Quantitative Reasoning Chapter 8 MTH105

 Chapter 8 covers information from all of the Quantitative Reasoning lessons and is the final chapter with the exam and final project. At this point you should have a pretty good understanding of everything but this will include more instruction if you forgot particular sections. 

Answers are in this color

Skills Quiz - Unit 8 Final Exam:

The city of Raleigh has 10400 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 200 randomly selected registered voters was conducted. 118 said they'd vote for Brown, 63 said they'd vote for Feliz, and 19 were undecided.

Describe the target population for this survey.

All citizens of Raleigh

All registered voters in Raleigh

All registered voters with telephones in Raleigh

The 200 voters surveyed

The 118 voters who said they'd vote for Brown

None of the above

The target population for the survey is "All registered voters in Raleigh" because the goal of the survey is to understand the voting preferences of the entire population of registered voters in Raleigh. The survey aims to make inferences about how all registered voters in the city might vote in the upcoming election based on the responses from the randomly selected sample of 200 registered voters.

This approach allows researchers to draw conclusions and make predictions about the entire population of registered voters in Raleigh, not just those who were surveyed. Therefore, the survey's target population encompasses all registered voters in the city.

The city of Raleigh has 8100 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 550 randomly selected registered voters was conducted. 304 said they'd vote for Brown, 239 said they'd vote for Feliz, and 7 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: The proportion should be a fraction or decimal, not a percent. 55.27% This sample statistic suggests that we might expect 4475 of the 8100 registered voters to vote for Brown.

The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is indeed the proportion calculated as:

Proportion for Brown = (Number who said they'd vote for Brown) / (Total number surveyed)

Proportion for Brown = 304 / 550 ≈ 0.553 (rounded to three decimal places)

So, the correct proportion of voters surveyed who said they'd vote for Brown is approximately 0.553 or 55.3% (rounded to the nearest tenth of a percent).

You want to estimate how many fish there are in a pond. Suppose you capture 135 fish, tag them, and throw them back into the pond. After a couple of days, you go back to the pond and capture 540 fish, of which 27 are tagged. An estimate for the number of fish in the pond is 2700 fish

You can use the mark and recapture method, also known as the Lincoln-Petersen index, to estimate the total number of fish in the pond. The formula for this estimate is:

Total population estimate = (Number of marked individuals in the first sample * Total number of individuals in the second sample) / Number of marked individuals in the second sample

In your scenario:

• Number of marked individuals in the first sample = 135
• Total number of individuals in the second sample = 540
• Number of marked individuals in the second sample = 27

Now, plug these values into the formula:

Total population estimate = (135 * 540) / 27

Total population estimate = 2700

So, an estimate for the number of fish in the pond is 2700.

Data was collected for 262 randomly selected 10 minute intervals. For each ten-minute interval, the number of people entering the atrium of a large mall were recorded. The data is summarized in the table below.

Number   of Guests	Frequency
140 – 149	56
150 – 159	77
160 – 169	28
170 – 179	78
180 – 189	23

What is the class width for this GFDT? 10

To find the class width for the given frequency distribution table (GFDT), you can use the following formula:

Class Width = (Upper Class Limit - Lower Class Limit) + 1

In this case, each class interval represents a range of 10 (e.g., 140 - 149, 150 - 159), so:

Lower Class Limit = 140 Upper Class Limit = 149

Now, plug these values into the formula:

Class Width = (149 - 140) + 1 Class Width = 9 + 1 Class Width = 10

So, the class width for this frequency distribution table is 10.

Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below.

Lengths (mm)	Frequency
160 - 162	1
163 - 165	16
166 - 168	71
169 - 171	108
172 - 174	83
175 - 177	18
178 - 180	3

What is the upper class limit for the seventh class?

upper class limit =180

To find the upper class limit for the seventh class, you can look at the last interval in the table, which is "178 - 180."

The upper class limit for this seventh class is 180 mm.

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 53 and a standard deviation of 6. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 47 and 59?

