A regression analysis of 117 homes for sale produced the following model, where price is in thousands of dollars and size is in square feet. Price =47.88+0.067 (Size) a) Explain what the slope of the line says about housing prices and house size. b) What price would you predict for a 2500-square-foot house in this market? c) A real estate agent shows a potential buyer a 1100 -square-foot house, saying that the asking price is $5500 less than what one would expect to pay for a house of this size. What is the asking price, and what is the $5500 called? a) Explain what the slope of the line says about housing prices and house size. A. For every $1000 increase in price of a house, the size is predicted to increase by 0.067 square feet. B. For every additional square foot of area of a house, the price is predicted to increase by $0.067. C. For every $1 increase in price of a house, the size is predicted to increase by 67 square feet. D. For every additional square foot of area of a house, the price is predicted to increase by $67. A regression analysis of 117 homes for sale produced the following model, where price is in thousands of dollars and b) What price would you predict for a 2500-square-foot house in this market? c) A real estate agent shows a potential buyer a 1100 -square-foot house, saying that the asking price is $5500 less than what one would expect to pay for a house of this size. What is the asking price? What is the $5500 called? A. Slope B. Residual C. Predicted value

Answer:

Step-by-step explanation:

Temperatures given:

Descending order of the numbers is:

Correct choice is E

The equation for the function that reflects the graph of y = x² across the x-axis, shifts it left 5 units, and down 4 units is f(x) = -(x + 5)² - 4.

To reflect the graph of y = x² across the x-axis, we need to change the sign of the entire function. Thus, we have f(x) = -x².

Next, to shift the graph left 5 units, we replace x with (x + 5), giving us f(x) = -(x + 5)².

Finally, to shift the graph down 4 units, we subtract 4 from the entire function, resulting in f(x) = -(x + 5)² - 4.

by reflecting the graph across the x-axis, shifting it left 5 units, and down 4 units, we obtain the equation f(x) = -(x + 5)² - 4. This equation describes a function that has the same shape as y = x² but with the desired transformations applied.

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The ultimate purpose of constructing a standard curve is to use it to calculate the concentration of a substance in solution.

What is a standard curve?

A standard curve is a graphical representation of a mathematical function that relates the concentration of a solution to the amount of light that passes through it. The majority of standard curves have a linear relationship between the dependent and independent variables. These curves are particularly useful for chemical tests that require the use of an instrument, such as a spectrophotometer.

A standard curve is created by generating a series of known concentrations of a specific compound in a solution. The absorption values are measured, and the data are then plotted on a graph. The resulting data points can then be utilized to create a standard curve, which can be used to identify the concentration of unknown samples.

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This situation does not contradict Rolle's Theorem because Rolle's Theorem requires the function to be continuous on a closed interval and differentiable on an open interval, which is not satisfied by f(x) = tan x in the interval (0, π).

To show that f(0) = f(π), we evaluate the tangent function at these points. At x = 0, tan(0) = 0, and at x = π, tan(π) = 0. Therefore, f(0) = f(π).

To investigate whether there exists a number c in the interval (0, π) such that f'(c) = 0, we need to find the derivative of f(x). The derivative of tan x is given by f'(x) = sec² x. However, the secant squared function is never equal to zero. Therefore, there is no c in the interval (0, π) where f'(c) = 0.

This situation does not contradict Rolle's Theorem because Rolle's Theorem requires certain conditions to be met. First, the function must be continuous on the closed interval [a, b], which is not satisfied by f(x) = tan x since it is not defined at x = π/2. Second, the function must be differentiable on the open interval (a, b), but f'(x) = sec^2 x is not defined at x = π/2. Thus, the requirements of Rolle's Theorem are not fulfilled, and its conclusion does not apply to f(x) = tan x in the interval (0, π).

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Answer:

x = 1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1. distribute 7 to x and 5.

42 = 7x + 35

2. subtract 35 on both sides.

7 = 7x

3. Divide by 7 for both sides.

1 = x

Could you be a bit more specific on what you are asking for help with? y=3xt7 is the final answer for a y=mx+b question. 3 is the slope and 7 is the y-intercept.

Answer:

A≈8.04m² is the answer

The value of x is 38.5 degrees.

To solve for x, we can use the fact that the angles in a triangle add up to 180 degrees.

First, let's focus on the triangle with angles 38°, x, and 38°. The sum of these angles must equal 180°, so we can write the equation:

38 + x + 38 = 180

Simplifying, we get:

x = 180 - 76

x = 104

So we know that x is equal to 104 degrees.

