Answer:yes
Step-by-step explanation:because there are more marbles than jars
Bob's golf score at his local course follows the normal distribution with a mean of 92.1 and a standard deviation of 3.8. What is the probability that the score on his next round of golf will be between 82 and 89?
Answer:
The probability is 0.20
Step-by-step explanation:
a) Lets revise how to find the z-score
- The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
* Lets solve the problem
- Bob's golf score at his local course follows the normal distribution
- The mean is 92.1
- The standard deviation is 3.8
- The score on his next round of golf will be between 82 and 89
- Lets find the z-score for each case
# First case
∵ z = (x - μ)/σ
∵ x = 82
∵ μ = 92.1
∵ σ = 3.8
∴ [tex]z=\frac{82-92.1}{3.8}=\frac{-10.1}{3.8}=-2.66[/tex]
# Second case
∵ z = (x - μ)/σ
∵ x = 89
∵ μ = 92.1
∵ σ = 3.8
∴ [tex]z=\frac{89-92.1}{3.8}=\frac{-3.1}{3.8}=-0.82[/tex]
- To find the probability that the score on his next round of golf will
be between 82 and 89 use the table of the normal distribution
∵ P(82 < X < 89) = P(-2.66 < z < -0.82)
∵ A z-score of -2.66 the value is 0.00391
∵ A z-score of -0.82 the value is 0.20611
∴ P(-2.66 < z < -0.82) = 0.20611 - 0.00391 = 0.2022
* The probability is 0.20
Normal distribution and z-scores are applied in this context. The z-scores for the given range are calculated, followed by finding the correlating probabilities from the z-table, resulting in the probability of Bob's next score falling within the range of 82-89.
Explanation:To answer this question, we will utilize the concept of z-scores in a normal distribution. A z-score basically explains how many standard deviations a data point (in this case, a golf score) is from the mean.
Firstly, we calculate the z-scores for the limits given. Here, 82 and 89. The formula we use is Z = (X - μ) / σ, where X is the golf score, μ is the mean, and σ is the standard deviation.
The calculated z-scores are then used as references, and we refer a z-table (also known as a standard normal table) to find the probabilities which correspond to these z-scores, and the result is a probability of Bob's next golf score being between 82 and 89.
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a. The following events are mutually exclusive: Living in California and watching American Idol. True or False b. The number of patients seen by an outpatient practice is an example of a discrete random variable. True or False
c.The law of large numbers states that as the number of times an event experiment is conducted increases, the likelihood of the actual probability of an event approaching the theoretical probability decreases. True or False
d. Measuring the time it takes for patients to enter the operating room is an example of a continuous random variable. True or False
Answer:
a) False. Because you can live in California AND watch American Idol at the same time
b) True. Because the number of patients is a whole number, like 1, 2 or 3. There is no 1.5 patient
c) False. The actual probability should become closer to the theoretical probablity
d) True
It is estimated that only 68% of drivers wear their safety belt. How many people should a police officer expect pull over until she finds a driver not wearing a safety belt
A.1
B 2
C 4
D 3
E 5
Answer:
D. 4
Step-by-step explanation:
Percent of drivers who wear seat belts = 68
Percent of drivers who do not wear seat belts = 100 - 68 = 32
Now, we know that for every 100 pull overs, 32 drivers will not be wearing belt.
32 drivers without seat-belt = 100 pullovers
1 driver without seat-belt = 100/32 pullovers
1 driver without seat-belt = 3.125 pullovers (4 pullovers)
So, a police officer should expect 4 pullovers until she finds a driver not wearing a seat-belt.
The police officer should expect to pull over approximately 4 drivers until finding one not wearing a safety belt.
To determine how many people a police officer should expect to pull over until she finds a driver not wearing a safety belt, given that only 68% of drivers wear their safety belt, follow these steps:
Step 1:
Calculate the probability of a driver not wearing a safety belt.
Since 68% of drivers wear their safety belt, the probability of a driver not wearing a safety belt is [tex]\( 1 - 0.68 = 0.32 \).[/tex]
Step 2:
Calculate the expected number of people to pull over.
