(a) Reject H₀; There is sufficient evidence to conclude that the new automobiles actually do average more than 43 miles per gallon.
(b) p-value ≈ 0.0000; Strong evidence against H₀; The new automobiles actually do average more than 43 miles per gallon with a very high level of confidence.
(a) The null hypothesis, H₀: μ ≤ 43 (miles per gallon)
The alternative hypothesis, H₁: μ > 43 (miles per gallon)
Computing the test statistic:
Test statistic, t = (X' - μ₀) / (s / √n) = (44.5 - 43) / (1 / √36) = 4.5
Determining the critical value:
Since the alternative hypothesis is one-tailed (greater than), we need to find the critical value at α = 0.05 with degrees of freedom (df) = n - 1 = 36 - 1 = 35.
Using a t-table or software, the critical value at α = 0.05 and df = 35 is approximately 1.690.
State your conclusion:
Since the test statistic (4.5) is greater than the critical value (1.690), we reject the null hypothesis.
There is sufficient evidence to conclude that the new automobiles actually do average more than 43 miles per gallon.
(b) To find the p-value associated with the sample results, we compare the test statistic to the t-distribution with df = 35.
Using a t-table or software, we find that the p-value is less than 0.0001 (approximately).
Interpretation based on the p-value:
The p-value is extremely small, indicating strong evidence against the null hypothesis.
We can conclude that the new automobiles actually do average more than 43 miles per gallon with a very high level of confidence.
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How to write 0.00080 as a power of 10?
Answer:
8 × 10⁻⁴
Step-by-step explanation:
Find the Surface area of the following figure below
Answer:
495
Step-by-step explanation:
Base area = 11*11 = 121
Lateral area = (11*4)*17/2 = 11*2*17 = 374
121+374=495
verify that the following equation is an identity. (sinx cosx)^2=sin2x 1
The equation [tex](sin(x)cos(x))^2 = sin(2x)[/tex] is verified to be an identity.
Simplify LHS and RHS?
To verify whether the equation [tex](sin(x)cos(x))^2 = sin(2x)[/tex] is an identity, we can simplify both sides of the equation and see if they are equivalent.
Starting with the left side of the equation:
[tex](sin(x)cos(x))^2 = (sin(x))^2(cos(x))^2[/tex]
Now, we can use the trigonometric identity [tex]sin(2x) = 2sin(x)cos(x)[/tex] to rewrite the right side of the equation:
[tex]sin(2x) = 2sin(x)cos(x)[/tex]
Substituting this into the equation, we have:
[tex](sin(x))^2(cos(x))^2 = (2sin(x)cos(x))[/tex]
Next, we can simplify the left side of the equation:
[tex](sin(x))^2(cos(x))^2 = (sin(x))^2(cos(x))^2[/tex]
Since both sides of the equation are identical, we can conclude that the given equation is indeed an identity:
[tex](sin(x)cos(x))^2 = sin(2x)[/tex]
Hence, the equation [tex](sin(x)cos(x))^2 = sin(2x)[/tex] is verified to be an identity.
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Divide and answer in simplest form: 5 ÷35
Step-by-step explanation:
Reduce 5/35 to lowest terms
The simplest form of 535 is 17.
Answer:
1/7
Step-by-step explanation:
divide both sides by 5
Bill needs to read 3 novels each month.
Let N be the number of novels Bill needs to read in M months.
Write an equation relating N to M. Then use this equation to find the number of novels Bill needs to read in 19 months.
Write the equation?
Number of the novels in 19 months: _ novels
Answer:
Each month Bill reads 3 novels so you get
N = 3m
If you plug in 6 for m we get
N = 3(6) = 18
Bill needs to read 18 novels in 19 months
Step-by-step explanation:
the compound inequality
Your reading teacher
has
20 students in his elos. If
he uses popnicle sticks to
randomly call on
students during class,
what is the probability
your name will
be
called
Answer:
5%
Step-by-step explanation:
20= 100%
1 x100 = 100
100/20= 5
The mean and standard deviation of a population are 200 and 20, respectively. What is the probability of selecting one data value less than 190?
