A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 25 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Which of the following is the value of the appropriate test statistic?A. z = -2.4736B. z = 2.4736C. tdf=−2.4736D. td f=2.4736

Answer:

3/16

Step-by-step explanation:

3/4÷4=3/16

Since there are 4 people, not 3, divide the remaining pizza by 4.

Given:

There are given the vector to find the magnitude:

Explanation:

To find the magnitude, first, we need to find the vector for -4w.

Then,

From the given vector:

Then,

The magnitude of the given vector is:

Now,

For the direction of the vector:

Then,

Then,

Final answer:

The magnitude and direction of the given vector is shown below:

Hence, the correct option is D.

Answer:

The entire clock measures 360 degrees. As the clock is divided into 12 sections. The distance between each number is equivalent to 30 degrees (360/12)

I hope this helps you!

The revenue function is R = 25q, the cost function is C = 2000 + 20q, and the profit function is P = 5q - 2000.

The revenue function in terms of quantity can be calculated as follows:

Revenue (R) = q x p

Where: "q" is the quantity of units sold

"p" is the price per unit

At the break even point:

10,000 = 400p

p = 25 birr per unit

At the break even point, the total cost is equal to the total revenue:

Total cost = Total revenue = 10,000 birr

Fixed cost = 2000 birr

Variable cost (VC) = Total cost - Fixed cost

VC = 10,000 - 2000 = 8000 birr

The cost function in terms of quantity can be expressed as:

Cost (C) = FC + VC x q

C = 2000 + 20q

The profit function can be calculated as the difference between revenue and cost:

Profit (P) = R - C

P = 25q - (2000 + 20q)

P = 5q - 2000

Therefore, the revenue function is R = 25q,

the cost function is C = 2000 + 20q, and

the profit function is P = 5q - 2000.

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Answer:

the pattern is they all end at the same length

Step-by-step explanation:

Answer:

a = (19/-6)b

Step-by-step explanation:

2a + 6b = 1/5(4a + 11b)

10a + 30b = 4a + 11b

10a + 19b = 4a

19b = -6a

(19/-6)b = a

Answer:4m+16<40

Step-by-step explanation:

m=magazines

She's planning on buying a number of magazines (m) with a cost of $4 so it would be "4m".

She's planning on buying a book for $16 also so

4m+16

She wants to have a price all under 40 so

4m+16 < 40

Answer:

\(x=2\)

Step-by-step explanation:

\(8 = 2^x + 4\)

\(8-4=2^x\)

\(4=2^x\)

\(2^2=2^x\)

\(2=x\)

\(check:\)

\(2^2+4\)

\(4+4\)

\(8\)

Given:

The trigonometric expression is,

Explanation:

Simplify the expression.

So equivalent expression is,

The probability that the average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night is 0.8413.

Probability is a branch of mathematics that deals with the measurement of the likelihood or chance of an event occurring. It is used to quantify uncertainty and make predictions based on incomplete information. In general, probability is defined as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur.

The basic concept of probability is based on the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if we toss a fair coin, the probability of getting heads is 1/2 or 0.5, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

We can use the central limit theorem to approximate the distribution of the sample mean, assuming that the sample size is large enough. Since the sample size is n=36, we can assume that the sample mean has a normal distribution with mean μ=6.1 and standard deviation σ/√n=0.6/√36=0.1.

Let X be the sample mean sleeping time per night. Then we need to find the probability P(X > 6), which can be transformed into a standard normal distribution using the formula:

Z = (X - μ) / (σ/√n)

where Z is the standard normal variable.

Substituting the given values, we get:

Z = (6 - 6.1) / (0.1) = -1

Now we need to find the probability that Z is greater than -1. Using a standard normal distribution table or calculator, we can find that the probability is approximately 0.8413.

Therefore, the probability that the average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night is 0.8413.

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Answer:

1) We know that tomatoes cost 56c per the pound, and he estimates that he bought 5 pounds of tomatoes. If we multiply 5 by 0.56 we get 2.8, which means that if he purchased 5 pounds of tomatoes, he would have spent only 20c more than he did, which is pretty close. So yes, his estimate is reasonable

2) Well, i dont hav any clear amount of money he can spend so, just remember, if you have 3 pounds per say, you multiply 3 by 0.56. And then you can find your answer

Hope that this helped to some extent!

Answer:

Step-by-step explanation:

Answer choices: 25, 5, 35} tenths divided by {Answer choices: 5, 25, 10} tenths is __. His estimate {Answer choices: is reasonable, is not reasonable}

Answer:

choice 2) 1/4(n - 64)

Step-by-step explanation:

1/4n - 16 = 1/4(n - 64)

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

Answer:

Please help me important question in image

Step-by-step explanation:Please help me important question in image

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Answer:

The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.

