b. What is the slope of the line containing the points?

c. What does the slope represent in this problem?

d. What is the y‐intercept of the line that contains the points?

e. What does the y‐intercept represent in this context?

f. What is the equation that represents the line?

Answer:

17550

Step-by-step explanation:

I am pretty sure you multiply them all together. If not sorry.

Answer:  344 yd²

Step-by-step explanation:

You can find the Area of the full block and then subtract the portion on the top right thats cut out

A(full block)=LA+2B          P= 9+9+16+16=50    h=10     B=(9)(16)

= Ph+2B              P, perimeter of Base;   h, height    B, area of base

=(50)(10)+2(144)

=788 yd²

A(cut out) = LA +2B         P=13+13+4+4=34     h=10   B=(13)(4)=52

=Ph +2B

=34(10)+2(52)

=444 yd²

Now subtract the 2 areas and that will give you your shape

A(shape)=A(full block)-A(cut out)

A(shape)= 788-444=344 yd²

Answer:

516.99

Step-by-step explanation:

i just answered it and it told me the correct answer after i did it

Answer:

To determine the density of the mixture, we need to first find the total volume of the mixture, which can be calculated by adding the volumes of metal A and metal B.

The volume of metal A can be calculated using the formula:

Volume = Mass / Density

So, the volume of metal A is:

Volume of A = 3.3g / 2.7g/cm³ = 1.2222... cm³ (rounded to four decimal places)

Similarly, the volume of metal B is:

Volume of B = 2.4g / 4.8g/cm³ = 0.5 cm³

The total volume of the mixture is therefore:

Total Volume = Volume of A + Volume of B

= 1.2222... cm³ + 0.5 cm³

= 1.7222... cm³ (rounded to four decimal places)

To find the density of the mixture, we can use the formula:

Density = Mass / Volume

The total mass of the mixture is:

Total Mass = Mass of A + Mass of B

= 3.3g + 2.4g

= 5.7g

So, the density of the mixture is:

Density = Total Mass / Total Volume

= 5.7g / 1.7222... cm³

= 3.3103... g/cm³ (rounded to four decimal places)

Therefore, the density of the mixture is approximately 3.3103 g/cm³

Step-by-step explanation:

Based on the information given, Ben Brenner should include $16,000 in income on his federal income tax return. This includes the $10,000 awarded in punitive damages, $5,000 in kickbacks on the sale of goods, and $1,000 increase in the value of an asset. The money borrowed from the bank is not considered income for tax purposes.

Based on the given information, Ben Brenner should include the following amounts in his income for his federal income tax return:

1. Jury awarded punitive damages: $10,000
2. Kickbacks on the sale of goods: $5,000

The money borrowed from the bank ($8,000) is not considered income, and the increase in the value of an asset ($1,000) is also not taxable until the asset is sold.

So, the total amount to include in his income for the federal income tax return would be:

$10,000 (punitive damages) + $5,000 (kickbacks) = $15,000

Therefore, the correct answer is option a. $15,000

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Based on the monthly data on the price of bitcoin, the average monthly growth rate can be calculated by taking the difference in price from the previous month and dividing it by the previous month's price. Using the average monthly growth rate, you can estimate the future value of your $1,000 Bitcoin investment.

Once this is done for each month, the resulting growth rates can be averaged to find the average monthly growth rate. As for the standard deviation of the monthly growth observations, this can be calculated using a statistical software or a calculator that has the capability to perform statistical calculations. Without the actual data, it is not possible to provide an exact answer to the question. However, it is important to note that investing in bitcoin can be volatile and unpredictable, so it is important to do thorough research and understand the potential risks before making any investment decisions. To estimate the average monthly growth rate and standard deviation of your Bitcoin investment, follow these steps:
1. Compile the monthly price data for Bitcoin.
2. Calculate the monthly growth rate for each month by using the formula: (Current Month Price - Previous Month Price) / Previous Month Price.
3. Add up all the monthly growth rates and divide the sum by the number of months in your data sample. This will give you the average monthly growth rate for Bitcoin.
4. To calculate the standard deviation, first find the variance. Subtract the average monthly growth rate from each individual growth rate, square the result, and find the average of these squared differences.
5. Finally, take the square root of the variance to get the standard deviation.