Do not enter the percent symbol.
ans =68%

Using the empirical rule (also known as the 68-95-99.7 rule), we can approximate the percentage of data within certain standard deviations of the mean for a bell-shaped distribution. In this case:

• About 68% of the data falls within one standard deviation of the mean.
• About 95% falls within two standard deviations of the mean.
• About 99.7% falls within three standard deviations of the mean.

Given that the mean is 53 and the standard deviation is 6, we want to find the percentage of daily phone calls between 47 and 59. These values are within one standard deviation of the mean in both directions.

So, approximately 68% of daily phone calls fall between 47 and 59.

Use the spinner below.



P(7) = $\frac{1}{12}$​112​

It's a 1 in 12 to hit a number there for 1/12 is the answer. 

A card is drawn randomly from a standard 52-card deck. Find the probability of the given event.
(a) The card drawn is 8
The probability is : $\frac{1}{13}$113​​Correct${\displaystyle \frac{\mathrm{}}{\mathrm{}}}$  

(b) The card drawn is a face card (Jack, Queen, or King)
The probability is : $\frac{3}{13}$313​​Correct${\displaystyle \frac{\mathrm{}}{\mathrm{}}}$  

(c) The card drawn is not a face card.
The probability is : $\frac{10}{13}$1013​​Correct${\displaystyle \frac{\mathrm{}}{\mathrm{}}}$  

To find the probability that the card drawn is not a face card, you can calculate the complement of the probability of drawing a face card. There are 3 face cards (Jack, Queen, and King) in each of the 4 suits (hearts, diamonds, clubs, and spades), for a total of 3 * 4 = 12 face cards in a standard 52-card deck.

So, the probability of drawing a face card is:

Probability(face card) = Number of face cards / Total number of cards = 12 / 52

To find the probability of not drawing a face card, subtract this probability from 1 (since the sum of all probabilities must equal 1):

Probability(not a face card) = 1 - Probability(face card) = 1 - (12 / 52)

Simplify:

Probability(not a face card) = (52 - 12) / 52 = 40 / 52 = 10 / 13

So, the probability of drawing a card that is not a face card is 10/13.

Suppose a jar contains 11 red marbles and 15 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

To find the probability that both marbles drawn are red, you can use the probability formula for dependent events:

Probability(both red) = (Probability of the first marble being red) * (Probability of the second marble being red, given that the first is red)

There are 11 red marbles out of a total of 26 marbles (11 red + 15 blue) in the jar initially. So, the probability of the first marble being red is:

Probability(first red) = Number of red marbles / Total number of marbles = 11 / 26

Now, if the first marble is red, there are 10 red marbles left, and the total number of marbles is reduced by 1 to 25. So, the probability of the second marble being red, given that the first is red, is:

Probability(second red | first red) = Number of remaining red marbles / Remaining total number of marbles = 10 / 25

Now, multiply these probabilities:

Probability(both red) = (11 / 26) * (10 / 25) = (11/26) * (2/5) = 22/130 = 11/65

So, the probability that both marbles drawn are red is 11/65.

A quick quiz consists of a multiple-choice question with 3 possible answers followed by a multiple-choice question with 3 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct.

Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = Correct%

To find the probability that both responses are correct when answering both questions with random guesses, you can use the multiplication rule for independent events.

Each question has 3 possible answers, and since the guesses are random, the probability of getting each question correct is 1/3.

So, the probability of both responses being correct is:

Probability(both correct) = Probability(correct on first question) * Probability(correct on second question) = (1/3) * (1/3) = 1/9

To express this probability as a percentage, multiply by 100:

Probability(both correct) = (1/9) * 100 = 11.1%

So, the probability that both responses are correct is 11.1% (rounded to one decimal place).

The table summarizes results from 982 pedestrian deaths that were caused by automobile accidents.

Driver Intoxicated?	Pedestrian Intoxicated?
	Yes	No
Yes	48	73
No	218	643

If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was intoxicated.

Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob =77.8

Find the coordinates of the point plotted below



Coordinates: (Correct,Correct)

The coordinate (4,3) represents a point in a two-dimensional Cartesian coordinate system. In this system:

• The first number, 4, represents the x-coordinate, which specifies the horizontal position of the point.
• The second number, 3, represents the y-coordinate, which specifies the vertical position of the point.

