You are performing a hypothesis test of a single population proportion. You find out that np is less than five. What must you do to be able to perform a valid hypothesis test

The information which the line of best fit predict about the increase in the minimum wage over the 70 year period is that: C) Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.

In Mathematics, a line of best fit is sometimes referred to as a trend line and it can be defined as a statistical or analytical tool that is commonly used in conjunction with a scatter plot, in order to determine whether or not there is any form of association and correlation between a data set.

Based on the scatter plot, an equation which represents the line of best fit include the following:

y = 0.096x - 0.488.

In this context, we can logically deduce that the initial minimum wage is  $0.488 and the average increase in minimum wage is equal to 0.096 dollars each year between 1940 and 2010.

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The domain and range of the function is

Domain: [ 0,∞ ), {x|x >= 0}

Range: [ 0, ∞ ),{y|y>= 0 }

Separate portion of the internet that is controlled by one organisation or person or that has addresses with a common suffix.

The range of a set of data is the distinction between the highest and lowest observations.

All x values that define an expression fall under its domain.

[ 0, ∞ ] is used to represent intervals.

Set-Builder Notation:{x | x>=0}

All legal y values are included in the range. To discover the range, use the graph.

[ 0,  ∞] is used to represent intervals.

Set-Builder Notation: {y | y >=0}.

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The series ∑ n=2 [infinity] (-1)^(n) / (n^(4-1) * n^(3)) can be classified as absolutely convergent, conditionally convergent, or divergent. To determine this, we need to analyze the convergence behavior of the series.

The given series can be rewritten as ∑ n=2 [infinity] (-1)^(n) / (n^(7)), where we combine the exponents. Now, we can apply the alternating series test to determine the convergence.

The alternating series test states that if the terms of a series alternate in sign and decrease in absolute value, then the series is convergent. In our case, the terms alternate in sign due to the (-1)^(n) factor, and the absolute value of the terms decreases since the exponent of n is increasing. Therefore, we can conclude that the series is convergent.

Furthermore, to determine whether the convergence is absolute or conditional, we need to investigate the convergence of the corresponding series obtained by taking the absolute value of the terms, which is ∑ n=2 [infinity] 1 / (n^(7)).

Since the series ∑ n=2 [infinity] 1 / (n^(7)) is a p-series with p = 7, and p is greater than 1, the series converges absolutely. Hence, the original series ∑ n=2 [infinity] (-1)^(n) / (n^(4-1) * n^(3)) is absolutely convergent.

In summary, the series ∑ n=2 [infinity] (-1)^(n) / (n^(4-1) * n^(3)) is absolutely convergent.

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Given m(x) and n(x), the rational function m(x)/n(x) is

a) The zeroes of the function are the values of x such that f(x)=0; then,

The zero of the function is at x=2.

b) Notice that the limits when x->+/- infinite are

This implies that there is an asymptote at y=0; however, notice that

Thus, the graph of f(x) crosses y=0; thus, there are no asymptotes even if the behavior of the function tends to zero.

c) The function's domain consists of every value of x such that the denominator of f(x) is different than zero. Notice that 1+x^2>=1 since x^2>=0; thus

d) n(x) and m(x) are polynomial function; thus both functions are continuous. Then,

Therefore, the rational function is indeed continuous for any value of x.

e) As we stated before, f(x) is defined for every value of x such that n(x) is different than zero, and n(x)>1 for every x. Thus, there are no values of x such that m(x)/n(x) is undefined.

f) As for the end behavior of the function, we found that the limits when x approaches +/- infinite are equal to zero. Therefore, the end behavior of the function is not positive nor negative since 0=-0

Answer:

$30.48<x<$53.34

Step-by-step explanation:

8 times per galleon: 14 times per gallon

Answer:

The answer is 6

Step-by-step explanation:

it can be written as 9/X = x/4

when you cross multiply, it gives you xsquare = 36

Therefore, X is 6

Answer:

AC=1.88

Step-by-step explanation:

cos 20 = AC/2

0.9397 = AC/2

AC = 1.88

The Lower Control Limit (LCL) of a 3.6 control chart is 44.1.

To construct an appropriate statistical process control chart for the average time taken in the execution of a set of computerized protocols, data was collected for 30 samples each of size 40, and the mean of all sample means was found to be 50. The standard deviation of the sample-means was known to be 4.5 seconds.

A control chart is a statistical tool used to differentiate between common-cause variation and assignable-cause variation in a process. Control charts are designed to detect when process performance is stable, indicating that the process is under control. When the process is in a stable state, decision-makers can make informed judgments and decisions on whether or not to change the process.