The expected number of people to pull over is the reciprocal of the probability of a driver not wearing a safety belt. So, it's [tex]\( \frac{1}{0.32} \).[/tex]
Step 3:
Perform the calculation.
[tex]\[ \frac{1}{0.32} \approx 3.125 \][/tex]
Step 4:
Interpret the result.
Since we can't pull over a fraction of a person, rounding up to the nearest whole number, the police officer should expect to pull over 4 drivers until finding one not wearing a safety belt.
So, the correct answer is option C: 4.
Factor the Higher degree polynomial
5y^4 + 11y^2 + 2
[tex]\bf 5y^4+11y^2+2\implies 5(y^2)^2+11y^2+2\implies (5y^2+1)(y^2+2)[/tex]
For this case we must factor the following polynomial:
[tex]5y ^ 4 + 11y ^ 2 + 2[/tex]
We rewrite [tex]y ^ 4[/tex]as [tex](y^ 2) ^ 2[/tex]:
[tex]5 (y ^ 2) ^ 2 + 11y ^ 2 + 2[/tex]
We make a change of variable:
[tex]u = y ^ 2[/tex]
We replace:
[tex]5u ^ + 11u + 2[/tex]
we rewrite the middle term as a sum of two terms whose product of 5 * 2 = 10 and the sum of 11.
So:
[tex]5u ^ 2 + (1 + 10) u + 2[/tex]
We apply distributive property:
[tex]5u ^ 2 + u + 10u + 2[/tex]
We factor the highest common denominator of each group.
[tex](5u ^ 2 + u) + (10u + 2)\\u (5u + 1) +2 (5u + 1)[/tex]
We factor again:
[tex](u + 2) (5u + 1)[/tex]
Returning the change:
[tex](y ^ 2 + 2) (5y ^ 2 + 1)[/tex]
ANswer:
[tex](y ^ 2 + 2) (5y ^ 2 + 1)[/tex]
a. The sample space consists of the results of a single probability experiment. True or False
Answer:
True
Step-by-step explanation:
The sample space consists of any possible outcome
Biologists estimate that the number of animal species of a certain body length is inversely proportional to the square of the body length.1 Write a formula for the number of animal species, N, of a certain body length as a function of the length, L. Use k as the constant of proportionality.
Answer:
[tex]N(L)=\frac{k}{L^2}[/tex]
Step-by-step explanation:
Here, N represents the number of animal species and L represents a certain body length,
According to the question,
[tex]N\propto \frac{1}{L^2}[/tex]
[tex]\implies N=\frac{k}{L^2}[/tex]
Where, k is the constant of proportionality,
Since, with increasing the value of L the value of N is decreasing,
So, we can say that, N is dependent on L, or we can write N(L) in the place of N,
Hence, the required function formula is,
[tex]N(L)=\frac{k}{L^2}[/tex]
Certainly! When we say that the number of animal species \( N \) is inversely proportional to the square of the body length \( L \), what we mean mathematically is that as the body length increases, the number of species decreases at a rate that is the square of the increase in length. This can be represented by the following formula:
\[ N = \frac{k}{L^2} \]
Here \( N \) is the number of species, \( L \) is the body length, and \( k \) is the constant of proportionality. This constant \( k \) represents the number of species at the unit body length (when \( L = 1 \)). The constant of proportionality is determined by the specific biological context, based on empirical data or theoretical considerations.
In this formula, \( L^2 \) denotes the body length squared, and the fraction represents the inverse relationship.
In summary, to find the number of species \( N \) for a given body length \( L \), we use the inverse square relationship with the constant of proportionality \( k \).
b7
__
b6
Multiply or divide as indicated.
For this case we have the following expression:
[tex]\frac {b ^ 7} {b ^ 6}[/tex]
By definition of division of powers of the same base, we have to place the same base and subtract the exponents, that is:
[tex]\frac {a ^ m} {a ^ n} = a ^ {n-m}[/tex]
So:
[tex]\frac {b ^ 7} {b ^ 6} = b ^ {7-6} = b ^ 1 = b[/tex]
Answer:
b
Answer: [tex]b[/tex]
Step-by-step explanation:
You need to remember a property called "Quotient of powers property". This property states the following:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
You can observe that the bases of the expression [tex]\frac{b^7}{b^6}[/tex] are equal, then you can apply the property mentioned before.
