Find the P-value of the hypothesis test described below a. 0.9582 b. 0.0250 c. 0.0418 d. 0.0836
e. 0.9164 A hypothesis test, at the 0.05 significance level, is conducted in order to determine if the percentage of US adults who expect a decline in the economy is equal to 50%. A random sample of 300 US adults includes 135 who expect a decline. Find the value of the test statistic.
a. -1.65
b. -1.73
c. 1.96
d. 1.75
e. 1.72

The approximate change formula for a function z=f(x,y) at the point (a,b) in terms of differentials is \(dz=f_y (a,b) dx + f_x(a,b) dy\). So, option a) is correct.

In calculus, the differential represents the principal part of the change in a function y=f(x) with respect to changes in the independent variable.

Differential, in mathematics, is an expression based on the derivative of a function, useful for approximating certain values of the function.

The derivative of a function can be used to approximate certain function values with a certain degree of accuracy.

The approximate change formula for a function z=f(x,y) at the point (a,b) in terms of differentials is given by the equation \(dz=f_y (a,b) dx + f_x(a,b) dy\), where \(f_x(a,b)\) and \(f_y(a,b)\) represents the partial derivatives of the function f(x,y) with respect to x and y, respectively, evaluated at the point (a,b).

So, option a) is correct.

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Answer:

x = 56

Step-by-step explanation:

Step 1: Write out equation

x + 20 + x + 48 = 180

Step 2: Combine like terms (x)

2x + 20 + 48 = 180

Step 3: Combine like terms (constants)

2x + 68 = 180

Step 4: Subtract 68 on both sides

2x = 112

Step 5: Divide both sides by 2

x = 56

Step-by-step explanation:

Given that,

Length, l = (3d+2) m

Width, b = (d+5) m

(a) Perimeter of the rectangle,

P = 2(l+b)

P = 2(3d+2+d+5)

= 2(4d+7)

P = 8d+14

(b) If P = 30 cm.

8d+14 = 30

8d = 16

d = 2

(c) l = (3(2)+2) = 8 m

b = (2+5) = 7 m

The area of this rectangle,

A = lb

A = 8×7

A = 56 cm²

Hence, this is the required solution.

Answer:

44

Step-by-step explanation:

Since a triangle has a total of 180 degrees, 62+44=136

180-136=44

Answer:

The first box is 4 and the second box is 4

The solution is
(\(\frac{3}{2}\),1)

Step-by-step explanation:

y = 2x -2  Subtract 2x from both sides

-2x + y = -2  Multiply all the way through by - 2

4x - 2y = 4  You are doing this so that you can add it to the first equation 4x + 2y = 8

     4x + 2y = 8

(+) 4x - 2y = 4

       8x       = 12  Divide both sides by 8

x = \(\frac{12}{8}\) = \(\frac{3}{2}\)

To find y substitute \(\frac{3}{2}\) for x and solve for y

y = 2x - 2

y = \(\frac{2}{1}\) x \(\frac{3}{2}\) - 2

y = 3 - 2

y = 1

Helping in the name of Jesus.

Answer:

Part A = 4x - 2y = 4

Part B = (1.5, 1)

Step-by-step explanation:

Part A:

y = 2x - 2

2y = 4x -4

4x - 4 = 2y

4x - 2y = 4

Part B:

4x + 2y = 8

2y = 8 - 4x

y = (8 - 4x)/2

y = 2x -2

(8 - 4x)/2 = 2x -2

8 - 4x = 4x - 4

8x = 12

x = 1.5

4x + 2y = 8

4(1.5) + 2y = 8

6 + 2y = 8

2y = 2

y = 1

(1.5, 1)

Answer:

x = 2/5 or 0.4

Step-by-step explanation:

5x + 3 = 5

      -3   -3

5x = 2

/5    /5

x = 2/5 or 0.4

The percentage of ACT composite scores are below 31 is 97.28%

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

Mean = 21.0

Standard deviation = 5.2

So, the z-score is

z = (x - mean)/SD

This gives

z = (31 - 21)/5.2

z = 1.923

So, the probability is

P = P(z < 1.923)

Using the table of z scores, we have

P = 0.97276

This gives

P = 97.28%

Hence, the percentage is 97.28%

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Yes, it is possible to prove that two triangles are congruent by using the AAS congruence theorem.

The AAS congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. This theorem can be used to prove that two triangles are congruent if two of the angles in the triangle and the side between them are congruent to two angles and the side between them of the other triangle. To prove congruence using the AAS congruence theorem, it is important to use the right angle and side measurements to ensure that the two triangles are congruent. If the measurements are correct, then the two triangles will be congruent.