Next, we can focus on the triangle with angles 2x, 38°, and 65°. Again, the sum of these angles must equal 180°, so we can write the equation:

2x + 38 + 65 = 180

Simplifying, we get:

2x = 77

x = 38.5

Therefore, the value of x is 38.5 degrees.

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Answer:

42 sheet of paper

Step-by-step explanation:

$7.84 divided by $0.16

This equals 42

After spending 7 dollars and 84 cents, 42 sheets of paper will be sold.

Answer:

X= - 6/20

Step-by-step explanation:

Find the lcm in both sides,,,

Do a cross multiple of the sides,

The probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

According to the given question.

A standard pair of dice is rolled.

So, the sample sapce for rolling a pair of dice = {(1,1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4),(5, 5),(5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

⇒ Total number of outcomes = 36

And, the outcomes for getting a sum of five on a sandard pair of six sided dice = {(2, 3), (3, 2), (4, 1), (1, 4)}

⇒ Total number of favorable outcomes = 4

As we know that " probability is the ratio of total number of favorable outcomes to the total number of outcomes".

Therefore,

The probability of rolling a sum of 5 on a standard pair of six-sided dice

= 4/36

= 1/9

Hence, the probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

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Answer:

if f(g(x)) = g(f(x)), then x is equal to zero.

Step-by-step explanation:

given:

f(x) = 2x²

g(x) = x + 1

then:

f(g(x)) = 2(x + 1)²

g(f(x) = 2x² + 1

so if:

f(g(x)) = g(f(x))

then:

2(x + 1)² = 2x² + 1

2(x² + 2x + 1) = 2x² + 1

2x² + 2x + 1 = 2x² + 1

2x = 0

x = 0

Answer:

21,798

Step-by-step explanation:

Answer:

21798

Step-by-step explanation:

add them all up step by step

Nastya's annual payments on the loan will be approximately $7,350.68 (rounded to the nearest cent).

To find Jean's equity as a percent of the house value, we need to calculate the equity and divide it by the house value, then multiply by 100 to get the percentage.

Jean's equity is the difference between the house value and the mortgage amount. So, the equity is $792078.31 - $600,000 = $192,078.31.

To calculate the percentage, we divide the equity by the house value and multiply by 100: ($192,078.31 / $792078.31) * 100 = 24.26%.

Therefore, Jean's equity as a percent of the house value is 24.26%.

Now, let's move on to Nastya's question.

To calculate Nastya's annual payments on a fully amortizing loan, we need to use the formula for calculating the monthly payment:

P = r * PV / (1 - (1 + r)^(-n))

Where:
P = Monthly payment
r = Monthly interest rate (annual interest rate / 12)
PV = Present value of the loan
n = Total number of payments

Given:
PV = $622,422
Annual interest rate = 5.2%
n = 10 years

First, we need to convert the annual interest rate to a monthly interest rate: 5.2% / 12 = 0.43333%.

Next, we substitute the values into the formula and solve for P:

P = (0.0043333 * 622422) / (1 - (1 + 0.0043333)^(-10))

Using a calculator, we get P ≈ $7,350.68.

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Answer:

504 in cubed

Step-by-step explanation:

I am assuming this is a rectangular prism, since you did not show a picture.

l x w x h

14 x 4 x 9

14 x 36

504

To determine if the yearbook photo is a dilation of the original photo, we need to compare the dimensions and check if there is a consistent scaling factor between the two.

Original photo dimensions: 4 inches by 6 inches.

Yearbook photo dimensions: 6 2/3 inches by 10 inches.

To check if it's a dilation, we can compare the ratios of corresponding sides:

Ratio of width:

Yearbook photo width / Original photo width = (6 2/3) / 4 = (20/3) / (12/3) = 20/12 = 5/3

Ratio of height:

Yearbook photo height / Original photo height = 10 / 6 = 5/3

The ratios of the corresponding sides are equal, with both being 5/3. This indicates that there is a consistent scaling factor of 5/3 between the original photo and the yearbook photo.

Therefore, the yearbook photo is indeed a dilation of the original photo, and the scale factor is 5/3. This means that each dimension of the yearbook photo is 5/3 times the corresponding dimension of the original photo.

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The values of the lengths of the sides and segments obtained using the equivalent ratios of the sides of similar triangles are;

1. AA

2. AA

3. 200 ft

4. 21 feet

5. 37.5 meters

6. 4.2 meters

7. 6 feet

Similar triangles are triangles that posses similar shape, but may have varied sizes.

1. Two angles in triangle ORS are congruent to two angles in triangle VUT, therefore, the triangles are similar by the Angle-Angle, AA similarity postulate

2. Whereby the angle ∠ABC is congruent to the angle ∠ADF, and the angle ∠ABC and ∠ADGF are corresponding angles, we get by the conversed of the corresponding angles theorem;

BC ║ DF

However, angle A is congruent to itself, by reflexive property, therefore;

Triangle ABC is similar to triangle ADF, according to the AA similarity postulate.

3. Using the proportional sides relationship between similar triangles or the definition of the tangent of an angle, we get;

50/12.5 = h/50

h = 50 × 50/12.5 = 200

The height of the building is 200 ft

4. Using similar triangles relationship, we get;

7/2 = h/6

h = (7/2) × 6 = 21

The height of the taller flagpole is 21 ft

5. Using the equivalent ratio of the sides of similar triangles, we get;

x/25 = 12/8

x = 25 × (12/8) = 37.5

The distance is 37.5 meters

6. The equivalent ratio of the sides of similar triangles indicates;

h/7 = 9/15

h = 7 × (9/15) = 4.2

The height of the brace is 4.2 meters

7. The ratios of the sides of similar triangles indicates that we get;

136/34 = h/(1 1/2)

h = 1 1/2 × (136/34) = 6

The height of the man is 6 feet

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Answer:

42

Step-by-step explanation:

6x8 = 48 90 - 48 = 42

Answer:

3.1 * 10^10

Step-by-step explanation:

we know 1 billion is 1,000,000,000

In scientific notation

1,000,000,000=1 * 10^9

To find the value of 31 Billion

Multiply the value of one billion for 31

so

31 * 1 * 10^9  = 31 * 10^9

= 3.1 *  10^10

Answer:

(f o g)(x) = \(\frac{4x+13}{4x+12}\)

Domain : (-∞, -3) ∪ (-3, ∞)

Step-by-step explanation:

Given : f(x) = \(\frac{x-4}{x-5}\)

            g(x) = 4x + 17

We have to find the value of (f o g)(x).

Since (f o g)(x) = f[g(x)]

                        = \(\frac{(4x+17)-4}{(4x+17)-5}\)

                        = \(\frac{4x+13}{4x+12}\)

For the Domain of the function (f o g)(x),

Given function is defined for (4x + 12) ≠ 0

4x ≠ -12

x ≠ -3

Therefore, Domain of the function will be : (-∞, -3) ∪ (-3, ∞)                    

The errors she made are She did not find the correct vertex; it should be at (8, 5) and She used the wrong area formula; it should be A = one-half b h, the incorrect options are B and C.

Error is an estimate of the standard deviation of the sampling distribution. It measures the variability of a considered sample statistic.

Supopse that we're given that:

Population standard deviation =\(\sigma\)

Size of sample we're working on = n

Then, the standard error can be calculated as:

\(SE = \dfrac{\sigma}{\sqrt{n}}\)

where SE denotes the standard error.

Given;

On a coordinate plane, 2 line segments are formed by points (1, 5), (5, 2), (12, 2).

She begins by finding the missing vertex on the graph to be point (9, 5).

Now,

The parallelogram is a simple quadrilateral with two parallel pairs of sides; The opposite or reverse sides of the parallelogram are of similar duration and the reverse angles of the parallelogram are of equivalent proportion;

The square has two sets of parallel sides, four right angles, and the four sides are identical. It's even a triangle and a parallelogram;

The rhombus is known as a four-sided parallelogram;

Therefore, the error will be in B and C.

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Answer:

couple? whaaaa-????????????

Answer:

1. Jerome and Jewel Jones are looking to buy their family home for their burgeoning brood. They are looking for a five-bedroom house. The average price of a five- bedroom house is GH¢450,000 in their locality. A bank offers the couple a 15- year mortgage facility at an interest rate of 24.5%. The bank also requires that the instalment payments do not exceed 30% of the couple’s monthly income. What should be the couple’s combined monthly income if they wish to take the facility?

2. You are willing to pay GH¢15,625 now to purchase a perpetuity that will pay you and your heirs GH¢1,250 each year, forever, starting at the end of this year. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year, annual payment, annuity instead of a perpetuity?

3. Desmodus Limited, a toy maker, prepares its accounts to 31 December each year. For the 2017 financial year the company paid a dividend of GH¢0.55 per share. Dividends paid are paid at the end of year but the 2017 were 80% lower than that of the previous year due to a difficult financial year. Members of the com- pany at its annual general meeting agreed not to pay dividends over the next two years and instead pay down the company’s bonds. Dividend payment will resume thereafter at the level of the 2017 dividends for three years. Management be- lieves that the company can afford to increase dividends at a rate of 4% thereafter for the foreseeable future. What is the intrinsic value of the company’s shares at the start of 2019 financial year if firms in the toy industry deliver returns of 13.5% on average?

4. YouhavejustjoinedtheMaaretsGroup,andyourbossasksyoutoreviewarecent analysis that was done to compare three alternative proposals to enhance the firm’s manufacturing facility. You find that the prior analysis ranked the proposals according to their IRR, and recommended the highest IRR option, Proposal A. You are concerned and decide to redo the analysis using NPV to determine whether this recommendation was appropriate. But while you are confident the IRRs were computed correctly, it seems that some of the underlying data regarding the cash flows that were estimated for each proposal was not included in the report. Here is the information you have, all amounts in millions of GH¢ o.:

PROPOSAL IRR YEAR 1 YEAR 2 YEAR 3 YEAR 4

A 60% -100 30 153 88

B 55% ? 0 206 95

C 50% -100 37 0 204+?

(a) Which projects would recommend based on the NPV of each proposal if the appropriate cost of capital is 10%?

(b) Would your recommendations be valid if the company has capital limitation of GH¢285 million? Explain your with appropriate detail.

Step-by-step explanation:

No, 4.379 is not a whole number, it is a decimal number.

Answer: No it is not a whole number.

Step-by-step explanation: Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers.

the boat is traveling in the direction of  68.2 degrees from the positive x-axis.

In mathematics, a vector is a mathematical object that has both magnitude and direction. Vectors are commonly used to represent physical quantities such as velocity, acceleration, and force. A vector can be represented by an arrow, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Given by the question.

The direction in which it travels is given by the arctan(y/x)=

arctan (-4/3) = -53.13 degrees = 36.87 degrees

To find the speed of the boat, we need to calculate the magnitude of the vector b, which represents the boat's velocity. Using the Pythagorean theorem, we can find the magnitude of b as follows:

|b| = sqrt (\((-2)^{2}\)  +\((-5)^{2}\)) = sqrt (4 + 25) = sqrt (29)

Therefore, the speed of the boat is approximately 5.39 meters per second.

To determine the direction of the boat in standard position, we use the arctan function to find the angle between the vector b and the positive x-axis. The angle can be calculated as:

theta = arctan (-5/-2) = arctan (2.5) = 1.19 radians or 68.2 degrees (rounded to one decimal place).

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Based on the evaluation of the subset consisting of vectors of the form is a subspace,

1. True, the set is a subspace.

2. True, the set contains the zero vector.

3. True, the set is closed under scalar multiplication.

4. True, the set is closed under vector addition.

To determine if the subset consisting of vectors of the form  \(\begin{bmatrix}x \\-2x \\0\end{bmatrix}\) is a subspace, we need to check if it satisfies the three conditions for being a subspace:

The set is closed under vector addition.

The set is closed under scalar multiplication.

The set contains the zero vector.

Let's evaluate each condition:

To check if the set is closed under vector addition, we take two arbitrary vectors from the set and add them together, \(\begin{bmatrix}a \\-2a \\0\end{bmatrix} + \begin{bmatrix}b \\-2b \\0\end{bmatrix} = \begin{bmatrix}a + b \\-2(a + b) \\0\end{bmatrix}\)

The resulting vector is of the same form as the vectors in the set, so the set is closed under vector addition.

To check if the set is closed under scalar multiplication, we take an arbitrary vector from the set and multiply it by a scalar \(c \cdot \begin{bmatrix}a \\-2a \\0\end{bmatrix} = \begin{bmatrix}ca \\-2ca \\0\end{bmatrix}\)

The resulting vector is of the same form as the vectors in the set, so the set is closed under scalar multiplication.

To check if the set contains the zero vector, we substitute  x=0 in the vector form: \(\begin{bmatrix}0 \\-2(0) \\0\end{bmatrix} = \begin{bmatrix}0 \\0 \\0\end{bmatrix}\)

The zero vector is in the set.

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