Therefore, you can make the division indicated in the exercise.
Then you get this result:
[tex]\frac{b^7}{b^6}=b^{(7-6)}=b[/tex]
(a) (8%) Compute the probability of an even integer among the 100 integers 1!, 2!, 3!, .., until 100! (here n! is n factorial or n*(n-1)*(n-2) *… 1) (b) (16%) Compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, …., 1+2+3+… + 99, and 1+2+3+… + 100
Answer:
(a) 99%
(b) 50%
Step-by-step explanation:
(a) All factorials after 1! have 2 as a factor, so are even. Thus 99 of the 100 factorials are even, for a probability of 99%.
__
(b) The first two sums are odd; the next two sums are even. The pattern repeats every four sums. There are 25 repeats of that pattern in 100 sums, so 2/4 = 50% of sums are even.
Solve the Equation for y . 9x +5y = -2
Answer:
[tex]\large\boxed{y=\dfrac{-9x-2}{5}}[/tex]
Step-by-step explanation:
[tex]9x+5y=-2\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\5y=-9x-2\qquad\text{divide both sides by 5}\\\\y=\dfrac{-9x-2}{5}[/tex]
Consider two algorithms that perform the same function, that run in n/4 and log2(n), respectively, where n ∈ N (i.e. natural numbers).(a) Plot these runtimes on the same graph with the values n ∈ [1, 50] (don’t forget labels). Provide the set of intervals over N, where n/4 is the strictly better algorithm to use (think greater than, not greater than or equal).
Answer:
[2, 15]
Step-by-step explanation:
The graph shows the n/4 algorithm to be better (smaller run time) for n in the range 2 to 15.
c. Using a standard deck of 52 cards, the probability of selecting a 4 of diamonds or a 4 of hearts is an example of a mutually exclusive event. True of False
Answer:
True
Step-by-step explanation:
If two events X and Y are mutually exclusive,
Then,
P(X∪Y) = P(X) + P(Y)
Let A represents the event of a diamond card and B represent the event of a heart card,
We know that,
In a deck of 52 cards there are 4 suit ( 13 Club cards, 13 heart cards, 13 diamond cards and 13 Spade cards )
That is, those cards which are heart can not be diamond card,
⇒ A ∩ B = ∅
⇒ P(A∩B) = 0
Since, P(A∪B) = P(A) + P(B) - P(A∩B)
⇒ P(A∪B) = P(A) + P(B)
By the above statement,
Events A and B are mutually exclusive,
Hence, the probability of selecting a 4 of diamonds or a 4 of hearts is an example of a mutually exclusive event is a true statement.
Suppose r(t) = cos t i + sin t j + 3tk represents the position of a particle on a helix, where z is the height of the particle above the ground. (a) Is the particle ever moving downward? When? (If the particle is never moving downward, enter DNE.) t = (b) When does the particle reach a point 15 units above the ground? t = (c) What is the velocity of the particle when it is 15 units above the ground? (Round each component to three decimal places.) v = (d) When it is 15 units above the ground, the particle leaves the helix and moves along the tangent line. Find parametric equations for this tangent line. (Round each component to three decimal places.)