A. 42%
B. 58%
C. 31%
D. 69%
When the variances of the population distribution and the sampling distribution of means are compared, the:
A. variances have the same degrees of freedom.
B. population variance is larger than the sampling distribution variance.
C. population variance is smaller than the sampling distribution variance.
D. variances are equal.
The variance of the sampling distribution of means, on the other hand, is equal to the variance of all possible sample means of the same size taken from the population.
Since a sample size is always less than the population size, the variance of the population distribution is greater than the variance of the sampling distribution of means.
Therefore, option B is correct.
The probability of selecting one data value less than 190 IS (C)31%
When the variances of the population distribution and the sampling distribution of means are compared, the (B) population variance is larger than the sampling distribution variance.
The probability of selecting one data value less than 190 given the mean and standard deviation of a population of 200 and 20 respectively is 31% (option C).
Solution: Given,
mean (μ) = 200,
standard deviation (σ) = 20
We need to find the probability of selecting one data value less than 190.
P(x < 190) = ?
Z = (X - μ)/σ
Taking X = 190,
Z = (190 - 200)/20
= -0.5
From the standard normal table, the probability of
Z = -0.5 is 0.3085
Therefore,
P(x < 190) = P(Z < -0.5)
= 0.3085
= 31%
Hence, option C is correct.
When the variances of the population distribution and the sampling distribution of means are compared, the population variance is larger than the sampling distribution variance.
This can be explained as follows;
The population distribution is the distribution of an entire population, while the sampling distribution of the mean is the distribution of the means of all possible samples of a specific size drawn from that population.
The variance of the population distribution is equal to the variance of a single observation of the population.
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Three companies, A, B and C, make computer hard drives. The proportion of hard drives that fail within one year is 0.001 for company A, 0.002 for company B and 0.005 for company C. A computer manufacturer gets 50% of their hard drives from company A, 30% from company B and 20% from company C. The computer manufacturer installs one hard drive into each computer.
(a) What is the probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year? [4 marks]
(b) I buy a computer that does experience a hard drive failure within one year. What is the probability that the hard drive was manufactured by company C? [4 marks]
(a) The probability of the chosen hard drive to fail within one year is 0.005.
(b) The probability that the hard drive was manufactured by company C is 3.95%.
(a) The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:
Probability of choosing hard drive from company A and failure within one year + Probability of choosing hard drive from company B and failure within one year + Probability of choosing hard drive from company C and failure within one year
P(A and F) = P(A) x P(F|A) = 0.5 x 0.001 = 0.0005
P(B and F) = P(B) x P(F|B) = 0.3 x 0.002 = 0.0006
P(C and F) = P(C) x P(F|C) = 0.2 x 0.005 = 0.0010
The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:
0.0005 + 0.0006 + 0.0010 = 0.0021 (or 0.21%)
(b) Let F be the event that the hard drive fails within one year and C be the event that the hard drive is manufactured by company C.
We want to calculate P(C|F), the probability that the hard drive was manufactured by company C, given that it failed within one year;
P(C|F) = P(C and F) / P(F) = [P(C) x P(F|C)] / [P(A) x P(F|A) + P(B) x P(F|B) + P(C) x P(F|C)]
P(C|F) = (0.2 x 0.005) / (0.5 x 0.001 + 0.3 x 0.002 + 0.2 x 0.005)
P(C|F) = 0.083 / 0.0021 = 0.0395 (or 3.95%)
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The probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.
(a) Let the random variable X denote the number of hard drives in the computer manufacturer's hard drives that fail within one year. The probability distribution of X can be found as follows:
[tex]P(X = 0) = 0.5(1 - 0.001) + 0.3(1 - 0.002) + 0.2(1 - 0.005) = 0.9957[/tex]
[tex]P(X = 1) = 0.5(0.001) + 0.3(0.002) + 0.2(0.005) = 0.0016[/tex]
Thus, the probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is 0.0016.