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The formula you provided is used to calculate the required sample size for a two-tailed test with a confidence level of 95%.

The condition for using this formula is that the sample size is not given and needs to be determined. This formula is not a derivative of any other formula, but rather a standalone equation used in statistics to determine sample size.

In the case where you want to determine the required sample size for a two-tailed test without a given value for 'n', you can use the formula n = (Z(α/2) + Z(β))² * (σ1² + σ2²) / Δ². The condition is a two-tailed test, meaning you are testing for the possibility of a relationship in both directions. This formula is a derivative of the more general sample size calculation for hypothesis testing, adjusted specifically for two-tailed tests. In your example, it appears that some values or symbols may be incorrect, so please double-check the information and let me know if you need further assistance.

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To compute Paasche's index for 2018 using 2010 as the base period, we need to use the formula:

Paasche's index = (current year prices * current year quantities) / (base year prices * current year quantities)

Using the given information, we have:

For Margarine:
- Current year prices: $2.00
- Current year quantities: 26
- Base year prices: $0.81
- Base year quantities: 20

Paasche's index for Margarine = (2.00 * 26) / (0.81 * 20) = 2.54

For Shortening:
- Current year prices: $1.88
- Current year quantities: 8
- Base year prices: $0.84
- Base year quantities: 1

Paasche's index for Shortening = (1.88 * 8) / (0.84 * 1) = 17.71

For Milk:
- Current year prices: $2.89
- Current year quantities: 63
- Base year prices: $1.44
- Base year quantities: 74

Paasche's index for Milk = (2.89 * 63) / (1.44 * 74) = 2.26

For Potato chips:
- Current year prices: $3.99
- Current year quantities: 34
- Base year prices: $2.91
- Base year quantities: 28

Paasche's index for Potato chips = (3.99 * 34) / (2.91 * 28) = 1.87

Therefore, the Paasche's index for 2018 using 2010 as the base period is:

Paasche's index = (2.54 + 17.71 + 2.26 + 1.87) / 4 = 6.34 (rounded to 2 decimal places)

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Answer:

5, 6, 7

Step-by-step explanation:

This question deals with linear equetion.

Let the first no. x , the 2nd one x + 1 and the 3rd no. will be x + 2 .

we have given that 3 consucetive sum are 18 so we write this equetion as

x + x + 1 + x + 2 = 18

3x + 3 = 18

3x = 18 - 3

3x = 15

3x/3 = 15/3

x = 5

so the 1st no. is 5

the 2nd no. is 5 + 1 = 6

the 3rd no. is 5 + 2 = 7

and the no. is 5, 6, 7

Answer:

The biconditional statement p <-> q is true when p and q have the same truth values and is false otherwise.

Step-by-step explanation:

This is because the biconditional is saying "p if and only if q"

A biconditional statement, written as "p if and only if q" or "p <--> q," is only true when both p and q have the same truth value. In other words, if p is true, then q must also be true for the biconditional statement to be true. Likewise, if p is false, then q must also be false.

Therefore, a biconditional statement is only true when the two statements being compared have equivalent truth values. A biconditional statement, represented as p ↔ q, is only true when both p and q have the same truth values. In other words, it is true when:

1. p is true and q is true, or
2. p is false and q is false.

A biconditional essentially means "p if and only if q." If both statements are true or both statements are false, then the biconditional is true. If one statement is true and the other is false, then the biconditional is false.

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Answer:

2a) The standard error is given by:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

  = sqrt[(5.10^2/16) + (5.23^2/16)]

  = 2.32

2b) The test statistic is given by:

t = (x1 - x2) / SE

 = (45.13 - 48.69) / 2.32

 = -1.53

2c) The p-value for a two-tailed test with alpha = 0.05 and degrees of freedom = 30 (n1 + n2 - 2) is 0.1384.

