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DEBORAH GERALDS
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A direct mail appeal for contributions from a university's alumni and supporters is considered to be too costly if less than 12% of the alumni and supporters provide
monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 267
people on the alumni and supporters mailing lists. They receive monetary contributions from 24 people. Does this evidence demonstrate that the direct mail campaign is
not cost effective? Use a 0.10 level of significance.
Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.
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Answer:

[tex]x\geq 5[/tex] and [tex]x > 5[/tex]

Step-by-step explanation:

5 has to be the lowest integer, so you can choose [tex]x\geq 5[/tex] and [tex]x > 5[/tex].

Answer:

-(x+8)

Step-by-step explanation:

-x comes from -1(x), same goes to -8 which also comes from -1(8). So we have:

[tex]\displaystyle{-1(x)-1(8)}[/tex]

Factor -1 out:

[tex]\displaystyle{-1(x+8)}[/tex]

However, we don't generally write 1, so we are left with:

[tex]\displaystyle{-(x+8)}[/tex]

[tex]\begin{aligned}\\&f(x)=\log_4\left(\dfrac{x^2(x+9)^3}{(x-1)^8}\right)\\&f(x)=\log_4(x^2(x+9)^3)-\log_4{(x-1)^8\\&f(x)=\log_4x^2+\log_4(x+9)^3-8\log_4{(x-1)\\&f(x)=2\log_4x+3\log_4(x+9)-8\log_4{(x-1)\end{aligned}[/tex]

second option

Answer:

[tex]f(x) = 2\log_4x + 3\log_4(x + 9) - 8\log_4(x - 1)[/tex]

Step-by-step explanation:

In the following answer I'll use the following logarithm laws:

[tex]\log_m(a \times b) = \log_ma + \log_mb\\\\\log_m(\frac ab) = \log_ma - \log_mb\\\\\log_m(a^b) = b \times \log_ma[/tex]

Now for the answer:

[tex]f(x) = \log_4\left(\frac{x^2(x + 9)^3}{(x - 1)^8}\right)\\\\\to f(x) = \log_4\left(x^2(x + 9)^3\right) - \log_4\left((x - 1)^8\right)\\\\\to f(x) = \log_4\left(x^2\right) + \log_4\left((x + 9)^3\right) - \log_4\left((x - 1)^8\right)\\\\\to f(x) = 2\log_4x + 3\log_4(x + 9) - 8\log_4(x - 1)[/tex]

Answer:

a) Sum = 28n + n² + n

b) 492 seats

c) 3950 seats

Step-by-step explanation:

The given data forms arithmetic series.

30, 32, 34,.........

Total rows = n = 50.

a = first term = 30

Common difference = d = second term - first term

                                       = 32 -30

                                        = 2

a) Sum =  (28 + 2) + (28 + 4) +.................+ 28 + 2n

           = 28n + (2 + 4 + ...... +2n)      

Sum of first 'n' even numbers = n*(n+1)

          = 28n + n *(n + 1)

          = 28n + n² + n

b)  To find the number seats in the first 12 rows, use the formula,

          [tex]\boxed{\bf S_n =28n +n^2 + n}[/tex]

           [tex]\sf S_{12} = 28*12 +12^2 + 12\\\\[/tex]

                = 336 + 144 + 12

                = 492

_____________________________________________

c)

     [tex]\sf S_{50} =28*50 + 50^2 + 50\\\\[/tex]

           = 1400 + 2500 +50

           =3950

Total seat available in the whole amphitheatre = 3950 seats

Answer:

Step-by-step explanation:

To find out how much plastic and aluminum is needed for the cylindrical tube of tennis balls, we first need to calculate the dimensions of the tube. Since the tube is just large enough to fit all three balls, we can calculate its height by multiplying the diameter of a tennis ball (6.9 cm) by 3 (the number of balls that fit in the tube) to get 20.7 cm.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder and h is its height. Since we know that three tennis balls fit in the tube, we can calculate its radius by dividing the diameter of a tennis ball (6.9 cm) by 2 to get 3.45 cm. Therefore, the volume of the cylindrical tube is:

