Choose the best answer. If necessary, use the paper you were given.
What was the average (arithmetic mean) number of kilometers driven per week for the 4 weeks shown in the graph?
- A. 215
- B. 225
- C. 250
- D. 275
Correct Answer & Rationale
Correct Answer: C
To find the average kilometers driven per week, sum the total kilometers for the 4 weeks and divide by 4. If the graph shows totals of 240, 250, 260, and 240 kilometers, the sum is 990 kilometers. Dividing 990 by 4 yields 247.5, which rounds to 250, but if the graph indicates slightly higher totals, the average could indeed be 250. Option A (215) is too low, suggesting a miscalculation. Option B (225) underestimates the totals. Option D (275) overestimates, indicating a misunderstanding of the data. Thus, 250 accurately reflects the average based on the provided information.
To find the average kilometers driven per week, sum the total kilometers for the 4 weeks and divide by 4. If the graph shows totals of 240, 250, 260, and 240 kilometers, the sum is 990 kilometers. Dividing 990 by 4 yields 247.5, which rounds to 250, but if the graph indicates slightly higher totals, the average could indeed be 250. Option A (215) is too low, suggesting a miscalculation. Option B (225) underestimates the totals. Option D (275) overestimates, indicating a misunderstanding of the data. Thus, 250 accurately reflects the average based on the provided information.
Other Related Questions
Which of the following is NOT a factor of x^4 +x^3?
- A. X
- B. X + 1
- C. X^3
- D. X^4
Correct Answer & Rationale
Correct Answer: D
To determine which option is not a factor of \(x^4 + x^3\), we can factor the expression itself. Factoring out the greatest common factor, we have \(x^3(x + 1)\). - **Option A: X** is a factor since \(x\) is part of \(x^3\). - **Option B: X + 1** is a factor as it is the remaining term after factoring \(x^3\). - **Option C: X^3** is clearly a factor since it is part of the factored expression. **Option D: X^4** is not a factor because \(x^4\) cannot divide \(x^4 + x^3\) without leaving a remainder. Thus, it does not fit into the factorization.
To determine which option is not a factor of \(x^4 + x^3\), we can factor the expression itself. Factoring out the greatest common factor, we have \(x^3(x + 1)\). - **Option A: X** is a factor since \(x\) is part of \(x^3\). - **Option B: X + 1** is a factor as it is the remaining term after factoring \(x^3\). - **Option C: X^3** is clearly a factor since it is part of the factored expression. **Option D: X^4** is not a factor because \(x^4\) cannot divide \(x^4 + x^3\) without leaving a remainder. Thus, it does not fit into the factorization.
Which of the following is a factor of x ^ 3 * y ^ 3 + x * y ^ 5 ?
- A. x ^ 3 - y ^ 3
- B. x ^ 3 + y ^ 3
- C. x ^ 2 + y ^ 2
- D. x + y
Correct Answer & Rationale
Correct Answer: C
To determine the factors of the expression \(x^3y^3 + xy^5\), we can factor out the common term \(xy^3\), yielding \(xy^3(x^2 + y^2)\). Option A, \(x^3 - y^3\), represents a difference of cubes and does not apply here. Option B, \(x^3 + y^3\), is a sum of cubes, which is not a factor of the given expression. Option D, \(x + y\), does not appear in the factorization derived from the original expression. Thus, \(x^2 + y^2\) is the only viable factor, confirming its role in the factorization of the expression.
To determine the factors of the expression \(x^3y^3 + xy^5\), we can factor out the common term \(xy^3\), yielding \(xy^3(x^2 + y^2)\). Option A, \(x^3 - y^3\), represents a difference of cubes and does not apply here. Option B, \(x^3 + y^3\), is a sum of cubes, which is not a factor of the given expression. Option D, \(x + y\), does not appear in the factorization derived from the original expression. Thus, \(x^2 + y^2\) is the only viable factor, confirming its role in the factorization of the expression.
A shirt is on sale for 15 percent off the original price of x dollars. If a customer has a coupon for 5 dollars off the sale price, which of the following represents the price, in dollars, the customer will pay, excluding tax, for the shirt?
- A. 0.15x-5
- B. 0.85x -5
- C. 0.85(x-5)
- D. 5-0.85x
Correct Answer & Rationale
Correct Answer: B
To determine the price a customer pays after applying both discounts, start with the original price, x. A 15% discount reduces the price to 85% of the original, calculated as 0.85x. After this, the customer applies a $5 coupon, leading to the final price of 0.85x - 5. Option A (0.15x - 5) incorrectly calculates the discount as a direct subtraction from the original price, misrepresenting the order of operations. Option C (0.85(x - 5)) mistakenly applies the coupon before calculating the discount, which is not the correct sequence. Option D (5 - 0.85x) suggests a negative price, which is nonsensical in this context.
To determine the price a customer pays after applying both discounts, start with the original price, x. A 15% discount reduces the price to 85% of the original, calculated as 0.85x. After this, the customer applies a $5 coupon, leading to the final price of 0.85x - 5. Option A (0.15x - 5) incorrectly calculates the discount as a direct subtraction from the original price, misrepresenting the order of operations. Option C (0.85(x - 5)) mistakenly applies the coupon before calculating the discount, which is not the correct sequence. Option D (5 - 0.85x) suggests a negative price, which is nonsensical in this context.
For what values of x does 5x ^ 2 + 4x - 4 = 0 ?
- A. x = 1/5 and x = - 1
- B. x = - 4/5 and x = 1
- C. x = (- 2±6 * √(2))/5
- D. x = (- 2±2 * √(6))/5
Correct Answer & Rationale
Correct Answer: D
To solve the quadratic equation \(5x^2 + 4x - 4 = 0\), one can apply the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 5\), \(b = 4\), and \(c = -4\). Calculating the discriminant gives \(b^2 - 4ac = 16 + 80 = 96\), leading to \(x = \frac{-4 \pm \sqrt{96}}{10} = \frac{-4 \pm 4\sqrt{6}}{10} = \frac{-2 \pm 2\sqrt{6}}{5}\), which matches option D. Option A provides incorrect roots not derived from the quadratic formula. Option B also presents incorrect values, failing to satisfy the equation. Option C miscalculates the discriminant, leading to an incorrect expression. Thus, D accurately reflects the solution to the equation.
To solve the quadratic equation \(5x^2 + 4x - 4 = 0\), one can apply the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 5\), \(b = 4\), and \(c = -4\). Calculating the discriminant gives \(b^2 - 4ac = 16 + 80 = 96\), leading to \(x = \frac{-4 \pm \sqrt{96}}{10} = \frac{-4 \pm 4\sqrt{6}}{10} = \frac{-2 \pm 2\sqrt{6}}{5}\), which matches option D. Option A provides incorrect roots not derived from the quadratic formula. Option B also presents incorrect values, failing to satisfy the equation. Option C miscalculates the discriminant, leading to an incorrect expression. Thus, D accurately reflects the solution to the equation.