Reference no: EM132296929

Mathematics For Management Questions -

Q1. When x = 3, the slope of the function f(x) = 4 + x + 2x2 is ___________.

Q2. Suppose that a stock is currently selling for $100. The change in the stock's price during the next year follows a normal random variable with a mean of $10 and a standard deviation of $20. What is the probability (rounded to the nearest hundredth) that the stock will sell for $85 or less in a year's time?

• 0.13
• 0.14
• 0.17
• 0.20
• 0.11

Q3. Suppose that 10% of all students at Cooley High play a winter sport, that 20% play a spring sport, and that 5% play both a winter and a spring sport. What is the probability that a randomly chosen student plays a winter or a spring sport?

• 30%
• 25%
• 35%
• 20%
• None of the above

Q4. Suppose that Joe Mauer has 150 hits in his 400 chances at bat. Assume that he will have 100 more chances at bat for the rest of the season. He needs ______ hits in his remaining chances at bat to ensure that he has hit .400. (Hitting .400 means he has gotten a hit during 40% of his at-bats.)

Q5. Evaluate

_i=1∑³i3

• $93.77
• $106.71
• $100.00
• $131.18
• None of the above

Q6. For the data in the file sandp.xlsx, the mode of the monthly returns (rounded to the nearest one tenth of a percent) is

Month	Returns
1881.02	-0.32%
1881.03	1.13%
1881.04	-0.32%
1881.05	4.50%
1881.06	1.23%
1881.07	-3.50%
1881.08	-2.36%
1881.09	0.81%
1881.10	-1.60%

• -0.5%
• 0.0%
• 0.2%
• 0.4%
• None of the above

Q7. For the data in the file sandp.xlsx, the median monthly return (rounded to the nearest one tenth of a percent) is

Month	Returns
1881.02	-0.32%
1881.03	1.13%
1881.04	-0.32%
1881.05	4.50%
1881.06	1.23%
1881.07	-3.50%
1881.08	-2.36%
1881.09	0.81%
1881.10	-1.60%

• 0.4%
• 0.5%
• 0.6%
• 1.0%
• 1.5%

Q8. Which of the following is the complete set of numbers for which the function f(x) = 3x3 - 6x2 is convex?

• x ≤ 0
• x ≥ 0
• x ≤ 1
• x ≥ 1
• None of the above

Q9. Let q = demand for a product and p = price in dollars charged for a product. Suppose that q = 10,000p-4. If you wanted to "invert" this relationship to express p as a function of q, you would obtain

• p = 10q-0.25
• p = 100q-0.5
• p = 10q0.25
• p = q0.25/10
• None of the above

Q10. Suppose that a die is tossed three times. What is the probability that at least one 6 will be tossed?

• 80/108
• 1/2
• 100/216
• 91/216
• None of the above

Q11. Today is January 1, 2015. The annual discount rate is 10%. Beginning in 2016, you will receive $10,000 on the first day of every year. What is the present value of this infinite sequence of cash flows?

• $60,000
• $70,000
• $110,000
• $90,000
• None of the above

Q12. Suppose that a fixed cost of $100,000 is incurred in producing a product. The unit cost of producing each product is $50, and each unit of the product is sold for $90. To break even, ______ units of the product must be sold.

Q13. Suppose that in 2012, ABC Industries earned a profit of $1400. You know that in 2012 profits grew by 40% from their 2011 level. Also, in 2011, profits grew by 25% from their 2010 level. The sum of the 2010 and the 2011 profits was

• $1600
• $1700
• $1800
• $1900
• None of the above

Q14. Suppose that the probability that it will rain on Saturday is 0.60. The probability that it will rain on Sunday is also 0.60. If it rains on one day, there is a 0.80 chance that it will rain the next day. What is the chance that it will rain at least one day during the weekend?

• 0.72
• 0.40
• 0.52
• 0.62
• None of the above

Q15. Britney is going to the candy store to buy 20 pieces of candy. She is going to buy chocolate candy and caramel candy. Each piece of chocolate candy costs 50 cents, and each piece of caramel candy costs 10 cents. You know that Britney spent $6.80 and bought 20 pieces of candy. She bought ______ pieces of chocolate.

Q16. Please download the file sandp.xlsx. The file contains monthly returns on the Standard & Poor's Index. For example, in February 1881 the Standard & Poor's Index dropped by 0.32%. Rounded to the nearest tenth of a percent, the mean monthly return on the S&P Index was

Month	Returns
1881.02	-0.32%
1881.03	1.13%
1881.04	-0.32%
1881.05	4.50%
1881.06	1.23%
1881.07	-3.50%
1881.08	-2.36%
1881.09	0.81%
1881.10	-1.60%

• 0.3%
• 0.4%
• 0.8%
• 1.0%
• 1.5%

Q17. Suppose that we create a histogram for the data in the file sandp.xlsx, with the boundaries for the bin ranges to the right.

The bin containing the most data points corresponds to monthly returns in the range

Bin
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5

• -20% to -10%
• -10% to 0%
• 0% to 10%
• 10% to 20%
• 20% to 30%

Q18. If you want to graph a function in Excel, select the data and then choose Insert from the ribbon. Next, choose the ______________ type of graph to create the desired view. The answer you type below should be one word.

Q19. Let q = demand for a product and p = price of a product in dollars. Suppose that q = 10,000p-3. Then a 1% increase in price will decrease demand by approximately ______ percent.

Q20. Here are the heights and weights of four residents of Smalltown, Nevada:

Height	Weight
69''	160 pounds
72''	175 pounds
75''	185 pounds
79''	220 pounds

The correlation between the height and the weight of these residents is

• .90
• .80
• .98
• .75
• .83

Q21. Suppose that a 3 of spades is drawn from a deck of cards. Let A = the event that the next card drawn is a heart and B = the event that the next card drawn is an ace. Is the following statement true or false?

Events A and B are independent.

• True
• False

Q22. The set of x satisfying -3x + 5 ≤ 17 is expressed as

• x ≤ -4
• x ≤ 2
• x ≥ -4
• x ≥ 4
• None of the above

Q23. The executives of an auto plant are thinking of buying a machine that today costs $10 million. During each of the next 5 years, they expect the machine to generate the profits given in the following table.

Year 1	Year 2	Year 3	Year 4	Year 5
$4 million	$3 million	$2 million	$2 million	$1 million

The payback period for the machine is

• between 1 and 2 years
• between 2 and 3 years
• between 3 and 4 years
• exactly 4 years
• exactly 5 years