Test Your Mathematical Skills: A Quiz For 12th Grade

Explanation
The given expression involves subtracting two sets of numbers within parentheses. First, we simplify the numbers within the first set of parentheses: 4 - 5 = -1. Next, we simplify the numbers within the second set of parentheses: 13 - 18 + 2 = -3. Finally, we subtract the result of the second set of parentheses from the result of the first set: -1 - (-3) = -1 + 3 = 2. Therefore, the correct answer is 2.

Explanation
The given expression is (4x^2 - 2x) - (-5x^2 - 8x). Simplifying this expression, we can remove the parentheses and combine like terms. The negative sign in front of the second set of parentheses means that we need to distribute the negative sign to each term inside the parentheses. Doing this, we get 4x^2 - 2x + 5x^2 + 8x. Combining like terms, we have 9x^2 + 6x. Therefore, the correct answer is 3x(3x + 2), which is equivalent to 9x^2 + 6x.

Explanation
The radius of a circle can be found by dividing the circumference by 2π. In this case, the given circumference is 3.14 meters. Dividing this by 2π (approximately 6.28) gives a radius of approximately 0.5 meters.

Explanation
The length of the wire can be calculated by multiplying the number of times the wire goes around the rod by the circumference of the rod. In this case, the wire goes 5 times around the rod, and the circumference of the rod is 12 cm. Therefore, the length of the wire is 5 times 12 cm, which equals 60 cm.

Explanation
Mary can complete 1 activity in 40 days, which means she can complete 1/40 of the activity in one day. Similarly, John can complete 1/50 of the activity in one day. When they work together, they can complete 1/40 + 1/50 = 9/200 of the activity in one day. To complete 2 activities, they need to work for 2 / (9/200) = 400/9 days, which is approximately 44.44 days.

Explanation
To guess any 5-digit code using "yes" or "no" questions, we need to consider that each question can only provide one bit of information. Since there are 10 possible digits (0-9) for each position in the code, we need to find the minimum number of questions required to narrow down the possibilities to just one code. In this case, the correct answer is 17, which means that it is possible to guess any 5-digit code by asking 17 "yes" or "no" questions.

Explanation
If we consider a cube with a side length of 2 units, it has 6 faces. When we paint one side of the cube, only 5 faces remain unpainted. However, if we divide the cube into one-unit cubes, each face of the original cube will be divided into 4 smaller faces. Therefore, the total number of painted faces will be 5 * 4 = 20, which is greater than the total number of unpainted faces (5). This means that the side length of the cube cannot be 2 units.

Explanation
The sum of the given addition can be simplified by noticing that each term is formed by concatenating a certain number of 9's. In this case, the last term consists of 21 9's. When we add these numbers, the sum of the digits in each column will be 9, except for the rightmost column which will be 1. Therefore, the three last digits of the sum will be 089.

Explanation
Let's assume the number of steps on the escalator is 'x'. When Jack walks up at a rate of one step per second, he takes 12 steps to reach the top. This means that the escalator is moving at a rate of (x-12) steps per second. Similarly, when Jack goes up at two steps per second, he takes 20 steps to reach the top. This means that the escalator is moving at a rate of (x-20) steps per second. We can set up two equations using this information: x - 12 = (x-20)/2 and x - 20 = (x-12)/1. Solving these equations, we find that x = 60. Therefore, there are 60 steps on the escalator.

Explanation
The given order of digits is in ascending order. To maintain this order and place the digit 1 in the correct position, it should be placed between the digits 9 and 7. This would result in the following order: 8 5 4 9 1 7 6 3 2.