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Yes, it is possible to prove that two triangles are congruent by using the AAS congruence theorem.

The AAS congruence theorem

it states that if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

This theorem can be used to prove that two triangles are congruent if two of the angles in the triangle and the side between them are congruent to two angles and the side between them of the other triangle.

To prove congruence using the AAS congruence theorem, it is important to use the right angle and side measurements to ensure that the two triangles are congruent. If the measurements are correct, then the two triangles will be congruent.

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Answer:

b

Step-by-step explanation:

1 mile = 3 laps.

3x7=21

21=hour

21/7=3

The soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day for the soft drink vendor, we need to use the formula P(x) = 0.001x^2 + 3x + 1800, where x is the number of cans of soda pop sold in one day.

To find the maximum profit, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex is given by -b/2a, where a = 0.001 and b = 3. Plugging in these values, we get x = -3/(2*0.001) = -1500.

Since the soft drink vendor cannot sell a negative number of cans, we know that the maximum profit occurs at the closest whole number to x = -1500, which is x = 1500.

To find the maximum profit per day, we can plug in x = 1500 into the profit function:

P(1500) = 0.001(1500)^2 + 3(1500) + 1800 = $5250

Therefore, the soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day and the number of cans needed to reach that profit, we'll first need to find the critical point of the given quadratic profit function, P(x) = -0.001x^2 + 3x - 1800.

Step 1: Find the derivative of P(x) with respect to x. This will give us the rate of change of profit as the number of cans sold changes.

P'(x) = -0.002x + 3

Step 2: Set the derivative equal to zero and solve for x. This will give us the critical point where the maximum profit occurs.

-0.002x + 3 = 0

x = 1500 cans

Step 3: Substitute the critical point (x = 1500) back into the profit function P(x) to find the maximum profit.

P(1500) = -0.001(1500)^2 + 3(1500) - 1800

P(1500) = $600

So, the maximum profit per day is $600, and the soft drink vendor must sell 1500 cans to reach the maximum profit.

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The maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

The profit function for the soft drink vendor is given by:

P(x) = \(0.001x^2 + 3x + 1800\)

To find the maximum profit, we need to find the vertex of the parabola represented by this function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

where a = 0.001 and b = 3. Substituting these values, we get:

x = -3 / (2 * 0.001) = -1500

Since the value of x cannot be negative in this context, we know that the maximum profit occurs at x = 1500. To find the maximum profit, we substitute this value of x into the profit function:

P(1500) =\(0.001(1500)^2 + 3(1500) + 1800 = $4800\)

Therefore, the maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

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Answer:

Step-by-step explanation:

6^0 + 6^0 + 6^0 + 6

= 1+1+1+6

= 9.

The value of the constant of variation include 8, 3.2, and 1.25

From the information given, when x = -0.5, y = -4.0. The constant will be:

y = kx

-4 = -0.5k

k = -4.0/-0.5

k. = 8

When x = 2.5, y = 8

y = kx

8 = 2.5k

k = 8/2.5

k = 3.2

When x = 4, y = 5

y = kx

5 = 4k

k = 5/4

k = 1.25

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Answer:

23

Step-by-step explanation:

put the numbers in numerical order and then cross off on both sides until there is only one number left (look at the process below!)

9,14,16,18,23,25,26,26,30

14,16,18,23,25,26,26

16,18,23,25,26

18,23,25

23

Answer:

10:33

Also YB better

Step-by-step explanation:

Answer: there will be 33 kids what is 33 divided by 10

                                                 3           r  3

Step-by-step explanation:  33÷ 10 = 30

Answer:

y = (x+3)2 - 12.

Step-by-step explanation:

Answer:

y = (x + 3)^2 - 6.

Step-by-step explanation:

y=x^2+6x+3

y = (x + 3)^2 - 9 + 3

y = (x + 3)^2 - 6.

There is one specific type of transformation that can cause a change in the period of a tangent or cotangent function, and that is a dilation.

A dilation is a transformation that stretches or compresses a function horizontally or vertically. When a tangent or cotangent function is dilated horizontally, the period of the function changes. The period of a tangent function is π, while the period of a cotangent function is also π.

If the function is dilated by a factor of k, then the new period will be π/k. This means that the function will oscillate faster if it is compressed horizontally (k > 1) and slower if it is stretched horizontally (k < 1). Therefore, it is important to consider the effects of dilations when analyzing the period of a tangent or cotangent function.

The type of transformation that could cause a change in the period of a tangent or cotangent function is called a "horizontal stretch" or "horizontal compression." These transformations affect the frequency of the function by scaling it horizontally, which in turn alters the period of the tangent or cotangent function.

