To find a number between 4/9 and 52%, first convert both to decimals. 4/9 ≈ 0.444... and 52% = 0.52. We are looking for a number n such that 0.444... < n < 0.52. Let's evaluate the choices: A) 3/7 ≈ 0.428, which is less than 0.444... B) 11/25 = 0.44, which is less than 0.444... C) 9/20 = 0.45, which is between 0.444... and 0.52. D) 8/15 ≈ 0.533, which is greater than 0.52. Thus, 9/20 is the only value in the specified range.

The phrase 'percent of' implies multiplication. Column A is 0.87 * 50. Column B is 0.50 * 87. Due to the commutative property of multiplication (a * b = b * a), the order of the factors does not change the product. Therefore, 0.87 * 50 = 50 * 0.87. The two quantities are equal. We can calculate both to verify: 0.87 * 50 = 43.5. 0.50 * 87 = 43.5.

To determine who had the highest score, we need to compare the three values by converting them to a common format, such as decimals. Alex's score: 4/5 = 0.80. Ben's score: 83% = 0.83. Chandra's score: 0.81. Comparing the decimals, 0.83 is the largest number. Therefore, Ben had the highest score.

Let's choose a value for x that is between -1 and 0. For example, let x = -1/2. Then Column A is -1/2. Column B is 1/(-1/2) = -2. Comparing -1/2 and -2, we see that -1/2 is greater because it is closer to zero on the number line. For any number x between -1 and 0, its reciprocal 1/x will be a number less than -1. A number between -1 and 0 is always greater than a number less than -1. Therefore, the quantity in Column A is always greater.

The concentration of juice in Mixture A is the amount of juice divided by the total amount of the mixture. The ratio is 2 parts juice to 5 parts water, so the total is 2+5=7 parts. The concentration is 2/7. To compare 2/7 with Mixture B's concentration of 30%, convert both to decimals or percentages. 2/7 ≈ 0.2857, which is 28.57%. Mixture B's concentration is 30%. Since 30% > 28.57%, Mixture B has a higher juice concentration.

To compare the values, convert all of them to decimals. 5/8 = 0.625. 0.62 remains 0.62. 62.8% = 0.628. 13/20 = 0.65. Comparing the decimals, 0.65 is the largest value. Therefore, 13/20 is the greatest.

First, convert all numbers to decimals to compare them easily. -3/5 = -0.6. -58% = -0.58. The numbers are -0.6, -0.61, -0.58, and -0.606. For negative numbers, the one with the largest absolute value is the smallest. So, the order from least to greatest is -0.61, -0.606, -0.6, -0.58. This corresponds to the list -0.61, -0.606, -3/5, -58%.

When comparing exponential expressions with the same positive integer exponent, you need to focus on the bases. Since both expressions have the same exponent $$y$$ (where $$y$$ is a positive integer), the key is determining which base is larger.

Let's compare the bases: $$\frac{3}{4} = 0.75$$ and $$\frac{4}{5} = 0.8$$. Since $$0.8 > 0.75$$, we know that $$\frac{4}{5} > \frac{3}{4}$$.

For any positive integer exponent, if the base is larger, the result will be larger. This means $$\left(\frac{4}{5}\right)^y > \left(\frac{3}{4}\right)^y$$ for any positive integer $$y$$. You can verify this with a simple example: when $$y = 2$$, $$\left(\frac{3}{4}\right)^2 = \frac{9}{16} = 0.5625$$ while $$\left(\frac{4}{5}\right)^2 = \frac{16}{25} = 0.64$$.

Choice A incorrectly suggests Column A is greater, likely from miscomparing the fractions or confusing the relationship between bases and results. Choice B is wrong because we can definitively determine the relationship—we have enough information since both bases are positive and different. Choice C is incorrect because the bases are different, so the exponential expressions cannot be equal for any positive integer exponent.

Therefore, D is correct: Column B is greater.

Study tip: When comparing exponential expressions with the same positive exponent, convert the bases to decimals to quickly see which is larger. The larger base always produces the larger result.

When comparing two positive fractions, taking the reciprocal reverses the inequality. Since it is given that a < b, it follows that 1/a > 1/b. We can test this with numbers. Let a = 1/3 and b = 1/2. Both are between 0 and 1, and 1/3 < 1/2. Column A is 1/(1/3) = 3. Column B is 1/(1/2) = 2. Since 3 > 2, the quantity in Column A is greater. This holds for any values of a and b that fit the given conditions.

Calculate the sale price for each column. Column A: The discount is (1/5) * $90 = $18. The sale price is $90 - $18 = $72. Column B: The discount is 15% of $85, which is 0.15 * $85 = $12.75. The sale price is $85 - $12.75 = $72.25. Comparing the two prices, $72.25 is greater than $72. Therefore, the quantity in Column B is greater.