MATH 407 Midterm: MATH 407 USC M 407 F 09f

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turquoisegnu128

31 Jan 2019

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Instructor s. lototsky (kap 248d; x0 2389; lototsky@math. usc. edu) Instructions: no books, notes, or calculators, you have 120 minutes to complete the exam, show your work. A total of 10 identical gifts are to be distributed among 7 children. Suppose that a and b are independent events for which p (a) = 0. 3 and p (b) = 0. 5. A population contains twice as many females as males. In this population, 5% of males and 0. 25% of females are color-blind. Compute the probability that the person is male. Let x be the di erence between the number of heads and the number of tails. Find (a) the possible values of x (note: x can be both positive and negative) (b) p (x = 0). Let x be a random variable with uniform distribution on [2, 5]. De ne the random variable y by y = ln x. compute the probability density function of the random variable y .

Related Questions

1. Evaluate the expression 2x - 2 for the value of x = -3

2. Factor: xsquare + 4x - 32 (x-4)(x+8) (x-4)(x-8) (x-4)(x-8) (x-16)

3. Factor: xsquare - 25 (x-5) (x+5)2 (x+5)(x-5) (x-5)(x-5)

4. Evaluate -u2v3 when u=4 and v=-2 128 64 32 -128

5. Using an online calculator, determine whether the value of x=7 is a solution of the equation. x Yes No

6. Explain why x=7 IS or IS NOT a solution of the equation. 7 + 1/x+2=8

7. Solve the equation and check your solution: -2 - 4x = 30

8. Solve the equation and check your solution: 67x - 24 = 3x + 8(8x - 3) 67 -3 -67 All real numbers

9. Solve the equation and check your solution. 5x/2 - x/6 = 14 10 6 7 9

10. Solve the quadratic equation by factoring: xsquare - 6x + 5 = 0 -1, 5 -1,-5 1,-5 1,5

11. The imaginary number i represents:

12. Find real numbers a and b such that the equation is true: a+ bi = 14 + 2i a=16, b=4 a=18, b=6 a=14, b=2 a=15, b=14

13. Find all solutions to the following equation. /4x - 8 = /4x + 9 x = -17/4 x=9 No solution x=-17

14. In a given amount of time, James drove twice as far as Rachel. Altogether they drove 120 miles. Write an equation to help find the number of miles driven by each. Use R as the variable to represent miles driven by Rachel and J for Jamesâ miles.

15. Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings. Be sure to save the equation you write, as you will use it to answer the next question in this quiz. 10h - .25=450 10h + .25(10h)=450 h -.25 (10h)=450 10h - .25(10h)=450

16. Using the equation you wrote in the previous problem, find the actual amount of hours Karen must work to take home $450 if she saves all of her earnings. Show your work. 17. The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width. Hint: Perimeter = width + length + width + length

18. Twice a number is added to the number and the answer is 80. Write an equation to solve this problem. 2n + n=80 2n = 80 2n + 80=n 80 + n=2n

19. If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.

20. Multiply the following binomials: (x + 5)(x - 5)

please use the following information to answer questions 1-6

Imagine you have graduated and have just gotten a job in a fictionalized version of Paducah, KY, home of the world famous Dippin' Dots (Links to an external site.)Links to an external site.. You got the job by pitching a truly marvelous idea: The Grand Cone-yan, an ice cream festival as grand as any Court Days (Links to an external site.)Links to an external site. or Apple Festival (Links to an external site.)Links to an external site..

The centerpiece of the festival is a 10 foot tall ice cream cone filled with local ice cream dots.

The day before the festival the contractors have brought the truck of ice cream, and begin to fill the cone. After only a single minute, there is a foot of ice cream in your frozen glass cone. Since the entire cone is only 10 feet tall, you decide to come back in 10 minutes to witness the final filling.

You are shocked when you return to find the cone has only been filled to the 2 foot mark! (The worker politely corrects you to say it is actually 2 feet and 2 inches.) You give it another 10 minutes, but the cone is only 2 foot 9 inches filled.

Not knowing what else to do, you make a spreadsheet of the progress.

Time (minutes)	0	1	10	20	30	60	120
Height (feet, inches)	0' 0"	1' 0"	2' 2"	2' 9"	3' 1"	3' 11"	4' 11"

You wonder why they have slowed down so much, so you keep checking in every hour.

Time (hours)	1	2	3	4	5	6
Height (feet, inches)	3' 11"	4' 11"	5' 8"	6' 3"	6' 6"	6' 11"

After six hours you are worried the entire festival might fail, but you won't give up! You keep spreadsheeting.

Time (hours)	7	8	9	10	11	12
Height (feet, inches)	7' 4"	7' 8"	7' 11"	8' 3"	8' 6"	8' 9"

After 12 hours, you take a quick trip home to change clothes, and return to your spreadsheeting.

Time (hours)	13	14	15	16	17	18
Height (feet, inches)	8' 11"	9' 2"	9' 5"	9' 7"	9' 9"	10' 0"

Finally, late in the night, around 3am, it is complete. Your masterpiece. The Grand Cone-yan. But why did it take so long? It took a lot longer than 10 minutes. Why did the workers slow down so much? The first minute finished the first foot, but three feet took 30 minutes instead of 3 minutes. And now it's 3am!

The workers say that they filled at a steady rate of 13 gallons per hour, and that any faster would run the risk of drain freeze.

Your responses

1. What is wrong with the following argument?

If you really did 13 gallons per hour, then the 10 foot cone should have only taken 10 / 13 = 0.7 hours, less than an hour tops.

2. What is wrong the following question?

How do you convert gallons into feet?

3. Find an authoritative source for the volume of a cone. Give the formula and explain what each part of the formula means in this problem.

4. Most formulas will have both radius and height. Find a reasonable source for the relationship between the radius and height of an ice cream cone. Give an expression like

R = H

5. Calculate the volume of the cone using your formula. At a constant rate of 13 gallons per hour, how long should it have taken to fill up?

You may use the approximate formula V=0.02908882 h3 if the formula you discovered does not match at all.

6. There should still be a discrepancy between the V=0.02908882 h3 and the spreadsheet. Can you explain what likely happened?

Solve all please.