In mathematical terms, the general form of a tangent function is y = A * tan(B(x - C)) + D, and for a cotangent function, it's y = A * cot(B(x - C)) + D. In these expressions, A represents the amplitude, B determines the horizontal stretch or compression, C is the phase shift, and D is the vertical shift.

The factor B directly affects the period of the function. For a tangent or cotangent function, the standard period is π. To find the new period after a horizontal transformation, you can use the formula: new period = (standard period) / |B|. Thus, by changing the value of B, the period of the tangent or cotangent function will be affected accordingly.

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A value which is in the domain of f(x) include the following: C. 4.

In Mathematics, a piecewise-defined function is a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the given piecewise-defined function, we can reasonably infer and logically deduce that it is defined over the interval -6 < x ≤ 0 and 0 < x ≤ 4.

In conclusion, a value of 4 is the only answer option that is in the domain of this piecewise-defined function.

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Complete Question:

Which value is in the domain of f(x)?

A.) –7

B.) –6

C.) 4

D.) 5

Answer:

y + 1 = \(\frac{1}{2}\) (x + 2)

Step-by-step explanation:

The equation of a line in point- slope form is

y - y₁ = m(x - x₁)

where m is the slope and (x₁, y₁ ) a point on the line

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, - 1 ) and (x₂, y₂ ) = (2, 1 )

m = \(\frac{1-(-1)}{2-(-2)}\) = \(\frac{1+1}{2+2}\) = \(\frac{2}{4}\) = \(\frac{1}{2}\) and (x₁, y₁ ) = (- 2, - 1 ) , then

y - (- 1) = \(\frac{1}{2}\)(x - (- 2) ) , that is

y + 1 = \(\frac{1}{2}\) (x + 2)

a) The subsets of S = {y, b, g} are: ∅, {y}, {b}, {g}, {y, b}, {y, g}, {b, g}, {y, b, g}.

b) The subsets of S = {y, b, g, r} are: ∅, {y}, {b}, {g}, {r}, {y, b}, {y, g}, {y, r}, {b, g}, {b, r}, {g, r}, {y, b, g}, {y, b, r}, {y, g, r}, {b, g, r}, {y, b, g, r}.

c) The number of subsets that can be created from S = {1, 0, 0} is 8.

d) Pseudocode to list all subsets of a set S and to list all sets of 2 from S is provided.

a) Given S = {y, b, g}, the subsets of S are:

∅, {y}, {b}, {g}, {y, b}, {y, g}, {b, g}, {y, b, g}

b) Given S = {y, b, g, r}, the subsets of S are:

∅, {y}, {b}, {g}, {r}, {y, b}, {y, g}, {y, r}, {b, g}, {b, r}, {g, r}, {y, b, g}, {y, b, r}, {y, g, r}, {b, g, r}, {y, b, g, r}

c) Given S = {1, 0, 0}, the number of subsets that can be created is 2^3 = 8.

d) Pseudocode to list all subsets of a set S:

function listSubsets(S):

   n = length(S)

   for i from 0 to (2^n - 1):

       subset = []

       for j from 0 to (n - 1):

           if (i & (1 << j)) != 0:

               subset.append(S[j])

       print(subset)

9) a) The number of ways to make a group of 2 out of S = {y, b, g} is C(3, 2) = 3.

b) Pseudocode to list all sets of 2 given S:

function listSetsOfTwo(S):

   n = length(S)

   for i from 0 to (n - 2):

       for j from (i + 1) to (n - 1):

           print(S[i], S[j])

C(n, k) represents the combination function, which calculates the number of ways to choose k elements from a set of n elements.

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The inequality that shows the minimum amount of Isaac is x ≥ $2,455.21

What is inequality?

An inequality is a mathematical statement that compares two expressions and expresses the relationship between them. It is represented by a symbol such as ">", "<", "≥", or "≤" and can be thought of as a generalization of an equation.

First, we need to find Isaac's monthly gross income. Since he has a bi-weekly gross income of $1,925, we can calculate his monthly gross income as follows:

Monthly gross income = bi-weekly gross income x 26 / 12 = $1,925 x 26 / 12 = $4,158.33

The debt-to-income ratio is the ratio of monthly debt payments to monthly gross income, expressed as a percentage.

We want to find the minimum amount by which Isaac needs to reduce his monthly debt payments to have a debt-to-income ratio of 35%.

