Elena makes a fruit punch by mixing 4 parts cranberry juice to 3 parts apple juice to 2 parts grape juice.if one batch of fruit punch includes 30 cups of apple juice,how large is this batch of fruit punch?

This batch has 90 cups of fruit punch

Step-by-step explanation:

Fruit punch=4 parts cranberry, 3 parts apple juice, 2 parts grape juice

Proportions for each=Number of parts/Total Parts

Cranberry proportion=4/(4+3+2)=4/9

Apple juice proportion=3/(4+3+2)=3/9=1/3

Grape juice proportion=2/(4+3+2)=2/9

There for;

Apple juice proportion×Total amount of fruit punch(T)=30 cups of apple juice

Replacing;

(1/3)×T=30

T=90 cups

Total amount of fruit punch=T=90 cups

This batch has 90 cups of fruit punch

So the answer is 2^-3

Step-by-step explanation:

The principle is the same no matter what the base.

Log_2 (7) + Log_2(3/28) - Log_2(6)

+ means multiply

- means divide

Log_2(7 * 3/28 /6)

Log_2(7/6 * 3/28)

Log_2(1/2 * 1/4)              3 divides into 6 twice. 7 divides into 28 four times

log_2 (1/8)

This is equivalent to 2^(-3)