Answer:
1
Step-by-step explanation:
One member in the graph only went one time which is fewer than two times.
Answer:
a. Fraction of earnings that Mariano put into each piggy bank is 1/12
b. Mariano earns $28.8
Step-by-step explanation:
Mariano divides his earning in a saving account and 3 piggy banks.
First , we have to know the fraction that we divide in the 3 piggy banks.
Piggy banks =Total earning-Saving account
Saving account 3/4,
Total earning is 1
to rest both term we have to get the same denominator , so we can say that the total earning is 4/4
Piggy banks =4/4-3/4=( 4-3)/4=1/4
Piggy banks =1/4
Each piggy bank will be 1/3 of that 1/4
1/3 x 1/4=
For fraction multiplication, multiply the numerators and then multiply the denominators to get
1×1/3×4=1/12
This fraction cannot be reduced.
b. Mariano adds $2.40
1/12 is 2.40
total earning is ?
We use cross-multiplication
a/b=c/d replacing (1/12)/2.40 = 1/ ?
So, the total earning (?) is 1 x 2.40/ (1/12)
= 2.40 x 12=$28.8
Whenever you multiply something, you just add it to itself that many times.
ex) 7 × 4 = 7 + 7 + 7 + 7.
Thus n × a = n + n + n + n....a times.
Trig was never my strong point but ok
remember the quotient rule
![\frac{dy}{dx} \frac{f(x)}{g(x)}=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%3D%5Cfrac%7Bf%27%28x%29g%28x%29-g%27%28x%29f%28x%29%7D%7B%28g%28x%29%29%5E2%7D)
so
remember the pythagorean identity sin²(x)+cos²(x)=1
so
![\frac{dy}{dx} \frac{1+sin(x)}{1-cos(x)}=\frac{cos(x)(1-cos(x))-sin(x)(1+sin(x))}{(1+cos(x))^2}=](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%5Cfrac%7B1%2Bsin%28x%29%7D%7B1-cos%28x%29%7D%3D%5Cfrac%7Bcos%28x%29%281-cos%28x%29%29-sin%28x%29%281%2Bsin%28x%29%29%7D%7B%281%2Bcos%28x%29%29%5E2%7D%3D)
![\frac{cos(x)-cos^2(x)-sin(x)-sin^2(x)}{(1+cos(x))^2}=](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29-cos%5E2%28x%29-sin%28x%29-sin%5E2%28x%29%7D%7B%281%2Bcos%28x%29%29%5E2%7D%3D)
![\frac{cos(x)-sin(x)-sin^2(x)-cos^2(x)}{(1+cos(x))^2}=](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29-sin%28x%29-sin%5E2%28x%29-cos%5E2%28x%29%7D%7B%281%2Bcos%28x%29%29%5E2%7D%3D)
![\frac{cos(x)-sin(x)-(sin^2(x)+cos^2(x))}{(1+cos(x))^2}=](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29-sin%28x%29-%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29%7D%7B%281%2Bcos%28x%29%29%5E2%7D%3D)
![\frac{cos(x)-sin(x)-(1)}{(1+cos(x))^2}=](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29-sin%28x%29-%281%29%7D%7B%281%2Bcos%28x%29%29%5E2%7D%3D)
![\frac{cos(x)-sin(x)-1}{(1+cos(x))^2}=](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29-sin%28x%29-1%7D%7B%281%2Bcos%28x%29%29%5E2%7D%3D)
![\frac{-sin(x)+cos(x)-1}{(1+cos(x))^2}=](https://tex.z-dn.net/?f=%5Cfrac%7B-sin%28x%29%2Bcos%28x%29-1%7D%7B%281%2Bcos%28x%29%29%5E2%7D%3D)
taht is the last option
thanks to jdoe0001 for showing me which identity to use