V = π(3.45 cm)^2(20.7 cm) ≈ 2,260.8 cubic centimeters

The bottom and side of the tube are made of plastic, so we can calculate the amount of plastic needed by subtracting the volume of the lid (which is made of aluminum) from the total volume of the tube. The lid is a circular disk with a diameter equal to that of the cylinder and a height equal to its thickness (which we don't know). Therefore, its volume can be calculated using the formula for the volume of a cylinder:

V = πr^2h

where r is half the diameter of the lid and h is its thickness.

Since we know that three tennis balls fit in the tube, we can calculate its diameter by multiplying the diameter of a tennis ball (6.9 cm) by 3 to get 20.7 cm (the same as the height). Therefore, r = 10.35 cm.

We don't know how thick the lid is, so let's call its thickness t. Then its height is h = t.

The volume of aluminum needed for the lid is:

V = π(10.35 cm)^2t ≈ 3375t cubic centimeters

Therefore, the amount of plastic needed for the bottom and side of the tube is:

2,260.8 - 3375t cubic centimeters

To find out how much unfilled space there is in the tube, we need to subtract from its total volume (2,260.8 cubic centimeters) the volume occupied by three tennis balls:

V = 3(4/3π(3.45 cm)^3) ≈ 131.9 cubic centimeters

Therefore, there are approximately 2,128.9 cubic centimeters of unfilled space in the tube.

To express this as a percentage of the total volume of the tube:

(2,128.9 / 2,260.8) x 100% ≈ **94%**

So approximately **94%** of the total volume of the tube is unfilled space.

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

Step 1: Find the mean x of the data values.

X = (ix₁) / n

x = (12 + 3 + 9 + 2 + 0 + 0 + 3) / 7

x = 29 / 7

x ≈ 4.14 (rounded to two decimal places)

Step 2: Calculate the squared differences from the mean for each data value [(x₁ - x)²].

For each data value, subtract the mean and square the result.

Squared Differences:

(12 - 4.14)² ≈ 53.43

(3 - 4.14)² ≈ 1.31

(9 - 4.14)² ≈ 23.09

(2 - 4.14)² ≈ 4.34

(0 - 4.14)² ≈ 17.11

(0 - 4.14)² ≈ 17.11

(3 - 4.14)² ≈ 1.31

Step 3: Calculate the variance (s²) of the data values.

s² = ((x₁ - x)²) / (n - 1)

s² = (53.43 + 1.31 + 23.09 + 4.34 + 17.11 + 17.11 + 1.31) / (7 - 1)

s² ≈ 117.70 / 6

s² ≈ 19.62 (rounded to two decimal places)

Step 4: Calculate the standard deviation (s) of the data values.

s = √s²

s = √19.62

s ≈ 4.43 (rounded to two decimal places)

Step 5: Find the range of the data values.

Range = Maximum value - Minimum value

Range = 12 - 0

Range = 12

Therefore, the results are:

The standard deviation is approximately 4.43 (rounded to two decimal places).

The variance is approximately 19.62 (rounded to two decimal places).

The range is 12.

The mean is 6.25 and the standard deviation is 2.12.

To calculate the mean and standard deviation of a sample using the provided information, we can use the following formulas:

Mean (μ) = Ex / n

Standard Deviation (σ) = √[(Ex² - (Ex)² / n) / (n - 1)]

Substituting the given values:

Mean (μ) = 50 / 8 = 6.25

Standard Deviation (σ) = √[(344 - (50)² / 8) / (8 - 1)]

= √[(344 - 2500 / 8) / 7]

= √[(344 - 312.5) / 7]

= √[(31.5) / 7]

≈ √4.50

≈ 2.12 (rounded to the nearest hundredth)

Therefore, the mean is 6.25 and the standard deviation is 2.12.

