Answer:
8.0
Step-by-step explanation:
Sin theta = opposite /hypotenuse
sin 53 = x/10
Multiply each side by 10
10 sin 53 = x
7.9863551
To the nearest tenth
x = 8.0
Answer:24
Step-by-step explanation:
40% 60 is just 0.4⋅60=24
We are given parent function: ![f(x)=2^x.](https://tex.z-dn.net/?f=f%28x%29%3D2%5Ex.)
We need to explain which graph would represent f(x) +1. function.
Please note: 1 is added to parent function f(x).
According to rule of transformations y= f(x)+K shifts K units up of parent function f(x).
For parent function f(x) =2^x, y-intercept is 1.
So, for f(x)+1 function y-intercept would be 2 because y-intercept 1 is being shifted 1 unit up, that is 2.
So, the shown graph would be correct graph for f(x)+1.
Answer:
![C(t)= \frac{1}{2} kg (2/3) ^ t](https://tex.z-dn.net/?f=C%28t%29%3D%20%5Cfrac%7B1%7D%7B2%7D%20kg%20%282%2F3%29%20%5E%20t)
Step-by-step explanation:
Original Question:
- Nana has a water purifier that filters 1/3 of the contaminants each hour. She used it to purify water that had 1/2 kilogram of contaminants. Write a function that gives the remaining amount of contaminants in kilograms, C(t), t hours after Nana started purifying the water.
Explanation:
- Each hour, the water purifier filters 1/3 of the contaminants, meaning that the contaminant reduces by 2/3. If the contaminant was 1kg (for example), the mass would be 2/3 kg after 1 hour- after 2 hours, it'll be 4/9 kg, so we see a pattern. We need to multiply the contaminant by 2/3 every single hour.
![C(t)= \frac{1}{2} kg (2/3) ^ t](https://tex.z-dn.net/?f=C%28t%29%3D%20%5Cfrac%7B1%7D%7B2%7D%20kg%20%282%2F3%29%20%5E%20t)
4⁻³ · 12⁰
Remember, if a power is ever negative, then you have to turn it into a fraction, and if a power is zero, then the whole number turns into 1 :)
4⁻³ turns into 1/4³ due to the fact that the power is negative.
So, our question now looks like this :
1/4³ · 1
Simplify.
1/64 · 1
Simplify.
Our answer is : 1/64
~Hope I helped!~