Integrated Math 2 - Unit 1 Lesson 1 Quiz

1. Express the relationship between height in inches and height in centimeters in a different but equivalent form.

You may choose to do this problem on a separate sheet of paper. Try to type your answer in the box below, though. Use * for multiplication, / for divisionor a fraction. Do not use spaces in the expression. [For example: 2*x=k <--- no spaces.] Use capital letters for the variables.

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2. In the United States, we usually measure a person's height in inches. In many other countries, they use centimeters to measure a person's height. The height in inches is a function of the height in centimeters according to the rule:

Is the function between height in inches and height in centimeters an example of direct variation, inverse variation, or neither? (You will explain your reasoning in the next question... keep this in mind) *For your answer type either: inverse variation OR direct variation. Use spaces correctly, all lower case letters, and include the word variation.

The function between height in inches and height in centimeters is an example of direct variation. In direct variation, as one variable increases, the other variable also increases in the same proportion. In this case, as the height in centimeters increases, the height in inches also increases.

Explanation

The function between height in inches and height in centimeters is an example of direct variation. In direct variation, as one variable increases, the other variable also increases in the same proportion. In this case, as the height in centimeters increases, the height in inches also increases.

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3. Andrew is 150 cm tall. How many inches tall is he? Round your answer to 1 decimal place.

Type the unit, inches, behind your numerical answer. Type a space after the number and use all lower case letters. Ex: ____ inches

Andrew's height is given in centimeters, but the question asks for his height in inches. To convert centimeters to inches, we can use the conversion factor that 1 inch is equal to 2.54 centimeters. By dividing Andrew's height in centimeters by the conversion factor, we get his height in inches. Rounding the answer to 1 decimal place gives us 59.1 inches.

Explanation

Andrew's height is given in centimeters, but the question asks for his height in inches. To convert centimeters to inches, we can use the conversion factor that 1 inch is equal to 2.54 centimeters. By dividing Andrew's height in centimeters by the conversion factor, we get his height in inches. Rounding the answer to 1 decimal place gives us 59.1 inches.

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4. Victoria is 67 inches tall. Find Victoria's height in centimeters. Round your answer to 2 decimal places.

Type your answer as ____ cm space after the number and use cm to represent centimeters.

To convert inches to centimeters, we multiply the number of inches by 2.54. Therefore, to find Victoria's height in centimeters, we multiply 67 inches by 2.54. The result is 170.18 cm, rounded to 2 decimal places.

Explanation

To convert inches to centimeters, we multiply the number of inches by 2.54. Therefore, to find Victoria's height in centimeters, we multiply 67 inches by 2.54. The result is 170.18 cm, rounded to 2 decimal places.

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5. If you are receiving radiation therapy for a tumor, the intensity of the radiation, R and your distance from the source, d are related by the rule:

Distance, d, is measured in methers and R is measured in mr/hr (milliroentgens per hour). Is this relationship an example of inverse or direct variation or neither? (You will explain your reasoning in the next question... keep this in mind) *For your answer type either: inverse variation OR direct variation. Use spaces correctly, all lower case letters, and include the word variation.

The relationship between the intensity of radiation and the distance from the source is an example of inverse variation. In inverse variation, as one variable (distance) increases, the other variable (intensity) decreases, and vice versa. This can be observed in the given scenario, as the distance from the source increases, the intensity of radiation decreases. The term "inverse variation power model" suggests that the relationship follows a power function, where the intensity is inversely proportional to the distance raised to a certain power.

Explanation

The relationship between the intensity of radiation and the distance from the source is an example of inverse variation. In inverse variation, as one variable (distance) increases, the other variable (intensity) decreases, and vice versa. This can be observed in the given scenario, as the distance from the source increases, the intensity of radiation decreases. The term "inverse variation power model" suggests that the relationship follows a power function, where the intensity is inversely proportional to the distance raised to a certain power.

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6. What is the intensity of the radiation 4 meters from the source? Show your work on a separate sheet of paper.

Put your answer in simplest form and type the unit mr/hr after the number as follows: ____ mr/hr (Space in between the number and the unit, but do not space anywhere else when typing the answer.

The question asks for the intensity of radiation 4 meters from the source. However, the given answer does not provide any explanation or work to support the answer. Therefore, it is not possible to determine how the answer of 20 mr/hr was obtained or whether it is correct.

Explanation

The question asks for the intensity of radiation 4 meters from the source. However, the given answer does not provide any explanation or work to support the answer. Therefore, it is not possible to determine how the answer of 20 mr/hr was obtained or whether it is correct.

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7. At what distance will the intensity be 6 mr/hr? Show your work on a separate sheet of paper.

Round your answer to one decimal place and include the distance unit, m, spaced after the numerical answer.

The correct answer is 7.3 m. This is the distance at which the intensity will be 6 mr/hr. The question asks for the distance at which the intensity is 6 mr/hr, and the answer provided is 7.3 m. It is important to round the answer to one decimal place and include the distance unit, m, after the numerical answer.

Explanation

The correct answer is 7.3 m. This is the distance at which the intensity will be 6 mr/hr. The question asks for the distance at which the intensity is 6 mr/hr, and the answer provided is 7.3 m. It is important to round the answer to one decimal place and include the distance unit, m, after the numerical answer.

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8. What is the constant of proportionality for the relationship?

If you type your answer as a fraction use / to represent the fraction bar. DO NOT space before or after the fraction bar. If you choose to write the constant of proportionality as a decimal round to 2 decimal places and type a 0 before the decimal as follows: 0.##

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