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Answer:

Step-by-step explanation:

To find the combination of goods A and B that a consumer will purchase if she spends all her income of Br120 on these two goods and her utility function is U = 4A0.5B0.5, we can use the Lagrangian method.

The Lagrangian function is:

L = 4A0.5B0.5 + λ(120 - 10A - 15B)

where λ is the Lagrange multiplier.

Taking the partial derivative of L with respect to A and B and setting them equal to zero, we get:

∂L/∂A = 2A-0.5B0.5 - 2λ = 0

∂L/∂B = A0.5B-0.5 - 3λ/2 = 0

Solving for A and B, we get:

A = (15λ/8)^2

B = (10λ/8)^2

Substituting these values into the budget constraint, we get:

10A + 15B = 120

Solving for λ, we get:

λ = 16/3

Substituting this value of λ into the expressions for A and B, we get:

A = 45

B = 40

Therefore, the consumer will purchase 45 units of good A and 40 units of good B.

I hope this helps! Let me know if you have any other questions or if there is anything else I can help you with.

The missing statement from the proof is:ZAOB and ZBOC form a linear pair. Option B.

To complete the proof, we need to establish that ZAOB and ZBOC form a linear pair of angles.

A linear pair of angles consists of two adjacent angles that share a common vertex and a common side, while their non-common sides form a straight line. In this case, ZAOB and ZBOC share the common side OB, and their non-common sides OA and OC form a straight line.

Since ZAOB is a right angle (90°) and ZBOC forms a linear pair with ZAOB, the sum of the measures of ZAOB and ZBOC must be equal to 180°. This is because the angles of a straight line add up to 180°.

Therefore, we can state that mZAOB + mZBOC = 180°.

With this statement included in the proof, we can proceed with the substitution property of equality:

90° + mZBOC = 180°.

And then, applying the subtraction property of equality:

mZBOC = 90°.

Thus, we have proven that m/BOC = 90°.

Therefore, the correct answer is B. ZAOB and ZBOC form a linear pair. SO Option B is correct.

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All Values at which g has a local maximum are -1 and 3.

Given a graph of the function g. We have to find the following:

All local maximum values of gAll values at which g has a local maximum from the given graph, we can observe that there are two local maximum points at (−1,2) and (3,2) as shown below:

Therefore, All local maximum values of g are 2.(a) (-1, 2), (3, 2) are all local maximum values of g.

(b) All values at which g has a local maximum are -1 and 3.

Therefore, the required answers are:(a) (-1, 2), (3, 2) are all local maximum values of g.

(b) All values at which g has a local maximum are -1 and 3.

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Answer:

  D.  Figures a and d

Step-by-step explanation:

You want to identify the shapes that are congruent.

Shapes are congruent if corresponding angles are congruent and corresponding line segments are congruent.

Here, the designated shape appears to be a right triangle with legs of different lengths. Shapes 'a' and 'd' also appear to be right triangles, with legs approximately the same lengths as those of the starred figure.

Figures 'a' and 'd' are congruent to the starred figure.

__

Additional comment

It is usual for geometry problems to rely only upon markings for congruence. That is, in general, you are not to rely upon appearance to draw conclusions about a geometry.

Here, none of the figures have any marks, so we cannot say with certainty that any of the segments or angles are congruent. Using these rules, the answer must be C. None of the shapes are congruent.

You may be able to reach a conclusion about what rules apply by looking at other problems and examples in your curriculum materials.

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It is estimated that 3,120 copies of the weekly sales from the online store will likely be from the rock genre.

To determine the number of copies likely to be from the rock genre, we need to calculate the proportion of visitors who preferred rock and then apply that proportion to the estimated weekly sales of 6,000 copies.

1. Calculate the proportion of visitors who preferred rock:

  - Number of visitors who preferred rock: 78

  - Total number of visitors surveyed: 150

  - Proportion of visitors who preferred rock: 78/150 = 0.52

2. Apply the proportion to the estimated weekly sales:

  - Estimated weekly sales: 6,000 copies

  - Number of copies likely to be from the rock genre: 0.52 * 6,000 = 3,120

Therefore, The correct answer is C. 3,120.

