Math Help
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Student: Kiare Mays Date: 06/15/20
Instructor: Valery Shemetov Course: MTH154 – Quantitative Reasoning (with MCR4)
Assignment: Section 6.3 Homework
Your mutual fund goes up % in the first year, then down % in the 2nd year, and finally up again % in the 3rd year. Complete parts a and b.
12.3 2.1 5.6
a) What is the average rate of return per year?
% (Do not round until the final answer. Then round to two decimal places as needed.)
b) If the fund plummets % in the 4th year, what is the average rate of return per year for the 4 years?31
% (Do not round until the final answer. Then round to two decimal places as needed.)
You average mph for the first miles of a trip and then mph for the next miles. Complete parts a and b.44 20 55 20
a) What is the average speed over the miles?40
mph (Type an integer or a decimal rounded to one decimal place.)
b) If you then average mph over the next miles what is the average speed over the miles?75 20 60
mph (Type an integer or a decimal rounded to one decimal place.)
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1: Types of means.
(1) arithmetic geometric harmonic
(2) arithmetic geometric harmonic
Determine whether to use the arithmetic mean, the geometric mean, or the harmonic mean to complete parts a and b.
Click the icon to view the three types of means.1
a) You mix equal weights of ( kg/ ), ( kg/ ), and ( kg/ ) together. What is the density of the resulting alloy? (Hint: Density is the rate of weight to volume, kg/ .)
Gold 19,320 m3 Europium 5243 m3 Aluminum 2712 m3
m3
To find the density of the resulting alloy, the (1) mean should be used and the density is
kg/ .m3
(Type an integer or a decimal rounded to one decimal place.)
b) If your veggie hot dog stand generates revenues of $ , $ , and $ at 3 events, what is your average revenue per event?
19,320 5243 2712
To find the average revenue per event, the (2) mean should be used and the average revenue is $ . (Round to the nearest cent as needed.)
The arithmetic mean, , is an average of n numbers. a1 + a2 +⋯ + an
n
The geometric mean, , is the average of change in growth where the rate of growth and/or decay changes over time.
n a1 • a2 •⋯ • an
The harmonic mean, , is the average of rates, as in travelling n miles at one rate and n miles at
another rate.
n 1
a1 +
1 a2
+⋯ + 1
an
Suppose the rate of return for a particular stock during the past two years was % and %. Compute the geometric mean rate of return. (Note: A rate of return of % is recorded as , and a rate of return of % is recorded as .)
5 35 5 0.05 35 0.35
The geometric mean rate of return is %. (Round to one decimal place as needed.)
Suppose the rate of return for a particular stock during the past two years was % and . Compute the geometric mean rate of return.
10 − 40%
The geometric mean rate of return is %. (Round to one decimal place as needed.)
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(1) more less
A company's stock price rose % in 2011, and in 2012, it increased %.1.7 17.1
a. Compute the geometric mean rate of return for the two-year period 2011 2012. (Hint: Denote an increase of % by .)
− 17.1 0.171
b. If someone purchased $1,000 of the company's stock at the start of 2011, what was its value at the end of 2012? c. Over the same period, another company had a geometric mean rate of return of %. If someone purchased $1,000
of the other company's stock, how would its value compare to the value found in part (b)? 32.11
a. The geometric mean rate of return for the two-year period 2011 2012 was %.− (Type an integer or decimal rounded to two decimal places as needed.)
b. If someone purchased $1,000 of the company's stock at the start of 2011, its value at the end of 2012 was $ . (Round to the nearest cent as needed.)
c. If someone purchased $1,000 of the other company's stock at the start of 2011, its value at the end of 2012 was
$ , which is (1) than the value from part (b). (Round to the nearest cent as needed.)
(1) more less
A company's stock price rose % in 2011, and in 2012, it increased %.3.9 75.8
a. Compute the geometric mean rate of return for the two-year period 2011 2012. (Hint: Denote an increase of % by .)
− 75.8 0.758
b. If someone purchased $1,000 of the company's stock at the start of 2011, what was its value at the end of 2012? c. Over the same period, another company had a geometric mean rate of return of %. If someone purchased $1,000 of
the other company's stock, how would its value compare to the value found in part (b)? 10.3
a. The geometric mean rate of return for the two-year period 2011 2012 was %.− (Type an integer or decimal rounded to two decimal places as needed.)
b. If someone purchased $1,000 of the company's stock at the start of 2011, its value at the end of 2012 was $ . (Round to the nearest cent as needed.)
c. If someone purchased $1,000 of the other company's stock at the start of 2011, its value at the end of 2012 was
$ , which is (1) than the value from part (b). (Round to the nearest cent as needed.)
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2: Data table for total rate of return
3: Geometric mean rate of return for stock market indices
The data in the accompanying table represent the total rates of return (in percentages) for three stock exchanges over the four-year period from 2009 to 2012. Calculate the geometric mean rate of return for each of the three stock exchanges.
