What is the length of the unknown leg of a right triangle that has one leg measuring 9 feet and a hypotenuse of 19 feet? (Round to the nearest tenth.)

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ATI TEAS 7

ATI TEAS 7 Test Bank

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Question 1 of 5

What is the length of the unknown leg of a right triangle that has one leg measuring 9 feet and a hypotenuse of 19 feet? (Round to the nearest tenth.)

Correct Answer: A

Rationale: To find the length of the unknown leg (a) of a right triangle, use the Pythagorean theorem: a² + 9² = 19². Substitute the known values, solve for a: a² + 81 = 361. Subtract 81 from both sides to get a² = 280. Taking the square root of 280 gives a ≈ 16.7 feet. Therefore, the correct answer is 16.7 feet. Choice B (16.0 feet) is incorrect as it does not accurately round to the nearest tenth. Choice C (17.4 feet) and choice D (8.4 feet) are incorrect as they do not match the calculated value using the Pythagorean theorem.

Question 2 of 5

How many feet are in 9 yards?

Correct Answer: D

Rationale: To convert yards to feet, you need to know that 1 yard is equal to 3 feet. Therefore, to find out how many feet are in 9 yards, you multiply 9 by 3, which equals 27 feet. Choice A (45 ft) is incorrect as it miscalculates by multiplying 9 by 5 instead of 3. Choice B (18 ft) incorrectly multiplies 9 by 2. Choice C (36 ft) is incorrect as it doubles the answer of 18 feet, which is also an incorrect calculation.

Question 3 of 5

A large pizza has a diameter of 9 inches. Which of the following is the area of the pizza in terms of pi?

Correct Answer: D

Rationale: To find the area of a circle, we use the formula A = πr², where r is the radius of the circle. In this case, the diameter is 9 inches, so the radius is half of the diameter, which is 4.5 inches. Substituting the radius into the formula, we get A = π(4.5)² = 20.25 πin². Therefore, the correct answer is 20.25 πin². Choices A, B, and C are incorrect because they do not correctly calculate the area using the radius of the circle.

Question 4 of 5

A sweater that normally sells for $78 is marked 15% off. Which of the following estimates the sale price of the sweater?

Correct Answer: B

Rationale: To find the sale price after a 15% discount, you calculate 15% of $78, which is $11.70. Subtracting $11.70 from the original price gives $66.30. Since the price is typically rounded, the estimated sale price is $66. Choice A, $12, is too low and does not reflect a 15% discount off $78. Choice C, $22, and choice D, $69, are also incorrect as they do not accurately estimate the sale price after a 15% discount.

Question 5 of 5

If a box of 55 syringes costs $660.00, what is the cost of four syringes?

Correct Answer: D

Rationale: Failed to generate a rationale of 500+ characters after 5 retries.

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