(b) Let the event H denote that the computer I buy experiences a hard drive failure within one year. Let the event Ci denote that the hard drive in my computer is manufactured by company
i. Then, using Bayes' theorem, we have:
[tex]P(C3 | H) = P(H | C3)P(C3) / P(H)[/tex]
We can find the values of the three probabilities in the above formula as follows:
P(H | C1) = 0.001
P(H | C2) = 0.002
P(H | C3) = 0.005
P(C1) = 0.5
P(C2) = 0.3
P(C3) = 0.2
[tex]P(H) = P(H | C1)P(C1) + P(H | C2)P(C2) + P(H | C3)P(C3)≈ 0.00135[/tex]
Thus, P(C3 | H) = 0.005(0.2) / 0.00135 ≈ 0.74
Therefore, the probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.
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please soon aaaaaaaaaaaaaaaaaaaaaaa
Answer:
3
Step-by-step explanation:
Carrie sewed a square blanket with an area of 225 in^2
What is the length of each side of the blanket?
A. 56.25 in
B. 15 in
C. 112.5 in
D. 10 in
Answer:
The answer is A 56.25
Step-by-step explanation:
Since a square has 4 sides, divide 225 by 4 to get 56.25. To check your answer multiply 56.25 x 4 to get 225 in^2.
Hope this helps! Pls mark Brainliest!
Answer:
a.56.25
Step-by-step explanation:
Emily played softball all weekend. She was wondering the difference in time between the shortest game and the longest game. Can you help her figure it out?
Answer:
hh
Step-by-step explanation:
Can someone explain pls I don’t understand how to do it lol
Find the volume of the
rectangular prism.
3 cm
9 cm
7 cm
V = [?] cm3
Answer:
189cm^3
Step-by-step explanation:
First, we need to find the formula of "how to find the volume of any prism":
length * width *height
* = multiply
So that means we need to do:
7cm * 9cm * 3cm
= 189cm^3
^ = exponent
Hope this helped :)
I really need help please and thank you
Answer:
117 Degrees
Step-by-step explanation:
plz give brailiest, the 1 and 117 are the exact same angle
Find two negative consecutive integers such that the square of the first is five more than the second. Find the integers.
Answer:
the two consecutive negative integers are -2 and -1.
Step-by-step explanation:
Represent these negative integers by m and n.
Then (because the integers are consecutive) n = m + 1, and m^2 = n + 5.
Substituting m + 1 for n in the second equation, we get:
m^2 = m + 1 + 5, or
m^2 - m - 6 = 0
This factors into (m - 3)(m + 2) = 0. The only negative root is -2.
Thus, the two consecutive negative integers are -2 and -1.
Check: Is the square of the first five more than the second?
Is (-2)^2 = -1 + 5? YES
The integers aer -2 and -1.
Pls help me plz either sdys
Answer:
44
Step-by-step explanation:
14x3.14 is 43.96 and that after being rounded to the nearest tenth becomes 44
What is the value of s?
_____units
Answer:
17
Step-by-step explanation:
by Pythagoras
[tex]8 {}^{2} + 15 {}^{2} = {x}^{2} [/tex]
x=17
Write two sentences to explain what taxes are.
Answer:
Taxes are money paid to the government, you need to pay these for the army , teachers, and it forms a better economy etc.!:) Have a nice day friend.
Step-by-step explanation:
rylee1015, it does matter because you are copying answers just to get points, and it might be wrong which is not fair, so stop it!!!:(
Scuba tanks arrive at a pressure test station for testing prior to shipment. The arrival rate is 16mins and the station test time averages 8 minutes per tank. Poisson distributions are assumed
A. What is the utilization of the test station?
B. What is the probability that a tank have to wait in the queue prior to testing?
C. What is the mean time a tank will spend in queue?
D. What is the mean time that a tank will spend in the system ?
E. What is the mean number of tanks that might be expected to be in queue at any time?
F. What is the mean number of tanks that might be expected to be in the system at any time ?
G. What is the probability of finding four or more tanks in the system at any time ?
H. Find the probability of 6 or more in the system
The probability of finding four or more tanks in the system at any time is approximately 0.95. The probability of having 6 or more tanks in the system is approximately 0.77.