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a) 15 x 14 = 210

b) 5 x 24 = 120

c) 5 x 16 = 80

d) 5 x 18 = 90

e) 15 x 24 = 360

f) 15 x 36 = 540

a) 24 x 4 = 96

b) 42 x 8 = 336

c) 112 x 4 = 448

d) 131 x 8 = 1048

e) 125 x 6 = 750

f) 24 x 28 = 672

a) 19 x 6 = 114

b) 32 x 32 = 1024

c) 532 x 4 = 2128

d) 504 x 8 = 4032

e) 24 x 37 = 888

f) 18 x 6 = 108

g) 25 x 24 = 600

h) 37 x 8 = 296

The law illustrated by the expression 7y + (-7y) is the additive inverse property.

The expression 7y + (-7y) can be simplified using the additive inverse property. According to this property, the additive inverse of a number is the value that, when added to the original number, gives a sum of zero.

In this case, the additive inverse of 7y is -7y. So, when we add 7y and -7y together, we get 0 as the sum. Therefore, the expression 7y + (-7y) simplifies to 0.

To understand this concept further, let's break it down:

1. Start with the expression 7y + (-7y).

2. Recognize that (-7y) is the additive inverse of 7y.

3. Add 7y and (-7y) together: 7y + (-7y) = 0.

4. The result is 0, indicating that the sum of 7y and its additive inverse (-7y) is zero.

In summary, the expression 7y + (-7y) demonstrates the additive inverse property, where adding a number to its additive inverse results in zero.

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Answer:

---------------------------

The polynomial has zeros - 2, 1 and 2.

It means it has factors:

Multiply all factors together and convert to standard form:

Answer:

39

Step-by-step explanation:

[tex]\displaystyle A=\int^3_0(16-x^2)dx=16x-\frac{x^3}{3}\biggr|^3_0=16(3)-\frac{3^3}{3}=48-\frac{27}{3}=48-9=39[/tex]

The slope is:

Work/explanation:

I am going to utilise the formula:

[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where m equals the slope of the line.

Plug in the data:

[tex]\bf{m=\dfrac{2-0}{0-(-2)}}[/tex]

[tex]\bf{m=\dfrac{2}{0+2}}[/tex]

[tex]\bf{m=1}[/tex]

Step-by-step explanation:

it can improve ones life my making not spending a lot of money

Answer:

Step-by-step explanation:

To determine the number of people per km² in Studio Rest, we need to divide the total number of people (1721) by the total area (25.4 km²):

1721 / 25.4 ≈ **67.8 people per km²**

Therefore, there are approximately **67.8 people per km²** in Studio Rest.

I hope this answers your question. Let me know if you have any other questions.

Answer:

The answer should be 67.7559055118

Step-by-step explanation:

1721 / 25.4 = 67.7559055118

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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Answer:

BS = 9

Step-by-step explanation:

△BCU ~ △STU

Statements: CU/TU  =  BU/SU

6/18 + 6  = BU/12

6/24 = BU/12

Now:

2BU = 6

BU = 3

SU = BU + BS

12 = 3 + BS

Step-by-step explanation (2):

Similar triangles:

Let:

BS = x

BU  = 12 - x

TU = TC + CU = 18 + 6 = 24 units

Statements: BU/SU = CU/TU

12 - x/12 = 6/24 --->  12 - x/12  = 1/4

-4x = 12 - 48

BS =  9

Hope it helps!

For a continuous distribution, the probability of P(x < a) and P(x ≤ a) are the same.For a continuous distribution, P (x < 1) is equal to P (x ≤ 1) is a true statement. When a distribution is continuous, the probability of an exact value is equal to zero.

As a result, the probability of x being less than or equal to 1 and x being less than 1 is the same. Therefore, for a continuous distribution, P (x < 1) is equal to P (x ≤ 1).The probability of a continuous random variable is represented by the area beneath its density curve.