The particle has position function
[tex]\vec r(t)=\cos t\,\vec\imath+\sin t\,\vec\jmath+3t\,\vec k[/tex]
Taking the derivative gives its velocity at time [tex]t[/tex]:
[tex]\vec v(t)=\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=-\sin t\,\vec\imath+\cos t\,\vec\jmath+3\,\vec k[/tex]
a. The particle never moves downward because its velocity in the [tex]z[/tex] direction is always positive, meaning it is always moving away from the origin in the upward direction. DNE
b. The particle is situated 15 units above the ground when the [tex]z[/tex] component of its posiiton is equal to 15:
[tex]3t=15\implies\boxed{t=5}[/tex]
c. At this time, its velocity is
[tex]\vec v(5)=-\sin 5\,\vec\imath+\cos5\,\vec\jmath+3\,\vec k\approx\boxed{0.959\,\vec\imath+0.284\,\vec\jmath+3\,\vec k}[/tex]
d. The tangent to [tex]\vec r(t)[/tex] at [tex]t=5[/tex] points in the same direction as [tex]\vec v(5)[/tex], so that the parametric equation for this new path is
[tex]\vec r(5)+\vec v(5)t\approx\boxed{(0.284+0.959t)\,\vec\imath+(-0.959+0.284t)\,\vec\jmath+(15+3t)\,\vec k}[/tex]
where [tex]0\le t<\infty[/tex].
please help :')
Typist Words Typed Minutes Typing
Ella 640 16
Harper 450 15
Owen 560 14
Shaquille 540 12
who typed quickest??
Ella
Harper
Owen
or
Shaquille
Answer:
owen
Step-by-step explanation:
Answer:
Shaquille
Step-by-step explanation:
To determine the unit rate for each, divide the number of words by the number of minutes typed.
Ella: 640÷16=40
Harper: 450÷15=30
Owen: 560÷14=40
Shaquille=540÷12=45
Since Shaquille's is the most, we can tell he typed fastest.
Hope this helps!
which expression is equivalent to (125^2/125^4/3)
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{125^2}{125^{\frac{4}{3}}}\implies \cfrac{(5^3)^2}{(5^3)^{\frac{4}{3}}}\implies \cfrac{5^{3\cdot 2}}{5^{3\cdot \frac{4}{3}}}\implies \cfrac{5^6}{5^4}\\\\\\ 5^6\cdot 5^{-4}\implies 5^{6-4}\implies 5^2\implies 25[/tex]
A number is thrift if it is a multiple of 2 or 3. How many thrift numbers are there between -15 and 15
(a) 18 (b) 9 (c) 19 (d) 15
Answer:
(a) 19.
Step-by-step explanation:
The even numbers in the given range are -14, -12, -10, -8, - 6 , -4 and -2. and 7 more of their positive values. Total 14.
The numbers divisible by 3 and not 2 are -9, -3, 3 and 9.
Also 0 is a multiple of any number
Thus, number of thrift numbers are 14 + 4 + 1 = 19 (answer).
Consider kite WXYZ. What are the values of a and b? a = 4; b = 10. a = 4; b = 40, a = 8; b = 10, a = 8; b = 40
Check the picture below.
let's recall that a kite is a quadrilateral, and thus is a polygon with 4 sides
sum of all interior angles in a polygon
180(n - 2) n = number of sides
so for a quadrilateral that'd be 180( 4 - 2 ) = 360, thus
[tex]\bf 3b+70+50+3b=360\implies 6b+120=360\implies 6b=240 \\\\\\ b=\cfrac{240}{6}\implies b=40 \\\\[-0.35em] ~\dotfill\\\\ \overline{XY}=\overline{YZ}\implies 3a-5=a+11\implies 2a-5=11 \\\\\\ 2a=16\implies a=\cfrac{16}{2}\implies a=8[/tex]
Answer:
D.)a = 8; b = 40
Step-by-step explanation:
it is on edgeinuity
A population has a mean mu μ equals = 87 and a standard deviation σ = 24. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 36 mu μx equals = nothing (Simplify your answer.) sigma Subscript x overbar σx equals = nothing (Simplify your answer.
Answer:
The mean of a sampling distribution of sample means is 87
The standard deviation of a sampling distribution of sample = 4
Step-by-step explanation:
* Lets revise some definition to solve the problem
- The mean of the distribution of sample means is called μx
- It is equal to the population mean μ
- The standard deviation of the distribution of sample means is
called σx
- The rule of σx = σ/√n , where σ is the standard deviation and n
is the size of the sample
* lets solve the problem
- A population has a mean (μ) is 87
∴ μ = 87
- A standard deviation of 24
∴ σ = 24
- A sampling distribution of sample means with sample size n = 36
∴ n = 36
∵ The mean of the distribution of sample means μx = μ
∵ μ = 87
∴ μx = 87
* The mean of a sampling distribution of sample means is 87
∵ The standard deviation of a sampling distribution of sample
means σx = σ/√n
∵ σ = 24 and n = 36
∴ σx = 24/√36 = 24/6 = 4
* The standard deviation of a sampling distribution of sample = 4
The mean of the sampling distribution of sample means is 87, identical to the population mean. The standard deviation of this sampling distribution is 4, which is the population standard deviation (24) divided by the square root of the sample size (36).
