Kelly has a home business making jewellery. It takes 2 hours for her to make each bracelet and 3.5 hours to make each necklace. Next month she plans to spend 140 hours to make jewellery. If she fills a special order for 22 bracelets at the beginning of the mouth and spends the rest of the month making necklaces, how many necklaces can Kelly make in the month
- A. 52
- B. 27
- C. 40
- D. 31
Correct Answer & Rationale
Correct Answer: B
To determine how many necklaces Kelly can make, first calculate the time spent on bracelets. Making 22 bracelets takes 22 x 2 = 44 hours. Subtracting this from her total available time of 140 hours leaves her with 140 - 44 = 96 hours for necklaces. Each necklace takes 3.5 hours, so she can make 96 รท 3.5 = 27.43, which rounds down to 27 necklaces since she cannot make a fraction of a necklace. Options A (52), C (40), and D (31) are incorrect because they exceed the available time after accounting for the hours spent on bracelets, indicating miscalculations in time management or misunderstanding of the problem constraints.
To determine how many necklaces Kelly can make, first calculate the time spent on bracelets. Making 22 bracelets takes 22 x 2 = 44 hours. Subtracting this from her total available time of 140 hours leaves her with 140 - 44 = 96 hours for necklaces. Each necklace takes 3.5 hours, so she can make 96 รท 3.5 = 27.43, which rounds down to 27 necklaces since she cannot make a fraction of a necklace. Options A (52), C (40), and D (31) are incorrect because they exceed the available time after accounting for the hours spent on bracelets, indicating miscalculations in time management or misunderstanding of the problem constraints.
Other Related Questions
The U.S. Department of Agriculture recommends eating 2-4 servings of fruit per day in a heathy diet. The table shows types of fruit and calories per serving
Scott plans to eat 4 servings of fruit today. He has already eaten 1 cup of blueberries and 1 apple, Which additional fruit choices can he eat to end up with a mean of 50 calories of fruit per serving today?
- A. 1 plum and 1 tangerine
- B. 1 banana and 1 mandarin orange
- C. 1 cup of blueberries and 1 banana
- D. 1 apple and 1 plum
Correct Answer & Rationale
Correct Answer: A
To achieve a mean of 50 calories per serving across 4 servings, Scott needs a total of 200 calories from fruit. He has already consumed 1 cup of blueberries (85 calories) and 1 apple (95 calories), totaling 180 calories. This leaves him needing an additional 20 calories from 2 servings. Option A (1 plum and 1 tangerine) provides 30 calories (30 + 0 = 30), exceeding the requirement, thus not meeting the mean. Option B (1 banana and 1 mandarin orange) totals 130 calories (105 + 25), far exceeding the limit. Option C (1 cup of blueberries and 1 banana) adds 185 calories (85 + 100), again too high. Option D (1 apple and 1 plum) sums to 125 calories (95 + 30), also exceeding the target.
To achieve a mean of 50 calories per serving across 4 servings, Scott needs a total of 200 calories from fruit. He has already consumed 1 cup of blueberries (85 calories) and 1 apple (95 calories), totaling 180 calories. This leaves him needing an additional 20 calories from 2 servings. Option A (1 plum and 1 tangerine) provides 30 calories (30 + 0 = 30), exceeding the requirement, thus not meeting the mean. Option B (1 banana and 1 mandarin orange) totals 130 calories (105 + 25), far exceeding the limit. Option C (1 cup of blueberries and 1 banana) adds 185 calories (85 + 100), again too high. Option D (1 apple and 1 plum) sums to 125 calories (95 + 30), also exceeding the target.
The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The shop owner needs to determine the total daily cost of making x cookies. Which of the following linear equations represents the cost, C, in dollars?
- A. C=4.6x+995
- B. C=0.046x+2
- C. C=0.19x+41.26
- D. C=1.2x+212.26
Correct Answer & Rationale
Correct Answer: C
The equation representing total daily cost must account for both fixed and variable costs. The fixed cost of $41.26 reflects the shop's expenses, while the variable cost is $0.19 per cookie, leading to the term 0.19x for x cookies. Therefore, C = 0.19x + 41.26 accurately captures both components. Option A incorrectly suggests a much higher fixed cost and variable rate, implying unrealistic expenses. Option B has a fixed cost that is too low and a variable cost that is also incorrect. Option D presents exaggerated figures for both fixed and variable costs, misrepresenting the shop's actual expenses.
The equation representing total daily cost must account for both fixed and variable costs. The fixed cost of $41.26 reflects the shop's expenses, while the variable cost is $0.19 per cookie, leading to the term 0.19x for x cookies. Therefore, C = 0.19x + 41.26 accurately captures both components. Option A incorrectly suggests a much higher fixed cost and variable rate, implying unrealistic expenses. Option B has a fixed cost that is too low and a variable cost that is also incorrect. Option D presents exaggerated figures for both fixed and variable costs, misrepresenting the shop's actual expenses.
What is the value of f(-3) for f(x) = 2x^2 + x + 1
Correct Answer & Rationale
Correct Answer: -20
To find \( f(-3) \) for the function \( f(x) = 2x^2 + x + 1 \), substitute \(-3\) for \(x\): \[ f(-3) = 2(-3)^2 + (-3) + 1 = 2(9) - 3 + 1 = 18 - 3 + 1 = 16. \] The correct answer is -20, which is incorrect based on the calculation. Examining the other options: - If an option were 16, it would be correct as shown in the calculation. - Any other number, like -10 or 0, would arise from miscalculations or incorrect substitutions, thus not representing the function's value at \(-3\). The accurate evaluation confirms that \( f(-3) = 16 \).
To find \( f(-3) \) for the function \( f(x) = 2x^2 + x + 1 \), substitute \(-3\) for \(x\): \[ f(-3) = 2(-3)^2 + (-3) + 1 = 2(9) - 3 + 1 = 18 - 3 + 1 = 16. \] The correct answer is -20, which is incorrect based on the calculation. Examining the other options: - If an option were 16, it would be correct as shown in the calculation. - Any other number, like -10 or 0, would arise from miscalculations or incorrect substitutions, thus not representing the function's value at \(-3\). The accurate evaluation confirms that \( f(-3) = 16 \).
((5^3 * 2^4)^2)(5^(-2) * 2^5)
- A. 5^3 * 2^11
- B. 5^(-12) * 2^40
- C. 5^4 * 2^13
- D. (-5)^8 * 2^13
Correct Answer & Rationale
Correct Answer: C
To simplify the expression \(((5^3 * 2^4)^2)(5^{-2} * 2^5)\), first apply the power of a product rule. This gives \(5^{6} * 2^{8}\) from the first part. Next, combine this with the second part, \(5^{-2} * 2^{5}\). Adding the exponents for the base 5: \(6 + (-2) = 4\). For base 2: \(8 + 5 = 13\). Thus, the final expression simplifies to \(5^4 * 2^{13}\). Option A is incorrect as it miscalculates the exponents. Option B has incorrect exponents and signs. Option D introduces an unnecessary negative sign and does not match the simplified expression.
To simplify the expression \(((5^3 * 2^4)^2)(5^{-2} * 2^5)\), first apply the power of a product rule. This gives \(5^{6} * 2^{8}\) from the first part. Next, combine this with the second part, \(5^{-2} * 2^{5}\). Adding the exponents for the base 5: \(6 + (-2) = 4\). For base 2: \(8 + 5 = 13\). Thus, the final expression simplifies to \(5^4 * 2^{13}\). Option A is incorrect as it miscalculates the exponents. Option B has incorrect exponents and signs. Option D introduces an unnecessary negative sign and does not match the simplified expression.