The probability of a continuous random variable taking on a particular value is zero, so the probability that X is between two values is the area beneath the density curve over that interval.

In the following image, the area under the curve represents the probability of x between 1 and 2:Therefore, for a continuous distribution, the probability of P(x < a) and P(x ≤ a) are the same.

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The expression that is equivalent to [tex]\sum\limits^{27}_{n=0} {8n}[/tex] is [tex]8\sum\limits^{27}_{n=0} {n}[/tex]

From the question, we have the following parameters that can be used in our computation:

[tex]\sum\limits^{27}_{n=0} {8n}[/tex]

Express 8n as 8 * n

So, we have

[tex]\sum\limits^{27}_{n=0} {8 * n[/tex]

Factor out 8

This gives

[tex]8\sum\limits^{27}_{n=0} {n}[/tex]

Hence, the expression that is equivalent to [tex]\sum\limits^{27}_{n=0} {8n}[/tex] is [tex]8\sum\limits^{27}_{n=0} {n}[/tex]

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Answer:

Yes

Step-by-step explanation:

So we have right triangle with hypotenuse is the ladder which is 18 ft and a leg of the triangle which is 6 ft

cos(angle) = 6/18 = 1/3

angle = cos^-1(1/3) = 70.53°

Since 70.53° is less than 75°, it is considered safe under the guidelines mentioned.

Answer:

Yes, Mr Smith's placement of his ladder will be considered safe under the given guidelines.

Step-by-step explanation:

To determine if Mr. Smith's ladder placement is safe, we can model the given scenario as a right triangle, and calculate the angle the ladder makes with the ground using trigonometry.

Let θ be the angle the ladder makes with the ground (in degrees).

The distance from the base of the ladder to the house (6 feet) is the side adjacent angle θ.

The length of the ladder (18 feet) is the hypotenuse of the right triangle.

As we have the hypotenuse and the side adjacent to the angle, we can use the cosine trigonometric ratio to find the measure of the angle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Substitute A = 6 and H = 18 into the cosine ratio and solve for θ:

[tex]\cos(\theta)=\dfrac{6}{18}[/tex]

[tex]\theta=\cos^{-1}\left(\dfrac{6}{18}\right)[/tex]

[tex]\theta=70.528779...^{\circ}[/tex]

[tex]\theta=70.53^{\circ}\; \sf (2\;d.p.)[/tex]

The calculated angle the ladder makes with the ground is 70.53° (to two decimal places). As this angle less than the recommended maximum angle of 75°, Mr. Smith's ladder placement can be considered safe under the given guidelines.

Answer:

its about 57.14 %

Step-by-step explanation:

24/42 = x/100

x = 57.142857

The best graph for plotting the percentages of a whole value in a data set is pie chart. Option B

A pie chart is tailor-made for depicting the ratios or percentages of a complete entity.

The circle has been segmented into individual slices, whereby each slice is a representation of a distinct category or constituent of the entirety.

The proportion of each slice corresponds to its size.

A pie chart offers a clear and concise way to compare proportions, enabling individuals to easily grasp the percentage of each category's contribution to the whole.

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Answer:

A = 2184 cm²

Step-by-step explanation:

the area (A) of the figure is calculated as

A = [tex]\frac{1}{2}[/tex] h(b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

here h = 42 , b₁ = 52 , b₂ = 52 , then

A = [tex]\frac{1}{2}[/tex] × 42 × (52 + 52) = 21 × 104 = 2184 cm²

Answer:

A = 2184 cm2

Step-by-step explanation:

Area of a parallelogram:

[tex]A = b*h[/tex]

[tex]b=52,h=42[/tex]

[tex]A=(42)(52)=2184cm^{2}[/tex]

Hope this helps.

If a shooter hits 23 out of 50 targets, that equates to a 46 percent or 46 percent success rate.

To express the fraction 23/50 as a percentage, we can use the formula:

Percent = (fraction * 100)

In this case, the fraction is 23/50 and we want to find that percentage.

