a mathematics test has a 42 ratio of data analysis problems to algebra problems if the test has 18 algebra problems how many data analysis problems ar
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ATI TEAS 7

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1. A mathematics test has a 4:2 ratio of data analysis problems to algebra problems. If the test has 18 algebra problems, how many data analysis problems are on the test?

Correct answer: C

Rationale: The ratio of 4:2 simplifies to 2:1. This means that for every 2 algebra problems, there is 1 data analysis problem. If there are 18 algebra problems, we can set up a proportion: 2 algebra problems correspond to 1 data analysis problem. Therefore, 18 algebra problems correspond to x data analysis problems. Solving the proportion, x = 18 * 1 / 2 = 9. Hence, there are 9 data analysis problems on the test. Therefore, the total number of data analysis problems on the test is 18 (algebra problems) + 9 (data analysis problems) = 27.

2. A driver drove 305 miles at 65 mph, stopped for 15 minutes, then drove another 162 miles at 80 mph. How long was the trip?

Correct answer: B

Rationale: To find the total trip duration, calculate the driving time for each segment and add the stop time. The driving time for the first segment is 305 miles รท 65 mph = 4.69 hours. The driving time for the second segment is 162 miles รท 80 mph = 2.025 hours. Adding the 15-minute stop (0.25 hours) gives a total time of 4.69 hours + 2.025 hours + 0.25 hours = 6.965 hours, which is closest to 6.69 hours (Choice B). Option A is incorrect as it miscalculates the total duration. Option C is incorrect as it overestimates the total duration. Option D is incorrect as it underestimates the total duration.

3. What is the median of Pernell's scores (81, 92, 87, 89, and 94)?

Correct answer: B

Rationale: To find the median, we first need to arrange the scores in ascending order: 81, 87, 89, 92, 94. Since there are five scores, the middle score would be the third one, which is 89. Hence, the median of Pernell's scores is 89. Choice A (87) is incorrect because it is the second score in the ordered list, not the middle one. Choice C (92) and Choice D (94) are also incorrect as they are not positioned in the middle of the ordered series.

4. The cost of renting a car is $50 per day plus $0.25 per mile driven. If a customer rents the car for 3 days and drives 120 miles, what is the total cost?

Correct answer: A

Rationale: To calculate the total cost, first, multiply the number of days by the cost per day: 3 days x $50/day = $150. Then, multiply the number of miles driven by the cost per mile: 120 miles x $0.25 = $30. Finally, add the two amounts together: $150 (daily cost) + $30 (mileage cost) = $180. Therefore, the correct total cost is $180, which corresponds to choice A. The other choices are incorrect because they do not reflect the accurate calculation of $150 for the daily cost and $30 for the mileage cost.

5. Simplify (x^2 - y^2) / (x - y)

Correct answer: A

Rationale: The expression ๐‘ฅ^2 - ๐‘ฆ^2 is a difference of squares, which follows the identity: ๐‘ฅ^2 - ๐‘ฆ^2 = (๐‘ฅ + ๐‘ฆ)(๐‘ฅ - ๐‘ฆ). Therefore, the given expression becomes: (๐‘ฅ^2 - ๐‘ฆ^2) / (๐‘ฅ - ๐‘ฆ) = (๐‘ฅ + ๐‘ฆ)(๐‘ฅ - ๐‘ฆ) / (๐‘ฅ - ๐‘ฆ). Since (๐‘ฅ - ๐‘ฆ) appears in both the numerator and the denominator, they cancel each other out, leaving ๐‘ฅ + ๐‘ฆ. Thus, the simplified form of (๐‘ฅ^2 - ๐‘ฆ^2) / (๐‘ฅ - ๐‘ฆ) is ๐‘ฅ + ๐‘ฆ. Therefore, the correct answer is A (x + y). Option B (x - y) is incorrect as it does not result from simplifying the given expression. Option C (1) is incorrect as it does not account for the variables x and y present in the expression. Option D ((x + y)/(x - y)) is incorrect as it presents the simplified form in a different format than the correct answer.

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