So, the point (4,3) is located 4 units to the right (horizontally) and 3 units up (vertically) from the origin, which is usually at (0,0).

Sketch a graph of y=-1/2x+1

1. Choose several x-values.
2. Calculate the corresponding y-values using the equation.
3. Plot the points (x, y).
4. Draw a straight line through the points.

Here's a table of values for plotting:

x	y = -\frac{1}{2}x + 1
0	1
2	0
4	-1
6	-2

Now, plot these points on a graph:

• Plot (0, 1).
• Plot (2, 0).
• Plot (4, -1).
• Plot (6, -2).

Once you've plotted these points, draw a straight line that passes through them. This line represents the graph of the equation $�=-\frac{1}{2}�+1$.

It should look like a line sloping downward from left to right with a slope of -1/2 and intersecting the y-axis at the point (0,1).

Write the equation of the line shown. Be sure to use the correct variable.

Equation: x = 8

The equation of the line shown is $�=8$. This equation represents a vertical line that intersects the x-axis at the point (8,0) and extends infinitely in both the positive and negative y-directions. This type of equation indicates that the value of x is always 8, regardless of the value of y, which is why it's a vertical line parallel to the y-axis.

A city's population in the year 

1953 was 

957,250. In 1995 the population was 963,550.

Compute the slope of the population growth (or decline) and choose the most accurate statement from the following:

The population is decreasing at a rate of 50 people per year.

The population is increasing at a rate of 150 people per year.

The population is decreasing at a rate of 100 people per year.

The population is decreasing at a rate of 150 people per year.

The population is increasing at a rate of 100 people per year.

The population is increasing at a rate of 50 people per year.

To compute the slope of the population growth (or decline) between 1953 and 1995, you can use the formula for slope:

Slope = (Change in Population) / (Change in Year)

Change in Population = Final Population - Initial Population = 963,550 - 957,250 = 6,300 Change in Year = Final Year - Initial Year = 1995 - 1953 = 42

Now, calculate the slope:

Slope = (6,300) / (42) = 150

The slope of the population growth is 150 people per year.

So, the most accurate statement is: "The population is increasing at a rate of 150 people per year."

If you drive for 9 hours and travel 270 miles, what is your rate?

30

To find your rate or speed, you can use the formula:

Rate (Speed) = Distance / Time

In your case, you traveled 270 miles in 9 hours, so:

Rate = 270 miles / 9 hours = 30 miles per hour

Your rate or speed is 30 miles per hour.

Out of 290 racers who started the marathon, 267 completed the race, 20 gave up, and 3 were disqualified. What percentage did not complete the marathon?

Correct %

Give your answer accurate to at least 1 decimal place.

To find the percentage of racers who did not complete the marathon, you need to add the number of racers who gave up and those who were disqualified, and then divide that sum by the total number of racers who started the marathon. Finally, multiply by 100 to express it as a percentage.

Number who gave up + Number who were disqualified = 20 + 3 = 23

Now, calculate the percentage who did not complete the marathon:

Percentage = (Number who did not complete / Total number who started) * 100 Percentage = (23 / 290) * 100 Percentage = (0.0793) * 100 Percentage ≈ 7.93%

So, approximately 7.93% of the racers did not complete the marathon.

When Ibuprofen is given for fever to children 6 months of age up to 2 years, the usual dose is 5 milligrams (mg) per kilogram (kg) of body weight when the fever is under 102.5 degrees Fahrenheit. How much medicine would be usual dose for a 18 month old weighing 25 pounds?

Correct milligrams

Round your answer to the nearest milligram.

To calculate the usual dose of Ibuprofen for an 18-month-old weighing 25 pounds, you'll need to convert the weight from pounds to kilograms because the usual dose is given in milligrams per kilogram (mg/kg).

1 pound is approximately equal to 0.453592 kilograms.

So, to convert 25 pounds to kilograms:

Weight in kilograms = 25 pounds * 0.453592 kg/pound ≈ 11.34 kg

Now that you have the weight in kilograms, you can calculate the usual dose:

Usual dose = Weight (in kg) * Dose (in mg/kg)

Usual dose = 11.34 kg * 5 mg/kg ≈ 56.7 mg

So, the usual dose of Ibuprofen for an 18-month-old weighing 25 pounds is approximately 56.7 milligrams.

