Question : Suppose that z varies jointly with x and y and that z : 2163519
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the expression is rational.
221) The fixed monthly payment required to amortize a loan of L dollars over a term of n months at an annual interest rate of r is given by ((Lr/12)/1 - (1 + (r/12))-n). Evaluate this expression when L = $200,000, r = 0.07, and n = 360 months .
A) $1264.07
B) $1463.67
C) $1397.14
D) $1330.60
Solve the proportion.
222) (1/3) = (x/18)
A) 18
B) 6
C) 3
D) 15
223) (3/5) = (x/15)
A) 11
B) 9
C) 6
D) 15
224) (6/8) = (x/24)
A) 48
B) 6
C) 18
D) 144
225) (14/x) = (9/18)
A) 28
B) 252
C) 14
D) 126
226) (9/x) = (23/138)
A) 15
B) 54
C) 9
D) 106
Write a proportion that models the situation described. Then, solve the proportion for x.
227) 11 is to 12, as 3 is to x
A) (11/12) = (3/x); x = (38/11)
B) (11/12) = (3/x); x = (36/11)
C) (11/12) = (x/3); x = (33/10)
D) (11/12) = (x/3); x = (11/4)
228) A rectangle has sides of 6 and 11. In a similar rectangle, the longer side is 44 and the shorter side is x.
A) (6/11) = (x/44); x = 26
B) (6/11) = (x/44); x = 24
C) (6/11) = (44/x); x = (242/3)
D) (6/11) = (44/x); x = (487/6)
229) If 3.3 ounces of oil are to be added to 16.5 gallons of gasoline, then x ounces of oil should be added to 39.5 gallons of gasoline.
A) (3.3/16.5) = (x/39.5); x = 7.9 ounces
B) (3.3/16.5) = (x/39.5); x = 8.1 ounces
C) (3.3/16.5) = (x/39.5); x = 7.8 ounces
D) (16.5/3.3) = (x/39.5); x = 197.5 ounces
230) If at a given speed a car can travel 142.8 miles on 6 gallons of gasoline, then the car can travel x miles on 102 gallons of gasoline at that speed.
A) (142.8/6) = (x/102); x = 2435 miles
B) (6/142.8) = (x/102); x = 2427.6 miles
C) (142.8/6) = (x/102); x = 2427.6 miles
D) (6/142.8) = (x/102); x = 2435 miles
Solve the problem.
231) Suppose that y is directly proportional to x and that y = 40 when x = 8. Find the constant of proportionality k. Then use y = kx to find y when x = 17.
A) k = 5; y = 85
B) k = - 5; y = - 85
C) k = 7; y = 119
D) k = 320; y = (320/17)
232) Suppose that y is directly proportional to x and that y = 39 when x = 6. Find the constant of proportionality k. Then use y = kx to find y when x = 15.
A) k = 6.5; y = 112.5
B) k = 234; y = (78/5)
C) k = 6.5; y = 97.5
D) k = 6.25; y = 93.75
233) Suppose that y is directly proportional to x and that y = 14.4 when x = 6. Find the constant of proportionality k. Then use y = kx to find y when x = 15.
A) k = 2.6; y = 36
B) k = 86.4; y = (86.4/15)
C) k = 2.4; y = 39
D) k = 2.4; y = 36
234) Suppose that y is directly proportional to x and that y = 3.5 when x = 7. Find the constant of proportionality k. Then use y = kx to find y when x = 10.
A) k = 1.5; y = 4
B) k = 24.5; y = (49/20)
C) k = 0.5; y = 5
D) k = 0.5; y = 4
235) Suppose that y is inversely proportional to x and that y = 40 when x = 9. Find the constant of proportionality k. Then use y = (k/x) to find y when x = 8.
A) k = (40/9); y = (320/9)
B) k = 180; y = 22.5
C) k = 360; y = 45
D) k = 72; y = 9
236) Suppose that y is inversely proportional to x and that y = 17.5 when x = 5. Find the constant of proportionality k. Then use y = (k/x) to find y when x = 25.
A) k = 3.5; y = 87.5
B) k = 80; y = 3.2
C) k = 87.5; y = 3.5
D) k = 95; y = 3.8
237) Suppose that y is inversely proportional to x and that y = 26.4 when x = 6. Find the constant of proportionality k. Then use y = (k/x) to find y when x = 36.
A) k = 176.4; y = 4.9
B) k = 4.4; y = 158.4
C) k = 158.4; y = 4.4
D) k = 146.4; y = 4.4
238) Suppose that y is inversely proportional to x and that y = 3.5 when x = 7. Find the constant of proportionality k. Then use y = (k/x) to find y when x = 10.
A) k = 9.8; y = (49/50)
B) k = 24.5; y = (49/20)
C) k = 4.9; y = (49/20)
D) k = 0.5; y = 5
Solve the problem. Round amounts to the nearest tenth if necessary.
239) Suppose that z varies jointly with x and y and that z = 405 when x = 9 and y = 15. Find the constant of variation k. Then use z = kxy to find z when x = 3 and y = 4.
A) k = 5; z = 60
B) k = 54,675; z = (18225/4)
C) k = 0.3; z = 3.6
D) k = 3; z = 36
240) Suppose that z varies jointly with x and y and that z = 1080 when x = 9 and y = 16. Find the constant of variation k. Then use z = kxy to find z when x = 3 and y = 10.
A) k = 7.8; z = 234
B) k = 7.5; z = 225
C) k = 155,520; z = 5184
D) k = 7.3; z = 219
