1. Stating the hypotheses. In each of the following situations a significance test for a population mean ? is called for. Identify the null hypothesis H0 and the alternative hypothesis Ha in each case. Make sure to use proper notation! (Note: in Blackboard quiz, ?x-bar? means x ?, the sample mean.
(a) A company produces an item that is supposed to have a six inch hole punched in the center. A quality control inspector is concerned that the machine which punches the hole is ?out-of-control?. In an effort to test this, the inspector is going to gather a random sample of items punched by the machine and measure the diameter of the holes.
(b) A forestry company is concerned about its percentage of on-the-job accidents. Ideally, there would be no accidents, but the company decides to set its standard at 0.01%. The safety engineer takes a sample of 12 months and finds that per 1000 employee, 1.3 accidents were reported with a sample standard deviation of 0.47.
(c) A company sells 24-ounce (710-mL) bottles of natural spring water. A quality control engineer wants to check that bottle manufacturing process is on target. The resulting mean volume is 708 mL with a standard deviation of 6 mL.
(d) The FMA Company has designed a new type of 16 lb bowling ball. They believe that this ball would improve a person?s bowling score. The company knows that the average man who bowls in a scratch league with the company?s old ball has a bowling score of 155. The variance of these scores is 100. The company asks a random sample of 100 men bowling in scratch leagues to bowl for five weeks with their new ball. The mean bowling score for these men with the new ball is 170. There is no reason to believe the variance is any different with the new ball.
(e) A school principal wants to test if it is true that high school juniors use the computer more than 3.2 hours a day. He selects a random sample of 50 high school juniors and finds out that they use the computer an average of 3.1 hours a day.

Answer:

316.78

Step-by-step explanation:

area of 360 circle = pi*radius*radius

area of 360 circle = pi*11*11

area of 360 circle = pi*11*11

area of 360 circle = 380.13

360/300 = 380.13/x

114039/360 = x

x=316.775

step-by-step explanation:

remember if you add the given lengths, they must be greater than each other.

4+4=9 so no

9+4 = 13 which is greater than our number. We can make an isosceles triangle.

9+9 is greater than four so it works.

Answer:

probably 14 centimeters

Step-by-step explanation:

I put the new forgis on the jeep

The sine function that matches the equation in the graph is given as follows:

y = 2sin(x) - 2.

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The function varies between -4 and 0, for a difference of 4, hence the amplitude is given as follows:

A = 4/2

A = 2.

The function varies between -4 and 0, instead of between -2 and 2, for a vertical shift of -2, hence the coefficient C is given as follows:

C = -2.

The period of the function is of 2π, hence the coefficient B is given as follows:

B = 1.

Thus the function is:

y = 2sin(x) - 2.

The graph is given by the image presented at the end of the answer.

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In this case, the likelihood function is the product of the Poisson probability mass function evaluated at each data point in the training data. To compute the log-likelihood, we take the natural logarithm of this product. To maximize the log-likelihood function, we take the derivative of it with respect to the parameter and set it equal to zero. Solving for the parameter gives us the maximum likelihood estimate.

To help you with your question, let's go through the process of using maximum likelihood estimation (MLE) for a Poisson distribution step by step.

1. Given training data drawn from a Poisson distribution, we have the probability mass function (PMF) as:
P(X=k) = (λ^k * e^(-λ)) / k!, where k is a non-negative integer and λ is the parameter we want to estimate.

2. The likelihood function, which is the joint probability of obtaining the sample given the model, is the product of individual probabilities:
L(λ) = Π P(X_i=k_i), for i = 1 to n, where n is the number of data points.

3. For MLE, we compute the log-likelihood function, which is the natural logarithm of the likelihood function:
log(L(λ)) = Σ log(P(X_i=k_i)), for i = 1 to n.

4. Plugging in the PMF, the log-likelihood becomes:
log(L(λ)) = Σ [k_i * log(λ) - λ - log(k_i!)], for i = 1 to n.

5. To maximize the log-likelihood function, we take its derivative with respect to λ and set it to 0:
d(log(L(λ))) / dλ = Σ [k_i/λ - 1] = 0.

6. Solve for the MLE estimate of λ:
λ_MLE = Σ k_i / n, where n is the number of data points.

The resulting estimate for λ, λ_MLE, is in accordance with the definition of λ in a Poisson distribution, as it represents the average number of events in the sample. The resulting estimate for the Poisson distribution parameter is the sample mean of the training data. This is in accordance with the definition of the Poisson distribution, where the mean and variance are equal to the parameter lambda.