For a sample size of 40, the LCL formula for the x-bar chart is: LCL = x-bar-bar - 3.6 * σ/√n

Where: x-bar-bar is the mean of the means

σ is the standard deviation of the mean

n is the sample size

Putting the values, we have: LCL = 50 - 3.6 * 4.5/√40

LCL = 50 - 2.138

LCL = 47.862 or 44.1 (approximated to one decimal place)

Therefore, the LCL of a 3.6 control chart is 44.1.

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Answer:

50

Step-by-step explanation:

Step 1:

(x ÷ 2) × 6 = 150

Step 2:

x ÷ 2 = 25

Answer:

x = 50

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The limit of the given function as "x" approaches zero is 5/3

Given the limit of a function expressed as:

Substitute the value of x into the function to have:

\( \lim_{x \to 0} \frac{sin(2x)+sin(3x)}{2x+sin(3x)} \\ =\frac{sin(2(\infty))+sin(3(0))}{2(0)+sin(3(0))} \\ =\frac{0}{0} (ind) \)

Apply the l'hospital rule by differentiating the function as shown:

\( \lim_{x \to 0} \frac{2cos(2x)+3cos(3x)}{2+3cos(3x)} \\=\frac{2cos(2(0))+3cos3(0))}{2(0)+3cos(3(0))} \\=\frac{2+3}{3}\\ =\frac{5}{3} \)

Hence the limit of the given function as "x" approaches zero is 5/3

They have the same slope, the lines are parallel to one another.

If two non-vertical lines that are in the same plane has the same slope, then they are said to be parallel. Two parallel lines won't ever intersect.

The slopes of two perpendicular lines are negative reciprocals. The product of the slopes of two perpendicular lines is -1

We need to put these equations into y=mx+b format.

3x-5y=20

-5y=-3x+20. (take 5x from both sides)

y=3/5 x -4 ( divide both sides by -3)

The slope is 3/5

y=3/5x-1

The slope is 3/5

Therefore, we can conclude that the lines are parallel to each other as they have same slope.

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Option A is the correct answer which is t=(v-u)/a

This equation defines the behaviour of a physical scheme in order of its movement as a function of time in Newtonian mechanics

where:

v= final velocity

u= initial velocity

t= time

a= acceleration

Now from the following equation

v-u=at(rearrange the term)

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After graphing the equations, we found that the solution of the given pair of equations is (2,5).

What is meant by an equation?

A formula called an equation uses the equals symbol (=) to denote the equality of two expressions. An equal sign ("=") links two expressions together to form an equation. The two expressions on either side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero. As we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.

The complete question is given below.

The equations are:

y = 7x - 9

y = 3x - 1

A) y = 7x - 9

 Slope = 7

 y - intercept = (0,-9)

  y = 3x - 1

slope = 3

y - intercept = (0,-1)

Now we can graph these equations.

B) The solution of this pair of equations is the point where both the lines intersect. This can be seen in the graph below.

The intersecting point is (2,5).

Therefore after graphing the equations, we found that the solution of the given pair of equations is (2,5).

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Answer: 380 ft

Step-by-step explanation: To find the length in between, you simply subtract the numbers.

1,515 - 1,135 = 380

Therefore, the ladder needs to be extended 380 ft.

Answer:

Step-by-step explanation:

1 yard is about 36 inches.

A square yard in square inches will therefore be:

= 36 * 36

= 1,296 inch²

He needs 497 square inches of gray fabric. In square yards that will be:

= 497/1,296

= 0.38 yard² of gray material

He needs 746 square inches of yellow:

= 746/1,296

= 0.58 yard² of yellow.

The range of the function f(x) = 4x + 9 is R = {-7, 1, 9, 17}. Option D is the correct option.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given function is f(x) = 4x + 9.

The domain of the function is  D = {-4, -2, 0, 2}.

To find the rage of the function putting x = -4, -2, 0, 2 in the given function:

When x = -4

f(-4) = 4(-4) + 9

f(-4) = -16 + 9

f(-4) = -7

When x = 0

f(0) = 4(-0) + 9

f(0) = 0+ 9

f(0) =9

When x = 2

f(2) = 4(2) + 9

f(2) = 8 + 9

f(2) = 17

The set of the value of f(x) at  x = -4, -2, 0, 2 is the range of the function.

The range of the function is R = {f(-4), f(-2), f(0), f(2)} = {-7, 1, 9, 17}

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The given observations suggest that the increase in population is directly proportional to the number of children born and the number of surviving children.

According to the question,

We have the following information:

An article in the New York times noted that the human population has shown a significant increase in height. when the relationship of height to reproductive success in humans was examined across three decades (1935-1967), height had a positive correlation to the number of children born and the number of surviving children.

