The expression you would use is 15 + .65x = 80. If you solve for x, Beth swam 100 laps.
Hope its correct and good luck :)
G(2) = 2 + 4/3 = 10/3
f(g(x)) = f(g(2)) = (10/3)^2 + 20/3 + 3 = 187/9 = 20 7/9 answer
![\bf 1~~,~~\stackrel{-3\cdot 1}{-3}~~,~~\stackrel{-3\cdot -3}{9}~~,~~\stackrel{-3\cdot 9}{-27}~~,~~\stackrel{-3\cdot -27}{81}](https://tex.z-dn.net/?f=%5Cbf%201~~%2C~~%5Cstackrel%7B-3%5Ccdot%201%7D%7B-3%7D~~%2C~~%5Cstackrel%7B-3%5Ccdot%20-3%7D%7B9%7D~~%2C~~%5Cstackrel%7B-3%5Ccdot%209%7D%7B-27%7D~~%2C~~%5Cstackrel%7B-3%5Ccdot%20-27%7D%7B81%7D)
notice, the "common ratio" is -3, thus their sum is just
1 + (-3) + 9 + (-27) + 81.
Answer: ![24\sqrt{3}](https://tex.z-dn.net/?f=24%5Csqrt%7B3%7D)
Step-by-step explanation:
You need to remember that
can be written in the following for:
![a^{\frac{1}{n}}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Knowing this and given the expression
, you need to multiply the numbers inside the parentheses:
![(12)^{\frac{3}{2}}](https://tex.z-dn.net/?f=%2812%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D)
Rewrite it in this form:
![=\sqrt{12^3}==\sqrt{1,728}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B12%5E3%7D%3D%3D%5Csqrt%7B1%2C728%7D)
Descompose 1,728 into its prime factors:
![1,728=2*2*2*2*2*2*3*3*3=2^6*3^3](https://tex.z-dn.net/?f=1%2C728%3D2%2A2%2A2%2A2%2A2%2A2%2A3%2A3%2A3%3D2%5E6%2A3%5E3)
Applying the Product of power property, which states that:
![(a^m)(a^n)=a^{(m+n)}](https://tex.z-dn.net/?f=%28a%5Em%29%28a%5En%29%3Da%5E%7B%28m%2Bn%29%7D)
You can say that:
![=\sqrt{1,728}=\sqrt{2^6*3^2*3}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B1%2C728%7D%3D%5Csqrt%7B2%5E6%2A3%5E2%2A3%7D)
Simplifying, you get:
![=2^3*3\sqrt{3}=24\sqrt{3}](https://tex.z-dn.net/?f=%3D2%5E3%2A3%5Csqrt%7B3%7D%3D24%5Csqrt%7B3%7D)
like chicken hate chicken total
like fish 22 15 37
hate fish 36 27 63
total 58 42 100
percentage of survey who did not like chicken or fish = 27/100 = 27%
the survey results reveal a greater dislike for fish...because 63% dislike fish and 42% dislike chicken