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Variations Gateway

 1. 

Wind chill factor (W) varies directly with temperature (T) and inversely with the wind velocity (v). If k is the constant of proportionality, which formula represents this relationship?
A)
mc001-1.jpg
B)
mc001-2.jpg
C)
mc001-3.jpg
D)
mc001-4.jpg
 

 2. 

n varies directly as p and the constant of variation is mc002-1.jpg.  Which equation represents the relationship?
A)
n = mc002-3.jpgp.
B)
n = p - mc002-4.jpg
C)
n = mc002-5.jpgp
D)
n = p + mc002-6.jpg
 

 3. 

c varies directly as d and c = 1 when d = 5. What is the constant of variation?
A)
4
B)
mc003-3.jpg
C)
mc003-4.jpg
D)
–4
 

 4. 

Which equation represents an inverse variation?
A)
mc004-3.jpg
B)
mc004-4.jpg
C)
mc004-5.jpg
D)
mc004-6.jpg
 

 5. 

In which graph is y a direct variation of x?
A)
mc005-1.jpg
C)
mc005-3.jpg
B)
mc005-2.jpg
D)
mc005-4.jpg
 

 6. 

If t varies directly as u and t = 5 when u = 3, what is the value of t when u = 9?
A)
1.667
B)
0.6
C)
15
D)
5.4
 

 7. 

Hannah was looking a picture of herself and 3 friends.  She measured the height of her image as 7 centimenters.  If Hannah is acutally 65 inches tall, which equation can she use to find h, the actual height in inches, of one of her friends who is c centimeters tall in the picture?
A)
h = 7c
B)
h = mc007-2.jpgc
C)
h = mc007-3.jpgc
D)
h = mc007-4.jpgc
 

 8. 

A electrician bills his customers $70 for each hour he works.  If a client’s bill is $850, which equation could be used to find the number of hours worked?
A)
mc008-2.jpg
B)
mc008-3.jpg
C)
mc008-4.jpg
D)
mc008-5.jpg
 

 9. 

Dora’s paycheck earnings, p, varies directly as the number of hours, h, she works. If she works 15 hours and earns $126.00, what should she earn if she worked 29 hours?
A)
$140.00
B)
$141.00
C)
$243.60
D)
$170.00
 

 10. 

In the table, y varies directly with x.

x
10
15
20
25
y
6
9
12
15

Which equation best describes the data?
A)
mc010-1.jpg
B)
mc010-2.jpg
C)
mc010-3.jpg
D)
mc010-4.jpg
 

 11. 

Distance, d, varies directly as time, t, when speed remains constant. If d is 175 kilometers when t is 5 hours, what is the constant speed?
A)
875 kmh
B)
170 kmh
C)
35 kmh
D)
mc011-2.jpg kmh
 

 12. 

For a group of objects made of the same material, the weight of an object varies directly with its volume. If an object that has a volume of 14 cubic centimeters weighs 30 grams, what is the constant of variation?
A)
0.47
B)
30
C)
2.14
D)
14
 

 13. 

The circumference, c, of a circle varies directly as the diameter, d, of the circle. If k is the constant of variation, which equation represents that situation?
A)
mc013-1.jpg
B)
mc013-2.jpg
C)
mc013-3.jpg
D)
mc013-4.jpg
 

 14. 

In which table does y not vary directly as x ?
A)
mc014-1.jpg
C)
mc014-3.jpg
B)
mc014-2.jpg
D)
mc014-4.jpg
 

 15. 

Which of the following graphs shows a direct variation?
A)
mc015-1.jpg
C)
mc015-3.jpg
B)
mc015-2.jpg
D)
mc015-4.jpg
 

 16. 

Which of the following tables indicates that x and y vary directly?
A)
mc016-1.jpg
B)
mc016-2.jpg
C)
mc016-3.jpg
D)
mc016-4.jpg
 

 17. 

The time it takes to travel a given distance varies inversely as the average rate of travel.  Averaging 45 miles per hour, it takes Paula 4 hours to drive to Airy.  If it took him 5 hours and 20 minutes to reach Airy on her last trip, what was her average rate of travel?
A)
31.8 mph
B)
32.7 mph
C)
33.8 mph
D)
34.8 mph
 

 18. 

Hooke’s law states that the force required to stretch a spring varies directly with the distance the spring is stretched. If a 16-pound force stretches a spring 4 inches, what force is required to stretch the spring 9 inches?
A)
25 lbs
B)
80 lbs
C)
36 lbs
D)
59 lbs
 

 19. 

Boyle’s Law states that, for a fixed amount of gas, the volume of the gas at a constant temperature is inversely proportional to the pressure. If a certain gas occupies 10.32 liters at a pressure of 49.3 centimeters of mercury (cm Hg), what is the approximate pressure when the volume is increased to 12 liters?
A)
41.3 cm Hg
B)
42.4 cm Hg
C)
44.5 cm Hg
D)
46.6 cm Hg
 

 20. 

In which of the following is w directly proportional to u and inversely proportional to the cube of v?
A)
mc020-1.jpg
B)
mc020-2.jpg
C)
mc020-3.jpg
D)
mc020-4.jpg
 

 21. 

Assuming k is a constant of variation, which equation represents a situation in which m varies jointly as p and q?
A)
mc021-1.jpg
B)
mc021-2.jpg
C)
mc021-3.jpg
D)
mc021-4.jpg
 

 22. 

Which equation represents the statement:          “g is inversely proportional to h.”?
A)
mc022-1.jpg
B)
mc022-2.jpg
C)
mc022-3.jpg
D)
mc022-4.jpg
 

 23. 

A farmer pumps water from an irrigation well to water his field. The time it takes to water the field varies inversely with the rate at which the pump operates. It takes 20 hours to water the field when the pumping rate is 650 gallons per minute. If he adjusts the pump so that it pumps at a rate of 400 gallons per minute, about how long will it take to water the field?
A)
12.3 hours
B)
44.8 hours
C)
32.5 hours
D)
36 hours
 

 24. 

Which equation represents the statement

e is inversely proportional to f and directly proportional to the cube of g”?
A)
mc024-1.jpg
B)
mc024-2.jpg
C)
mc024-3.jpg
D)
mc024-4.jpg
 

 25. 

The time it takes to do a job is inversely proportional to the number of workers. If 8 workers can do a job in 5 weeks, then 14 workers can do the same job in --
A)
1.43 weeks
B)
2.86 weeks
C)
4.29 weeks
D)
5.71 weeks
 



 
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