A long year-end status report for work is 82 pages long. You need to print 14 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.24 each.

7.44

The population of a town increased from 3900 in 2006 to 5200 in 2010. Find the absolute and relative (percent) increase.

Absolute increase: Correct

Relative increase: Correct %

Give answers accurate to at least 1 decimal place.

To find the relative (percent) increase, you can use the following formula:

Relative Increase (%) = [(New Value - Old Value) / Old Value] * 100%

In this case:

Old Value (population in 2006) = 3900 New Value (population in 2010) = 5200

Relative Increase (%) = [(5200 - 3900) / 3900] * 100%

Relative Increase (%) = (1300 / 3900) * 100%

Relative Increase (%) = 33.33%

So, the relative (percent) increase in the town's population from 2006 to 2010 is 33.33%.

Starting in the year 2012, the number of speeding tickets issued each year in Middletown is predicted to grow according to an exponential growth model. During the year 2012, Middletown issued 230 speeding tickets (P0=230). Every year thereafter, the number of speeding tickets issued is predicted to grow by 5%. If Pn denotes the predicted number of speeding tickets during the year 2012+n, then Write the recursive formula for Pn Pn=1.05 Write the explicit formula for Pn Pn=230(1.05)n If this trend continues, how many speeding tickets are predicted to be issued in 2030?

553.52242374895

A population of 30 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 30% per year.

Estimate the population after one year

${\displaystyle {�}_1}$ = $39$39​Correct  

Estimate the population after two years

P2=49.37194875

To estimate the population after two years, you can use the exponential growth formula:

${�}_{�}={�}_0(1+�{)}^{�}$

Where:

• ${�}_{�}$ is the population after $�$ years.
• ${�}_0$ is the initial population (30 deer in this case).
• $�$ is the annual growth rate (30% or 0.30 as a decimal).
• $�$ is the number of years.

For one year, we already calculated it to be ${�}_1=39$.

A population of beetles are growing according to a linear growth model. The initial population (week 0) is P0=7, and the population after 7 weeks is P7 =77 Find an explicit formula for the beetle population after n weeks Pn= 7+n*10 After how many weeks will the beetle population reach 297?

29

To find out after how many weeks the beetle population will reach 297, you can set up and solve the equation:

${�}_{�}=7+�\cdot 10=297$

Now, isolate the variable $�$ by first subtracting 7 from both sides of the equation:

$�\cdot 10=297-7$

$�\cdot 10=290$

Finally, divide both sides by 10 to solve for $�$:

$�=\frac{290}{10}$

$�=29$

So, it will take 29 weeks for the beetle population to reach 297.

A researcher interested in Springfield citizens' shopping habits surveys a randomly selected group of 200 Walmart shoppers. 76% of those surveyed indicated that price was more important to them than where an item was produced. The researcher concluded that "about three quarters of the people in Springfield are more concerned with cost than where an item is made." This conclusion might be invalid because: the sample is not representative of the population. there was no control group. the size of the sample is too small. 76% is not exactly three quarters. None of the above

The conclusion might be invalid because: the sample is not representative of the population.

The researcher surveyed only Walmart shoppers, which may not be representative of the entire population of Springfield. People who shop at Walmart might have different preferences than those who shop at other stores, and therefore, the conclusion drawn from this sample may not accurately reflect the preferences of the entire population.

Calculate the average (mean) of the data shown, to two decimal places

x
22.9
17.3
4.8
12.8
26.2

16.8

To calculate the average (mean) of the given data, you need to sum all the values and then divide by the number of data points. Here's the calculation:

Average (mean) = (22.9 + 17.3 + 4.8 + 12.8 + 26.2) / 5

Average (mean) = 83.0 / 5

Average (mean) = 16.8

So, the average of the data is 16.8 when rounded to two decimal places.

Use the graph to identify the z and y intercepts of the graph. Note the scale on each axis since they may not be the same. x intercept=(6,0) y intercept=(0,9)

You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $3.19 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.69 a pound. Is it worth the extra drive?