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The graph that represents the given piecewise function has a range of

R: (-∞, 0) ∪ (0,2] ∪ (4, ∞).

A piecewise function is a combination of subfunctions that are defined with different intervals in the domain.

The range of the piecewise function is the union of all the ranges of the subfunctions.

The given piecewise function is

g(x) = x², x < 0

      = 1/2 x, 0 < x ≤ 4

      = x, x > 4

The domain and range for the subfunctions in the given piecewise function are:

for g(x) = x²; Domain is {x < 0} and Range is (-∞, 0)

for g(x) = 1/2 x; Domain is {0 < x ≤ 4} and Range is (0, 2]

for g(x) = x; Domain is {x > 4} and Range is (4, ∞)

Then, the range of the given piecewise function is

Range: (-∞, 0) ∪ (0, 2] ∪ (4, ∞)

Thus, the graph shown in the question is the correct one.

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Answer: c, its da 3rd graph

Step-by-step explanation:

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.

To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.

First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.

We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.

1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:

  0 = x^2 + 2x - 3.

  This quadratic equation can be factored as (x + 3)(x - 1) = 0.

  Therefore, x = -3 or x = 1.

2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.

3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).

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a. If a friend says his grade is 12 points lower than your grade, it means your grade is greater than his grade, if your grade is represented by x, then the grade of your friend can be found by subtracting 12 from your grade, this can be written as:

b. If x represents your friend's grade instead of yours, then to find your grade you need to add 12 to his grade, it can be represented as:

The correct answers are B. and D.

Option B is the correct option for the total area of the shape which is approximate 8049 ft².

An isosceles triangle is a polygon with three sides, where two of the sides have equal length.

Suppose the equal sides of Isosceles triangle is 'a',

so we can say that by Isosceles triangle rule: 70 = a√2

or side of Isosceles triangle (a) = 35√2 ft         (by Pythagoras theorem)

Area of isosceles triangle (A₁) = \(\frac{1}{2}\) × (Side of Isosceles triangle)²

                                                 = \(\frac{1}{2}\) × (35√2)² = 1225 ft²

Area of two square (A₂) =  2 × a × a

                                       = 2 × 35√2 × 35√2  = 4900 ft²

Area of quadrant circle (A₃) = (πr²)/4

                                              = 3.14 × (35√2)² × (1/4) = 1923.25 ft²

Total area of the shape = A₁ + A₂ + A₃

                                       = 1225 + 4900 + 1923.25 = 8048.25 ft²

Therefore, the total area of the shape is approximate 8049 ft²

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A.  The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.

B. No, the project does not meet the company's cash payback criteria.

C.  Yes, the project does meet the net present value criteria for acceptance.

A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.

                $55,440 / $7,700 = 7.2 years

To solve for the net present value, we say

Net Present Value = ∑ [(Cash inflow in period t) / (1 + \(r^{t}\)] - Initial Investment.

NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63

+ ($7,700 / (1 + 0.08)²) = 6601.51

+ .($7,700 / (1 + 0.08)³ = 6112.51

+ ($7,700 / (1 + 0.08)⁴) = 5659.73

+ ($7,700 / (1 + 0.08)⁵) = 5240.49

+ ($7,700 / (1 + 0.08)⁶) = 4 852.31

+ ($7,700 / (1 + 0.08)⁷) = 4492.88

+($7,700 / (1 + 0.08)⁸)  = 4160.07

+ ($27,600 / (1 + 0.08)⁸)) = 14911.42

- $55,440

We add all these values together and subtract by  $55,440

7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440

59160.55 - 55,440

NPV = 3720.55

B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.

C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.

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Answer:

434

Step-by-step explanation:

We can think of this problem like this:

\(\frac{percentage}{100} * number = newnumber\)

in this case, our percentage is 140, and our number is 310.

So lets plug in our values and solve!

\(\frac{140}{100} * 310 = newnumber\)

=

\(1.4*310 = newnumber\)

=

\(1.4*310 = 434\)
Hope this helps! :3

Note:

This formula can be changed depending on what your trying to find.

For instance, if you had one hundred and forty percent of what number is 310, we could rewrite this formula as:
\(\frac{100}{percentage}*number=newnumber\)

Which then would equal

\(\frac{100}{140}*310= \frac{310}{1.4}= 221.43\)

Hope this all helps! :3
if you have any other questions, feel free to let me know!

