1. a total of three freshmen, five sophomores, 3 juniors and 4 seniors are eligible for a $3000 scholarship, a $2000 scholarship and a $1000 scholarship. in how many different ways can these scholarships be awarded if at least two of them must go to senior

So those scholarships can be awarded in 13*12 = 156 different ways ensuring that at least two of them go to seniors.

Step-by-step explanation:

In this problem, there are three scolarships.

The first step to solve this question is ensuring that two seniors receive their scolarships.

There are 4 seniors, and we must guarantee two scolarships to them. If senior A receives the first scolarship and senior B the second, or A receives the second and B the first, it is the same thing, so the order does not interfere with the problem. It means it is a combination problem.

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The formula for the number of possible combinations of r objects from a set of n objects is:

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So, for the senior scolarships, we have combinations of two(scolarships) objects from a set of four(seniors) objects: So

There are 12 ways to ensure two of those scolarships to those seniors.

The are 13 students vying for the last scolarship(hree freshmen, five sophomores, 3 juniors and two seniors that didn't get the first two).

So those scholarships can be awarded in 13*12 = 156 different ways ensuring that at least two of them go to seniors.

step-by-step explanation:

the first 5 right here the next 5 i will upload as separate question

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer