Jake's mom buys pizza for him every time he completes 15 Imagine Math Lessons. Brandon's mom buys cookies for him every time he completes 9 Imagine Math Lessons. How many lessons will they have completed when they earn pizza and cookies at the same time?

45 lessons

Step-by-step explanation:

Here, we want to know the number of lessons that both of them would have completed when they earn pizza and cookies at the same time

From the question, we are told that they earn cookies and pizza when they complete 9 and 15 lessons respectively.

So to know the number of lessons completed, we need to find the lowest common multiple of the number of cookies and the numbers of pizza

That will be lowest common multiple of 9 and 15

This is 45

step-by-step explanation:

the answer is 128

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."