Explanation:When working with populations and sampling distributions, the Central Limit Theorem is critical for understanding the behavior of sample means. Given a population with mean (μ) and standard deviation (σ), the mean of the sampling distribution of sample means will be the same as the population mean, and the standard deviation of the sampling distribution (σx) is equal to the population standard deviation divided by the square root of the sample size (n).
In this instance, the population has a mean (μ) of 87 and a standard deviation (σ) of 24. For a sample size (n) of 36, the mean of the sampling distribution of sample means (μx) is equal to the population mean:
μx = μ = 87
The standard deviation of the sampling distribution of sample means (σx) is calculated as follows:
σx = σ / √ n = 24 / √ 36 = 24 / 6 = 4
Therefore, the mean of the sampling distribution is 87, and standard deviation is 4.
evaluate the function at the fiven values of the variables:
f(x)= 5x^2 + 5x *+ 3
a f (-3)
b f (-9)
Answer:
f(-3)=5x^2+5x*3
-f*3=5x^2+5*3x
-3f=5x^2+15x
f=-5x(x+3)/3
f(-9)=5x^2+5x*3
-f*9=5x^2+5*3x
-9f=5x^2+15x
f=-5x(x+3)/9
Step-by-step explanation:
hope it helps you?
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips.
(a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive?
(b) What is the probability that a randomly selected bag contains fewer than 1125 chocolate chips?
(c) What proportion of bags contains more than 1225 chocolate chips?
(d) What is the percentile rank of a bag that contains 1425 chocolate chips?
The probability of an event can be computed by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
Probability
The probability of an event can be computed by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
The probability exists a branch of mathematics that deals with calculating the likelihood of a given event's happening, which is defined as a number between 1 and 0. An event with a probability of 1 can be regarded as a certainty.Utilizing the TI-83, 83+, 84, 84+ Calculator to estimate these probabilities
Go to 2nd DISTR, and select item 2: normalcdf
The syntax is: normalcdf (lower bound, upper bound, mean, standard deviation)
a) P(1100 <= X <= 1500)
= normalcdf(1100, 1500, 1252, 129)
= 0.8534
b) P(X < 1125)
= normalcdf(-1E99, 1125, 1252, 129)
= 0.1624
c) P(X > 1200)
= normalcdf(1200, 1E99, 1252, 129)
= 0.6566 = 65.66%
d) P(X < 1000)
= normalcdf(-1E99, 1000, 1252, 129)
= 0.0254 = approx. 3rd percentile
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Pretend you're playing a carnival game and you've won the lottery, sort of. You have the opportunity to select five bills from a money bag, while blindfolded. The bill values are $1, $2, $5, $10, $20, $50, and $100. How many different possible ways can you choose the five bills? (Order doesn't matter, and there are at least five of each type of bill.)
The total number of ways are:
462
Step-by-step explanation:When we are asked to select r items from a set of n items that the rule that is used to solve the problem is:
Method of combination.
Here the total number of bills of different values are: 7
i.e. n=7
( $1, $2, $5, $10, $20, $50, and $100 )
and there are atleast five of each type of bill.
Also, we have to choose 5 bills i.e. r=5
The repetition is allowed while choosing bills.
