Nokea
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.
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Which proportion yields a different number for the unknown compared to the others?
- A. 2/3 = x/6
- B. 4/5 = x/10
- C. 3/4 = x/8
- D. 5/6 = x/12
Correct Answer: D
Rationale: To find the value of x in each proportion, cross multiply. For proportion A, x = 4; for B, x = 8; for C, x = 6; and for D, x = 10. Hence, proportion D yields a different value for x compared to the others. Choices A, B, and C all result in unique values for x, but these values are distinct from the value obtained in proportion D.
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)
Half of a circular garden with a radius of 11.5 feet needs weeding. Find the area in square feet that needs weeding. Round to the nearest hundredth. Use 3.14 for π.
- A. 2.4
- B. 207.64
- C. 15.1
- D. 30.1
Correct Answer: B
Rationale: The formula for the area of a full circle is calculated as Area = π (radius²). When finding the area of half a circle, we multiply by 0.5. Thus, the formula becomes Area = 0.5 π (radius²). Given that the radius of the circular garden is 11.5 feet, the calculation using π = 3.14 is as follows: Area = 0.5 3.14 (11.5²) = 0.5 3.14 132.25 = 0.5 415.27 = 207.64 square feet. Therefore, the correct answer is B. Choices A, C, and D are incorrect because they do not reflect the correct calculation for finding the area of half a circular garden with a radius of 11.5 feet.
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.
What is the median of the data set: 3, 5, 7, 9, 11?
- A. 3
- B. 7
- C. 9
- D. 5
Correct Answer: B
Rationale: To find the median of a set of numbers, you arrange them in ascending order and then find the middle value. Given the data set 3, 5, 7, 9, 11, when arranged in ascending order, becomes 3, 5, 7, 9, 11. The middle value in this set is 7, making it the median. Choice A (3) is the smallest value, not the middle value. Choice C (9) and Choice D (5) are not the middle values of the set either. Therefore, the correct answer is B (7).