Nokea
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.
You may also like to solve these questions
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)
What is the difference between two equal numbers?
- A. Negative
- B. Positive
- C. Zero
- D. Not enough information
Correct Answer: C
Rationale: The difference between two numbers is found by subtracting one from the other. When two numbers are equal, subtracting them results in 0, because any number minus itself is always 0. Therefore, the difference between two equal numbers is always zero, making option C the correct answer. Option A ('Negative') and option B ('Positive') are incorrect as they do not represent the result of subtracting two equal numbers, which always yields zero. Option D ('Not enough information') is also incorrect as the difference between two equal numbers is definitively known to be zero.
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.
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.
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.