Of the 30 girls who tried out for lacrosse team 12 were selected. of the 40 boys that tried out 16 were selected. are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls? explain.

Girls;

Total number of girls who tried out = 30

Number of girls who got selected = 12

Ratio of girls on team to girls who tried out =  = 2 : 5

Boys;

Total number of boys who tried out = 40

Number of boys who got selected = 16

Ratio of boys on team to boys who tried out =  = 2 : 5

Hence, the ratios are the same.

8) If the base of the exponents match on both sides of the equal sign, then the exponents can be set equal to each other.

So since (5ˣ)⁵ = 5³⁵, the base 5 is on both sides.

5(x) = 35

5x = 35

Divide by 5 on both sides to isolate the variable.

x = 7

9) Without evaluating (much) you can tell by common sense that (2⁵)(10⁵) is bigger.

The exponents are the same so you can multiply the bases. 4x5 = 20. 2 x 10 = 20. Now, just look at the exponents to see which is bigger. 5 > 4. Therefore, (2⁵)(10⁵) is bigger.

10) Nicholas's second statement is false. (2⁶)(2⁶) is the same as (2⁶)². In this case since they have the same base, you would multiply the exponents. 6 x 2 = 12. Therefore, (2⁶)(2⁶) = 2¹²