Scale Factor

A random sample of 50 students from a school shows that 28 students prefer online classes over traditional classes. Predict how many students out of 200 would prefer online classes.

• 112

• 56

• 140

• 100

Answer explanation

Since 28 out of 50 students prefer online classes, the proportion is 28/50. Extrapolating to 200 students gives 112 students who would prefer online classes.

A survey conducted on a random sample of 120 people in a town shows that 60 people own a pet. If the town has 4800 people, how many people in the town are likely to own a pet?

• 2400

• 1200

• 1800

• 3000

Answer explanation

Since 60 out of 120 people own a pet in the sample, we can estimate that 2400 out of 4800 people in the town likely own a pet (60/120 = 2400/4800). Therefore, the correct answer is 2400.

In a random sample of 200 seeds, 140 seeds germinated. Predict the number of seeds that would germinate if 1000 seeds were planted.

• 700

• 500

• 600

• 800

Answer explanation

To find the number of seeds that would germinate if 1000 seeds were planted, use the proportion method: (140 seeds germinated / 200 seeds) = (x seeds germinated / 1000 seeds). Solving for x gives 700 seeds germinated.

A random sample of 80 books at a library showed that 32 books were fiction. Predict the total number of fiction books in a library that has 400 books.

• 160

• 200

• 140

• 120

Answer explanation

To find the total number of fiction books in the library, we can set up a proportion: 32 books out of 80 are fiction, so 400 books would have (32/80) * 400 = 160 fiction books.

In a survey, 45 out of a random sample of 150 people said they prefer tea over coffee. Predict how many people would prefer tea in a city of 30,000 people.

• 9000

• 15000

• 4500

• 12000

Answer explanation

Since 45 out of 150 prefer tea, the ratio is 45/150. Applying this ratio to 30,000 people gives 9000 people who would prefer tea.

A study on a random sample of 250 cars passing through a toll booth shows that 75 cars are from out of state. Predict the number of out-of-state cars among 1000 cars passing through the toll booth.

• 300

• 250

• 200

• 350

Answer explanation

To predict the number of out-of-state cars among 1000 cars, use the ratio from the sample: 75/250 = x/1000. Solving for x gives 300.

In a random sample of 60 apples from a farm, 12 apples were found to be rotten. If the farm has 3000 apples, predict the number of rotten apples.

• 600

• 240

• 120

• 480

Answer explanation

To predict the number of rotten apples, use the ratio of rotten apples in the sample to the total apples in the farm: (12/60) * 3000 = 240 rotten apples.

What is the scale factor from the small fry to the large fry?

• 1/3

• 48

• 4

• 3

What is the scale factor from triangle ABC to triangle DEF?

• 1/2

• 7/14

• 2

• 10/20

• 0.25
• 0.5
• 2
• 1/2