MATH201 Lecture Notes - Lecture 3: Upper Class

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redwalrus66

22 Jul 2016

School

University of Delaware

Department

Mathematics

Course

MATH201

Professor

Mwerinde Patrick

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Document Summary

Consider the following data set and construct both a frequency table and a histogram. One-way commuting distance in miles for 40 workers in downtown dallas, texas: 16 n = 40 largest = 47 smallest = 1 range = 47 1 = 46 miles. We chose 6: now we must determine class width, class width = range/# of classes, answer is rounded to the nearest whole number b. i. Our class width = 46/6 = 7. 7 which rounds up to 8: choose a starting point that is less than or equal to the first entry. Count by the class width: these are the lower class limits a. i. Since our 1st point is 1 and our class width is 8, we start with 1 and count up by 8 a. iii. Notice we have 6 classes: the upper class limits are the integers that fit within each class.

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)

1. One of the tables below contains (x,y) values that weregenerated by a linear function. Determine which table, and thenwrite the equation of the linear function represented by the

Table #1 x 2 5 8 11 14 17 20 y 1 3 7 13 21 31 43

Table #2 x 1 2 3 4 5 6 7 y 10 13 18 21 26 29 34

Table #3 x 2 4 6 8 10 12 14 y 1 6 11 16 21 26 31

2. Give an example of each of the following:

A function whosedomain is [2, infinity)

An arithmeticsequence

A system of equationswith no solutions

3. For f(x) =1/x^2-3, find:

f(3)
f(2+h)

4. For f(x) = 1/x-5and g(x) = x^2+2, find:

1. (fog)(x)

2. (gof)(6)

5. For the sequencegiven by a (subscript n) = 4n+5 an=4n+5, answer the following:

Find the first fiveterms

Find the sum of thefirst 25 terms.

Is this an arithmeticsequence? If so, how can you tell? If not, why not?

6. Graph the areabound by y<1/2x+6, x+3y>=12, x>=0, and x<=12

7. For the functiondefined by:

f(x)= {x^2,x<=1}

{2x+1,x>1}

a. evaluate f(0)

b. graph f(x)

8. Solve thefollowing system of equations algebraically. Verify your solutioneither graphically or by using matrices.

3x-y=0

5x+2y=22

9. Solve thefollowing system of equations algebraically. Verify your solutioneither graphically or by using matrices

8x-2y=5

-12x+3y=7

10.Given matricesA, B, and C below, perform the indicatedoperations if possible. If the operation is not possible, explainwhy.

A (3x3) [1st 2, -1,0] [2nd 0, 5, 0.3] [3rd 1, 4, 10]

B (3x3) [1st 5, 0, 2][2nd 1, -3, 9] [3rd2, 0, 4]

C (1x1) [1, 3, 5]

1.3A+B

2. B+C

3. CA

11. Given the tablebelow, evaluate the following:

x	-3	-2	-1	0	1	2	3	4	5
f(x)	10	20	30	40	50	60	70	80	90
g(x)	-1	-2	-3	-4	-5	-6	-7	-8	-9

a.(3f+2g(1) b. (fog)(-1)

12.Express the following function, F(x) as a composition of twofunctions f and g

f(x)= x^2/(x^2+4)

13.You have a coupon for your favorite clothing store for $25 off anypurchase of more than $50. The store is also running a 20%-off saleon its entire inventory. Let x be the original price, f(x)be the price with the $25 coupon applied, and g(x) be the pricewith the 20% discount applied.

a.Write an expression for f(x)

b.Write an expression for g(x)

c.What would the expression (fog)(x) represent?

d.What would the expression (gof)(x) represent?

e.If the store allows you to apply both the 20% discount and the$25-off coupon, does it matter which you apply first? How do youknow?

For this scenario, the manager at Shooters needs to know how advertising will effect customer turn out. In other words, how much should he spend each week in order to get the biggest return on his money. To that end, the manager at Shooters also recorded data relating how much he spent on weekly advertisements, such as fliers and commercials, with how many customers he had each week.

Week	Ad $, a	People, q	Week	Ad $, a	People, q	Week	Ad $, a	People, q
1	$ 50	112	19	$ -	81	37	$ 200	195
2	$ 150	182	20	$ 300	190	38	$ 300	205
3	$ 200	188	21	$ 150	176	39	$ 250	193
4	$ 200	184	22	$ 50	127	40	$ 100	147
5	$ 150	167	23	$ 200	187	41	$ 50	123
6	$ -	77	24	$ 200	189	42	$ 250	191
7	$ 150	173	25	$ 300	203	43	$ 50	120
8	$ -	71	26	$ 150	168	44	$ -	89
9	$ 100	149	27	$ 100	153	45	$ 300	198
10	$ 200	193	28	$ 200	194	46	$ 200	189
11	$ 250	191	29	$ 200	182	47	$ -	82
12	$ 100	146	30	$ 250	200	48	$ -	87
13	$ 100	155	31	$ 50	125	49	$ -	76
14	$ 150	177	32	$ 300	189	50	$ 100	159
15	$ 50	124	33	$ 150	173	51	$ 50	121
16	$ 150	177	34	$ 300	205	52	$ 50	120
17	$ 100	148	35	$ 200	182
18	$ -	76	36	$ -	80

) Use this data to determine a model that describes the number of people q who come to Shooters as a quadratic function of the amount of money spent on ads.

Give a graph of the customer versus advertising data. Then state the formula that expresses how many customers he can expect based on advertising expenses, q(a).

2) Use the derivative of the quadratic function you found in question 1 to determine what amount should be spent on advertising each week in order for Shooters to achieve a maximum number of customers? How many customers would come if the owner spent the maximum on advertising?

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MATH201 Lecture Notes - Lecture 3: Upper Class

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