answer:The area of a rectangle is calculated by multiplying its length by its width, so the area of the rectangle is 3 inches * 6 inches = 18 square inches. The area of a square is calculated by multiplying its side length by itself, so the area of the square is 5 inches * 5 inches = 25 square inches. Therefore, the difference in area between the two shapes is 25 square inches - 18 square inches = 7 square inches. 7 The answer is: 7

answer:We want to find the value of X in the given situation. The probability that a two-digit number ab and both a and b are divisible by X can be calculated by considering the possible outcomes and the favorable outcomes. There are 36 possible outcomes when two fair 6-sided dice are tossed. To find the favorable outcomes, we need to determine the values of a and b that satisfy the conditions: ab is a two-digit number and both a and b are divisible by X. For ab to be a two-digit number, a cannot be 0. Since a and b are digits, they can take values from 1 to 6. We need to find the values of a and b that are divisible by X. Given that the probability is frac{1}{9}, we can write: frac{text{number of favorable outcomes}}{text{number of possible outcomes}} = frac{1}{9} Let's consider the possible values of X and calculate the probability for each value. If X = 1, then all the values of a and b are divisible by 1, and there are 36 favorable outcomes. frac{36}{36} = 1 If X = 2, then a and b can take the values 2, 4, and 6. There are 9 favorable outcomes. frac{9}{36} = frac{1}{4} If X = 3, then a and b can take the values 3 and 6. There are 4 favorable outcomes. frac{4}{36} = frac{1}{9} If X = 4, then a and b can take the values 4. There is 1 favorable outcome. frac{1}{36} = frac{1}{36} If X = 5 or X = 6, there are no favorable outcomes because none of the values of a and b are divisible by 5 or 6. Therefore, the only value of X that gives a probability of frac{1}{9} is X = 3. The value of X is 3. The answer is: 3

answer:We can solve this system of equations by multiplying the first equation by 3 and the second equation by 4, then subtracting the second equation from the first: begin{align*} 9p + 12q &= 24 16p + 12q &= 52 hline -7p &= -28 p &= 4. end{align*} Substituting this value of p into either of the original equations, we find 4(4) + 3q = 13, so 16 + 3q = 13, and 3q = -3. Therefore, q = boxed{-1}.The answer is: -1

answer:We are given that the mean of 6, 9, and 18 is equal to the mean of X and y. To find the value of y, we need to determine the value of X. The mean of a set of numbers is found by summing all the numbers and dividing by the total count. For the given set of numbers, the mean is: (6 + 9 + 18) / 3 = 33 / 3 = 11 Since the mean of X and y is also 11, we can set up the equation: (X + y) / 2 = 11 Multiplying both sides by 2, we get: X + y = 22 Given that the value of y is 10, we can substitute it into the equation: X + 10 = 22 Subtracting 10 from both sides, we find: X = 12 The value of X is 12. The answer is: 12