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Linear Equations, Subsets, Interst and Probability (14 Problems)

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1) Which of the following equations describe the same line as the equation

3x+ 4y =5?

a. y = (3/4)x + 5
b. 6x + 8y = 5
c. y = (3/4)x + 5/4
d. 5 - 3x - 4y = 0
e. none of the above

2) The equation of the vertical line passing through (-3,5) is

a. x = -3
b. x = 5
c. y = -3
d. y = 5
e. none of the above

3) Determine which of the following points lie on the graph of the linear equation
4x + 5y = 20.

a) (0, -4)
b) (-5, 8)
c) (0, 0)
d) (5, 4)
e) (-4, 20)

4) Which of the following points satisfy the linear inequality 2x + 4y (less than or equal to symbol) 7 ?

a) (2, 4)
b) (-1, 3)
c) (0, 2)
d) (1, 1)
e) none of the above

5) The y-intercept of the line passing through point (14, 12) and having slope 2/7 is

a) (0, -4)
b) (0, 24/7 )
c) ( 0, 8)
d) (0,12)
e) none of the above

6) Consider the following sets:

U = {all professors}
A= {female professors}
B= {professors under 40 years of age}

(A "union symbol" B)' is the set

a. { professors who are male or 40 or older}
b. { male professors who are 40 or older}
c. {professors who are male and under 40}
d. {professors who are female or under 40}
e. none of the above

7) The number of events associated with a sample space having n outcomes is

a) n
b) n to the second power
c) 2 to the "nth" power
d) n!
e) none of the above

8) The probability of getting a black card or an ace in one draw from an ordinary deck of 52 cards is

i. 26/52
ii. 28/52
iii. 29/52
iv. 30/52
v. none of the above

9) An urn contains 4 white balls and 3 red balls. The balls are drawn from the urn, one at a time without replacement, until 2 white balls have been drawn. Let X be the number of the draw on which the second ball is white ball is drawn. The value which may be are

i. 1,2,3,4,5
ii. 2,3,4,5,6,7
iii. 2,3,4,5
iv. 1,2,3,4,5,6
v. none of the above

10. A church sells 2000 lottery tickets on a new car worth $7000. Each ticket costs $5. If you buy one ticket, your expected winning is

1. -1999 / 400
2. - 3 / 2
3. - 599 / 400
4. 7 / 2
5. none of the above

11. The variance of a probability distribution

vi. is large if the mean is large
vii. is small if the mean is large
viii. is always smaller than the mean
ix. has little practical value
x. none of the above

12. If Z is the standard normal random variable, then Pr(Z greater than or equal to symbol 0.6)

xi. .2254
xii. .2743
xiii. .5987
xiv. .7257
xv. none of the above

13. A loan of $9000 is to be repaid with monthly payments for 4 years at 12% interest compounded monthly. Calculate the monthly payment

xvi. $147.00
xvii. $264.38
xviii. $211.37
xix. $237.00
xx. none of the above

14. How much money can you borrow at 12% interest compounded monthly if you agree to pay $200 at the end of the month for three years in addition a balloon payment of $2000 at the end of the third year?

xxi. $6021.50
xxii. $1377.85
xxiii. $7419.35
xxiv. $8021.50
xxv. none of the above

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Linear Equations, Subsets, Interest and Probability are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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1) Answer: d
3x+4y=5, then move left to the right and get 0=5-3x-4y, so 5-3x-4y=0

2) Answer a
A vertical line has the form x=a. It passes through the point (-3,5), then a=-3. So the vertical line is x=-3

3) Answer b
When we plug in, we get 4*(-5)+5*8=-20+40=20, which satisfies the equation 4x+5y=20

4) Answer d
We plug in (1,1), then 2*1+4*1=6<=7 holds. Thus (1,1) satisfies the inequality 2x+4y<=7

5) Answer c
By the point-slope form, the equation of the line is y-12=(2/7)(x-14). To find y-intercept, we set x=0, then we get y-12=(2/7)*(-14)=-4. Then y=8. So the y-intercept is (0,8).

6) Answer d
A union B means either female professors or professors under 40. So the statement d is correct.

7) Answer c

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