Hence, the formula is given by:
[tex]C(n+r-1,r)[/tex]
Hence, we get:
[tex]C(7+5-1,5)\\\\i.e.\\\\C(11,5)=\dfrac{11!}{5!\times (11-5)!}\\\\C(11,5)=\dfrac{11!}{5!\times 6!}\\\\\\C(11,5)=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{5!\times 6!}\\\\\\C(11,5)=\dfrac{11\times 10\times 9\times 8\times 7}{5!}\\\\\\C(11,5)=\dfrac{11\times 10\times 9\times 8\times 7}{5\times 4\times 3\times 2}\\\\\\C(11,5)=462[/tex]
Hence, the answer is:
462
There are 462 different possible ways to choose five bills from a set of seven types with repetition allowed.
To determine the number of different ways to choose five bills from a set of bills with values $1, $2, $5, $10, $20, $50, and $100, we can use the combinatorial concept known as "combinations with repetition."
Given:
- Bill values: [tex]\( \{1, 2, 5, 10, 20, 50, 100\} \)[/tex]
- Total number of types of bills: ( n = 7 )
- Number of bills to choose: ( r = 5 )
The formula for combinations with repetition (also known as "stars and bars") is:
\[
\binom{n + r - 1}{r}
\]
Substituting the values ( n = 7 ) and ( r = 5 ):
[tex]\[\binom{7 + 5 - 1}{5} = \binom{11}{5}\][/tex]
Now, calculate [tex]\( \binom{11}{5} \):[/tex]
[tex]\[\binom{11}{5} = \frac{11!}{5!(11-5)!} = \frac{11!}{5! \cdot 6!}\][/tex]
First, compute the factorials:
[tex]\[11! = 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\]\[5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\]\[6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720\][/tex]
Next, compute [tex]\( \frac{11!}{6!} \):[/tex]
[tex]\[\frac{11!}{6!} = 11 \times 10 \times 9 \times 8 \times 7\]\[= 11 \times 10 = 110\]\[110 \times 9 = 990\]\[990 \times 8 = 7920\]\[7920 \times 7 = 55440\][/tex]
Now, compute:
[tex]\[\frac{55440}{120} = 462\][/tex]
Therefore, the number of different possible ways to choose the five bills is:
[tex]\[\boxed{462}\][/tex]
Stones are thrown horizontally, with the same initial velocity, from the tops of two different buildings, A and B. The stone from building A lands 4 times as far from the base of the building as does the stone from building B. What is the ratio of building A's height to building B's height?
In this Physics problem, we calculate the horizontal distance a stone travels when thrown horizontally from a cliff to determine the ratio of heights between two buildings.
Explanation:The horizontal distance the stone will travel can be calculated using the formula:
d = v*t
Where d is the distance, v is the initial velocity, and t is the time of flight. Using the information given, we can calculate the distance the stone from block A will travel, and then find the ratio of building A's height to building B's height.
You are going to play two games. The probability you win the first game is 0.60. If you win the first game, the probability you will win the second game is 0.75. If lose the first game, the probability you win the second game is 0.55. What is the probability you win exactly one game? (Round your answer to two decimal places)
The probability that you win exactly one game is:
0.37
Step-by-step explanation:The probability you win the first game is 0.60. If you win the first game, the probability you will win the second game is 0.75. If lose the first game, the probability you win the second game is 0.55.The probability that you win exactly one game is:
Probability you win first but not second+Probability you win second but not first.
= 0.60×0.25+0.40×0.55
= 0.37
( since probability of losing second game when you win first is: 1-0.75=0.25
and probability that you lose first game is: 1-0.60=0.40 )
Final answer:
The probability of winning exactly one game, rounded to two decimal places, is 0.37.
Explanation:
Probability of winning the first game = 0.60
Probability of winning the second game if the first game is won = 0.75
Probability of winning the second game if the first game is lost = 0.55
To find the probability of winning exactly one game, we calculate the probability of winning the first game and losing the second game, plus the probability of losing the first game and winning the second game:
Probability of winning 1st and losing 2nd = (0.60 * 0.25) = 0.15Probability of losing 1st and winning 2nd = (0.40 * 0.55) = 0.22Total Probability of winning exactly one game: 0.15 + 0.22 = 0.37Use the power rules for exponents to simplify the expression. (Type as a fraction, use exponential form)
Answer: [tex]\bold{\dfrac{h^9}{g^9}}[/tex]
Step-by-step explanation:
The power rule is "multiply the exponents".