First, determine what information you need to answer this question, then click here to display that info (along with other info).

• Going to the further store is cheaper
• Going to the close store is cheaper

Correct

The cheaper option saves you $1.81

A city currently has 123 streetlights. As part of a urban renewal program, the city council has decided to install 3 additional streetlights at the end of each week for the next 52 weeks.

How many streetlights will the city have at the end of 50 weeks?

Correct streetlights

Project #8 Finances

                                               

Must show calculations/formula for credit. Any answer given with no calculations/descriptions of how arrived at answers shown will result in no credit for that answer. If utilizing excel must state/describe your formulas used and your inputs

 

I strongly suggest you use excel for this project. The calculations are accomplished much simpler, quicker, and more accurate than doing the formulas by hand. The video embedded in your Canvas course provide a step-by-step process of how to go about it.

 

1.       The following chart is data over an 8-month period that shows how much a company spent in advertising and the sales revenue for that month

 

MONTH	ADVERTISING $	SALES $
March	800	57000
April	2400	89100
May	3450	97500
June	1500	56000
July	3700	99000
Aug	1500	56000
Sept	2200	95000
Oct	2150	78800

 

a) What is the correlation coefficient? (round to 2 decimals) describe how you utilized excel to arrive at this number (recommended) or show the formula you utilized to arrive at this answer

For correlation use CORREL(B2: B9, C2: C9), for slope use SLOPE(D2: D9,C2:C9) and for intercept use INTERCEPT(D2 : D9, C2: C9) in the excel sheet.

 

 

 

b) Is it a positive or negative correlation? It’s a strong positive linear relationship of 0.82.

 

 

c)       Would you say it is a strong correlation, weak correlation, or no correlation? What is the indicator that led you to that conclusion? strong positive correlation between advertising expenses and sales

Calculate the means of advertising expenses

Advertising Expenses = (800 + 2400 + 3450 + 1500 + 3700 + 1500 + 2200 + 2150) / 8 = 17,700 / 8 = 2,212.50

Sales = (57,000 + 89,100 + 97,500 + 56,000 + 99,000 + 56,000 + 95,000 + 78,800) / 8 = 538,400 / 8 = 67,300

Calculate the numerator

Numerator = (800 - 2,212.50)(57,000 - 67,300) +

            (2400 - 2,212.50)(89,100 - 67,300) +

            (3450 - 2,212.50)(97,500 - 67,300) +

            (1500 - 2,212.50)(56,000 - 67,300) +

            (3700 - 2,212.50)(99,000 - 67,300) +

            (1500 - 2,212.50)(56,000 - 67,300) +

            (2200 - 2,212.50)(95,000 - 67,300) +

            (2150 - 2,212.50)(78,800 - 67,300)

 

Numerator = (-1412.50)(-10300) +

            (187.50)(21700) +

            (1237.50)(30200) +

            (-712.50)(-11300) +

            (1487.50)(31700) +

            (-712.50)(-11300) +

            (-12.50)(27700) +

            (-62.50)(11500)

 

Numerator = 14597750

 

Calculate the denominators

Σ(xi - x̄)^2 = (800 - 2,212.50)^2 +

              (2400 - 2,212.50)^2 +

              (3450 - 2,212.50)^2 +

              (1500 - 2,212.50)^2 +

              (3700 - 2,212.50)^2 +

              (1500 - 2,212.50)^2 +

              (2200 - 2,212.50)^2 +

              (2150 - 2,212.50)^2

 

Σ(Value of advertising each month – mean of advertising expenses)^2 = 564062.50

 

Σ(Sales for each month – Mean of sales)^2 = (57,000 - 67,300)^2 +

              (89,100 - 67,300)^2 +

              (97,500 - 67,300)^2 +

              (56,000 - 67,300)^2 +

              (99,000 - 67,300)^2 +

              (56,000 - 67,300)^2 +

              (95,000 - 67,300)^2 +

              (78,800 - 67,300)^2

 

Σ(Value of sales for each month – value of mean sales)^2 = 1,104,820,000

Calculate correlation coefficient

r = Numerator / sqrt(Σ(advertising each month – mean of advertising expenses)^2 * Σ(value of sales for each month – Mean of sales)^2)