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a. The population of the city can be modeled using the exponential growth function:

y = 600(1 + 0.018)^x

with x being years from 0 to 10, where x = 0 corresponds to the year 2010. We can create a table to show the population for each year from 2010 to 2020:

(you can see above)

We can see from the table that the population of the city is increasing each year, and the rate of increase is accelerating. This is because the growth function is exponential, not linear. We know it is exponential because the function has a power of x in the exponent, which causes the rate of growth to increase over time. If the function were linear, the rate of growth would be constant.

b. To predict the population in 2025, we can use the same function with x = 15 (since 2025 is 15 years after 2010):

y = 600(1 + 0.018)^15

y ≈ 846.5 (in thousands)

Therefore, we can predict that the population of the city in 2025 will be approximately 846,500 citizens.

The functions represented by the graphs are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

f(x) = |x|

The function g(x) is a translation down two units of the parent function f(x), hence it is given as follows:

g(x) = |x| - 2.

The function h(x) is a translation up three units of the parent function f(x), hence it is given as follows:

h(x) = |x| + 3.

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(a)The test statistic is -1.684

(b) degrees of freedom for a T distribution = 15

(c)the p-value is 0.05

We will be conducting a t-test to determine if the modifications made by the manufacturer have successfully reduced the noise level of the mowers.

(a) First, we need to find the test statistic (t-value). We can calculate it using the formula:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

t = (79.6 - 82) / (5.7 / sqrt(16))

t = (-2.4) / (5.7 / 4)

t = -2.4 / 1.425

t ≈ -1.684 (rounded to three decimal places)

(b) To find the degrees of freedom for a T distribution, we use the formula:

df = sample size - 1

df = 16 - 1

df = 15

(c) To find the p-value, we look up the t-value and the degrees of freedom in a t-distribution table or use a calculator or software that can calculate the p-value for a one-tailed t-test. In this case, we have:

t = -1.684 and df = 15

Using a calculator or software, we find:

p-value ≈ 0.0568 (rounded to four decimal places)

Now, we compare the p-value with the significance level (0.05). Since the p-value (0.0568) is greater than the significance level (0.05), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the modifications have reduced the noise level of the mowers at a 5% significance level.

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A random variable Y has the density Function f(y) = { ey, y<0, 0, otherwise

a.[tex]E(e^(3Y/2)) = [1/5] - [3e^(5/2)/10][/tex]

b.[tex]M(t) = 1/[(1-t)(t+1)][/tex]

c.[tex]V(Y) = ∫(y^2 + 2y + 1)eydy[/tex] [tex]= [y^2e^y]/2 - ∫ye^ydy + [ye^y]/2 - ∫e^y[/tex]

a. To find [tex]E(e^(3Y/2))[/tex], we use the definition of expected value, which is the integral of the product of the random variable and its probability density function. We have: [tex]E(e^(3Y/2))[/tex] [tex]= ∫e^(3y/2)f(y)dy[/tex] [tex]= ∫e^(3y/2)eydy[/tex], y<0 .Using integration by parts, we let [tex]u = e^(3y/2)[/tex] and [tex]dv = e^y dy[/tex]. Then, [tex]du/dy = (3/2)e^(3y/2)[/tex]and [tex]v = e^y[/tex].

[tex]E(e^(3Y/2))[/tex] [tex]= ∫e^(3y/2)eydy[/tex] [tex]= [e^(3y/2)e^y/2] - ∫(3/2)e^(3y/2)e^y/2dy[/tex]

[tex]= [e^(5y/2)]/5 - [3/5]∫e^(5y/2)dy[/tex]

[tex]= [e^(5y/2)]/5 - [3e^(5y/2)/10] + C[/tex]

Since f(y) = 0 for y ≥ 0, we know that [tex]E(e^(3Y/2))[/tex] only depends on the integral of [tex]e^(3y/2)[/tex]for y < 0. Evaluating the above expression at y = 0, we get:

[tex]E(e^(3Y/2)) = [1/5] - [3e^(5/2)/10][/tex]

b. To find the moment generating function (MGF) for Y, we use the definition of the MGF, which is the expected value of [tex]e^(tY)[/tex] for all t in a neighborhood of 0. We have:

[tex]M(t) = E(e^(tY))[/tex] [tex]= ∫e^(ty)f(y)dy[/tex][tex]= ∫e^(ty)eydy[/tex] , y<0

Using integration by parts as before, we get:

[tex]M(t) = ∫e^(ty)eydy[/tex] [tex]= [e^(ty)e^y]/(t+1) - ∫(t+1)(e^(ty)e^y)/(t+1)dy[/tex]

[tex]= [e^(ty+2y)]/(t+1) - (t+1)M(t)[/tex]

Simplifying, we get:

M(t)(t+1) = 1/(1-t)

M(t) = 1/[(1-t)(t+1)]

c. To find V(Y), we first need to find the mean or expected value of Y. Using the definition of expected value, we have:

E(Y) = ∫yf(y)dy = ∫yeydy, y<0. Using integration by parts once more, we get: E(Y) = ∫yeydy [tex]= [ye^y] - ∫e^ydy[/tex] = -1 . The mean of Y is -1.

We use the definition of variance, which is the expected value of the squared difference between the random variable and its mean. We have:

[tex]V(Y) = E[(Y - E(Y))^2][/tex][tex]= ∫(y + 1)^2f(y)dy[/tex] [tex]= ∫(y^2 + 2y + 1)eydy[/tex], y<0

Using integration by parts for the third time, we get:

[tex]V(Y) = ∫(y^2 + 2y + 1)eydy[/tex][tex]= [y^2e^y]/2 - ∫ye^ydy + [ye^y]/2 - ∫e^y[/tex]

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The significance level is set at 5%, and the probability of the result is 0%, which is less than the significance level. The result is statistically significant.

We are given that;

The probability of the result=(7.7/9.2/4.6/5/7.8)%

Now,

To determine the probability of the treatment group’s mean being lower than the control group’s mean by 15 points or more, we need to find the difference between the two sample means and compare it to the standard error of the difference. The standard error of the difference can be estimated using the formula:

SE = √(s1^2 / n1) + (s2^2 / n2)

where s1 and s2 are the sample standard deviations and n1 and n2 are the sample sizes.

Assuming that the treatment group is group 1 and the control group is group 2, we can plug in the values given in the question:

SE = √(9.2^2 / 30) + (7.7^2 / 30)

SE = √3.02

SE = 1.74

The difference between the two sample means is:

x1 - x2 = 85 - 100

x1 - x2 = -15

To find the probability of this difference or lower, we need to find the z-score and use a normal distribution table or calculator3:

z = (x1 - x2) / SE

z = (-15) / 1.74

z = -8.62

Using a normal distribution table or calculator, we can find that P(z ≤ -8.62) ≈ 0, which means that the probability of the treatment group’s mean being lower than the control group’s mean by 15 points or more is very close to zero.

Therefore, by probability the answer will be statistically significant.

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Answer:

I believe the answer is 49°

The correct answer is not listed in the options, so there might have been a mistake in the question or the choices provided. To find the fourth ordered pair using the two sequences, we need to apply each rule to the previous result, starting from the given starting points.

Using Rule 1, starting from 1:
- Multiply by 2: 1 x 2 = 2
- Add one third: 2 + (1/3) = 7/3
So the first term of the fourth ordered pair is 7/3.
Using Rule 2, starting from 0:
- Add one half: 0 + 1/2 = 1/2
- Multiply by 4: (1/2) x 4 = 2
So the second term of the fourth ordered pair is 2.
Therefore, the fourth ordered pair is (7/3, 2).

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Option D (9) is not a probability and is not a possible answer choice for a probability question.

To find the probability of the intersection of events A and B (denoted as P(A ∩ B)), we need to know how many elements are in both A and B. Since there are 2 repeated elements between the events, this means that there are a total of 7 - 2 = 5 distinct elements between them.

Therefore, P(A ∩ B) = 5/7.

Note that none of the answer choices provided match this result exactly. Option A is the closest with a probability of 4/7, but this is the probability of A alone, not the intersection of A and B. Option B (2/7) is the probability of B alone and option C (5/7) is the probability of either A or B occurring, not the intersection.

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The  speed of the moving end of the sprinkler in feet per minute is 34.48 food per hour

Speed in mathematics is defined as the distance an object travels in a given amount of time. Also, It can be calculated using the formula Speed = Distance ÷ Time, where distance is equal to the time taken to travel and time is equal to the number of seconds needed to travel.