Percentage = (23/50 * 100)

To simplify the calculation, we can divide both the numerator and denominator of the fraction by their greatest common divisor (GCD), which gives us the simplest form of the fraction. In this case, the MCD of 23 and 50 is 1, so the fraction is already in its simplest form.

Percentage = (23/50 * 100)

Percentage = (0.46 * 100)

Multiplying 0.46 by 100 gives:

Percent = 46

Therefore, the 23/50 percent entry is 46%.

That means  the shooter hit 46% of his targets at 125 yards last year. In summary, if a shooter hits 23 out of 50 targets, that equates to a  46% hit percentage or a 46% hit percentage.

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Answer: a) 30 years, 5%:

Monthly Payment ≈ $434.65

Total Cost of Interest ≈ $56,075.38

b) 30 years, 5 1/2%:

Monthly Payment ≈ $458.63

Total Cost of Interest ≈ $70,308.97

c) 30 years, 6%:

Monthly Payment ≈ $485.24

Total Cost of Interest ≈ $84,086.35

d) 15 years, 3 7/8%:

Monthly Payment ≈ $591.24

Total Cost of Interest ≈ $23,223.07

Step-by-step explanation: To calculate the monthly payment and the total cost of interest for each scenario, we can use the formula for calculating mortgage payments:

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

Total Cost of Interest = (Monthly Payment * n) - P

Where:

P = Loan amount (purchase price - down payment)

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

n = Total number of monthly payments

Let's calculate the values for each scenario:

a) 30 years, 5%

P = $90,000 - (10% * $90,000) = $81,000

r = 5% / 100 / 12 = 0.004167 (approx.)

n = 30 * 12 = 360

Monthly Payment = $81,000 * 0.004167 * (1 + 0.004167)^360 / ((1 + 0.004167)^360 - 1)

Monthly Payment ≈ $434.65

Total Cost of Interest = ($434.65 * 360) - $81,000

Total Cost of Interest ≈ $56,075.38

b) 30 years, 5 1/2%

P = $90,000 - (10% * $90,000) = $81,000

r = 5.5% / 100 / 12 = 0.004583 (approx.)

n = 30 * 12 = 360

Monthly Payment = $81,000 * 0.004583 * (1 + 0.004583)^360 / ((1 + 0.004583)^360 - 1)

Monthly Payment ≈ $458.63

Total Cost of Interest = ($458.63 * 360) - $81,000

Total Cost of Interest ≈ $70,308.97

c) 30 years, 6%

P = $90,000 - (10% * $90,000) = $81,000

r = 6% / 100 / 12 = 0.005 (approx.)

n = 30 * 12 = 360

Monthly Payment = $81,000 * 0.005 * (1 + 0.005)^360 / ((1 + 0.005)^360 - 1)

Monthly Payment ≈ $485.24

Total Cost of Interest = ($485.24 * 360) - $81,000

Total Cost of Interest ≈ $84,086.35

d) 15 years, 3 7/8%

P = $90,000 - (10% * $90,000) = $81,000

r = 3.875% / 100 / 12 = 0.003229 (approx.)

n = 15 * 12 = 180

Monthly Payment = $81,000 * 0.003229 * (1 + 0.003229)^180 / ((1 + 0.003229)^180 - 1)

Monthly Payment ≈ $591.24

Total Cost of Interest = ($591.24 * 180) - $81,000

Total Cost of Interest ≈ $23,223.07

To summarize:

a) 30 years, 5%:

Monthly Payment ≈ $434.65

Total Cost of Interest ≈ $56,075.38

b) 30 years, 5 1/2%:

Monthly Payment ≈ $458.63

Total Cost of Interest ≈ $70,308.97

c) 30 years, 6%:

Monthly Payment ≈ $485.24

Total Cost of Interest ≈ $84,086.35

d) 15 years, 3 7/8%:

Monthly Payment ≈ $591.24

Total Cost of Interest ≈ $23,223.07