a marketing research organization wishes to estimate the proportion of television viewers who watch a particular prime-time comedy on may 24th. the proportion is thought to be about 0.30. what is the least number(sample size) of viewers that should be randomly selected to ensure that a 95% confidence interval for the true proportion of viewers will have a width of 0.06 or less?

Answer: y=8x-58

Step-by-step explanation:

1. find the slope

Since the new line is parallel to the first one that means the slope of 8x will remain the same.

2. plug it into the point slope formula y-y1=m(x-x1)

which would look like

y-(-2)=8(x-7)

3. solve for y

y-(-2)=8(x-7)

y+2=8x-56

y=8x-58

Answer: 14

Step-by-step explanation:

87.5% of 105 is 91.875 (91)

105-91=14

The equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3

The line is passing through the point = (-6,-3)

The slope of the line = 0

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

(y-(-3)) = 0×(x-(-6))

We have to convert this equation the slope intercept form

Slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

(y-(-3)) = 0×(x-(-6))

y+3 = 0×(x+6)

y+3 = 0

y = -3

Hence, the equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3.

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Answer:

9

Step-by-step explanation:

t < 13 - 4

t < 9

again as far as it goes

a) Number of employees that prefer coffee are [tex]\frac{3}{7}[/tex].

b) Percentage of employees don't like either tea or coffee is 30.4%

c) Number of employees that prefer tea are [tex]\frac{28}{105}[/tex]

The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively. A fraction only informs us of the number of parts that make up the whole. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. [tex]\frac{1}{2}[/tex], for instance, is a fraction.

Given Data

In a work survey, it was found that:

28 employees preferred tea

45 employees preferred coffee

32 didn't like either

a) Number of employees that prefer coffee

= 45

Fraction:

= [tex]\frac{45}{105}[/tex]

= [tex]\frac{3}{7}[/tex]

b) Percentage of employees don't like either tea or coffee

= [tex]\frac{32}{105}[/tex] × 100

= 30.4%

c) Number of employees that prefer tea.

= 28

= [tex]\frac{28}{105}[/tex]

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The length of the guy wire to the nearest foot is 42 feet.

The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.

The situations forms a right angle triangle.

Therefore, the length of the guy wire can be found as follows:

Using trigonometric ratios, we can find the angle the guy wire made with the ground.

tan ∅ = opposite / adjacent

tan ∅ = 5 / 15

∅ = tan ⁻¹ 1 / 3

∅ = 18.4349488057

∅ = 18.43°

Therefore, let's find the length of the guy wire using the angle.

cos 18.43° =  adjacent / hypotenuse

0.94871060813 = 40 / h

h = 40 / 0.94871060813

h = 42.162488395

Therefore,

length of the guy wire = 42 feet

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Answer: You could assume that X=8 and y=0

Step-by-step explanation:

Answer:

Solutions below.

Step-by-step explanation:

This Question involves the concept of intercepts of a graph.

Intercepts of a graph are namely the x-intercept and y-intercept.

x-intercept is when y = 0. Example: (3,0)

y-intercept is when x = 0. Example: (0,9)

We are given the equation: x + 4y = 8

To find x-intercept, we can substitute y = 0 into the equation to obtain the value of x.

x + 4(0) = 8

x + 0 = 8

x = 8

Coordinates: (8, 0)

To fins y-intercept, we can substitute x = 0 into the equation to obtain the value of y.

0 + 4y = 8

4y = 8

y = 8 ÷ 4

y = 2

Coordinates: (0, 2)

The approximate probability that between 70 and 90 is 0.728.

Using normal distribution,

Mean = xbar = np = 400 × 0.2 = 80

Standard deviation = √[np(1-p)] = √(80 × 0.8) = 8

To ensure that the distribution is normal,

np ≥ 10

80 ≥ 10

And,

np(1-p) ≥ 10

80(0.8) = 320 ≥ 10

Hence, we use the z-tables for this

a) Convert 75 and 100 into standardized scores.

A value's standardized score is equal to the value minus the mean divided by the standard deviation.

z = (x - xbar) ÷ σ

For 75

z = (75 - 80) ÷ 8 = - 0.625

For 100

z = (100 - 80) ÷ 8 = 2.5

To calculate the approximate likelihood that between 75 and 100 (inclusive) mufflers will be replaced under warranty.

P(75 ≤ x ≤ 100) = P(-0.625 ≤ z ≤ 2.5)

For these probabilities, use data from the normal probability table.

P(75 ≤ x ≤ 100)

= P(-0.625 ≤ z ≤ 2.5)

= P(z ≤ 2.5) - P(z ≤ -0.625)

= 0.994 - 0.266

= 0.728

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The measurement pairs that could be the dimensions of rectangle B include:

A. 6cm by 1.5cm

D. 18cm by 4.5vm

F. 80cm by 20cm

From the information, Rectangle A measures 12 cm by 3cm. Therefore, it should be noted that the scale factor is:

= 12/3

= 4/1

Therefore, the options should also have that same constant of 4:1

In this case, 6cm by 1.5cm, 18cm by 4.5cm, and 80cm by 20cm all possess this. This illustrates the concept of equivalent dimensions since they all have a ratio of 4:1.

The complete question is written below.

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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.

A. 6 cm by 1.5 cm

B.10 cm by 2 cm

C. 13 cm by 4 cm

D.18 cm by 4.5 cm

E.80 cm by 20 cm

Answer:

Step-by-step explanation:

2nd one

Answer:

You can add up to 5 each time, so we just need to multiply 5 by 40 although we already have the first three terms.

A: 40*5 = 200

Step-by-step explanation:

21 + 200 = 221

D

1) Taking the function g(x)= (x+1) (x-2) (x+5), as we can see this a 3rd degree ploynomial

g (x)= (x+1) (x-2) (x+5)

g(x) =x³+4x²-7x-10

As the coefficient is positive, then we'll have

Examining the options, we have as the roots S={-5,-1,2} So the answer is D

Answer:

37

Step-by-step explanation:

Use PEMDAS, in this case, start with multiplication: (2)(-7), don't forget there is a minus sign in front of the two which is important later, then move on to dividing (-9) by (-3). Then you are left with 20-(-14)+3, which is the same as 20+14+3, which equals 37.

The 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521

In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. Exponential decay differs from linear decay in that the decay factor depends on a percentage of the initial sum, meaning that the amount by which the original sum may be lowered will fluctuate over time as opposed to a linear function, which reduces the original sum by the same amount each time.

Given,

10 hour decay factor = 0.2722

Let us calculate the one-hour decay factor first,

One-hour decay factor = (10 hour decay factor)^1/10 = (0.2722)^1/10 = 0.8779

Now, Calculating the 5-hour decay factor,

5 hour decay factor = ( 1 hour decay factor )^5 = (0.8779)^5 = 0.521

Hence, the 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521

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If:

so:

Or:

0.32 liters

(b)

We need to find the volume of the rectangular prism, therefore:

However, we need to express the volume in liters, so:

Since we need to know the amount of mango juice:

Hello there. To solve this question, we'll have to remember some properties about trigonometric functions and the right triangle.

We want to find x such that:

We'll use the second right triangle to show what we want.

First, given a triangle:

We know that the hypotenuse will be:

But most importantly, the tangent of the angles α and β can be calculated by only using the legs of the triangle: it is the ratio between the opposite side and the adjacent side to an angle.

and

Now look at the triangle we have:

We can easily check that:

So it would be good to find something that relates the ratio between those two numbers: the tangent of 60º!!

Therefore, we have:

And the solution to x is:

A proportion is an equation in which two ratios are set equal to each other. No option is satisfying the proportion

Ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other.

In the given question, rayon drove 320 miles in 5 hours to complete the first part of his trip. 12 hours to drive 768 miles.

we can write this

320miles/5 = 768 miles/12

320miles/768 miles=5/12

In option d the values are not given in a correct way. It doesnot hold for the proportion.

Hence no option is correct.

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The resulting value for the quotient of 21 and a equals 30 is 7/10.

The result of dividing two numbers is known as the quotient. Six divided by two results in the number three.

Latin's "how many times" is the meaning of the word "quotient." That is really logical. For instance, the quotient of a and b is a/b

Given the statement "the quotient of 21 and a equals 30", this can be written mathematically as;

21/a = 30

Cross multiply

30a = 21

Divide both sides by 30

30a/30 = 21/30

a = 21/30

a = 7/10

Hence the value of a from the equivalent expression is 7/10.

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The value that Sarah must she get on the third test to have at least 90% test average is represented by the inequality x ≥ 96.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.

In this case, Sarah has 85 and 89 on her first two math 23 tests.

Let the third test be represented as x. This will be illustrated as:

(85 + 89 + x) / 3 ≥ 90

Cross multiply

85 + 89 + x ≥ 90 × 3

174 + x ≥ 270

Collect like terms

x ≥ 270 - 174

x ≥ 96

The value is x ≥ 96.

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The transformation from the graph of B to the graph of P is a vertical stretch by a scale factor of 2

From the question, the function definitions are given as

B(m) = 5m

P(m) = 10m

Rewrite the function P(m) as follows

P(m) = 2 x 5m

Substitute B(m) = 5m in the equation P(m) = 2 x 5m

P(m) = 2 x B(m)

When a function is represented as

f(x) = kg(x), then the transformation is a vertical stretch by k

Hence. the transformation a vertical stretch by 2

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<EOG =90° AS INDICATED IN THE DIAGRAM

<EOF+<FOG=<EOG(THEY MAKE THE ANGLE)

[tex]27 + 3y = 90 \\ 3y = 90 - 27 \\ 3y = 63 \\ \frac{3y}{3} = \frac{63}{3} \\ y= 21[/tex]

<AOB =180°( STRAIGHT LINE )

<AOE+EOF+<FOG+<GOB=<AOB(THWY MAKE THE ANGLE)

[tex]x + 27 + 3(21) + 8x + 18 = 180[/tex]

[tex]x + 27 + 63 + 8x + 18 = 180 \\ x + 8x + 27 + 63 + 18 = 180 \\ 9x - + 108 = 180 \\ 9x = 180 - 108 \\ 9x =72 \\ \frac{9x}{9} = \frac{72}{8} \\ x = 9[/tex]

ATTACHED IS THE SOLUTION

Answer:

  x = 3⁴

Step-by-step explanation:

You want the exponential form of log₃(x) = 4.

It can be helpful to remember that a logarithm is an exponent of the base of the logarithm.

  log₃(x) = 4   ⇔   x = 3⁴

The exponential form is x = 3⁴.

The truck can haul 1102 pounds.

According to the question,

We have the following information:

A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.

(We will not directly convert ton into pounds. We will follow the following steps.)

Now, we know that 1 ton is equal to 1000 kilograms.

So, half ton makes 500 kg.

Now, to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg is equal to 2.205 pounds.

1 kg = 2.205 pounds

500 kg = (500*2.205) pounds

500 kg = 1102.5 pounds

Hence, the truck can haul 1102.5 pounds.

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Given:

Aim:

We need to graph the given function.

Explanation:

Replace x =-4 in the given equation.

We get the point (-4, 4).

Replace x = 0 in the given equation.

We get the point (0,1).

Replace x =4 in the equation.

We get the point ( 4, -2).

Mark the points (-4, 4), (0,1), and ( 4, -2) on the graph and join them by ray.

Final answer:

The graph of the given eqaution:

The table that represents a linear function is Table 1. Thus, the correct option is A.

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.

Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.

We know that, slope m= (y2-y1)/(x2-x1)

Table 1:

Put (x1, y1)=(1, 5) and (x2, y2)=(2, 9) in slope formula

That is, (9-5)/(2-1)

= 4

Similarly, the slope between last two points is (9-5)/(4-1)

=4

Table 2:

Put (x1, y1)=(1, -5) and (x2, y2)=(2, 10) in slope formula

That is, (10+5)/(2-1)

= 15

Similarly, slope between last two points (20+15)/(4-3)

=35

Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.

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4x^4-10x^3-15x^2+27x

(use foiling)

ANSWER:
94.2m^3

STEP BY STEP:

V = 1/3 x PI x R^2 x h = 1/3 x 3.14 x 3^2 x 10 =94.2^3

Answer:

V = 94.25m³

I don't have enough time to show work because I have to go, but I hope this helped.