I.E.D. Warm-up Quiz #1 Spring 2013

Explanation
To evaluate the expression 2(a + b) - 3c, we substitute the given values for a, b, and c. Plugging in a = 3, b = 7, and c = 8, we get 2(3 + 7) - 3(8). Simplifying further, we have 2(10) - 24, which equals 20 - 24. Finally, subtracting 24 from 20 gives us -4. Therefore, the correct answer is -4.

Explanation
To find the value of the expression 3(z - 7) + 12 when z = -3, we substitute -3 for z in the expression. This gives us 3(-3 - 7) + 12. Simplifying further, we have 3(-10) + 12, which is equal to -30 + 12. Adding these values, we get -18. Therefore, the value of the expression is -18.

Explanation
When the value of w is substituted into the equation on the right, it results in the value of 8.

Explanation
The odds of rolling a number less than or equal to three on a number cube can be determined by counting the favorable outcomes and dividing it by the total number of possible outcomes. In this case, the favorable outcomes are rolling a one, two, or three, which gives us three favorable outcomes. The total number of possible outcomes on a number cube is six, since there are six sides. Therefore, the odds of rolling a number less than or equal to three is 3/6, which simplifies to 1/2.

Explanation
The probability of randomly selecting a marble that is not red can be calculated by dividing the number of marbles that are not red by the total number of marbles. In this case, there are 5 blue marbles, 10 purple marbles, and 7 white marbles, which adds up to 22 marbles that are not red. The total number of marbles is 5 + 10 + 7 + 18 = 40. Therefore, the probability is 22/40, which simplifies to 11/20.

Explanation
To solve the equation (2a-4) / 6 = 3/4, we can cross multiply to eliminate the fractions. Multiplying both sides of the equation by 6 gives us 2a - 4 = 18/4. Simplifying the right side gives us 2a - 4 = 9/2. Adding 4 to both sides gives us 2a = 17/2. Finally, dividing both sides by 2 gives us a = 17/4. Therefore, the correct answer is 17/4.

Explanation
To find out how much gas would be used on a 250-mile trip, we can set up a proportion using the given information. The ratio of miles to gallons for the 375-mile trip is 375 miles/17 gallons. We can set this equal to the ratio of miles to gallons for the 250-mile trip, which is 250 miles/x gallons. Cross-multiplying and solving for x, we get x = (250 * 17) / 375 = 11.3 gallons. Therefore, the correct answer is 11.3 gallons.

Explanation
The probability of drawing the king of hearts from a standard 52-card deck is 1/52. This is because there is only one king of hearts in the deck, and there are a total of 52 cards. Therefore, the chance of drawing the king of hearts is 1 out of 52 possible outcomes.

Explanation
To solve the proportion, we can cross-multiply. Multiply 5 by 30 and divide the result by 15 to find the value of w. This gives us w = 10.

Explanation
To solve the given equation, we can start by isolating the variable n. First, we multiply both sides of the equation by 2 to eliminate the fraction: 3n + 4 = 22. Then, we subtract 4 from both sides to get 3n = 18. Finally, we divide both sides by 3 to solve for n, giving us n = 6.