Pre-algebra Mid Term Exam Fall 2011

1. Jasmine is building birdhouses. It takes her $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math»$ hours to build 4 birdhouses. Which of the following is an equivalent rate?

14 hours to build 18 birdhouses

28 hours to build 35 birdhouses

7 hours to build 8 birdhouses

21 hours to build 28 birdhouses

The equivalent rate can be determined by finding the ratio of the number of birdhouses to the number of hours. In this case, the ratio for the correct answer is 8 birdhouses in 7 hours. This can be simplified to a rate of 1 birdhouse in 7/8 hours, which is equivalent to 7 hours to build 8 birdhouses.

Explanation

The equivalent rate can be determined by finding the ratio of the number of birdhouses to the number of hours. In this case, the ratio for the correct answer is 8 birdhouses in 7 hours. This can be simplified to a rate of 1 birdhouse in 7/8 hours, which is equivalent to 7 hours to build 8 birdhouses.

2. Which of the following does not represent a rational number?

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Explanation

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3.

F

G

H

J

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Explanation

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4. In July 2005 the United States imported approximately 10.3 million barrels of oil per day. Canada supplied about 16% of the imported oil. Which of these is closest to the number of barrels of oil the United States imported from Canada each day?

5.7 million

1.6 million

2.1 million

0.2 million

Canada supplied approximately 16% of the 10.3 million barrels of oil that the United States imported in July 2005. To find the number of barrels of oil imported from Canada each day, we can calculate 16% of 10.3 million. This comes out to be 1.648 million barrels. Since we are looking for the closest number, the answer of 1.6 million barrels is the best approximation.

Explanation

Canada supplied approximately 16% of the 10.3 million barrels of oil that the United States imported in July 2005. To find the number of barrels of oil imported from Canada each day, we can calculate 16% of 10.3 million. This comes out to be 1.648 million barrels. Since we are looking for the closest number, the answer of 1.6 million barrels is the best approximation.

5.

Between 43 units and 45 units

Between 88 units and 90 units

Between 8 and 9 units

Between 9 and 10 units

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Explanation

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6. The expression shown below describes a sequence of numbers. 2n + 3 If n represents the position of a number in this sequence, which sequence of numbers does this expression describe?

5, 8, 11, 14, 17, ...

5, 7, 9, 11, 13, ...

2, 3, 5, 8, 13, 21, ...

2, 5, 8, 11, 14, ...

The expression 2n + 3 generates a sequence of numbers where each number is obtained by multiplying the position of the number (n) by 2 and then adding 3. This means that the sequence will start with 3 (when n = 1), then 5 (when n = 2), 7 (when n = 3), and so on. Therefore, the correct answer is 5, 7, 9, 11, 13, ...

Explanation

The expression 2n + 3 generates a sequence of numbers where each number is obtained by multiplying the position of the number (n) by 2 and then adding 3. This means that the sequence will start with 3 (when n = 1), then 5 (when n = 2), 7 (when n = 3), and so on. Therefore, the correct answer is 5, 7, 9, 11, 13, ...

7. Tim recorded that 27 out of 63 customers used a shopping cart at a grocery store. Based on these results, about how many customers out of 350 can be expected to use a shopping cart?

110

260

90

150

Based on the given information, Tim recorded that 27 out of 63 customers used a shopping cart. To find out how many customers out of 350 can be expected to use a shopping cart, we can set up a proportion. The proportion is 27/63 = x/350, where x represents the number of customers out of 350. By cross-multiplying, we get 63x = 27 * 350, which simplifies to 63x = 9450. Dividing both sides by 63, we find that x is approximately equal to 150. Therefore, we can expect about 150 customers out of 350 to use a shopping cart.

Explanation

Based on the given information, Tim recorded that 27 out of 63 customers used a shopping cart. To find out how many customers out of 350 can be expected to use a shopping cart, we can set up a proportion. The proportion is 27/63 = x/350, where x represents the number of customers out of 350. By cross-multiplying, we get 63x = 27 * 350, which simplifies to 63x = 9450. Dividing both sides by 63, we find that x is approximately equal to 150. Therefore, we can expect about 150 customers out of 350 to use a shopping cart.

8. Jodie wants to buy a shirt regularly priced at $20. The shirt is on sale for 15% off the regular price. Which equation can be used to determine s, the sale price of the shirt, not including tax?

The equation that can be used to determine the sale price of the shirt, not including tax, is s = 20 - (0.15 * 20). This equation calculates the discount amount by multiplying the regular price by the discount percentage (15%), and then subtracts that amount from the regular price to get the sale price.

Explanation

The equation that can be used to determine the sale price of the shirt, not including tax, is s = 20 - (0.15 * 20). This equation calculates the discount amount by multiplying the regular price by the discount percentage (15%), and then subtracts that amount from the regular price to get the sale price.

9.

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Explanation

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10. Which equation best represents the data in the table below?

X	0	3	6	9	12
y	3	7	11	15	19

The equation y = 4x + 3 best represents the data in the table. This is because the y-values increase by 4 each time the x-values increase by 3, and the initial y-value is 3 when x = 0.

Explanation

The equation y = 4x + 3 best represents the data in the table. This is because the y-values increase by 4 each time the x-values increase by 3, and the initial y-value is 3 when x = 0.