The given parameters are

The distance is = 50-foot long

Time is given as = 1.45 hours

Speed = Distance/Time

Speed = 50 foot long/1.45 hurs

Therefore the Speed = 34.48 food per hour

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43 4/5 cups of cheese is needed to make 10 pizzas.

We will use the Unitary method, that is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.

Given that it takes 4 3/4 cups of cheese, 7/8 cups of olives, and 2 5/8 cups of sausage to make a signature pizza.

For making one pizza, amount of cheese needed =  4 3/8 cups = 35/8  cups.

Now the total amount of cheese needed to make 10 pizzas, we need to multiply  35/8  cups by 10.

So, 350/8  cups = 43 4/5 cups

Thus,  43 4/5 cups of cheese is needed.

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Answer:B

Step-by-step explanation:

The functions categorized as decay or growth are

From the question, we have the following parameters that can be used in our computation:

y = 2250(1-0.9)^x

y=10.(1+0.04)^x

An exponential function is represented as

y = ab^x

If b > 0, then it is a growth function

Otherwise, it a decay function

using the above as a guide, we have the following:

y = 2250(1-0.9)^x -- decay

y=10.(1+0.04)^x -- growth

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The dimension of the board either 4 by 6 square inches or 6 by 4 square inches.

We know that,

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

here,

let the length of the board be x, and width be w,

The perimeter of the rectangle board  = 20

2 (l + w) = 20

l + w = 10

l = 10 - w

Now,

area of the board = 24

l × w = 24

(10 - w)w = 24

10w - w² = 24

w² -10w + 24 =0

(w - 4)(w -6) = 0

So,

w = 4 or 6

Now,

Lengths = 10 - 4 or 10 - 6

             =  6 or 4

Thus, the dimension of the board either 4 by 6 square inches or 6 by 4 square inches.

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Using diagonals from a common vertex, the number of triangles that could be formed from a 19-gon  is 16 triangles.

If you choose a vertex of a 19-gon, then you can draw diagonals from this vertex to 16 other vertices of the 19-gon (not including adjacent vertices).

Each of these diagonals will form a triangle with the chosen vertex. Therefore, the number of triangles that can be formed using diagonals from a common vertex of a 19-gon is 16 triangles.

When you choose a vertex of a 19-gon, you can draw diagonals to 16 other vertices of the 19-gon. Each of these diagonals forms a distinct triangle with the chosen vertex. Therefore, the total number of triangles that can be formed is 16.

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To maximize the likelihood function, we take the derivative with respect to θ and set it equal to zero: d/dθ[L(θ|X1,X2,...,Xn)]=−n/θ+(X1+X2+⋯+Xn)/θ2=0.

The MLE for θ in the exponential distribution is simply the sample mean of the observed data.

The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson point process. X1,X2,...,XnX1,X2,...,Xn is a random sample of size n from this distribution, which means that each XiXi is an independent and identically distributed random variable with the same exponential distribution.

The probability density function (pdf) of the exponential distribution is given by f(x:θ)=(1/θ)e−x/θ, where θ is the scale parameter. This means that the probability of observing a value x from the distribution is proportional to e−x/θ, with the constant of proportionality being 1/θ.

To estimate the value of θ based on the observed data, we can use the method of maximum likelihood estimation (MLE). The likelihood function for the sample X1,X2,...,XnX1,X2,...,Xn is given by L(θ|X1,X2,...,Xn)=∏i=1n(1/θ)e−Xi/θ=(1/θ)n e−(X1+X2+⋯+Xn)/θ.

Solving for θ, we get θ=(X1+X2+⋯+Xn)/n, which is the sample mean.

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Answer:

Ais 66 and B is 40% C is 60%

Step-by-step explanation:

I know A is correct but not b or c hope this helps

Therefore, the linearization of f(x) = cos(x) at a = π/2 is L(x) = π/2 - x.

The linearization of a function f(x) at a point a is given by:

L(x) = f(a) + f'(a)(x - a)

where f'(a) denotes the derivative of f(x) evaluated at x = a.

In this case, we have:

f(x) = cos(x)

a = π/2

First, let's find f'(x):

f'(x) = -sin(x)

Then, we can evaluate f'(a):

f'(π/2) = -sin(π/2) = -1

Next, we can plug in the given values into the formula for linearization:

L(x) = f(a) + f'(a)(x - a)

L(x) = cos(π/2) + (-1)(x - π/2)

L(x) = 0 - x + π/2

L(x) = π/2 - x

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The correct statement about the function is given as follows:

D. As x approaches positive infinity, f(x) approaches positive infinity.

The function for this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

At the points where the interval changes, which are x = 0 and x = 2, the function is not defined, meaning that:

On the interval 0 < x < 2, the function is defined as follows

f(x) = -x² - 4x + 1.