 

r = 14597750 / sqrt(564062.50 * 1,104,820,000)

 

r = 0.82399 = 0.82 (rounded to two decimal places)

confirms that there is indeed a strong positive correlation between advertising expenses

 

 

d)      What is the linear equation (y = mx + b form) that best approximates the relationship between advertising dollars spent(x) and sales revenue(y) based on the above 8 months of data? (round to 2 decimals for the slope and the y intercept) describe how you utilized excel to arrive at this equation (recommended) or show the formula you utilized to arrive at your equation

Select a blank cell and enter the following linear regression formula:

=LINEST(C2:C9, B2:B9, TRUE, TRUE)

Step 2: Press Ctrl + Shift + Enter to enter the formula as an array formula. Excel will display the slope, y-intercept, and other regression-related statistics in the adjacent cells.

Step 3: Retrieve the slope and y-intercept values from the array result.

Step 4: Use the slope and y-intercept to form the linear equation (y = mx + b).

Slope (m): 22.34

Y-Intercept (b): 29847.29

y = 22.34x + 29847.29

 

 

 

 

e)      What sales revenue would the company expect for the following advertising spending? Round to nearest cent show calculation

y = 22.34x + 29847.29

x is the advertising spending in dollars

y is the estimated sales revenue

a)       3000

y = 22.34 * 3000 + 29847.29

y = 67065.29

The company would expect sales revenue of approximately $67,065.29

 

b)      2100

y = 22.34 * 2100 + 29847.29

y = 56997.69

The company would expect sales revenue of approximately $56,997.69

c)       1300

y = 22.34 * 1300 + 29847.29

y = 53313.69

The company would expect sales revenue of approximately $53,313.69.

f)        If you were in charge of the advertising department how much would you spend on each of the next 4 months on advertising and how and why did you arrive at your decision?

Nov

Jan

Feb

March

Please give a brief explanation as to how and why you came up with your advertising spending for the above 4 months.

From the data we can see that the more money being used for advertising the more profit in sales if advertising money is more than 2200 then the expected sales will be over 85k I would go with 2600 since any more advertising then that doesn’t generate a noticeable difference in sale and we would make the most out of profit by making spending 2600.

Example: You want to buy a $18,500 car. The company is offering a 3% interest rate for 4 years.

What will your monthly payments be?

I will do this one for you and show you how I want you to describe your formula/inputs in excel if that is how you choose to go about solving problems 2 through 5 - which I strongly recommend. If you choose to perform the calculations by hand show the formula used with values.

Excel:

Formula used: PMT

Rate input: .03/12

NPer input: 4*12

Pv input: 18500

Answer: $409.49 per month

2.       You want to buy a $24,500 car. The company is offering a 3% interest rate for 5 years.

PMT(0.0025, 60, -6000) = $409.49

a.       What will your monthly payments be? Round to the nearest cent.

                         $409.49

b.       Assuming you pay that monthly amount for the entire 5 years, what is the total amount of money you will pay during those 5 years for the car?

Total amount paid = Monthly payment * Total number of monthly payments

Total amount paid = $409.49 * 60

Total amount paid = $24,569.40

c.       How much interest will you pay during those 5 years?

Interest Paid = Total amount paid - Original principal amount

Interest Paid = $24,569.40 - $24,500

Interest Paid = $69.40 

3.       You have $360,000 saved for retirement. Your account earns 5% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 25 years?

Monthly Payment = (360000 * 0.004167 * (1 + 0.004167)^300) / ((1 + 0.004167)^300 - 1)

Monthly Payment = (360000 * 0.004167 * 1.945176) / (1.945176 - 1)

Monthly Payment = (753.6636) / 0.945176

Monthly Payment = 797.42

You will be able to withdraw approximately $797.42 per month to sustain the withdrawals for the entire period.

4.       You deposit $700 each month into an account earning 3% interest compounded monthly.

a) How much will you have in the account in 15 years?

