Use the data below, showing a summary of highway gas mileage for several observations, to decide if the average highway gas mileage is the same for midsize cars, SUV’s, and pickup trucks. Test the appropriate hypotheses at the α = 0.01 level.
n Mean Std. Dev.
Midsize 31 25.8 2.56
SUV’s 31 22.68 3.67
Pickups 14 21.29 2.76

The linear equation in terms of the units {x} produced per hour as → y = 4.5 + 0.75x.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that an entrepreneur passes to his workers 4.50 dollars per hour plus an additional amount of 0.75 dollars per unit produced.

We can write a linear equation in terms of the units {x} produced per hour as -

y = 4.5 + 0.75x

Therefore, the linear equation in terms of the units {x} produced per hour as → y = 4.5 + 0.75x.

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{Question in english -

An entrepreneur passes to his workers 4.50 dollars per hour plus an additional amount of 0.75 dollars per unit produced. Write a linear equation / for the saland per hour u in terms of the units x produced per hour.}

To determine if a graph represents a polynomial function, an important factor to consider is the degree of the polynomial.

Function is the process or state of instruction that text inputs performance is specific tax and produce an output functional key components of programming language allowing the quarters to create complex commands with simple instruction for example a function can be used to add two numbers round together or to generate a random number function can also be combined to create more complex sequence of instruction.

Polynomial functions are continuous, smooth curves that can have no more than a certain number of turning points. To determine the least degree possible for a polynomial function, one must first identify the number of turning points the graph has.

Turning points are points on a graph where the curve changes direction. In a polynomial graph, these points are called inflection points. The number of turning points a polynomial graph has is equal to the degree of the polynomial minus one. For example, a cubic polynomial graph will have two turning points, while a quartic polynomial graph will have three.

In order to determine if a graph is a polynomial function, one must first identify the number of turning points the graph has. Once the number of turning points has been identified, the least degree of the polynomial can be determined. If the graph has fewer turning points than the degree of the polynomial minus one, then the graph is not a polynomial function. If the graph has the same number of turning points as the degree of the polynomial minus one, then the graph is a polynomial function.

For example, if a graph has three turning points, then the least degree of the polynomial is four. In this case, the graph is a polynomial function. On the other hand, if a graph has five turning points, then the least degree of the polynomial is six. In this case, the graph is not a polynomial function.

In conclusion, to determine if a graph represents a polynomial function, one must first identify the number of turning points the graph has. Once the number of turning points has been identified, the least degree of the polynomial can be determined. If the graph has fewer turning points than the degree of the polynomial minus one, then the graph is not a polynomial function. If the graph has the same number of turning points as the degree of the polynomial minus one, then the graph is a polynomial function.

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Answer:

96

Step-by-step explanation:

becuase 4 more than 8 is 12. and 12 times 8 is 96

The steps Sergey could use to solve the quadratic equation by completing the square is 5(x2 + 4x) = –7

We should know that in completing the square method both sides of the equation are made perfect squares.

The given equation is 5x²+20x-7=0

Solving this equation by completing the square method we have

5(x²+4x+4)=-7

This means that (x+2)=±√27/5

Simplifying further we have

5(x²+4x)=7

Then expanding to make ²HS a perfect square we have

5(x²+4x+4)=7+20

This means that 5(x²+4x)=-7

Therefore the step he could use is 5(x²+4x)=-7\

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Answer:

Step-by-step explanation:

hello, it seems this is problematic im sorry but I'm not sure if you could put a better picture.

The expected number of people out of 700 to order plain vanilla ice cream flavor is given as follows:

b. 224 people.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Out of 3 x 50 = 150 people surveyed, 17 + 15 + 16 = 48 ordered plain vanilla ice cream, hence the probability of a person ordering plain vanilla ice cream flavor is given as follows:

p = 48/150

Then, out of 700 people, the expected number of people to order the plain vanilla flavor is given as follows:

700 x 48/150 = 224 people.

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Answer:

Your answer is correct

Step-by-step explanation:

Use the rules of exponents to simplify the expression.

To raise a power to another power, multiply the exponents.

Multiply 6 by 2.

The correct option is the third.

Answer:

The GFC of 22 and 32 is 2

Step-by-step explanation:

Answer:

The slope of a line is a measure of the steepness of the line. It is calculated as the rise (the change in the y-coordinate) divided by the run (the change in the x-coordinate).

To find the slope of a line given two points on that line, you can use the following formula:

slope = (y2 - y1) / (x2 - x1)

If we plug in the coordinates (-4,2) and (2,-5) into this formula, we get:

slope = (-5 - 2) / (2 - (-4))

Simplifying this fraction, we get:

slope = -7 / 6

Simplifying further, we get:

slope = -7/6

So the slope of the line through the points (-4,2) and (2,-5) is -7/6.

Step-by-step explanation:

The percentage of buyers is approximately 68.26% of buyers of new houses paid between \($149,000\) and \($151,000\) .

We are given that the prices of the new homes are normally distributed with a mean of \($150,000\) and a standard deviation of $1000.

Using the 68-95-99.7 rule, we know that: approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the data falls within two standard deviations of the mean, approximately 99.7% of the data falls within three standard deviations of the mean.

In order to determine the proportion of customers who spent between $149,000 and , we must first determine the z-scores for these values:

z1 = (149,000 - 150,000) / 1000 = -1 z2 = (151,000 - 150,000) / 1000 = 1

Now, we can determine the proportion of data that falls between z1 and z2 using the z-table or a calculator. The region to the left of z1 is 0.1587, and the area to the left of z2 is 0.8413, according to the z-table. Thus, the region bounded by z1 and z2 is:

0.8413 - 0.1587 = 0.6826

We can get the percentage of consumers who spent between by multiplying this by 100% is  \($149,000\)  and \($151,000\):

0.6826 x 100% = 68.26%

Therefore, the standard deviation of customers who paid between is \($149,000\) and \($151,000\)  for this model of new homes.

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The absolute value equation that represents the minimum and maximum heights is  mathematically given as

|x-65| ≤ 10.

It is a certainty that the person with the smallest stature in a class measures 55 inches, while the one with the highest stature measures 75 inches.

Generally, the equation for the midpoint of maximum and minimum value  is  mathematically given as

midpoint = (max + min)/2

midpoint  =(75+55)/2

midpoint = 130/2

midpoint  =65

The difference between the extremes and the middle point is that

d=(max-min) /2

d= (75-55)/2

d  = 20/2

d= 10

The equation for absolute value is as follows:

|x-midpoint| ≤ Difference.

|x-65| ≤ 10.

In conclusion, As a result, the needed equation for an absolute value, which depicts the lowest and highest possible heights, is

|x-65| ≤ 10.

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The total number of grapes bought in a day is 1600 .

An equation is a mathematical statement which relates two algebraic expression with an equal sign.

It is given that

34 customers buy a bag of grapes at Jery's Market.

There are an average of 47 grapes in each bag.

Let the no. of grapes = x

Then

x = 34 * 47

x = 1598

rounded to the nearest ten

The total number of grapes bought in a day is 1600 .

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Answer:

Step-by-step explanation:

y ≤ - 2x + 3

y ≤ x + 3

Answer:

(4, 0)

Step-by-step explanation:

The circumference of a circle is \(2 \pi r\) where r is the radius.

In this case, \(2 \pi r = 10 \pi\).  Divide both sides of the equation by \(2\pi\) to get

\(r=5\)

The center of the circle is on the x-axis, so the intercepts are 5 units to the left of the center and 5 units to the right of the center.  The two intercepts are (-1-5, 0) and (-1+5, 0).  The point that is on the positive x-axis is (4, 0).

See attached image.

Using proportions, it is found that the blue team paints faster.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

For this problem, to find which team paints faster, we have to find the team that has the highest proportion of square meters painted per hour, dividing these amounts as given in the problem. Hence the proportions are found as follows:

2.5 > 2, hence, due to the higher value of the proportion, the blue team paints faster.

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The following percentages are listed below:

In this question we have seven cases of real life situations in which percentages are used. Mathematically speaking, percentages are represented by the following expression:

x = r / r' × 100       (1)

Where:

Now we proceed to determine quantities related to percentages:

2.8 mm as a per cent of 2.24 cm

x = (2.8 mm / 22.4 mm) × 100 %

x = 12.5 %

What per cent of 1.5 m is 60 cm?

x = (60 cm / 150 cm) × 100 %

x = 40 %

What per cent of 2 kg is 125 g?

x = (125 g / 2000 g) × 100

x = 6.25 %

What per cent of R 6 to 40 p?

x = (40 / 600) × 100

x = 6.667 %

What per cent of a day is 10 h?

x = (10 h / 24 h) × 100

x = 41.667 %

What per cent of 7 1 / 3 m in 5 1 / 2 m ?

x = [(11 / 2) / (22 / 3)] × 100 %

x = 75 %

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Answer:

Plane Z or plane VTX.

Step-by-step explanation:

From the picture attached,

ST pierces the plane at a point T.

That means line ST is perpendicular to the horizontal plane Z or plane VTX.

Since, S is a point lying on line ST it will not lie on the vertical plane VTX Or plane Z.

Therefore, point S is not contained in the plane Z.

Answer:

8

Step-by-step explanation:

Answer:

The area of the shaded region is 27 units^2.

Step-by-step explanation:

Area of outer square = 6^2 = 36 units^2

Area of inner square = 3^2 = 9 units^2

Area of shaded region

= 36 units^2 - 9 units^2 = 27 units^2

The area of a shaded region in a unit grid can be found either by subtracting the area of unshaded regions from the total grid area or by adding up the areas of identifiable shapes within the shaded region.

To find the area of the shaded region without counting every square, you can use a few different strategies, such as identifying and subtracting the area of unshaded regions from the total grid area, or recognizing and adding together larger, easily countable shapes within the shaded region.

For example, if your grid is 10x10 units, the total area would be 100 square units. If, within that grid, there are 20 unshaded squares, you can subtract this from the total area to find the area of the shaded region. So, 100 total square units - 20 unshaded square units = 80 shaded square units. This approach works best when the number of unshaded squares is relatively small or easily countable.

Alternatively, if the shaded region forms easily identifiable shapes (like a 5x5 square or a 3x10 rectangle), you can add the areas of these shapes together to get the total shaded area. This approach works best when the shaded region forms a few large, simple shapes.

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The required value of the sum of the decimal values is 0.5536. Option c is correct.

Given that,
0.4 + 0.143 + 0.3706 =

It is defined as a decimal number that only consists of repeating digits after a certain interval after the decimal. For example, 94.642642642..., 213.569569... etc.

Here,
To simplify 0.4 + 0.143 + 0. 3706 we transform it into
= 0.0400 + 0.1430 + 0.3706
= 0.1830 + 0.3706
= 0.5536

Thus, the required value of the sum of the decimal values is 0.5536. Option c is correct.

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The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Correct question is;

You represent a chemical company that is being sued for paint damage to automobiles. You want to support the claim that the mean repair cost per automobile is more than $650. How would you write the null and alternative hypotheses?

A) State the null and alternative hypotheses in words (context of the problem)

B) Write the null and alternative hypotheses in appropriate symbols (population parameters μ, σ or p)

C) Describe in words Type I error (the consequence of rejecting a true null hypothesis.)

D) Describe in words Type II error (the consequence of failing to reject a false null hypothesis.)

Answer:

A)In words;

Null hypothesis is that the cost is $650

Alternative hypothesis is that the cost is not $650

B) Null hypothesis; μ = 650

Alternative hypothesis; μ ≠ 650

C) Type I Error will be to make a claim that the repair cost is not $650, when it is actually $650.

D) Type II Error will be to make a claim that the repair cost is not $650, but fail to reject the claim that it is $650.

Step-by-step explanation:

We are told that You want to support the claim that the mean repair cost per automobile is more than $650.

Thus;

A)In words;

Null hypothesis is that the cost is $650

Alternative hypothesis is that the cost is not $650

B) Null hypothesis; μ = 650

Alternative hypothesis; μ ≠ 650

C) Type I Error will be to make a claim that the repair cost is not $650, when it is actually $650.

D) Type II Error will be to make a claim that the repair cost is not $650, but fail to reject the claim that it is $650.

Answer: C

Step-by-step explanation: Brainliest please

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

B. 7i

Step-by-step explanation:

first we need to find the root of the expression

\(\sqrt{-49} = \sqrt{49} *\sqrt{-1} \\ \\ \sqrt{49} = 7\\\\and\\\\ \sqrt{-1} = i\)

so the answer is B. 7i

Hello

        S        a         T

2a + 6  /            /
          /             /       a + 17
        /             /
   V          a         U

you want ST = VU (it's good) and SV = TU (not good)

2a + 6 = a + 17

2a - a = 17 - 6

a = 9

Answer:

Step-by-step explanation:

x+9

Let x, be 4

4+9=13

given condition,

x+9<4x

4+9<4(4)

13<16

The answer is:

Work/explanation:

Our inequality is:

\(\sf{x+9 < 4x}\)

Flip it

\(\sf{4x > x+9}\)

Solve

\(\sf{4x-x > 9}\)

Combine like terms

\(\sf{3x > 9}\)

Divide each side by 3

\(\sf{x > 3}\)