Answer:

1/6 + 1/2 = 2/3

Step-by-step explanation:

a/b The decay can be modeled by this equation, (1 - r), the r being the rate of decay. So it would be 1-0.115. (0.115 is your answer for a) You have to convert the percent into a decimal by moving the deicmal place two places to the left. 0.885 is your answer for b.

c. For function notation, that just means write an equation. So you want your decay times your inital.  V(t)=15000(0.885)^x. We get the V(t) from the directions that they want us to put it in; it's basically y.

d. Since it's two years, plug in 2 for x. This shows the decay after two years

V(t)=15000(0.885)^2

e. As with d, plug in 10 for x. V(t)=15000(0.885)^t

If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and  \(\frac{9K}{8}\)

Spring stiffness is a characteristic that describes the relationship between load and deflection. If k is stiffness, P is load, and x is deflection, P = kx. The smaller the deflection at a constant load, the stiffer the spring, k.

Given that,

If spring A has a spring constant which is 8 times spring B's spring constant,

Let us assume,

A spring is cut into two parts of length La and Lb

Also given that La : Lb

La : Lb = 1 : 8

The total of spring constant is = 1 + 8 = 9

If the length of spring is L , then La

La = \(\frac{L}{9}\)

And length of B , Lb

Lb = \(\frac{8L}{9}\)

We know, for spring force , spring constant or stiffness of spring is inversely proportional to length of spring .

K ∝ 1 / L

If initial spring constant is k then,

kL= KaLa = KbLb

Then,

Ka = \(\frac{K}{\frac{1}{9} }\)

Ka = 9K

And Kb = \(\frac{K}{\frac{8}{9} }\)

Kb = \(\frac{9K}{8}\)

Hence, stiffness of A is given by, 9K

Stiffness of B is given by  \(\frac{9K}{8}\)

Therefore,

If spring A has a spring constant which is 8 times spring B's spring constant then the ratio of their periods is = 9K and  \(\frac{9K}{8}\)

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P(X ≤ 2.39)= 0.9967, P(X ≥ -2.39) = 0.3808, P(|X| ≥ 2.39)  = 0.0388 ,P(|X + 3| ≥ 2.39) can be rewritten as P(X + 3 ≤ -2.39) + P(X + 3 ≥ 2.39)=  0.0388,  P(X < 5) = 1 AND P(|X| < 5) =  0.34 with X is a normal random variable .

To solve the given problems, we need to standardize the normal random variable X using the formula Z = (X - μ)/σ, where μ is the mean and σ is the standard deviation.

a) P(X ≤ 2.39) = P(Z ≤ (2.39 - (-3))/2) = P(Z ≤ 2.695) = 0.9967

b) P(X ≥ -2.39) = P(Z ≥ (-2.39 - (-3))/2) = P(Z ≥ 0.305) = 0.3808

c) P(|X| ≥ 2.39) = P(X ≤ -2.39) + P(X ≥ 2.39) = P(Z ≤ (-2.39 - (-3))/2) + P(Z ≥ (2.39 - (-3))/2) = P(Z ≤ -1.805) + P(Z ≥ 2.695) = 0.0354 + 0.0034 = 0.0388

d) P(|X + 3| ≥ 2.39) can be rewritten as P(X + 3 ≤ -2.39) + P(X + 3 ≥ 2.39)

= P(Z ≤ (-2.39 - (-3))/2) + P(Z ≥ (2.39 - (-3))/2) = P(Z ≤ -1.805) + P(Z ≥ 2.695) = 0.0354 + 0.0034 = 0.0388

e) P(X < 5) = P(Z < (5 - (-3))/2) = P(Z < 4) = 1

f) P(|X| < 5) = P(-5 < X < 5) = P((-5 - (-3))/2 < Z < (5 - (-3))/2) = P(-4 < Z < 4) = 0.9987

g) Let the value that X exceeds with a probability of 0.33 be x. Then, we need to find the value of x such that P(X > x) = 0.33. Using the standard normal distribution table, we can find that the z-score for the 0.33 probability is 0.44. So, we can solve for x as follows:

0.33 = P(X > x) = P(Z > (x - (-3))/2) = P(Z > (x + 3)/2)

0.44 = 1 - P(Z ≤ (x + 3)/2)

P(Z ≤ (x + 3)/2) = 1 - 0.44 = 0.56

Using the standard normal distribution table, we can find that the z-score for the 0.56 probability is 0.17. So, we can solve for x as follows:

0.56 = P(Z ≤ (x + 3)/2) = P(Z ≤ (x + 3)/2)

0.17 = (x + 3)/2

x = 0.34

Therefore, with a probability of 0.33, variable X exceeds the value of 0.34.

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Answer:

B

Step-by-step explanation:

The parenthesis will go away because there is nothing for them to be multipled by