What is the value of the expression 2j - 7jkm when j = 5, k = -14, and m = -3?
Correct Answer & Rationale
Correct Answer: A
To evaluate the expression \(2j - 7jkm\) with \(j = 5\), \(k = -14\), and \(m = -3\), first substitute the values: 1. Calculate \(2j\): \(2 \times 5 = 10\). 2. Calculate \(7jkm\): \(7 \times 5 \times -14 \times -3 = 1470\). 3. Combine the results: \(10 - 1470 = -1460\). Thus, the value of the expression is \(-1460\). Other options are incorrect because they either miscalculate the substitutions or the arithmetic operations involved, leading to different results that do not match the evaluated expression.
To evaluate the expression \(2j - 7jkm\) with \(j = 5\), \(k = -14\), and \(m = -3\), first substitute the values: 1. Calculate \(2j\): \(2 \times 5 = 10\). 2. Calculate \(7jkm\): \(7 \times 5 \times -14 \times -3 = 1470\). 3. Combine the results: \(10 - 1470 = -1460\). Thus, the value of the expression is \(-1460\). Other options are incorrect because they either miscalculate the substitutions or the arithmetic operations involved, leading to different results that do not match the evaluated expression.
Other Related Questions
The equation and the graph represent two linear functions.
Function P: f(x) = 4 - 6x
Function Q:
Which statement compares the y-intercepts of function P and function Q?
- A. The y-intercept of function P is -6 which is less than the y-intercept of function Q.
- B. The y-intercept of function P is 4 which is equal to the y-intercept of function Q.
- C. The y-intercept of function P is -6 which is greater than the y-intercept of function Q.
- D. The y-intercept of function P is 4 which is greater than the y-intercept of function Q.
Correct Answer & Rationale
Correct Answer: D
Function P, represented by the equation \( f(x) = 4 - 6x \), has a y-intercept of 4, which is found by evaluating \( f(0) \). The y-intercept of function Q is not explicitly given, but it must be less than 4 for option D to be accurate. Option A incorrectly states that the y-intercept of P is -6. Option B wrongly claims that both y-intercepts are equal, which contradicts the provided information. Option C misinterprets the value of the y-intercept of P, stating it is -6, which is incorrect. Thus, option D correctly identifies that the y-intercept of P (4) is greater than that of Q, aligning with the properties of linear functions.
Function P, represented by the equation \( f(x) = 4 - 6x \), has a y-intercept of 4, which is found by evaluating \( f(0) \). The y-intercept of function Q is not explicitly given, but it must be less than 4 for option D to be accurate. Option A incorrectly states that the y-intercept of P is -6. Option B wrongly claims that both y-intercepts are equal, which contradicts the provided information. Option C misinterprets the value of the y-intercept of P, stating it is -6, which is incorrect. Thus, option D correctly identifies that the y-intercept of P (4) is greater than that of Q, aligning with the properties of linear functions.
An expression for a company's cost to make n bicycles is -0.017n? - 6.8n + 690. An expression for the revenue from selling these n bicycles is 70n. Profit is revenue minus cost. Which is an expression for the profit for making and selling n bicycles?
- A. -0.017n^2 - 76.8n + 690
- B. 0.017n^2 + 76.8n - 690
- C. 0.017n^2 + 63.2n + 690
- D. -0.017n^2 + 63.2n + 690
Correct Answer & Rationale
Correct Answer: D
To find the profit from selling n bicycles, subtract the cost expression from the revenue expression. The cost is given as -0.017n² - 6.8n + 690, and the revenue is 70n. Calculating profit: Profit = Revenue - Cost = 70n - (-0.017n² - 6.8n + 690) simplifies to 70n + 0.017n² + 6.8n - 690, which results in 0.017n² + 63.2n - 690. Option D, -0.017n² + 63.2n + 690, incorrectly presents the quadratic term with the wrong sign. Options A and B incorrectly combine terms or misrepresent the coefficients. Option C miscalculates the constant term. Thus, only option D maintains the correct profit structure.
To find the profit from selling n bicycles, subtract the cost expression from the revenue expression. The cost is given as -0.017n² - 6.8n + 690, and the revenue is 70n. Calculating profit: Profit = Revenue - Cost = 70n - (-0.017n² - 6.8n + 690) simplifies to 70n + 0.017n² + 6.8n - 690, which results in 0.017n² + 63.2n - 690. Option D, -0.017n² + 63.2n + 690, incorrectly presents the quadratic term with the wrong sign. Options A and B incorrectly combine terms or misrepresent the coefficients. Option C miscalculates the constant term. Thus, only option D maintains the correct profit structure.
The world's highest suspension bridge spans the Arkansas River at a height of 1,053 feet above the water. If a ball is dropped from the bridge. The height of the ball, In feet, after t seconds can be modeled by the equation f(t)= -16(t)^2 + 1053. How many feet above the water is the ball 7 seconds after being dropped?
Correct Answer & Rationale
Correct Answer: A
To determine the height of the ball 7 seconds after being dropped, substitute \( t = 7 \) into the equation \( f(t) = -16(t)^2 + 1053 \). Calculating this gives \( f(7) = -16(7)^2 + 1053 = -16(49) + 1053 = -784 + 1053 = 269 \) feet. Option A provides this correct height of 269 feet. Other options are incorrect because they result from miscalculations or incorrect substitutions into the equation. For example, using an incorrect value for \( t \) or failing to properly apply the formula leads to heights that do not reflect the physics of the scenario.
To determine the height of the ball 7 seconds after being dropped, substitute \( t = 7 \) into the equation \( f(t) = -16(t)^2 + 1053 \). Calculating this gives \( f(7) = -16(7)^2 + 1053 = -16(49) + 1053 = -784 + 1053 = 269 \) feet. Option A provides this correct height of 269 feet. Other options are incorrect because they result from miscalculations or incorrect substitutions into the equation. For example, using an incorrect value for \( t \) or failing to properly apply the formula leads to heights that do not reflect the physics of the scenario.
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 owner has decided to take out a loan to purchase updated equipment. A bank has agreed to loan the owner $2,000 for the purchase of the equipment at a simple interest rate of 4.69% payable annually.
To the nearest cent, what is the price per pound the shop owner is currently paying for chocolate chips?
- A. $0.10
- B. $4.38
- C. $0.23
- D. $4.28
Correct Answer & Rationale
Correct Answer: D
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.