Suppose 90 out of 120 people said they like to work out and 5 out of every 18 of the people who like to work out have a gym membership. at the same rates, in a group of 216 people, predict how many you would expect to have a gym membership.

In a group of 216 people, I would expect 45 people to have a gym membership.

Step-by-step explanation:

Given :

90 out of 120 people said they like to work out

5 out of every 18 of the people who like to work out have a gym membership.

To Find : At the same rates, in a group of 216 people, predict how many you would expect to have a gym membership.

Solution :

Let x out of 216 like to work out

We are given that 90 out of 120 people said they like to work out

Since the rate is same for both the cases

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⇒

⇒

⇒

Thus 162 out 216 like to work out.

Since we are given that 5 out of every 18 has membership

So, first we need to calculate how many groups of 18 are there in 162

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⇒

So, there are 9 groups of 18 in 162 people

Since we know that out of 1 group of 18 there are 5 people who has membership

So,  if there are 9 groups of 18 so there will 9*5 = 45 people who will have membership .

Hence , in a group of 216 people, I would expect 45 people to have a gym membership.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.