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 Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

• y=1344x

• y=100x

• y=5.25x

• y=4/21x

Answer explanation

Since y varies directly with x, we can express this as y = kx. Given y = 84 when x = 16, we find k = 84/16 = 5.25. Thus, the equation is y = 5.25x, which is the correct choice.

Do the ratios form a proportion?

• Yes, they form a proportion.

• No, they do not form a proportion.

Answer explanation

Yes, the ratios form a proportion because they maintain a constant ratio when compared. This means that the cross products of the ratios are equal, confirming they are proportional.

Every 30 seconds, you can text 35 words. How many words can you type in an hour? 

• 2,300

• 4,200

• 540

• 1,800

Answer explanation

In one hour, there are 120 half-minute intervals. If you can text 35 words every 30 seconds, then in an hour, you can type 35 words x 120 intervals = 4,200 words. Thus, the correct answer is 4,200.

What type of proportion does the table represent?

• Direct

• Inverse

• I dont' know

Answer explanation

The table represents a direct proportion because as one variable increases, the other variable also increases at a constant rate. This relationship indicates that the two quantities are directly related.

The amount of money earned on a job is directly proportional to the number of hours worked.  If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

• $2

• $308

• $1.57

• $265

Answer explanation

To find the earnings for 22 hours, first determine the hourly rate: $70.00 / 5 hours = $14.00/hour. Then, multiply the hourly rate by 22 hours: $14.00 * 22 = $308. Thus, the correct answer is $308.

What type of variation does this scenario represent?
The length of time you charge your cell phone
and the battery power 

• direct variation

• inverse variation

• joint variation

• none of these

Answer explanation

The scenario shows that as you increase the charging time of your cell phone, the battery power also increases. This indicates a direct relationship, hence it represents direct variation.

The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

• 8 painters

• 10 painters

• 9 painters

• 11 painters

Answer explanation

The relationship is inverse: hours = k / painters. With 6 painters in 27 hours, k = 162. To find painters for 18 hours, set 18 = 162 / painters, giving 9 painters. Thus, 9 painters are needed.

The width of a rectangle varies inversely with its length. if the width is 4 when the length is 18, find the width when the length is 8.

• 9

• 72

• 36

• 2

Answer explanation

The width (W) and length (L) of the rectangle are inversely related: W = k/L. Given W = 4 when L = 18, we find k = 4 * 18 = 72. For L = 8, W = 72/8 = 9. Thus, the width when the length is 8 is 9.

2.The amount of money spent at the gas station varies directly with the number of gallons purchased. When 9.5 gallons of gas were purchased the cost was $36.52. How much would 12 gallons of gas cost?

• Direct Variation

• Inverse Variation

Answer explanation

The cost of gas varies directly with the gallons purchased, meaning if you buy more gas, the cost increases proportionally. Since 9.5 gallons cost $36.52, we can find the cost for 12 gallons using direct variation.

The number of kilograms of water in a person’s body varies directly as the person’s mass.  A person with a mass of 90 kg contains 60 kg of water.  How many kilograms of water are in a person whose mass is 75 kg?

• 50 kg water

• 72 kg water

• 94 kg water

• 150 kg water

Answer explanation

The ratio of water to mass is 60 kg water for 90 kg mass, or 0.67 kg water/kg mass. For 75 kg, water = 75 kg * 0.67 = 50 kg. Thus, a person with 75 kg mass contains 50 kg of water.