MATHEMATICS

1. Find the circumference and area of the circle having the given diameter. d = 12 cm

The circumference is 37.7 cm.

(Round to the nearest tenth as needed.)

The area is 113.0 cm 2.

(Round to the nearest tenth as needed.)

 2. An oval track is made by erecting semicircles on each end of a 56 m by 112 m rectangle. Find the length of the track and the area enclosed by the track. The length of the track is 400 m. (Round to the nearest whole number.) The area enclosed by the track is 8734 m2. (Round to the nearest whole number.) 3. Find the surface area and the volume of the cylinder. Surface area = 226.08 cm- Volume = 251.2 cm3 (Round to the nearest hundredth.) YOU ANSWERED: 276.0 5 cm

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4. At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins, one with radius 4 inches and the other with radius 6 inches. Compute the surface area and volume for each pumpkin. Then find the surface-area-to-volume ratio for both pumpkins. Which pumpkin has the larger ratio?

The surface area of the pumpkin with a 4-inch radius is 201 in2.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

The volume of the pumpkin with a 4-inch radius is 267.9 in3.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

The surface area of the pumpkin with a 6-inch radius is

452.47 in2.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

The volume of the pumpkin with a 6-inch radius is

904.3 in3.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

Which pumpkin has the larger surface-area-to-volume ratio? The pumpkin with a 6-inch radius

The pumpkin with a 4-inch radius YOU ANSWERED: 452

5. Find the angular size of a circular object with a 2-inch diameter viewed from a distance of 6 yards.

The angular size of the object is 0.53

(Do not round until the final answer. Then round to the nearest hundredth as needed.)

6. A mountain peak rises from sea level to a summit elevation of 3894 ft over a horizontal distance of 15,842 ft. Find the grade of the peak.

The grade of the peak is 25 %.

(Round to the nearest percent as needed.)

7. On the map (right), the length of each 1 east-west block is — mile and the length of 5 Theater Grocery store E • • e Library 1 4 S A L L; • • : 41 _ • •each north-south block is —4 mile. Victoria has

to walk from the library to the theater. Find the shortest walking distance. Then find the straight-line distance (‘as the crow flies’) between the two locations.

What is the shortest walking distance? 2.1 mi Bus stop — mi 5

(Round to the nearest hundredth as needed.)

What is the straight-line distance?

1.68 mi

(Round to the nearest hundredth as needed.)

8. A triangular lot is 160 ft on one side and has a

160 property line of length 900 ft. Find the area of the lot in acres. (Figure not drawn to scale)

Areage, acre(s)

(Round to the nearest hundredth as needed.)

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 9. Given that the pair of triangles is similar, find the length of the side labeled n. 60 30 n = 25

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10. To get to a cabin, Dana can ride a bicycle west from a parking lot along the edge of a rectangular reservoir for 1.2 miles, and then south along the edge for 0.5 miles. Or she can row a boat directly from the parking lot. If Dana can ride 1.4 times as fast as she can row, which is the faster route?

Choose the faster route below. Rowing a boat

2_40 Riding a bicycle

11. The population of a town is increasing by 632 people per year. State whether this growth is linear or exponential. If the population is 1300 today, what will the population be in five years?

Is the population growth linear or exponential? 110 linear

exponential

 What will the population be in five years? 4460

12. During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 25% per month. State whether this increase was linear or exponential. If your food bill was \$160 in one month during this period, what was it three months later?

Was the growth in inflation linear or exponential? -kV exponential

linear

What was the monthly food bill after three months? \$ 313

(Round to the nearest dollar as needed.)

13. A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 21? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)

How many grains of wheat should be placed on square 21? 1048576 grains

How many total grains of wheat should be on the board after the the grains of wheat have been placed on square 21?

2,097,151 grains

What is the total weight of all the grains of wheat on the board after the grains of wheat have been placed on square 21?

299.6 pounds

(Round to the nearest tenth as needed.)