Hamburger: $3.25
Medium Fries: $1.45
Medium Drink: $1.39
Answer:
Part a) ![n=-8.017176](https://tex.z-dn.net/?f=n%3D-8.017176)
Part b) ![n=9.700465](https://tex.z-dn.net/?f=n%3D9.700465)
Step-by-step explanation:
Part a) we have
![9^{(n+10)}+3=81](https://tex.z-dn.net/?f=9%5E%7B%28n%2B10%29%7D%2B3%3D81)
Solve for n
Subtract 3 both sides
![9^{(n+10)}+3-3=81-3](https://tex.z-dn.net/?f=9%5E%7B%28n%2B10%29%7D%2B3-3%3D81-3)
![9^{(n+10)}=78](https://tex.z-dn.net/?f=9%5E%7B%28n%2B10%29%7D%3D78)
take log both sides
![log[9^{(n+10)}]=log[78]](https://tex.z-dn.net/?f=log%5B9%5E%7B%28n%2B10%29%7D%5D%3Dlog%5B78%5D)
![(n+10)log[9]=log[78]](https://tex.z-dn.net/?f=%28n%2B10%29log%5B9%5D%3Dlog%5B78%5D)
![(n+10)=log[78]/log[9]](https://tex.z-dn.net/?f=%28n%2B10%29%3Dlog%5B78%5D%2Flog%5B9%5D)
----> using a calculator
![n=-8.017176](https://tex.z-dn.net/?f=n%3D-8.017176)
Part b) we have
![11^{(n-8)}-5=54](https://tex.z-dn.net/?f=11%5E%7B%28n-8%29%7D-5%3D54)
Solve for n
Adds 5 both sides
![11^{(n-8)}-5+5=54+5](https://tex.z-dn.net/?f=11%5E%7B%28n-8%29%7D-5%2B5%3D54%2B5)
![11^{(n-8)}=59](https://tex.z-dn.net/?f=11%5E%7B%28n-8%29%7D%3D59)
take log both sides
![log[11^{(n-8)}]=log[59]](https://tex.z-dn.net/?f=log%5B11%5E%7B%28n-8%29%7D%5D%3Dlog%5B59%5D)
![(n-8)log[11]=log[59]](https://tex.z-dn.net/?f=%28n-8%29log%5B11%5D%3Dlog%5B59%5D)
![(n-8)=log[59]/log[11]](https://tex.z-dn.net/?f=%28n-8%29%3Dlog%5B59%5D%2Flog%5B11%5D)
----> using a calculator
![n=9.700465](https://tex.z-dn.net/?f=n%3D9.700465)
the following are my reminders in using this module
Answer:
Option B: 0.4
Step-by-step explanation:
We have 20 dots.
Such that each column represents the repetitions for each proportion.
So:
0.1 -> 3 times
0.2 -> 1 time
0.3 -> 4 times
0.4 -> 6 times
0.5 -> 3 times
0.6 -> 3 times
Now we can compute the mean of these values, and that will be the best estimation we can make with the given data.
Remember that for a set of N values:
{x₁, x₂, ..., xₙ}
The mean is:
![M = \frac{x_1 + x_2 + ... + x_n}{N}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7Bx_1%20%2B%20x_2%20%2B%20...%20%2B%20x_n%7D%7BN%7D)
In this case we have the set of 20 points described above, then the mean is:
![M = \frac{3*0.1 + 1*0.2 + 4*0.3 + 6*0.4 + 3*0.5 + 3*0.6}{20} = 0.37](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B3%2A0.1%20%2B%201%2A0.2%20%2B%204%2A0.3%20%2B%206%2A0.4%20%2B%203%2A0.5%20%2B%203%2A0.6%7D%7B20%7D%20%3D%200.37)
Rounding to the first place after the decimal point, we get:
M = 0.4
Then the correct option is option B.