There are 7 campers for every 2 counselors at summer camp. How many counselors are there if there are 84 campers?

24 counselors

Step-by-step explanation: Our first step in this problem is to write down the unit ratio that is involved. In this case, it's campers/counselors.

Next, we set up our proportion.

We know that at this summer camp, there are 7 campers for every 2 counselors so we have 7/2 and we're asked how many counselors are at the summer camp if there are 84 campers so that's 84/x.

Notice that the 84 campers must go on the top of the second ratio because our unit ratio tells us that we put campers over counselors.

Solving from here, we use the means-extremes property

to get (7)(x) or 7x equals (2)(84) or 168.

So we have 7x = 168.

Now dividing both sides of the equation by 7, we find that x = 24.

So, there are 24 counselors for 84 campers at the summer camp.

10/60

step-by-step explanation:

if you divide 10 by 60 the answer is 0.166666 while if you divide or solve the other problems it equals 0.6

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1