The derivative is then given as follows:

f'(x) = -2x - 4.

-2x - 4 is positive for x < -2, hence the function is increasing only for x < -2.

Thus option d is correct, as:

1/2(∞) + 3 = ∞.

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The product of the two matrices is  [2 - 3]    x  [1  -  4]

                                                            [ 3   2]       [4     1]

option B.

A product matrix is also known as matrix multiplication, which involves the multiplication of two matrices, to get or simply to a single matrix.

For example, if P and Q are the two matrices, then the product of the two matrices P and Q are denoted by:

Y = PQ.

For the given question; we have the first matrix as; (2 - 3i) and the second matrix as (1 - 4i).

Matrix (2 - 3i) is transformed to [2 - 3]

                                                   [ 3   2]

Matrix (1 - 4i) is transformed to [1  -  4]

                                                  [4     1]

The product of the two matrices =  [2 - 3]    x  [1  -  4]

                                                          [ 3   2]       [4     1]

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Answer:

In a 30°-60°-90° right triangle, the length of the shorter leg is 1/2 the length of the hypotenuse, and the length of the longer leg is √3 times the length of the shorter leg. In the equilateral triangle, the perimeter is (2)(4√3)(3) = 24√3, and the apothem is 4.

π(8^2) - (1/2)(24√3)(4)

= 64π - 48√3 square units

= about 117.92 square units

The only possible degree for the polynomial p+q is 11.

Given the degree of polynomial p is 11 and the degree of polynomial q is 7, we can find all possible degrees of the polynomial p+q by considering their highest-degree terms.

When adding polynomials, the resulting polynomial will have the degree that corresponds to the highest-degree term. In this case, we have two options:

1. The highest-degree terms of both polynomials are of different degrees. In this case, the degree of p+q will be the maximum of the two given degrees, which is max(11, 7) = 11.

2. The highest-degree terms of both polynomials are of the same degree and their coefficients have opposite signs, causing them to cancel out when added. In this scenario, the degree of p+q will be less than the maximum degree, i.e., less than 11.
However, given that the degrees of p and q are different (11 and 7), it is not possible for their highest-degree terms to cancel out.

Therefore, the only possible degree for the polynomial p+q is 11.

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By using the model, the missing values that complete the expression include the following:

48 + 32 = 8(6 + 4).

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of big rectangle = L × B

48 = 8 × 6

Area of small rectangle = L × B

32 = 8 × 4

For the required expression, we have:

48 + 32 = 8(6 + 4).

80 = 8(10)

80 = 80

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Step-by-step explanation:

See image:

In mutually exclusive data, you cannot find any overlap or intersection between the categories or events being analyzed.

This means that the occurrence of one event or category precludes the occurrence of the other. On the other hand, in dependent data, the occurrence of one event or category may have an effect on the occurrence of the other, and thus, they are not completely independent or separate. Therefore, in both cases, you cannot find any shared or common outcomes or occurrences between the categories or events being analyzed.

You cannot find a direct correlation or causal relationship between mutually exclusive or dependent data. In mutually exclusive events, the occurrence of one event prevents the occurrence of the other, meaning they cannot happen at the same time. In dependent events, the probability of one event happening is influenced by the outcome of a previous event. Due to these characteristics, it is not possible to establish a direct correlation or causal relationship between such events.

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Answer: 2.09

Step-by-step explanation: 0.85e^0.075(12)

The smallest number that appears in both lists is 11. Therefore, the least possible value of n that satisfies both conditions is 11.

To find the least possible value of n, we need to find the smallest number that satisfies both conditions.

We can start by listing out some numbers that have a remainder of 2 when divided by 3: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179, 182, 185, 188, 191, 194, 197, 200, 203, 206, 209, 212, 215, 218, 221, 224, 227, 230, 233, 236, 239, 242, 245, 248, 251, 254, 257, 260, 263, 266, 269, 272, 275, 278, 281, 284, 287, 290, 293, 296, 299, and so on.

Out of these numbers, we need to find the ones that also have a remainder of 1 when divided by 5. The numbers that have a remainder of 1 when divided by 5 are: 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, and so on.

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