A Simple Math IQ Quiz

Explanation
To find the value of a/b, we divide the value of a (1.9) by the value of b (0.6). Dividing 1.9 by 0.6 gives us approximately 3.17 when rounded to 2 decimal places. Therefore, the correct answer is 3.17.

Explanation
To find 1/4 of the sum of 260 and 64, we first need to calculate the sum which is 324. Then, we divide this sum by 4 to find the 1/4 value. Therefore, 1/4 of 324 is 81.

Explanation
672 is evenly divisible by 7 because it can be divided by 7 without leaving a remainder.

Explanation
To find 2/3 of 192, we can multiply 192 by 2 and then divide the result by 3. This gives us (192 * 2) / 3 = 384 / 3 = 128. Therefore, the correct answer is 128.

Explanation
There are 5,280 feet in a mile. To find 2/3 of a mile, we can multiply 5,280 by 2 and then divide by 3. This gives us 3,520 feet, which is the correct answer.

Explanation
To calculate the number of different ways the cars of a three-car train can be arranged, you can use the concept of permutations. In this case, you want to arrange three distinct cars, so you would use a permutation of 3 objects taken 3 at a time.

The formula for permutations is:

[P(n, r) = frac{n!}{(n - r)!}]

where:
- (P(n, r)) is the number of permutations of (n) objects taken (r) at a time.
- (n!) is the factorial of (n), which is the product of all positive integers from 1 to (n).
- ((n - r)!) is the factorial of (n - r).

For your three-car train, you have three cars, so (n = 3), and you want to arrange all three, so (r = 3).

Using the permutation formula:

[P(3, 3) = frac{3!}{(3 - 3)!} = frac{3!}{0!} = frac{6}{1} = 6]

There are 6 different ways to arrange the cars of the three-car train.

Explanation
The width of a cube is equal to its height, so if the height of the cube is 10 inches, then the width would also be 10 inches.

Explanation
To write 4^3 without an exponent, we need to multiply 4 by itself three times. This can be written as 4 × 4 × 4, which equals 64.

Explanation
The example 2 x (1/2) = 1 shows the "Multiplicative Inverse" because when a number is multiplied by its multiplicative inverse, the result is always 1. In this case, 2 is multiplied by the multiplicative inverse of 2, which is 1/2, resulting in 1.

Explanation
The prime factorization of 100 is 2 x 2 x 5 x 5 because it can be expressed as a product of prime numbers. The number 100 can be divided by 2, resulting in 50. Then, 50 can be divided by 2 again, resulting in 25. Finally, 25 can be divided by 5, resulting in 5. Therefore, the prime factorization of 100 is 2 x 2 x 5 x 5.