Click the icon to view data table for total rate of return for stock market indices.2 Click the icon to view data table for total rate of return for platinum, gold, and silver.3
a. Compute the geometric mean rate of return per year for the stock indices from 2009 through 2012.
For stock exchange A, the geometric mean rate of return for the four-year period 2009-2012 was %. (Type an integer or decimal rounded to two decimal places as needed.)
For stock exchange B, the geometric mean rate of return for the four-year period 2009-2012 was %. (Type an integer or decimal rounded to two decimal places as needed.)
For stock exchange C, the geometric mean rate of return for the four-year period 2009-2012 was %. (Type an integer or decimal rounded to two decimal places as needed.)
b. What conclusions can you reach concerning the geometric mean rates of return per year of the three market indices?
A. Stock exchange B had a higher return than exchange C and a much higher return than exchange A.
B. Stock exchange C had a much higher return than exchanges A or B. C. Stock exchange A had a much higher return than exchanges B or C. D. Stock exchange A had a higher return than exchange C and a much higher return than
exchange B.
c. Compare the results of (b) to those of the results of the precious metals. Choose the correct answer below.
A. All three stock indices had lower returns than any of the precious metals. B. Silver had a much higher return than any of the three stock indices. Both gold and platinum had
a worse return than stock index C, but a better return than indices A and B.
C. Silver had a worse return than stock index C, but a better return than indices A and B. Gold had a better return than index B, but a worse return than indices A and C. Platinum had a worse return than all three stock indices.
D. All three stock indices had higher returns than any of the precious metals.
Year A B C 2012 8.61 12.77 15.85 2011 4.57 0.00 − 2.25 2010 11.00 11.54 16.18 2009 18.99 23.35 43.15
Metal Geometric mean rate of return Platinum %14.85
Gold %16.54 Silver %20.96
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4: Data table for total rate of return
5: Geometric mean rate of return for stock market indices
In 2009 2012, the value of precious metals changed rapidly. The data in the accompanying table represents the total rate of return (in percentage) for platinum, gold, and silver from 2009
–
through 2012. Complete parts (a) through (c) below.
Click the icon to view data table for total rate of return for platinum, gold, and silver.4 Click the icon to view the geometric mean rate of return for stock market indices.5
a. Compute the geometric mean rate of return per year for platinum, gold, and silver from 2009 through 2012.
The geometric mean rate of return for platinum during this time period was %. (Type an integer or decimal rounded to two decimal places as needed.)
The geometric mean rate of return for gold during this time period was %. (Type an integer or decimal rounded to two decimal places as needed.)
The geometric mean rate of return for silver during this time period was %. (Type an integer or decimal rounded to two decimal places as needed.)
b. What conclusions can you reach concerning the geometric mean rates of return of the three precious metals?
A. Platinum had a higher return than silver and a much higher return than gold. B. Platinum had a much higher return than silver and gold. C. Silver had a much higher return than gold and platinum. D. Gold had a higher return than silver and a much higher return than platinum.
c. Compare the results of (b) to those of the results of the stock indices. Choose the correct answer below.
A. Silver had a much higher return than any of the three stock indices. Both gold and platinum had a worse return than stock index C, but a better return than indices A and B.
B. All three metals had lower returns than any of the stock indices. C. Silver had a worse return than stock index C, but a better return than indices A and B. Gold had
a better return than index B, but a worse return than indices A and C. Platinum had a worse return than all three stock indices.
D. All three metals had higher returns than any of the stock indices.
Year Platinum Gold Silver 2012 5.8 0.2 56.6 2011 − 23.9 9.6 − 9.1 2010 23.3 30.6 14.8 2009 55.1 23.5 46.3
Stock indices Geometric mean rate of return A %9.96 B %11.28 C %22.49
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The half-life of a certain element is days, meaning every days the amount is cut in half. Complete parts (a) through (d) below.
15.5 15.5
(a) Fill in the following table.
Days Grams 0 40 15.5
31.0
46.5
(Round to two decimal places as needed.)
(b) What is the average percent change per day over the first days?15.5
% (Round to two decimal places as needed.)
(c) Write down an equation for the amount of the element left after d days in the form: A = A • (1 + r)0 d
A = 40 • (1 − 4.37%)d
A = 40 • (1 + 4.37%)d
A = 40 • (0.0437)d
A = 40 • (1.0437)d
(d) How much is left after 3 days?
grams (Round to one decimal place as needed.)
The average cost of gas dropped from a high of $ per gallon on June 1, 2015 to a low of $ on February 1, 2016. Complete parts (a) through (c) below.
2.81 1.65
(a) What is the average percent change in gas price per month?
% (Round to one decimal place as needed.)
(b) What is the decay factor associated to this rate?
(Round to three decimal places as needed.)
(c) Write down an equation for the price of gas m months after June 1, 2015 in the form: P = P • (1 + r)0 m
A. P = 2.81 • (1 − 0.936)m
B. P = 2.81 • (1.064)m
C. P = 2.81 • (0.064)m
D. P = 2.81 • (0.936)m
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