2d) Since the p-value (0.1384) is greater than the level of significance (0.05), we fail to reject the null hypothesis that there is no difference in the cost of high end red and white wines. Therefore, we cannot conclude that there is a significant difference in the cost of high end wines.

Therefore, there are 45 different combinations of meals that Yann and Camille can order if they refuse to order the same dish.

This problem involves counting the number of ways two people can choose different dishes from a menu of 10 items, without repeating any dish. To solve this problem, we can use the formula for combinations, which is given by:

C(n, k) = n!/[(n-k)! k!]

where n is the total number of items, and k is the number of items we want to choose. In this case, we want to choose 2 items from a menu of 10, so we have:

C(10, 2) = 10!/[(10-2)! 2!]

= (10 x 9)/2

= 45

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The value of x in the similar triangle is 12 units. The triangle are similar because they only vary in sizes but have the same shape.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The triangles are also similar because they have the same shape but different sizes.

Hence, let's find the value of x as follows:

3 / 9 = 4  / x

cross multiply

3x = 36

divide both sides by 3

x = 36 / 3

x = 12

Therefore, the value of x is 12 units.

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The probability of choosing the first chip a white, then the second chip, not Black is 2/15.

The probability of choosing the first chip a white, then the second chip, not Black is determined as follows:

There are a total of 10 chips, 4 whites, and 6 blacks

The probability of choosing the first chip, a white = 4/10 or 2/5

Then without replacement, there are now 3 white chips and 6 black chips.

The probability of not choosing a black is the probability of picj=king another white chip

Probability of another white chip = 3/9 or 1/3

Therefore;

P(white and not a black) = 4/10 * 1/3

P(white and not a black) = 4/30

P(white and not a black) = 2/15

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Complete question:

Suppose a bag contains 4 white chips and 6 black chips. You randomly choose one of the chips. Without replacing the first chip, you choose a second chip. Find the probability of choosing the first chip a white, then the second chip, not a Black.

4/45

1/10

2/25

1/9

The speed of the boat is approximately 9.21 km/h.

In order to ascertain the speed of the boat, we must find out the number of kilometers traversed by it and the amount of time taken for traveling that distance.

The traveled distance by the boat is equal to the space between two points,

or the magnitude of (final position vector - initial position vector),

which in this case is (-7i - 3j). Hence, the total distance of sqrt((-7)^2 + (-3)^2) kilometers is obtained.

Regarding the amount of time taken to travel that predetermined distance, it computes to be 2 hours 45 minutes, or 2.75 hours.

Therefore, through simple division, the speed of the boat can be determined at roughly 9.21 km/h, which results when you divide the traveled distance of sqrt(58) by the time taken in hours, that is, 2.75.

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The area of the square enclosure is calculated as Area = AB² = 5² = 25 square units.

To find the length of the fourth side of the square, find the distance between points C(7,4) and D(x,y). AB and CD are parallel and perpendicular to each other, so they have the same length. Hence,

AB = CD = √((4-0)² + (0-3)²) = 5

Using this distance to find coordinates at point D:

D(x,y) = A(0,3) + (-5,-5) = (-5,-2)

Now to find the length of each side of the square:

AB = CD = √((4-0)² + (0-3)²) = 5

BC = AD = √((7-4)² + (4-0)²) = 5

Therefore, the area of the square enclosure is:

Area = AB² = 5² = 25 square units.

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Using the definite integral, it is determined that the driver is 108 miles from his home at 1:00 PM.

We need to find the distance travelled by the driver between 11:00 AM and 1:00 PM.

The velocity of the driver is given by v(t) = 54t − 24t^2.

We can find the distance travelled by finding the definite integral of v(t) with respect to t, between 0 and 2 (since the driver leaves at 11:00 AM and we need to find the distance travelled by 1:00 PM, which is 2 hours later).

[tex]\int\limits^0_2[/tex]v(t) dt   =    [tex]\int\limits^0_2[/tex](54t − 24t²) dt

= [27t² - 8t³] between 0 and 2

= [27(2)² - 8(2)³] - [27(0)² - 8(0)³]

= 108 - 0

= 108 miles

Therefore, the driver is 108 miles away from his home at 1:00 PM.

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Answer: To determine the probability that there exists a triangle with side lengths x, y, and z, we need to find the probability that the three side lengths satisfy the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Since x, y, and z are independent and uniformly distributed on [0, 1], the probability density function of each variable is f(t) = 1 for 0 ≤ t ≤ 1 and 0 otherwise.

We can use geometric probability to determine the probability that x, y, and z satisfy the triangle inequality. Imagine a cube with side length 1, where the x-axis represents the value of x, the y-axis represents the value of y, and the z-axis represents the value of z. The region of the cube where x + y > z, x + z > y, and y + z > x corresponds to a tetrahedron with vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1), as shown below:

    (0,1,0)         (1,0,0)

       *---------------*

      /|              /|

     / |             / |

    /  |            /  |

(0,0,1)  *----------/---* (1,0,1)

   |   / (0,0,0)  |   /

   |  /           |  /

   | /            | /

   |/             |/

   *---------------* (0,1,1)

  (0,1,1)        (1,1,0)

The volume of this tetrahedron is 1/6 of the volume of the cube, since each of the four triangular faces has half the area of a face of the cube.

Therefore, the probability that x, y, and z satisfy the triangle inequality (i.e., that there exists a triangle with side lengths x, y, and z) is equal to the volume of this tetrahedron, which is 1/6.

Hence, the probability that there exists a triangle with side lengths x, y, and z is 1/6, or approximately 0.1667.

The probability that there exists a triangle with side lengths x, y, and z is 1/6 or approximately 0.1667.  The probability that there exists a triangle with side lengths x, y, and z can be found by determining the probability that the three sides satisfy the triangle inequality.

This inequality states that the sum of any two sides must be greater than the third side.

Since x, y, and z are chosen uniformly from [0, 1], we can assume that they are continuous random variables with a uniform distribution over the interval [0, 1].

Therefore, the probability that the three sides satisfy the triangle inequality can be found by integrating the joint probability density function of x, y, and z over the region where the triangle inequality holds. This region can be described as the set of all (x, y, z) that satisfy the following three conditions:

1) x + y > z
2) x + z > y
3) y + z > x

To find the probability, we integrate the joint probability density function over this region:

P(triangle exists) = ∫∫∫ R f(x, y, z) dxdydz

where R is the region defined by the three conditions above, and f(x, y, z) is the joint probability density function of x, y, and z, which is 1 over the interval [0, 1] since they are uniformly distributed.

Evaluating this triple integral is a bit tricky, but it turns out that the probability is 1/6. Therefore, the probability that there exists a triangle with side lengths x, y, and z is 1/6, which is approximately 0.1667.

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Answer:

Perpendicular

Given the following vectors:

[tex]\vec u =-5 \hat i +8 \hat j\\\vec v =56 \hat i +35 \hat j\\[/tex]

We are asked to determine whether vectors u and v are parallel or perpendicular.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

How do we do this?

To determine whether two vectors are parallel, the result of their cross product is zero.

To determine whether two vectors are perpendicular, the result of their dot product is zero.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\bold{Given \ two \ vectors...}\\\vec a=a_x \hat i + a_y \hat j +a_z \hat k\\\\\vec b=b_x \hat i + b_y \hat j +b_z \hat k\\[/tex]

[tex]\bold{Cross \ Product} \Rightarrow \vec a \times \vec b= \begin{vmatrix}\hat i & \hat j & \hat k\\a_x & a_y & a_z\\b_x & b_y & b_z\end{vmatrix} \rightarrow \begin{vmatrix}a_y & a_z \\b_y & b_z \end{vmatrix} \hat i- \begin{vmatrix}a_x & a_z \\b_x & b_z \end{vmatrix} \hat j+\begin{vmatrix}a_x & a_y \\b_x & b_y \end{vmatrix} \hat k[/tex]

[tex]\bold{Dot \ Product} \Rightarrow \vec a \cdot \vec b = a_xb_x+a_yb_y+a_zb_z[/tex]

Note: The result of the cross product is a vector while the result of a dot product is a scalar.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Cross product:

[tex]\vec u \times \vec v = \begin{vmatrix}\hat i & \hat j & \hat k\\-5 & 8 & 0\\56 & 35 & 0\end{vmatrix}[/tex]

[tex]\Longrightarrow \begin{vmatrix} 8 & 0 \\ 35 & 0 \end{vmatrix} \hat i- \begin{vmatrix}-5 & 0 \\56 & 0 \end{vmatrix} \hat j+\begin{vmatrix}-5 & 8 \\56 & 35 \end{vmatrix} \hat k[/tex]

[tex]\Longrightarrow [(8)(0)-(0)(35)]\hat i -[(-5)(0)-(0)(56)]\hat j +[(-5)(35)-(8)(56)] \hat k[/tex]

[tex]\Longrightarrow (0)\hat i (0)\hat j +[-175-448] \hat k[/tex]

[tex]\Longrightarrow (0)\hat i (0)\hat j +(-623) \hat k[/tex]

[tex]Thus, \ \boxed{\vec u \times \vec v = 0\hat i + 0\hat j -623 \hat k}[/tex]

Which does not equal zero. So, these vectors aren't parallel.

Now, dot product:

[tex]\vec u \cdot \vec v = (-5)(56)+(8)(35)+(0)(0)[/tex]

[tex]\Longrightarrow \vec u \cdot \vec v = -280+280+0[/tex]

[tex]Thus, \ \boxed{ \vec u \cdot \vec v = 0}[/tex]

The dot product of vectors u and v equals zero. These vectors are perpendicular!

Answer:

Step-by-step explanation:

The answer is B because it goes 7,9,9,9,10,12,14,14,16 The number in the middle is the median(10) 4 on each side so second number from the front is your Q1 (9) second number from the back is your Q2 (14) smallest number is 7 and biggest nimber is 14 so that is your min. and max. so your answer is D

Answer:

ANSWER: 59/ 60

Step-by-step explanation:

What should be subtracted to get 1 / 2 ?( 3 / 4 + 1 / 3 + 2 / 5 )

to get 1 / 2A.3 / 4 = 3.00 ÷ 4 = .75 *.1 / 3 = 1.000 ÷ 3 = .333 * .2 / 5 = 2.0 ÷ 5 = .4 * ..75 + .33 + .4 = 1.48…75+.33.40 == 1.48 *OR3 / 4 = 45 / 60+1 /3 = 20 / 602 / 5 = 24 / 60 ======== 89 / 60 = 1 29/601 29 /60 = 1 29/60 === 0 89/60—0 1/2 ==== 0 30/ 60=—0 30/60 =====================0 59/ 60

Answer:

undetermined

you need more info, what does x equal?
This is only true if x=0

if equation 6 × ∎ = 420 then the value of ∎ is 70.

Given that 6 × ∎ = 420

We have to find the value ∎

Let us consider ∎  as x

6×x=420

To find the value of x we have to divide both sides by 6

x=420/6

x=70

Hence, if 6 × ∎ = 420 then the value of ∎ is 70.

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The sample standard deviation of the heights (in inches) of 10 adult males is approximately 1.464 inches.

To find the sample standard deviation of the heights of the 10 adult males, follow these steps:

1. Calculate the mean (average) height:

(70+72+71+70+69+73+69+68+70+71) / 10 = 703 / 10 = 70.3 inches.

2. Subtract the mean from each height and square the result:

[tex][(70-70.3)^2, (72-70.3)^2, ... (71-70.3)^2].[/tex]

3. Calculate the sum of these squared differences:

0.09+2.89+0.49+0.09+1.69+7.29+1.69+5.29+0.09+0.49 = 19.31.

4. Divide the sum by (n-1), where n is the sample size: [tex]19.31 / (10-1) = 19.31 / 9 = 2.145.[/tex]
5. Take the square root of the result: √2.145 = 1.464 (rounded to 3 decimal places).

The sample standard deviation of the heights of the 10 adult males is approximately 1.464 inches.

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Answer:

Down

Step-by-step explanation:

The correct generalization about the height of the trees is given as follows:

The IQR is 160 feet. The middle half of cedar trees have heights that vary by 160 feet at most.

The ordered heights of the trees are given as follows:

16, 40, 49, 130, 200, 210.

The data-set is divided into two halves, as follows:

The quartiles are given as follows:

The interquartile range represents how much the middle 50% of elements vary, and is the difference of the third quartile by the first quartile, hence:

IQR = 200 - 40 = 60.

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Answer: (4x+7)-(x+1) = 4x + 7 - x - 1 = 3x + 6.

Therefore, (4x+7)-(x+1) = 3x + 6.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Distribute the Negative sign

(4x +7 ) + (-x - 1)

2. Remove Paranthesis

4x + 7- x - 1

3. Solve

4x - x + 7 - 1

3x + 6

4. (optional) Factor out the 3

3(x+2)

The answer is 3x + 6 or 3(x+2)

A confidence interval is a range of values that is likely to contain the true value of an unknown parameter with a certain level of confidence.

We can use the formula for the confidence interval of a proportion:

p±z α/2√p(1− p)/n

where $\hat{p}$ is the sample proportion, $n$ is the sample size, and $z_{\alpha/2}$ is the critical value from the standard normal distribution.

In this case, we have $\hat{p} = \frac{14}{130} = 0.1077$ and $n=130$. Using a table or calculator, we find that $z_{\alpha/2} = 2.33$ for a 98% confidence interval.

Plugging in the values, we get:

0.1077±2.33 √0.1077(1−0.1077)/130

Simplifying, we get:

(0.063,0.153)

So the answer is (A).

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The point estimator of the mean percentage of airline reservations canceled on the day of the flight is the midpoint of the 95% confidence interval, which is (3% + 9%) / 2 = 6%.

The point estimator of the mean percentage of airline reservations being canceled on the day of the flight is the midpoint of the confidence interval, which is (3% + 9%) / 2 = 6%. Therefore, the point estimator of the mean percentage of reservations that are canceled on the day of the flight is 6%.

This means that based on the data, we can estimate that the mean percentage of airline reservations being canceled on the day of the flight is around 6%. However, since this is a point estimate, there is some uncertainty associated with it. The 95% confidence interval provides a range of values within which we can be 95% confident that the true mean percentage of cancellations falls. In this case, we can be 95% confident that the true mean percentage of cancellations on the day of the flight falls between 3% and 9%.

Overall, the interval and the point estimator provide us with useful information about the mean percentage of airline reservations being canceled on the day of the flight and allow us to make informed decisions and predictions about future cancellations.

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Answer:

Total amount ≈ $115,952.40 (rounded to 2 decimal places)

Step-by-step explanation:

To calculate the total amount Kyle will pay over 30 years, we need to first determine his annual mortgage payment. We can use the mortgage formula to do this:

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

Where:

M = monthly mortgage payment

P = principal loan amount (in this case, $40,000)

r = monthly interest rate (annual interest rate / 12)

n = total number of payments (loan term in years * 12)

In Kyle's case:

P = $40,000

Annual interest rate = 9% = 0.09

r = 0.09 / 12 = 0.0075

Loan term = 30 years

n = 30 * 12 = 360 payments

Plug these values into the formula:

M = 40,000 * 0.0075 * (1 + 0.0075)^360 / ((1 + 0.0075)^360 - 1)

M ≈ $322.09 (rounded to 2 decimal places)

Now that we have the monthly mortgage payment, we can calculate the total amount paid over 30 years:

Total amount = Monthly mortgage payment * number of payments

Total amount = $322.09 * 360

Total amount ≈ $115,952.40 (rounded to 2 decimal places)

So, Kyle will pay approximately $115,952.40 over 30 years for his mortgage.

Answer:

Step-by-step explanation:

C:  (-4, 3)

r = √16 = 4

D:  [-8, 0]     -8<x<0

R: [-1, 7]     -1<y<7

The given equation is in standard form, so you can get the (h,k) values right from the equation.

To get the Domain and Range, it's easiest to graph the circle (use an online graphing calculator like Desmos), then see that x goes from -8 to 0, and y goes from -1 to 7.