An English teacher has 6 short stories, 4 novels, and 23 poems to choose from. How many ways can he assign one of each to his class?

552

Step-by-step explanation:

This is a problem of permutation which can be solved by rule of fundamental counting principle.

This principle states that if there "m" ways of doing one thing and "n" ways of doing other. Then no. of ways in which both the things can be done together is "m*n". This can be extended for m, n, p,r, s things and so on.

example: if there are 5 shirts and 3 trousers then number of ways in which the shirts and trousers can be worn is 5*3 = 15 ways.

The given problem is on similar concepts.

here  6 short stories, 4 novels, and 23 poems have to be assigned to his class.

Thus it can be done in 6*4*23 = 552 ways.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.