A. The utilization of the test station is calculated by dividing the average service rate (1 tank per 8 minutes) by the arrival rate (1 tank every 16 minutes). Utilization = Service rate / Arrival rate = 1/2 = 0.5 or 50%.
B. The probability that a tank has to wait in the queue prior to testing can be calculated using the queuing theory formula for the M/M/1 queue. In this case, the utilization (ρ) is 0.5. The formula for the probability of waiting in the queue (Pw) is Pw = ρ^2 / (1 - ρ) = 0.5^2 / (1 - 0.5) = 0.25 / 0.5 = 0.5 or 50%.
C. The mean time a tank spends in the queue can be calculated using Little's Law, which states that the mean number of customers in a stable system (L) is equal to the arrival rate (λ) multiplied by the mean time spent in the system (W). In this case, L = λ * W. The mean number of tanks in the queue (Lq) can be calculated using Lq = λ * Wq, where Wq is the mean time spent in the queue. Given λ = 1/16 tanks per minute and Lq = 8 tanks, we can rearrange the equation to solve for Wq: Wq = Lq / λ = 8 / (1/16) = 128 minutes / 16 = 8 minutes.
D. The mean time a tank spends in the system (queue + test) is equal to the mean time spent in the queue (Wq) plus the mean service time (1/8 tanks per minute). Therefore, the mean time in the system (Ws) is Ws = Wq + 1/μ = 8 + 1/8 = 8.125 minutes.
E. The mean number of tanks expected to be in the queue at any time can be calculated using Little's Law: Lq = λ * Wq. Given λ = 1/16 tanks per minute and Wq = 8 minutes, we can calculate Lq: Lq = (1/16) * 8 = 0.5 tanks.
F. The mean number of tanks expected to be in the system at any time can be calculated using Little's Law: L = λ * Ws. Given λ = 1/16 tanks per minute and Ws = 8.125 minutes, we can calculate L: L = (1/16) * 8.125 = 0.507 tanks.
G. The probability of finding four or more tanks in the system at any time can be calculated using the Poisson distribution formula. By summing the probabilities for four, five, and more tanks, we get 0.043.
H. The probability of having 6 or more tanks in the system can also be calculated using the Poisson distribution formula, which results in a probability of 0.002.
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Which pair of equations below is a result of constructing the altitude, h, in triangle ABC?
Answer:
the answer is A:
sinA=h/c
sinC=h/a
Step-by-step explanation:
edge 2020
The pair of equations is sinA=h/a cosC=h/a
What is trigonometry?
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms.
When a altitude is drawn from the base of the triangle
we can write
sinA=height/ a where a, is the side length of AB
also,cos C=height/a where a, is the side length of AB
Therefore,The pair of equations is where a, is the side length of AB
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A party store sold a total of 4,032 balloons since they open 42 days ago.they sold the same amount of balloons each day how many balloons did the party store sell each day since it opened?
A 86 balloons
B 90 balloons
C 92 balloons
D 96 balloons
Answer:
D)
Step-by-step explanation:
Sana maka tulong po
shout out tga pagadian
The figures are similar. find x.
whats 10k - 90 = -10
Answer:
k = 8
Step-by-step explanation:
10*8 - 90 = -10
:/
Complete the equation
the figures are similar find X
Answer:
X=14.4Step-by-step explanation:
As triangles are similar
The ratio of the sides must be equal
so..
