Explanation

Explanation

Explanation

5 (as 9^n - 4^n is a difference of two odd powers, which is always divisible by 5)

13 (as 9^n - 4^n can be rewritten as (13-4)^n - 4^n, which is always divisible by 13)

Explanation

To simplify the expression, follow the order of operations:

(-20) + (-8) ÷ (-2) x 3

Divide -8 by -2: -8 ÷ (-2) = 4

Multiply 4 by 3: 4 x 3 = 12

Add -20 and 12: (-20) + 12 = -8

The correct answer is: -8

Explanation

1/log3(60) + 1/log4(60) + 1/log5(60)

= log60(3) + log60(4) + log60(5) (using the change of base formula)

= log60(3×4×5) (using the product rule of logarithms)

= log60(60)

= 1 (since log60(60) is equal to 1)

So the correct answer is: 1

Explanation

Step 1: Counting 7s in the ones place

Numbers where 7 appears in the ones place:

7, 17, 27, 37, 47, 57, 67, 77, 87, 97 → 10 times

Step 2: Counting 7s in the tens place

Numbers where 7 appears in the tens place:

70, 71, 72, 73, 74, 75, 76, 77, 78, 79 → 10 times

Step 3: Adjust for double counting

77 has two sevens, so we counted it twice.

Total occurrences:

10 (ones place) + 10 (tens place) = 20 times

Explanation

Since you are 5th in a queue starting from either end  so there are 2 persons to your left and 2 to your right

∴∴ Total number of persons are

5+2+2= 9

Explanation

To round off 87.321756 to 5 significant figures, we look at the 6th significant figure, which is 6.

Since it's greater than 5, we round up the 5th significant figure.

87.321756 becomes 87.322

Explanation

Find the least common multiple (LCM) of 10, 11, and 17.

The LCM of 10, 11, and 17 is the smallest number that is a multiple of all three numbers.

Calculate the LCM.

The prime factorization of the numbers is:

10 = 2 × 5

11 = 11

17 = 17

The LCM is the product of the highest powers of all prime factors: LCM = 2 × 5 × 11 × 17 = 1870.

Explanation

To find the common factors, let's list the factors of each number:

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 45: 1, 3, 5, 9, 15, 45

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

The common factors are 1 and 3.