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A sign stating 'Do Not Enter' is in the shape of a square with side lengths of 75 centimeters. What is the area in square centimeters?
- A. 150
- B. 300
- C. 5,325
- D. 5,625
Correct Answer: D
Rationale: The formula for the area of a square is given by the square of its side length: Area = side side. For this problem, the side length of the square is 75 centimeters. To find the area, you multiply 75 by itself: 75 75 = 5,625 square centimeters. Thus, the area of the square is 5,625 cm². This shows that option D is correct. Choices A, B, and C are incorrect as they do not correspond to the correct calculation of the area of a square with a side length of 75 centimeters.
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Which statement about multiplication and division is true?
- A. The product of the quotient and the dividend is the divisor.
- B. The product of the dividend and the divisor is the quotient.
- C. The product of the quotient and the divisor is the dividend.
- D. None of the above.
Correct Answer: C
Rationale: In division, the dividend is the number being divided, the divisor is the number you are dividing by, and the quotient is the result. Multiplying the quotient by the divisor gives the original dividend. This is the reverse of the division operation. Therefore, the correct statement is that the product of the quotient and the divisor equals the dividend, making option C correct. Choices A and B provide incorrect relationships between the terms dividend, divisor, quotient, and product, making them inaccurate. Option D is a general statement that does not provide the correct relationship between multiplication and division terms.
Jayden rides his bike for 5/8 miles. He takes a break and rides another 3/4 miles. How many miles does he ride?
- A. 1 3/8 miles
- B. 1 1/2 miles
- C. 1 7/8 miles
- D. 2 miles
Correct Answer: A
Rationale: To find the total distance Jayden rides, you need to add the fractions 5/8 + 3/4. To add these fractions, you must ensure they have a common denominator. In this case, the common denominator is 8. So, 5/8 + 3/4 = 5/8 + 6/8 = 11/8. Since 11/8 can be simplified to 1 3/8, Jayden rides a total of 1 3/8 miles. Choice B (1 1/2 miles), Choice C (1 7/8 miles), and Choice D (2 miles) are incorrect as they do not accurately represent the total distance calculated by adding the two fractions, which is 1 3/8 miles.
Evaluate the expression -3 x 5.
- A. -15
- B. -2
- C. 2
- D. 15
Correct Answer: A
Rationale: The correct answer is A, which is -15. When you multiply -3 by 5, you get -15. The negative sign in front of the 3 indicates a negative value, and when multiplied by a positive number like 5, the result remains negative. Choices B, C, and D are incorrect because they do not reflect the correct multiplication of -3 and 5.
How much hydrochloric acid (HCl) is necessary to make 2.5 liters of a 5:1 solution of water (in liters) to HCl (in grams)?
- A. 0.5 grams
- B. 2 grams
- C. 5 grams
- D. 12.5 grams
Correct Answer: C
Rationale: To create a 5:1 solution in 2.5 liters, 0.5 liters are needed for HCl, which translates to 5 grams. The correct answer is 5 grams, as this amount corresponds to the 5:1 ratio specified in the solution. Choices A, B, and D are incorrect because they do not align with the 5:1 ratio and the volume of the solution.
Solve the inequality for the unknown.
- A. x > 5
- B. x < 5
- C. x >= 5
- D. x <= 5
Correct Answer: A
Rationale: When solving an inequality, the direction of the inequality sign changes depending on the operation performed. In this case, if the given inequality simplifies to x > 5, it means that the unknown value x must be greater than 5 for the inequality to hold true. Therefore, x > 5 is the correct solution. Option A is correct. Choices B, C, and D are incorrect because they do not correctly represent the relationship between x and 5 based on the given inequality.