[tex]\frac{x}{8} =\frac{9}{5}[/tex]
[tex]x=\frac{9*8}{5}[/tex]
[tex]x=14.4[/tex]
hope it helps...
have a great day!!
x=-2
Identify what's the slope and what's the y-intercept
Answer:
There is no slope and no y-intercept.This is a line that is parallel to Y-axis
Which scenario would most likely show a negative association between the variables? A. the height of a tree and the amount of time it takes to climb to the top of the tree
B. the number of people in the mall and the number of cars in the parking lot
C. miles traveled in a car and the amount of gasoline used
D. time spent reading a book and the number of pages left to read
Answer: i would say B because it makes the most sence
Step-by-step explanation:
Two spheres A and B of mass 7.5 kg and 6.3 kg respectively are separated by a distance of 0.59 m. Calculate the magnitude of the gravitational force A exerts on B and B exerts on A. force A exerts on B force B exerts on A If the force between the spheres is now 3.50 times 10-9 N, how far apart are their centers?
To calculate the magnitude of the gravitational force A exerts on B and B exerts on A, we can use Newton's law of universal gravitation:
[tex]F = (G * m1 * m2) / r^2[/tex]
where F is the gravitational force, G is the gravitational constant (approximately [tex]6.67430 *10^-11 N m^2 / kg^2)[/tex], m1 and m2 are the masses of the two spheres, and r is the distance between their centers.
For the force A exerts on B:
[tex]F_AB = (G * m_A * m_B) / r^2[/tex]
Substituting the given values: m_A = 7.5 kg, m_B = 6.3 kg, and r = 0.59 m:
F_AB = (6.67430 × 10^-11 N m^2 / kg^2) * (7.5 kg) * (6.3 kg) / (0.59 m)^2
Calculating the above expression gives the magnitude of the gravitational force A exerts on B.
For the force B exerts on A, we use the same formula:
[tex]F_BA = (G * m_A * m_B) / r^2[/tex]
Substituting the given values: m_A = 7.5 kg, m_B = 6.3 kg, and r = 0.59 m:
[tex]F_BA = (6.67430 * 10^-11 N m^2 / kg^2) * (6.3 kg) * (7.5 kg) / (0.59 m)^2[/tex]
Calculating the above expression gives the magnitude of the gravitational force B exerts on A.
To find the distance between the centers of the spheres when the force between them is 3.50 times 10^-9 N, we rearrange the formula to solve for r:
r = √((G * m_A * m_B) / F)
Substituting the given values: m_A = 7.5 kg, m_B = 6.3 kg, and F = 3.50 × 10^-9 N:
r = √[tex]((6.67430 * 10^-11 N m^2 / kg^2) * (7.5 kg) * (6.3 kg) / (3.50 *10^-9 N))[/tex]
Calculating the above expression gives the distance between the centers of the spheres.
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let y=f(x) be the particular solution to the differential equation dydx=ex−1ey with the initial condition f(1)=0 . what is the value of f(−2) ?
To find the value of f(-2) given the differential equation dy/dx = e^(x-1) * e^y with the initial condition f(1) = 0, we can use separation of variables and solve the differential equation.
Starting with the given differential equation:
dy/dx = e^(x-1) * e^y
Separating variables by multiplying both sides by dx and e^(-y):
e^(-y) dy = e^(x-1) dx
Now, we can integrate both sides of the equation:
∫ e^(-y) dy = ∫ e^(x-1) dx
Integrating the left side with respect to y and the right side with respect to x:
e^(-y) = e^(x-1) + C
Applying the initial condition f(1) = 0, where x = 1 and f(1) = 0:
e^(-0) = e^(1-1) + C
1 = 1 + C
C = -2
Substituting the value of C back into the equation:
e^(-y) = e^(x-1) - 2
Now, we can find the value of f(-2) by substituting x = -2 into the equation:
e^(-y) = e^(-2-1) - 2
e^(-y) = e^(-3) - 2
To find the value of f(-2), we need to solve for y:
e^(-y) = 2 - e^(-3)
y = -ln(2 - e^(-3))
Therefore, the value of f(-2) is f(-2) = -ln(2 - e^(-3)).
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what is the scale factor in the dilation?
PLEASE HURRY!!!
Answer: 1/3
Step-by-step explanation:
2.5:7.5
3:9
just simplify