Future value = 700 * ((1 + 0.0025)^180 - 1) / 0.0025

Future value = 700 * (1.488949 - 1) / 0.0025

Future value = 700 * 0.488949 / 0.0025

Future value = 700 * 195.5796

Future value = 137,005.72

b) How much total money will you put into the account?

Monthly deposit amount (P) = $700

Total number of deposits (n) = 15 * 12 = 180 (15 years * 12 months per year)

Total money put into the account = Monthly deposit amount * Total number of deposits

Total money put into the account = $700 * 180

Total money put into the account = $126,000

So, you will put a total of $126,000 into the account over 15 years by making monthly deposits of $700 each

c) How much total interest will you earn?

Total interest earned = Future value - Total amount deposited

Total interest earned = $137,005.72 - $126,000

Total interest earned = $11,005.72

5.       Suppose you want to have $800,000 for retirement in 20 years. Your account earns 7% interest compounded annually.

a) How much would you need to deposit in the account today?

Present value = 800000 / (1 + 0.07)^20

Present value = 800000 / 2.6532977

Present value = 301570.88

        b) How much interest will you earn?

Interest Earned = Future value  - Initial deposit

Interest Earned = $800,000 - $301,570.88

Interest Earned = $498,429.12

So, you will earn approximately $498,429.12 in interest over 20 years with a $301,570.88 initial deposit and a 7% annual interest rate compounded annually.

6.       You deposit $2800 in a savings account paying 6.5% simple interest. The solution to this problem is not accomplished by an excel formula. Use the formula I = PRT where T is in years

a) How much interest will you earn in 18 months?

P (Principal amount) = $2800

R (Interest rate per year) = 6.5% = 0.065 (in decimal form)

T (Time in years) = 18 months = 18 / 12 = 1.5 years

Interest=P×R×T

Interest = 2800 x 0.065 x 1.5

Interest = 2800 x 0.0975

Interest = 273

So, you will earn $273 in interest over 18 months with a $2800 deposit in a savings account paying 6.5% simple interest. 

b) How much will be in your account at the end of 18 months?

Total amount = Principal amount + Interest earned

Total amount = $2800 + $273

Total amount = $3073

So, you will have $3,073 in your account at the end of 18 months with a $2800 deposit in a savings account paying 6.5% simple interest.

1. Correlation Coefficient: To calculate the correlation coefficient, you can use Excel's CORREL function. Assuming that the "Advertising" data is in column B and the "Sales" data is in column C, you can enter the following formula in an empty cell:

   less
   =CORREL(B2:B9, C2:C9)
   

   This will give you the correlation coefficient.

2. Positive or Negative Correlation: If the correlation coefficient is positive, it indicates a positive correlation. If it's negative, it's a negative correlation.

3. Strength of Correlation: The strength of the correlation can be judged based on the absolute value of the correlation coefficient. If it's close to 1 (either positive or negative), it's a strong correlation. If it's closer to 0, it's a weak correlation.

4. Linear Equation: To find the linear equation, you can use Excel's LINEST function. Assuming your data is in the same columns as before, you can enter these formulas in empty cells:

   For the slope (m):

   php
   =LINEST(C2:C9, B2:B9, 1, TRUE)
   

   For the y-intercept (b):

   php
   =LINEST(C2:C9, B2:B9, 1, TRUE)
   

   This will give you the equation in the form of y = mx + b.

5. Sales Revenue Based on Advertising Spending: To calculate the sales revenue based on advertising spending, you can use the equation you found in the previous step. For example:

   For $3000 spending:

   scss
   =230 * (1.05^8) * 3000
   

   For $2100 spending:

   scss
   =230 * (1.05^8) * 2100
   

   For $1300 spending:

   scss
   =230 * (1.05^8) * 1300
   

6. Advertising Spending for Next 4 Months: This is a subjective decision. You can calculate it based on your desired advertising-to-sales ratio or budget constraints. For example, if you want to allocate 10% of your expected sales revenue to advertising:

   For November:

   scss
   =230 * (1.05^8) * (0.10 * Sales_R revenue for November)
   

   Similar calculations can be made for January, February, and March.

For parts 2 to 5, I can provide the calculations based on your inputs. Please specify the interest compounding frequency for part 2, as it's essential for accurate calculations.