Algebra 1 Quiz Lesson 2-7 To 2-11

1. On a map, the distance between Jacksonville, FL and Tallahassee, FL is about 8 inches. According to the scale, 1 inch represents 20 miles. About how far apart are the two cities? (leave the number as the answer).

The scale on the map states that 1 inch represents 20 miles. Since the distance between Jacksonville and Tallahassee on the map is 8 inches, we can multiply 8 by 20 to find the actual distance between the two cities. Therefore, the two cities are about 160 miles apart.

Explanation

The scale on the map states that 1 inch represents 20 miles. Since the distance between Jacksonville and Tallahassee on the map is 8 inches, we can multiply 8 by 20 to find the actual distance between the two cities. Therefore, the two cities are about 160 miles apart.

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2. A utility worker is 5.5 feet tall and is castig a shadow 4 feet long. At the same time, a nearby utility pole casts a shadow 20 feet long. Find the height of the utility pole. (leave the number as the answer).

The height of the utility pole can be found using the concept of similar triangles. The ratio of the height of the utility worker to the length of their shadow is the same as the ratio of the height of the utility pole to the length of its shadow. Therefore, we can set up the proportion: (Height of utility worker)/(Length of utility worker's shadow) = (Height of utility pole)/(Length of utility pole's shadow). Plugging in the given values, we get (5.5 feet)/(4 feet) = (Height of utility pole)/(20 feet). Solving for the height of the utility pole, we find that it is 27.5 feet.

Explanation

The height of the utility pole can be found using the concept of similar triangles. The ratio of the height of the utility worker to the length of their shadow is the same as the ratio of the height of the utility pole to the length of its shadow. Therefore, we can set up the proportion: (Height of utility worker)/(Length of utility worker's shadow) = (Height of utility pole)/(Length of utility pole's shadow). Plugging in the given values, we get (5.5 feet)/(4 feet) = (Height of utility pole)/(20 feet). Solving for the height of the utility pole, we find that it is 27.5 feet.

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3. A rectangle has an area of 48 . Every dimension of the rectangle is multiplied by a scale factor and the new rectangle has an area of 12 . What was the scale factor? (leave the number as the answer).

The scale factor is the ratio of the new area to the original area. In this case, the new area is 12 and the original area is 48. Therefore, the scale factor is 12/48 = 1/4 = 0.25. However, none of the given answer choices match this value. So, the correct answer is not available.

Explanation

The scale factor is the ratio of the new area to the original area. In this case, the new area is 12 and the original area is 48. Therefore, the scale factor is 12/48 = 1/4 = 0.25. However, none of the given answer choices match this value. So, the correct answer is not available.

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4. Solve the proportion A hair salon rent booths for $200 per month plus a 5% commission on receipts. How rent does Qiana owe for one month when her receipts total $4500? (leave the number as the answer).

Qiana owes $425 for one month's rent. This is calculated by adding the $200 base rent to the 5% commission on her receipts, which is $225 (5% of $4500). The total rent owed is $200 + $225 = $425.

Explanation

Qiana owes $425 for one month's rent. This is calculated by adding the $200 base rent to the 5% commission on her receipts, which is $225 (5% of $4500). The total rent owed is $200 + $225 = $425.

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5. After 9 mounts, the simple interest earned on an investment of $1200 is $72. Find the interest rate. (leave the number as the answer).

After 9 months, the simple interest earned on an investment of $1200 is $72. To find the interest rate, we can use the formula for simple interest: Interest = (Principal * Rate * Time) / 100. Plugging in the given values, we have 72 = (1200 * Rate * 9) / 100. Solving for the rate, we get Rate = (72 * 100) / (1200 * 9) = 8%. Therefore, the interest rate is 8%.

Explanation

After 9 months, the simple interest earned on an investment of $1200 is $72. To find the interest rate, we can use the formula for simple interest: Interest = (Principal * Rate * Time) / 100. Plugging in the given values, we have 72 = (1200 * Rate * 9) / 100. Solving for the rate, we get Rate = (72 * 100) / (1200 * 9) = 8%. Therefore, the interest rate is 8%.

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6. The sales tax rate is 8.25%. estimate the sales tax on the book taht costs $18.50.

The sales tax rate is 8.25%, which means that for every dollar spent, 8.25 cents will be added as tax. To estimate the sales tax on the book that costs $18.50, we can multiply the cost by the tax rate. 8.25% of $18.50 is approximately $1.53. Therefore, the correct answer is 1.53.

Explanation

The sales tax rate is 8.25%, which means that for every dollar spent, 8.25 cents will be added as tax. To estimate the sales tax on the book that costs $18.50, we can multiply the cost by the tax rate. 8.25% of $18.50 is approximately $1.53. Therefore, the correct answer is 1.53.

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7. After 8 mounts, the simple interest earned annually on an investment of $4500 is $165. What is the interest rate?