So we can set up the following inequality:

Minimum monthly debt payments / Monthly gross income ≤ 35% / 100%

Substituting the given values, we get:

$3,915 / $4,158.33 ≤ 0.35

Simplifying this inequality, we get:

0.9407 ≤ 0.35

This inequality is not true, so we made an error in our calculations. Let's check the calculation of monthly gross income. We should have:

Monthly gross income = bi-weekly gross income x 26 / 12 = $1,925 x 26 / 12 = $4,158.33

This calculation is correct. The problem is that the minimum monthly debt payments of $3,915 are already higher than what is allowed by the debt-to-income ratio of 35%. In fact, the maximum monthly debt payments Isaac can have to satisfy the 35% debt-to-income ratio is:

Maximum monthly debt payments = Monthly gross income x 35% = $4,158.33 x 35% = $1,454.92

Therefore, the minimum amount by which Isaac needs to reduce his monthly debt payments is:

$3,915 - $1,454.92 = $2,460.08

Rounding this to two decimal places, we get $2,460.09, which is closest to the fourth option:

x ≥ $2,455.21

Hence,  the inequality that shows the minimum amount of Isaac is x ≥ $2,455.21

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Answer:

a. B is the correct equation

b. u = 5.8 sin(64°) = 5.2

Answer:

A

Step-by-step explanation:

If x is the number of shirts you multiy by 15. 2.25 is the additional cost

Answer:

Thanks, you are so generous

Step-by-step explanation:

Answer:

Thank you so much, you are the best!

Step-by-step explanation:

The probability that 2 of these 4 foxes have been tagged is 0.6316 (approx).Therefore, Option A is the correct answer.

Given that a forest contains 20 foxes, of which 5 were captured, tagged, and then released. A month later, 4 of the 20 foxes are again captured.

We need to find the probability that 2 of these 4 have been tagged.

We can use combinations to solve this problem as order doesn't matter while selecting 2 tagged foxes from 5 tagged foxes.

The total number of ways to choose 2 foxes from the 5 tagged foxes is:

n(S) = \(^5C_2\) = 10

The total number of ways to choose any 2 foxes from 20 foxes is:

n(E) =\(^{20}C_2\)

=>  (20 * 19) / (2 * 1) = 190

Hence, the probability that 2 of these 4 foxes have been tagged is:

P(2 foxes are tagged out of 4 foxes) = (Number of ways of selecting 2 tagged foxes out of 5) × (Number of ways of selecting any 2 foxes out of 20)/(Total number of ways of selecting any 2 foxes out of 20)P(2 foxes are tagged out of 4 foxes)

=>  5C2 * 16C2 / 20C2

=>  (10 * 120) / 190 = 0.6316 (approx)

Hence, the probability that 2 of these 4 foxes have been tagged is 0.6316 (approx).Therefore, Option A is the correct answer.

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The following set of equations can be used to represent this situation:

4b + 3c = 134

3b + 3c = 120

In this approach, b stands for the price per box of monochrome brochures, whereas c stands for the price per box of color  brochures.

Christian ordered two batches of brochures; the first equation shows the cost of the first batch, and the second equation shows the cost of the second batch.

The replacement approach can be used to solve this system. By focusing on just one side of the first equation, we may find the value of b:

4b = 134 - 3c

The second equation can therefore be changed to use this expression for b in place of b :

3(134 - 3c) + 3c = 120

This equation can be written as:

402 - 9c + 3c = 120

Combining related concepts gives us:

-6c = -282

When we multiply both sides by -6, we get:

c = 47

The value of b can then be determined by reintroducing this value into the first equation as follows:

4b = 134 - 3(47) (47)

If we simplify, we get:

4b = 134 - 141

This equation can be written as:

4b = -7

When we multiply both sides by 4, we get:

b = -1.75

As a result, the price each box of monochrome brochures is $-1.75, whereas the price per box of color brochures is $47.

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Answer:

34 inches

Step-by-step explanation :

54/360 X 20

The excel statement to estimate the test average of these 4 grades is -

An average is the sum of many numbers divided by the total of numbers. It is also known as the arithmetic mean.

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For a equation of the form:

m = slope

b = y-intercept

for:

(5)

(7)

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x < 9

Interval Notation:

(-∞ ,9)

Answer:

Correct: e, b, g

incorrect: c, a

Step-by-step explanation:

The angle adjacent (across from) to the given angle is the same as the given angle. So that means that f=128.

360° in a circle

128+128=256 degrees taken in the circle

360-256=104 degrees remaining in the circle

c and e are adjacent so we know they're the same. We can divide the remaining degrees by 2.

104/2=52

c=52, e=52

Assuming the two lines are parallel, because they have the same line intersecting them, the bottom degrees are the same as the top.

b=128, g=52, h=128, a=52