You must understand that the exponent of both h and g is 1.
Multiply 1 times 9 for both variables.
[tex]\bigg(\dfrac{h}{g}\bigg)^9=\bigg(\dfrac{h^1}{g^1}\bigg)^9=\dfrac{h^{1\times 9}}{g^{1\times 9}}=\large\boxed{\dfrac{h^9}{g^9}}[/tex]
s f(-x)= x^2 -1 odd, even or neither
Answer:
f(x) = f(-x) = x^2 -1 is an even function
Step-by-step explanation:
When f(x) = f(-x), the function is symmetrical about the y-axis. That is the definition of an even function.
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An odd function is symmetrical about the origin: f(x) = -f(-x).
f p(x) and q(x) are arbitrary polynomials of degreeat most 2, then the mapping< p,q >= p(-2)q(-2)+ p(0)q(0)+ p(2)q(2)defines an inner product in P3.Use this inner product to find < p,q >, llpll, llqll, and the angletetha, between p(x) and q(x) forp(x) = 2x^2+6x+1 and q(x) = 3x^2-5x-6.< p;q >= ?llpll = ?llqll= ?
We're given an inner product defined by
[tex]\langle p,q\rangle=p(-2)q(-2)+p(0)q(0)+p(2)q(2)[/tex]
That is, we multiply the values of [tex]p(x)[/tex] and [tex]q(x)[/tex] at [tex]x=-2,0,2[/tex] and add those products together.
[tex]p(x)=2x^2+6x+1[/tex]
[tex]q(x)=3x^2-5x-6[/tex]
The inner product is
[tex]\langle p,q\rangle=-3\cdot16+1\cdot(-6)+21\cdot(-4)=-138[/tex]
To find the norms [tex]\|p\|[/tex] and [tex]\|q\|[/tex], recall that the dot product of a vector with itself is equal to the square of that vector's norm:
[tex]\langle p,p\rangle=\|p\|^2[/tex]
So we have
[tex]\|p\|=\sqrt{\langle p,p\rangle}=\sqrt{(-3)^2+1^2+21^2}=\sqrt{451}[/tex]
[tex]\|q\|=\sqrt{\langle q,q\rangle}=\sqrt{16^2+(-6)^2+(-4)^2}=2\sqrt{77}[/tex]
Finally, the angle [tex]\theta[/tex] between [tex]p[/tex] and [tex]q[/tex] can be found using the relation
[tex]\langle p,q\rangle=\|p\|\|q\|\cos\theta[/tex]
[tex]\implies\cos\theta=\dfrac{-138}{22\sqrt{287}}\implies\theta\approx1.95\,\mathrm{rad}\approx111.73^\circ[/tex]
The question is about calculating an inner product, norms, and the angle between two polynomials in a two-dimensional space, represented by their coefficients. We use the provided polynomials and input values from the question to calculate these values.
Explanation:The mathematics problem given refers to calculating the inner product and magnitude of two polynomials, as well as the angle between them, if they are represented in a two-dimensional space.
To find the values asked in this problem, we will use the given polynomials p(x) = 2x^2+6x+1 and q(x) = 3x^2-5x-6. The inner product < p,q > is calculated as follows: p(-2)q(-2) + p(0)q(0) + p(2)q(2).
To find the magnitudes, or norms, ||p|| and ||q||, we need to solve the expression for < p,p > and < q,q > respectively, and then take the square root of the result. The angle between the vectors, denoted as Theta (θ), can be computed using the formula cos θ = < p,q > / (||p||*||q||). Because cos θ is the cosine of the angle, θ = arccos(< p,q > / (||p||*||q||)).
Note that the exact value of the inner product, norms, and angle depends on the input values of -2, 0, and 2 for each polynomial.
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Upper A 4-ft-tall fence runs parallel to a wall of a house at a distance of 24 ft. (a) Find the length of the shortest ladder that extends from the ground to the house without touching the fence. Assume the vertical wall of the house and the horizontal ground have infinite extent. (a) Let L be the length of the ladder, x be the distance from the base of the ladder to the fence, d be the distance from the fence to the house and b be the distance from the ground to the point the ladder touches the house. What is the objective function, in terms of x?
