I.E.D. Warm-up Quiz #4

Explanation
To find the value of the expression, we substitute the given value of z into the expression. So, when z = -3, we have 3(-3 - 7) + 12. Simplifying this expression, we get 3(-10) + 12, which further simplifies to -30 + 12. Finally, combining like terms, we get -18 as the result.

Explanation
The odds of rolling a number less than or equal to three on a number cube can be found by determining the number of favorable outcomes (rolling a 1, 2, or 3) and dividing it by the total number of possible outcomes (rolling any number from 1 to 6). In this case, there are three favorable outcomes (1, 2, and 3) and six possible outcomes (1, 2, 3, 4, 5, and 6). 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 found by dividing the number of marbles that are not red by the total number of marbles in the bag. In this case, there are 5 blue marbles, 10 purple marbles, and 7 white marbles, making a total of 22 marbles that are not red. The total number of marbles in the bag is 5 + 10 + 7 + 18 = 40. Therefore, the probability is 22/40, which simplifies to 11/20.

Explanation
To solve the equation, we need to isolate the variable "a". First, we can multiply both sides of the equation by 6 to eliminate the fraction. This gives us 4a-4 = 36. Then, we can add 4 to both sides to get 4a = 40. Finally, we divide both sides by 4 to solve for "a", which gives us a = 10.

Explanation
To find the amount of gas used on a 250-mile trip, we can set up a proportion using the given information. Since the car used 17 gallons of gas for a 375-mile trip, we can set up the proportion 375/17 = 250/x, where x represents the amount of gas used on the 250-mile trip. Cross-multiplying, we get 375x = 17 * 250. Dividing both sides by 375, we find that x = (17 * 250) / 375 = 11.3. Therefore, the amount of gas used on a 250-mile trip would be 11.3 gallons.

Explanation
The probability of drawing a jack from a standard 52-card deck is 1/13. This is because there are 4 jacks in the deck (one jack of each suit - hearts, diamonds, clubs, and spades) and a total of 52 cards. Therefore, the probability of drawing a jack is equal to the number of favorable outcomes (4) divided by the total number of possible outcomes (52), which simplifies to 1/13.

Explanation
The given proportion states that the ratio of w to 30 is equal to the ratio of 6 to 20. To solve this proportion, we can cross-multiply. Multiplying 6 by 30 and 20 by w gives us 180 = 20w. Dividing both sides by 20, we find that w = 9.

Explanation
To solve the equation, we need to isolate the variable n. We can start by multiplying both sides of the equation by 3 to eliminate the fraction. This gives us 3n + 6 = 33. Next, we can subtract 6 from both sides to isolate the term with n, resulting in 3n = 27. Finally, we divide both sides by 3 to solve for n, giving us n = 9. Therefore, the correct answer is n = 9.

Explanation
By substituting the given values into the expression, we can evaluate 2(a + b) - 3c as 2(3 + 7) - 3(8). Simplifying further, we get 2(10) - 24, which equals 20 - 24. Finally, subtracting 24 from 20 gives us -4 as the result.

Explanation
To find the value of the expression, we substitute the given value of z, which is -4, into the expression. Thus, we have 3(-4 - 7) + 12. Simplifying the expression inside the parentheses, we get 3(-11) + 12. Multiplying -11 by 3 gives us -33, so the expression becomes -33 + 12. Finally, adding -33 and 12 gives us -21. Therefore, the value of the expression is -21.

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 (15 blue + 13 purple + 12 white) by the total number of marbles (15 blue + 13 purple + 12 white + 8 red). This simplifies to (40/60), which can be further simplified to 2/3. Therefore, the probability is 1/6.

Explanation
To solve the equation (2a-4) / 6 = 3/4, we can first cross multiply to eliminate the fractions. This gives us (2a-4) * 4 = 6 * 3. Simplifying further, we get 8a - 16 = 18. Adding 16 to both sides of the equation, we have 8a = 34. Finally, dividing both sides by 8, we find that a = 34/8, which simplifies to 17/4.

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

Explanation
The given proportion is w/30 = 5/15. To solve this proportion, we can cross-multiply. Cross-multiplying gives us 15w = 150. To isolate w, we divide both sides of the equation by 15. This gives us w = 10. Therefore, the correct answer is w = 10.

Explanation
To solve the equation (3n + 4) / 2 = 11, we need to isolate the variable n. First, we can multiply both sides of the equation by 2 to eliminate the fraction. This gives us 3n + 4 = 22. Then, we can subtract 4 from both sides to isolate the term with n. This gives us 3n = 18. Finally, we can divide both sides by 3 to solve for n, which gives us n = 6. Therefore, the correct answer is n = 6.