The interest rate can be calculated by dividing the annual interest earned ($165) by the principal amount ($4500) and multiplying by 100 to convert it to a percentage. Therefore, the interest rate is 3.67%. However, the given answer options are 5.5 and 5.5%, both of which are incorrect.

Explanation

The interest rate can be calculated by dividing the annual interest earned ($165) by the principal amount ($4500) and multiplying by 100 to convert it to a percentage. Therefore, the interest rate is 3.67%. However, the given answer options are 5.5 and 5.5%, both of which are incorrect.

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8. Estimate the tax on a digital camera taht costs $399 with a 6.25% sales tax. (leave the number as the answer).

The correct answer is 24.94. To calculate the tax on the digital camera, we multiply the cost of the camera ($399) by the sales tax rate (6.25%). This gives us $24.9375, which rounds up to $24.94. Therefore, the correct answer is 24.94.

Explanation

The correct answer is 24.94. To calculate the tax on the digital camera, we multiply the cost of the camera ($399) by the sales tax rate (6.25%). This gives us $24.9375, which rounds up to $24.94. Therefore, the correct answer is 24.94.

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9. A pharmacy discount card gives the user 40% off prescriptions. Mr. Allen's cholesterol medicadion normally costs $96.50. What is the final price with the discount card?

The final price with the discount card can be calculated by subtracting 40% of the original price from the original price. 40% of $96.50 is $38.60. Subtracting $38.60 from $96.50 gives us $57.90.

Explanation

The final price with the discount card can be calculated by subtracting 40% of the original price from the original price. 40% of $96.50 is $38.60. Subtracting $38.60 from $96.50 gives us $57.90.

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10. Ron has a model car. The scale of the model to the actual car is 1:10. The length of the model car is 15 inches. How long os the actual car? (leave the number as the answer).

The scale of the model car to the actual car is 1:10. This means that every inch on the model car represents 10 inches on the actual car. The length of the model car is 15 inches, so the length of the actual car would be 15 multiplied by 10, which equals 150 inches. Therefore, the length of the actual car is 150 inches.

Explanation

The scale of the model car to the actual car is 1:10. This means that every inch on the model car represents 10 inches on the actual car. The length of the model car is 15 inches, so the length of the actual car would be 15 multiplied by 10, which equals 150 inches. Therefore, the length of the actual car is 150 inches.

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11. Solve the proportion

-2

8

-4

4

To solve the proportion, we need to cross-multiply. Multiply the first term of the first ratio (-2) with the second term of the second ratio (4), and multiply the second term of the first ratio (8) with the first term of the second ratio (-4). This gives us (-2 * 4) = (-4 * 8). Simplifying this equation gives us -8 = -32. Therefore, the answer is -4.

Explanation

To solve the proportion, we need to cross-multiply. Multiply the first term of the first ratio (-2) with the second term of the second ratio (4), and multiply the second term of the first ratio (8) with the first term of the second ratio (-4). This gives us (-2 * 4) = (-4 * 8). Simplifying this equation gives us -8 = -32. Therefore, the answer is -4.

12. Solve the proportion

1

2

3

4

not-available-via-ai

Explanation

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13. Find the value 50% of 98

59

69

49

39

To find 50% of 98, we divide 98 by 2. This gives us 49, which is the correct answer.

Explanation

To find 50% of 98, we divide 98 by 2. This gives us 49, which is the correct answer.

14. Find the value 130% of 50

55

58

65

68

To find 130% of 50, we can multiply 50 by 1.3. This gives us 65. Therefore, the correct answer is 65.

Explanation

To find 130% of 50, we can multiply 50 by 1.3. This gives us 65. Therefore, the correct answer is 65.

15. Find the value 18 is 40% of what number?

35

95

25

45

If 18 is 40% of a number, we can set up the equation 0.4x = 18, where x represents the unknown number. To solve for x, we divide both sides of the equation by 0.4. This gives us x = 18/0.4 = 45. Therefore, the number that 18 is 40% of is 45.

Explanation

If 18 is 40% of a number, we can set up the equation 0.4x = 18, where x represents the unknown number. To solve for x, we divide both sides of the equation by 0.4. This gives us x = 18/0.4 = 45. Therefore, the number that 18 is 40% of is 45.

16. A gas station purchases fuel at a wholesale price of $1.75 per gallon. The price is marked up 8%. What is the selling proce per gallon?

$1.80

$1.90

$1.89

$2.00

The gas station purchases fuel at a wholesale price of $1.75 per gallon. To calculate the selling price, we need to add the markup percentage. The markup percentage is 8% of $1.75, which is $0.14. Adding this markup to the wholesale price gives us a selling price of $1.89 per gallon.

Explanation

The gas station purchases fuel at a wholesale price of $1.75 per gallon. To calculate the selling price, we need to add the markup percentage. The markup percentage is 8% of $1.75, which is $0.14. Adding this markup to the wholesale price gives us a selling price of $1.89 per gallon.