Answer:
(a) shortest ladder length ≈ 35.7 ft (rounded to tenth)
(b) L = (d/x +1)√(16+x²) . . . . where 16 is fence height squared
Step-by-step explanation:
It works well to solve the second part of the problem first, then put in the specific numbers.
We have not been asked anything about "b", so we can basically ignore it. Using the Pythagorean theorem, we find the length GH in the attached drawing to be ...
GH = √(4²+x²) = √(16+x²)
Then using similar triangles, we can find the ladder length L to be that which satisfies ...
L/(d+x) = GH/x
L = (d +x)/x·√(16 +x²)
The derivative with respect to x, L', is ...
L' = (d+x)/√(16+x²) +√(16+x²)/x - (d+x)√(16+x²)/x²
Simplifying gives ...
L' = (x³ -16d)/(x²√(16+x²))
Our objective is to minimize L by making L' zero. (Of course, only the numerator needs to be considered.)
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(a) For d=24, we want ...
0 = x³ -24·16
x = 4·cuberoot(6) ≈ 7.268 . . . . . feet
Then L is
L = (24 +7.268)/7.268·√(16 +7.268²) ≈ 35.691 . . . feet
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(b) The objective function is the length of the ladder, L. We want to minimize it.
L = (d/x +1)√(16+x²)
The objective function for the length of the ladder in terms of x is L = sqrt((x+b)^2 + d^2).
Explanation:To find the length of the shortest ladder that extends from the ground to the house without touching the fence, we can use the concepts of similar triangles. Let L be the length of the ladder, x be the distance from the base of the ladder to the fence, d be the distance from the fence to the house, and b be the distance from the ground to the point the ladder touches the house. In terms of x, the objective function for the length of the ladder is:
L = sqrt((x+b)^2 + d^2)
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The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are ( r, 67.4°). What is the value of the polar coordinate r in this case?
Answer:
r ≈ 13.01
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Cos = Adjacent/Hypotenuse
cos(67.4°) = 5.00/r . . . . . . filling in the given values
Solving for r gives ...
r = 5.00/cos(67.4°) ≈ 13.01
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Check your requirements for rounding. We rounded to 2 decimal places because the x-coordinate, 5.00, was expressed using 2 decimal places.
If (x - 3)2 = 5, then
x=-315
Ox= 3+V5
Ox= 5+13
Answer:
x = 3 ±sqrt(5)
Step-by-step explanation:
(x - 3)^2 = 5
Take the square root of each side
Sqrt( (x - 3)^)2 =±sqrt( 5)
x-3 = ±sqrt(5)
Add 3 to each side
x-3+3 = 3 ±sqrt(5)
x = 3 ±sqrt(5)
A rectangular pyramid has a volume of 90 cubic feet. What is the volume of a rectangular prism with the same size base and same height?
Answer:
30 cubic feet
Step-by-step explanation:
Here we are given the volume of rectangular pyramid as 90 cubic feet as we are required to find the volume of rectangular prism.
For that we need to use the theorem which says that
the volume prism is always one third of the volume of the pyramid . Whether it is rectangular of triangular base. Hence in this case also the volume of the rectangular prism will be one third of the volume of the rectangular pyramid.
Volume of Rectangular prism = [tex]\frac{1}{3}[/tex] * Volume of rectangular pyramid
= [tex]\frac{1}{3}[/tex] * 90
= 30
Answer:
270 is the answer just took test.
Step-by-step explanation:
Which of the following is most likely the next step in the series?
Answer:
D
Step-by-step explanation:
It's a repeating pattern
Answer:
D
Reasoning:
the pattern keeps the previous color and alternates between blue and red. The pattern is also increasing in number by 1. Therefore there would be no reason for the fourth step to change previous color or numbers. That eliminates A and B. For C, since the pattern is adding a different color clockwise in each step, it is more likely that the pattern will continue to alternate, therefore D is most likely.