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Eric buys 5 1/2 pounds of apples each week for four weeks. How many total pounds does he buy?
- A. 22 pounds
- B. 20 pounds
- C. 18 pounds
- D. 24 pounds
Correct Answer: A
Rationale: To find the total pounds of apples Eric buys, you need to multiply the pounds of apples bought each week (5 1/2 pounds) by the number of weeks (4 weeks). When you multiply 5 1/2 by 4, you get 22 pounds. Therefore, the correct answer is A. Choices B, C, and D are incorrect because they do not accurately calculate the total pounds purchased over the four weeks.
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Apply the polynomial identity to rewrite (a + b)².
- A. a² + b²
- B. 2ab
- C. a² + 2ab + b²
- D. a² - 2ab + b²
Correct Answer: C
Rationale: When you see something like (a + b)², it means you're multiplying (a + b) by itself:
(a + b)² = (a + b) (a + b)
To expand this, we use the distributive property (which says you multiply each term in the first bracket by each term in the second bracket):
Multiply the first term in the first bracket (a) by both terms in the second bracket:
a a = a²
a b = ab
Multiply the second term in the first bracket (b) by both terms in the second bracket:
b a = ab
b b = b²
Now, add up all the results from the multiplication:
a² + ab + ab + b²
Since ab + ab is the same as 2ab, we can simplify it to:
a² + 2ab + b²
So, (a + b)² = a² + 2ab + b².
This is known as a basic polynomial identity, and it shows that when you square a binomial (a two-term expression like a + b), you get three terms: the square of the first term (a²), twice the product of the two terms (2ab), and the square of the second term (b²).
Therefore, the correct answer is C (a² + 2ab + b²)
Write 290% as a fraction.
- A. 29/10
- B. 58/20
- C. 145/50
- D. 290/100
Correct Answer: D
Rationale: To convert a percentage to a fraction, you write the percentage as the numerator of the fraction over 100. Therefore, 290% is equivalent to 290/100, which simplifies to 29/10. Choices A, B, and C are incorrect because they do not represent 290% as a fraction by placing the percentage value over 100.
How many gallons are in 1,000 fluid ounces?
- A. 7.8125 gallons
- B. 15.625 gallons
- C. 31.25 gallons
- D. 62.5 gallons
Correct Answer: A
Rationale: To convert fluid ounces to gallons, you need to divide the number of fluid ounces by the number of fluid ounces in a gallon. Since there are 128 fluid ounces in a gallon, to find out how many gallons are in 1,000 fluid ounces, you divide 1,000 by 128. The correct calculation is 1,000 / 128 = 7.8125 gallons. Therefore, the correct answer is A. Choices B, C, and D are incorrect as they do not accurately represent the conversion from fluid ounces to gallons.
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.
Find the area in square centimeters of a circle with a diameter of 16 centimeters. Use 3.14 for π.
- A. 25.12
- B. 50.24
- C. 100.48
- D. 200.96
Correct Answer: D
Rationale: The formula for the area of a circle is: Area = π x (radius²). Given: Diameter = 16 cm, so Radius = Diameter / 2 = 16 / 2 = 8 cm. Now, calculate the area using π = 3.14: Area = 3.14 x (8²) = 3.14 x 64 = 200.96 cm². The correct answer is D (200.96 cm²) as it correctly calculates the area of the circle. Choices A, B, and C are incorrect as they do not represent the accurate area of the circle based on the given diameter and π value.