typed before the meeting starts
Answer:
Ethan can type 12 pages before the meeting starts.
Step-by-step explanation:
Given:
Number of pages he can type =2
Number of hours he can type 2 pages = [tex]\frac{1}8\ hrs[/tex]
We need to find number of pages he can type in [tex]\frac34\ hrs[/tex]
Solution:
Now first we will find number of pages in 1 hour
So we can say;
In [tex]\frac{1}8\ hrs[/tex] = 2 pages
In 1 hour = number of pages he can type in 1 hour
By Using Unitary method we get;
number of pages he can type in 1 hour = [tex]\frac{2}{\frac18} =\frac{2\times8}{1}=16\ pages[/tex]
Now we can say that;
In 1 hour = 16 pages
So [tex]\frac34\ hrs[/tex] = number of pages he can type in [tex]\frac34\ hrs[/tex]
Again By using Unitary method we get;
number of pages he can type in [tex]\frac34\ hrs[/tex] = [tex]16\times \frac34 = 12\ pages[/tex]
Hence Ethan can type 12 pages before the meeting starts.
Final answer:
Ethan has 3/4 hours to type and can complete two pages every 1/8 hour, resulting in a total of 12 pages typed before the meeting starts.
Explanation:
Ethan can type two pages every 1/8 hour. To find out how many pages he can type before the start of the meeting, we need to calculate the total pages he can type in the waiting time of 3/4 hours. Here's the step-by-step calculation:
Calculate the number of 1/8 hour intervals in 3/4 hours by dividing: (3/4) ÷ (1/8) = (3/4) × (8/1) = 6.
Since he types two pages every 1/8 hour, we find the total number of pages by multiplying the number of intervals by 2: 6 × 2 = 12 pages.
Therefore, Ethan can type a total of 12 pages before the meeting starts.