It means if the number of children born and the number of surviving children is more then the population will also increase.

In other words, it can be said population is directly proportional.

Hence, the given observations suggest that the increase in the population is directly proportional to the number of children born and the number of surviving children.

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The set {a: a ∈ P(x) and |a| = 2} is equal to {{a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}}.

Here is the step-by-step explanation:

1. Identify the set x and the condition for the set {a: a ∈ P(x) and |a| = 2}.
2. Find all the subsets of x with exactly 2 elements.
3. Write the set {a: a ∈ P(x) and |a| = 2} as the set of all the subsets of x with exactly 2 elements.
The set {a: a ∈ P(x) and |a| = 2} is the set of all subsets of x that have exactly 2 elements.

In this case, the set x = {a, b, c, d}, so the subsets of x with exactly 2 elements are

{a, b}, {a, c}, {a, d}, {b, c}, {b, d}, and {c, d}.

Therefore, the set {a: a ∈ P(x) and |a| = 2} is equal to {{a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}}.

In conclusion, the set {a: a ∈ P(x) and |a| = 2} is equal to {{a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}} when x = {a, b, c, d}.

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The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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The simplex method is a widely used algorithm for solving linear programming problems, which involve optimizing a linear objective function subject to linear constraints. False.

However, the simplex method does not explicitly require the variables to be nonnegative in order to find a solution.

The simplex method starts with an initial feasible solution and iteratively improves it by moving along the edges of the feasible region, ultimately reaching the optimal solution. During the iterations, the variables can take any real values, including negative values.

That being said, some variations of the simplex method, such as the dual simplex method, have been developed specifically to handle problems with nonnegativity constraints. These variations can be used when variables are required to be nonnegative.

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The probability that a randomly selected person will have an iq score of less than 80 is 0.0918 or 9.18%.

To find out the probability that a  randomly selected person will have an iq score of less than 80, we need to find out distribution of IQ scores in the population. IQ scores typically follow a normal distribution with a mean of 100 and a standard deviation of 15. Using this information, we can calculate the probability using a standard normal distribution table or by using statistical software.

Standardized score (Z) = (X - μ) / σ

where, X is the standardization value we need to calculate,  μ is the mean, and σ is the standard deviation.

Standardized score (Z) = 80 - 100 / 15 = -1.33

Looking at the standardized score in the  standard normal distribution table, we find that the corresponding probability is approximately 0.0918.

Therefore, the probability that a randomly selected person will have an iq score of less than 80 is 0.0918 or 9.18%.

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Answer:

350

Step-by-step explanation:

in every 140 calories there is 8 ounces

what about in 20 ounce of drink

140 calories ___8 ounce

? 20 ounce

140×20 =2800÷8=350

Answer:

S=68

T=44

Step-by-step explanation:

G=E=68

F=180-(2×68):44

Let's use the following properties:

so:

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

The probability of exactly one successes in five trials  is 0.20

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

The probability is calculated as

P(x) = nCx * p^x * (1 - p)^(n -x)

Where

n = 5

p = 5%

x = 1

Substitute the known values in the above equation, so, we have the following representation

P(1) = 5C1 * (5%)^1 * (1 - 5%)^(5 -1)

Evaluate

P(1) = 0.20

HEnce, the probability value is 0.20

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The number of ways are there of choosing ten balls from the box if the number of green balls must be in even numbers =15946 ways

To determine the number of ways of choosing ten balls from the box such that the number of green balls chosen is even, we need to consider the different possible combinations of green balls that could be chosen.

First, we can select 0 green balls, in which case we would need to choose all 10 balls from the 5 red and 8 yellow balls. This can be done in (5+8) choose 10 ways, which is 13 choose 10, or 286 ways.

Alternatively, we could choose 2, 4, or 6 green balls, and then select the remaining balls from the red and yellow balls. To count the number of ways of doing this, we can use the binomial coefficient formula.

The total number of ways of selecting 10 balls from the box is (6+5+8) choose 10, which is 19 choose 10, or 92,378 ways.

Therefore, the number of ways of choosing 10 balls from the box such that the number of green balls chosen is even is the sum of the number of ways of choosing 0, 2, 4, or 6 green balls, which is:

(6 choose 0)(13 choose 10) + (6 choose 2)(5 choose 8)(8 choose 0) + (6 choose 4)(5 choose 6)(8 choose 0) + (6 choose 6)(5 choose 4)*(8 choose 0)

Simplifying this expression gives a total of 15,946 ways.

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Answer:

15%

Step-by-step explanation:

\(\frac{7225-8500}{7225}=-15\%\)

Answer:

188

Step-by-step explanation: