For each relationship, state whether you believe there would be positive, negative, or no association. Explain your answer.a. A person's shoe size and length of hair.b. The distance traveled and the amount of gas in a car's gas tank.c. The amount of time studying and the grade in a class.

A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

How to determine the amount of carpet needed for a rectangular room?

To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.

The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),

18 feet ÷ 3 feet/yard = 6 yards

So the dimensions of the room in yards are 10 yards by 6 yards.

To find the total area of the room, we need to multiply the length and width,

10 yards × 6 yards = 60 square yards

Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

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16 sample points (possible outcomes as to the classifications) exist.

What is the combination?

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

Here, we have

Given: An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices.

There are 4 possible classifications for the president (freshman, sophomore, junior, senior) and 4 for the vice president.

A total of (4)(4) = 16 sample points.

Hence, 16 sample points (possible outcomes as to the classifications) exist.

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Answer:

\(4x^2-x+8\)

Step-by-step explanation:

First expand \((x-8)^2\).

\((x-8)(x-8)=x^2-16x+64\)

Now Add:

\((x^2-16x+64)+(3x^2+15x-56)\\(x^2+3x^2)+(-16x+15x)+(64-56)=\\4x^2-x+8\)

We want this:

3x^2 + 15x - 56 + (x - 8)^2

First, expand (x - 8)^2 using FOIL.

So, (x - 8)^2 = (x - 8)(x - 8).

(x - 8)(x - 8) = x^2 - 16x + 64.

We now add like terms.

3x^2 + 15x - 56 + x^2 - 16x + 64

4x^2 - x + 8

Done.

\(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

The given fraction is \(1\frac{3}{4}\).

\(1\frac{3}{4}\) feet can be written as a multiplication expression as follows: 1 foot × 1 3/4. This is because \(1\frac{3}{4}\) is the same as 1 + 3/4.

Furthermore, 3/4 can be written as 0.75, which is the same as 0.75 × 1 foot.

Therefore, the multiplication expression is 1 foot × \(1\frac{3}{4}\) = 1 foot × (1 + 0.75) = 1 foot × 1 + 1 foot × 0.75 = 1 foot + 1.75 feet.

Therefore, \(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

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Step-by-step explanation:

1ft=12in

1¾ft=x

x=12×7/4=21in

1¾ft=1¾×1 ft

Dilation involves transformation. The result is either an enlargement or a reduction of the original image. This depends on the scale factor. If the scale factor is greater than 1, enlargement occurs. If the scale factor is lesser than 1, a reduction occurs. Looking at the given question, the scale factor is 1/2 which is less than 1 thus, a reduction occurs.

We would reduce each coordinate by 1/2. The coordinates of the image after dilation would be

J(-4 * 1/2, - 1 * 1/2) K(0 * 1/2, 4 * 1/2) L(- 4 * 1/2, - 2 * 1/2)

It becomes

J(- 2, - 1/2) K(0, 2) L(- 2, - 1)

Answer:

Step-by-step explanation:

54(4/9)

216/9

24 sheets

Answer:

Suraj used 24 sheets of paper

Answer:

D

Step-by-step explanation:

Clockwise would mean a rotation to the right, and since the triangle is already plotted, just use the little picture turning icon( in the top right corner of the photo of the problem) to turn, and look at the triangle in the original graph to see how it moved.

Then click the button three more time until you get the photo right-side-up, and choose which option is the best answer.

Answer:

slope: 2/5

y intercept: 1

equation: y=2/5x+1

Step-by-step explanation:

You can see that the line is positive. Using the rise/run method you can see that the slope is 2/5. The y intercept is found about by finding the point that the line as crossed on the y axis. Put this together to make your equation!

Answer:

ok no explanation.

2 is the answer

Answer:

25

Step-by-step explanation:

none

Answer:

6+4×3+7=37

Step-by-step explanation:

6+4= 10

3x10=30

30+7=37

Answer:

infinite number of solutions

Step-by-step explanation:

\(\frac{4}{5}\) (x + 9) - \(\frac{1}{5}\) x = \(\frac{3}{5}\) (x + 12)

multiply through by 5 to clear the fractions

4(x + 9) - x = 3(x + 12) ← distribute parenthesis on both sides

4x + 36 - x = 3x + 36

3x + 36 = 3x + 36

since both sides are the same then any value of x will make the equation true.

Thus there are an infinite number of solutions

The maximum value of the function f (x) = -1.8x² + 7x - 11 to the nearest hundredth is,  - 4.19.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ f (x) = -1.8x² + 7x - 11

Now, We can differentiate with respect to x as;

⇒ f ' (x) = - 1.8 × 2x + 7 × 1 - 0

⇒ f ' (x) = - 3.6x + 7

Put f ' (x) = 0

⇒ - 3.6x + 7 = 0

⇒ 3.6x = 7

⇒ x = 1.94

Now, Again differentiate with respect to x as;

⇒ f ' (x) = - 3.6x + 7

⇒ f '' (x) = - 3.6 × 1 + 0

⇒ f '' (x) = - 3.6 < 0

Hence, Substitute x = 1.94 in function to get maximum value,

⇒ f (x) = -1.8x² + 7x - 11

⇒ f (x) = -1.8 (1.94)² + 7 × 1.94 - 11

⇒f (x) = - 6.77 + 13.58 - 11

⇒ f (x) = - 4.19

Thus, The maximum value = - 4.19

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Answer:

n ≈ 69.5

Step-by-step explanation:

using the cosine ratio in the right triangle

cos75° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{18}{n}\) ( multiply both sides by n )

n × cos75° = 18 ( divide both sides by cos75° )

n = \(\frac{18}{cos75}\) ≈ 69.5 ( to the nearest tenth )

Answer:

x=30o+n90on∈Z

Step-by-step explanation:

cos2x=sin(90o−2x)=sin(2x−30o)

Which mean 90o−2x=2x−30o+n360o

or 90o−2x+2x−30o=(2n+1)180o

The later cannot be true.

so x=30o+n90on∈Z

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The value of tan x is :

solution is in attachment !

1. Image 4:

A. In image 4, the main change from the previous image (image 3) is the addition of two squares.

B. If we choose figure 5 in image 4, we can see that its lengths are related to the figure in image 1.

C. The length of figure 5, which corresponds to 'a', and the length of figure 6, which corresponds to 'b', relate to the Pythagorean Theorem.

2. The visual proof demonstrates the Pythagorean Theorem by showing how the figures labeled 5 through 9 in image 4 are related to figures 2 and 10. Figure 5 represents side 'a' and figure 6 represents side 'b'.

1. Image 4:

A. In image 4, the main change from the previous image (image 3) is the addition of two squares. One square is attached to the side of the triangle with length 'a', and the other square is attached to the side of the triangle with length 'b'. These squares are constructed by transforming the previous image, specifically by adding the squares and adjusting their positions accordingly.

B. If we choose figure 5 in image 4, we can see that its lengths are related to the figure in image 1. The length of the bottom side of figure 5 is equal to 'a' (the length of the side of the triangle in image 1), and the length of the right side of figure 5 is equal to 'b' (the length of the other side of the triangle in image 1).

C. The length of figure 5, which corresponds to 'a', and the length of figure 6, which corresponds to 'b', relate to the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a^2 + b^2). In this case, figure 5 represents side 'a' and figure 6 represents side 'b'. So, their lengths squared (a^2 and b^2) added together equal the length of figure 7 squared (c^2).

2. The visual proof demonstrates the Pythagorean Theorem by showing how the figures labeled 5 through 9 in image 4 are related to figures 2 and 10. Figure 5 represents side 'a' and figure 6 represents side 'b'. When we combine these two figures and the square attached to the hypotenuse (c), we see that they perfectly fill the large square in figure 10. This shows that the area of the square on the hypotenuse (c^2) is equal to the sum of the areas of the squares on the other two sides (a^2 + b^2). This visual representation provides a clear and tangible demonstration of the Pythagorean Theorem.

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Answer:

-6 ≤ x < 0

Step-by-step explanation:

-6 + 7 = 1 and 1 is included in this inequality.  

0 + 7 = 7 and 7 is not included in this inequality.  

Therefore, -6 ≤ x < 0 is the answer.  

To graph, closed circle at -6 and open circle at 0.  

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The domain of function A and function B are compared by the statement of Option A: The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1.

What is a function?

A function is a fundamental concept in mathematics that relates a set of inputs (also known as the domain) to a corresponding set of outputs (sometimes referred to as the codomain). For each input, there exists exactly one output, and the output can be linked to its corresponding input in a unique manner.

The domain of a function refers to the set of all possible input values for which the function can produce an output.

In Function A, the domain consists of all real numbers greater than 0, since it is a logarithmic function that can take any positive number as an input.

In contrast, the domain of Function B includes all real numbers greater than or equal to 1, since it is a square root function that begins at (1,0) and continues to infinity.

This means that any number greater than or equal to 1 can be used as an input to produce a corresponding output.

It is essential to define the domain of a function accurately to ensure that the function is well-defined and to avoid potential errors or ambiguities in mathematical computations.

Therefore, the correct statement is A.

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to the right is P(z> Z)

so P(z>Z) = 0.9909

P(z< Z) = 1- 0.9909 = 0.0091

Closest values from a z-table

P(z< -2.37) = 0.00889 (-0.00011 away)

p(z< -2.36) = 0.00914 (+0.00014 away)

so the answer must be (c) since it is between -2.36 and -2.37

The function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

The function f(x,y) = x² + y² represents the sum of the squares of the variables x and y. To find the extreme values of this function, we need to take the partial derivatives with respect to x and y and set them equal to zero.

∂f/∂x = 2x = 0

∂f/∂y = 2y = 0

From these equations, we can see that the critical point occurs at (x,y) = (0,0).

To determine whether this is the maximum or minimum, we can use the second partial derivative test. The second partial derivatives are:

∂²f/∂x² = 2

∂²f/∂y² = 2

∂²f/∂x∂y = 0

At (0,0), ∂²f/∂x² > 0 and ∂²f/∂y² > 0, so the critical point is a minimum.

Therefore, the function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.

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Skipper's finance charge at the end of the billing period is given as follows:

$14.77.

The finance charge is obtained using simple interest, as there is a simple compounding per year for the debt, and the charge is the amount of interest accrued during the period of one month.

The amount of interest accrued after t years, using simple interest, is given as follows:

I(t) = Prt.

The parameters for the equation are given as follows:

Considering a period of one month = 1/12 of an year, the values of these parameters for this problem are given as follows:

P = 933, r = 0.19, t = 1/12.

Hence the finance charge for Skipper's purchase is calculated as follows:

I = 933 x 0.19 x 1/12 = $14.77.

(rounding to the nearest penny = nearest cent).

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11

Step-by-step explanation:

55 divide 5 = 11

11 + 3 = 15

5 × 11 = 55

Answer:

A = 8

Step-by-step explanation:

-5(a+3)=-55

-5a-15=

-55-5a=

-40-40/-5=8

a=8

All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.

Answer:

42 Units :)

Step-by-step explanation:

Answer:

B.42 on EDGE2022

Step-by-step explanation:

The solution to the system of given inequalities is (-7, 0).

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given system of inequalities are y> 2x-4 and y≤ -x-7.

The solution of the system of inequalities is the intersection region of all the solutions in the system.

x<y/2 +2 and x≤-y-7

The solution of the system of inequalities is (-7, 0)

Therefore, the solution to the system of given inequalities is (-7, 0).

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Answer: 2277 Newtons

Step-by-step explanation:

I will show you how to do this the Physics way, so first we must write down our given values.

gravitational field = gravity = 25.3 N/kg

Mass of the astronaut = 90kg

Fun fact: know that if you convert the Newtons to a different unit, Newtons = kg (m/s^2) so we can say that instead of N/kg, we can write it as m/s^2 because if we divide kg(m/s^2) with kg, you’ll end with m/s^2

If you’re in physics, we always work with m/s^2 for every acceleration that exists. So we basically have 25.3 m/s^2 for gravity.

To find the weight, we can use the F=ma formula but rewritten as Weight = mass * gravity

Weight = (90kg)(25.3 m/s^2) = Option D = 2277 Newtons

Correct Option is,

D) Buy, because the expected rate is greater than the required rate.

Now, Based on the information you've provided,

To calculate the required rate of return, we can use the SML formula as;

Required rate of return = risk-free rate + beta x (expected market return - risk-free rate)

Plugging in the numbers, we get:

Required rate of return = 8% + 0.85 x (16% - 8%)

                                   = 14.6%

Since the expected rate of return for Stock S is,

= dividend yield + growth rate

= (1.1 / 22 + 8%),

= 9.4%

which is higher than the required rate of return of 14.6%,

Here, the stock is undervalued and would be a good buy.

Therefore, the answer is, option D) Buy, because the expected rate is greater than the required rate.

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