What is the range of her scores?
- A. 100
- B. 120
- C. 440
- D. 2,250
Correct Answer & Rationale
Correct Answer: B
To determine the range of her scores, we subtract the lowest score from the highest score. If the highest score is 220 and the lowest is 100, the calculation is 220 - 100 = 120, which represents the range. Option A (100) misrepresents the range as it does not account for the difference between the highest and lowest scores. Option C (440) and Option D (2,250) are excessively high and do not reflect the actual spread of scores based on the provided data. Thus, 120 accurately represents the range of her scores.
To determine the range of her scores, we subtract the lowest score from the highest score. If the highest score is 220 and the lowest is 100, the calculation is 220 - 100 = 120, which represents the range. Option A (100) misrepresents the range as it does not account for the difference between the highest and lowest scores. Option C (440) and Option D (2,250) are excessively high and do not reflect the actual spread of scores based on the provided data. Thus, 120 accurately represents the range of her scores.
Other Related Questions
The price P, in dollars, that a store sets for an item is given by the equation P = C + 1/10 * C where C dollars is the store's cost for the item. If the store sets a price of $55.00 for an item, what is the store's cost for the item?
- A. $50.00
- B. $54.90
- C. $55.10
- D. $60.50
Correct Answer & Rationale
Correct Answer: A
To find the store's cost \( C \), we start with the equation \( P = C + \frac{1}{10}C \). This can be simplified to \( P = 1.1C \). Given that \( P = 55 \), we can set up the equation \( 55 = 1.1C \). Solving for \( C \) gives \( C = \frac{55}{1.1} = 50 \). Option A ($50.00) is correct, as it satisfies the equation. Option B ($54.90) incorrectly suggests a cost that would lead to a higher price than $55 when applying the markup. Option C ($55.10) implies a cost greater than the set price, which is illogical. Option D ($60.50) is also incorrect as it would result in a price far exceeding $55, making it unfeasible.
To find the store's cost \( C \), we start with the equation \( P = C + \frac{1}{10}C \). This can be simplified to \( P = 1.1C \). Given that \( P = 55 \), we can set up the equation \( 55 = 1.1C \). Solving for \( C \) gives \( C = \frac{55}{1.1} = 50 \). Option A ($50.00) is correct, as it satisfies the equation. Option B ($54.90) incorrectly suggests a cost that would lead to a higher price than $55 when applying the markup. Option C ($55.10) implies a cost greater than the set price, which is illogical. Option D ($60.50) is also incorrect as it would result in a price far exceeding $55, making it unfeasible.
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.
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.
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.