Nokea
Solve the equation for the unknown. 3x + 2 = 20
- A. x = 2
- B. x = 4
- C. x = 6
- D. x = 8
Correct Answer: C
Rationale: Simplify the equation step by step:
Subtract 2 from both sides:
3x + 2 - 2 = 20 - 2
3x = 18
Divide both sides by 3:
x = 18 · 3
x = 6
Therefore, the correct answer is C (x = 6).
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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.
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.
What is the result of multiplying 3/5 by 5/7?
- A. 3/7
- B. 1
- C. 2
- D. 4
Correct Answer: A
Rationale: To multiply fractions, multiply the numerators together and the denominators together. Multiplying 3/5 by 5/7 gives (3*5)/(5*7) = 15/35. This fraction simplifies to 3/7 by dividing the numerator and denominator by their greatest common factor, which is 5. Therefore, the correct answer is 3/7. Choices B, C, and D are incorrect as they do not result from multiplying 3/5 by 5/7.
What is the result of multiplying (3/5) by (5/8)?
- A. 3/8
- B. 3/5
- C. 15/40
- D. 3/30
Correct Answer: A
Rationale: To multiply fractions, multiply the numerators together and the denominators together. For (3/5) * (5/8), you get (3*5) / (5*8) = 15 / 40, which simplifies to 3/8. Therefore, the correct answer is A. Choice B (3/5) is incorrect as it is one of the original fractions being multiplied. Choice C (15/40) is the result of the multiplication but not simplified to its lowest terms. Choice D (3/30) is incorrect as the numerator is not the result of multiplying 3 and 5 together.
If a tree grows an average of 4.2 inches in a day, what is the rate of change in its height per month? Assume a month is 30 days.
- A. 0.14 inches per month
- B. 4.2 inches per month
- C. 34.2 inches per month
- D. 126 inches per month
Correct Answer: D
Rationale: The tree grows at an average rate of 4.2 inches per day. To find the rate of change per month, multiply the daily growth rate by the number of days in a month (30 days):
4.2 inches/day 30 days = 126 inches per month.
Therefore, the rate of change in the tree's height is 126 inches per month, making option D the correct answer. Option A is incorrect because it miscalculates the rate based on daily growth. Option B is incorrect as it doesn't account for the total days in a month. Option C is incorrect as it overestimates the monthly growth rate.