13. joe expects to spend at least $8500 on a used car, but he can’t afford to spend more than $12,000. which inequality could be used to describe the amount of money, x, that joe may spend on a car?

a12000 - 8500 < x
b8500 < x < 12000
cx = 8500 or x = 12000
dx < 8500 and x > 12000
e 8500 < x < 12,000
f not enough information

14. teenagers should sleep between 8 and 10 hours per night. sarah typically sleeps 2 hours less than this per night. which inequality describes the amount of time that sarah sleeps?

a10 < x < 12
b8 < x < 10
c6 < x < 12
d6 < x < 8
e 8 + 2 < 8 < 10
f 8 < x < 10 + 2

15. men need to intake between 2200 and 2800 calories daily. women need 600 fewer calories than this. write and solve an inequality to discover how many calories women should be taking in per day.

a2200 < x - 600 < 2800
b2200 > x < 2800
c600 < x < 1200
d1600 < x < 2800
e 1600 < x < 2200
f 2800 < x < 3200

16. the velocity of an object fired directly upward is given by v = 20 – 9.8t, where t is time in seconds. when will the velocity be between 10 and 20 meters per second?

a1.02s > t > 0 s
bt > 0
c3.57s < t < 2.5s
dt < 4.08s
e t < 3.06s
f 1s < t < 2s

17. if you invest $2000 at a rate of 8% per year, how many years will it take to earn at least $1000 in interest?

a9 years
b5.5 years
c6 years
d1 year
e 3.75 years
f 6.25 years

18. if you invest $5000 for 10 years, which inequality describes the interest rate needed to earn at least $1500 of interest?

a5000 > (1500)(10)x
bx > (10)(1500)(5000)
c10x < (1500)(5000)
d1500 < (5000)(10)x
e 5000x < (1500)(10)
f 5000 < x < (1500)(10)

19. the velocity of an object fired directly upward is given by v = 35 – 9.8t, where t is time in seconds. which inequality describes the velocity when t is between 0.5 and 1.5 seconds? (hint: remember that when you multiply an inequality by a negative number, you must switch the direction of the inequality.)

a20.3 > 35 - 9.8t > 30.1
b4.9 > t > 14.7
c0.5 < t < 1.5
dv < 30.1
e 20.3 < 35 - 9.8t < 30.1
f 14.7 > 35 - 9.8t > 4.9

20. what is the least amount of principal you can invest at an 8% interest rate to earn at least $1000 in interest in 3 years? (round your answer to the nearest dollar.)

a$240
b$5167
c$2
d$4167
e $6367
f cannot be determined