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In the ratio 0.6 : X :: 7 : 42, what is X?
- A. 3
- B. 3.6
- C. 4
- D. 4.2
Correct Answer: B
Rationale: To find the value of X in the given ratio, set up the proportion: (0.6/X) = (7/42). Simplifying this, we get (0.6/X) = (1/6). Cross multiplying gives 0.6 * 6 = X, which results in X = 3.6. Therefore, the correct answer is 3.6, representing the value of X in the given ratio.
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Solve for y if y = 3: 4y + 21/y
- A. 7.7
- B. 23/3
- C. 19
- D. 11
Correct Answer: C
Rationale: To find the value of the expression when y = 3, substitute y = 3 into the expression: 4(3) + 21/3. This simplifies to 12 + 7 = 19. Therefore, the correct answer is C, which is 19.
How many kilograms are in 2000 grams?
- A. 20 kilograms
- B. 2 kilograms
- C. 0.002 kilograms
- D. 0.2 kilograms
Correct Answer: B
Rationale: To convert grams to kilograms, you need to divide by 1000 since there are 1000 grams in a kilogram. Therefore, 2000 grams divided by 1000 equals 2 kilograms. The correct answer is 2 kilograms. Remember, when converting units, it is important to keep track of the conversion factor to ensure the correct transformation of measurements. In this case, multiplying or dividing by 1000 is a common conversion for grams to kilograms, moving the decimal point three places to the left or right.
An artist sells paintings at $5.50 each. She has 7 stands in town and pays $35 per stand. What was her profit if she sold an average of 11 paintings per stand?
- A. $245
- B. $178.50
- C. $175
- D. $423.50
Correct Answer: B
Rationale: To calculate the profit per stand, we first find the total revenue per stand by multiplying the number of paintings sold (11) by the price per painting ($5.50), which equals $60.50. Then, we subtract the stand cost ($35) from the total revenue to find the profit per stand: $60.50 - $35 = $25.50. Since the artist has 7 stands, the total profit is $25.50 * 7 = $178.50. Therefore, the correct answer is $178.50. The profit per stand is determined by subtracting the stand cost from the total revenue generated from selling paintings. Multiplying this profit per stand by the number of stands gives the total profit. In this scenario, the artist's profit from selling an average of 11 paintings per stand would amount to $178.50.
Ratio and Proportion: 200:2::20:X (Enter numeric value only.)
- A. 2
- B. 0.2
- C. 4
- D. 10
Correct Answer: B
Rationale: Correct Answer: B (0.2)
Rationale:
To solve this proportion problem, we can set up the equation:
200/2 = 20/X
Simplify the left side:
100 = 20/X
Cross multiply to solve for X:
100X = 20
Divide by 100 to isolate X:
X = 20/100
X = 0.2
Summary:
- Choice A (2) is incorrect as it does not match the calculated value of X.
- Choice C (4) is incorrect as it is not the correct answer derived from the proportion.
- Choice D (10) is incorrect as it does not align with the calculated value of X.
Divide: 4 2/3 · 2 3/4 =
- A. 1 23/33
- B. 2 8/9
- C. 3 21/3
- D. 4 23/4
Correct Answer: A
Rationale: To divide mixed numbers, convert them to improper fractions. For 4 2/3, the improper fraction is 14/3, and for 2 3/4, it is 11/4. When dividing 14/3 by 11/4, you get 154/33, which simplifies to 4 22/33 or 1 22/33. Therefore, the correct answer is 1 23/33, which is represented in mixed number form as 1 23/33.