So is doubling, first off, meaning, if the current amount say P, then when it doubles is 2P, or double that, or P + P, so the rate of growth is 100%, since it's doubling.
and is doing it every 9 hour cycle, thus
![\bf \textit{Periodic/Cyclical Exponential Growth}\\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &650\\ r=rate\to 100\%\to \frac{100}{100}\to &1.00\\ t=\textit{elapsed time}\to &10\\ c=period\to &9 \end{cases} \\\\\\ A=650(1 + 1)^{\frac{10}{9}}\implies A=650(2)^{\frac{10}{9}}\implies A=650\sqrt[9]{2^{10}}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BPeriodic%2FCyclical%20Exponential%20Growth%7D%5C%5C%5C%5C%0AA%3DP%281%20%2B%20r%29%5E%7B%5Cfrac%7Bt%7D%7Bc%7D%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D%5Ctextit%7Baccumulated%20amount%7D%5C%5C%0AP%3D%5Ctextit%7Binitial%20amount%7D%5Cto%20%26650%5C%5C%0Ar%3Drate%5Cto%20100%5C%25%5Cto%20%5Cfrac%7B100%7D%7B100%7D%5Cto%20%261.00%5C%5C%0At%3D%5Ctextit%7Belapsed%20time%7D%5Cto%20%2610%5C%5C%0Ac%3Dperiod%5Cto%20%269%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D650%281%20%2B%201%29%5E%7B%5Cfrac%7B10%7D%7B9%7D%7D%5Cimplies%20A%3D650%282%29%5E%7B%5Cfrac%7B10%7D%7B9%7D%7D%5Cimplies%20A%3D650%5Csqrt%5B9%5D%7B2%5E%7B10%7D%7D)
As rolling a one on a fair die has a probability of 1/6, on average it is likely that a one will be rolled around once every six rolls, therefore the game’s expected value is 0 because in six rolls one roll will yield 50 and the other five rolls -10 each granting a net total of 0.
Answer:
g=79
h=55
j=75
Step-by-step explanation:
1. When a transversal intersects two parallel lines corresponding angles, angles that are located in the same relative position an intersection of transversal and two or more straight lines, are congruent. Therefore g=79.
2. Since the two lines are parallel same side interior angles are supplementary. This means they add up to 180. So to find h solve the equation h+125=180. Once solved you get 55.
3. Like question 2, these angles are same side interior and therefore supplementary. To find j solve the equation j+105=180, which gets j=75.
The correct formula for this is as follows:
where n is the number of compounding periods per year, and r is the annual interest rate as a decimal,
Plugging the given values into the formula, we get:
This equation can be simplified to:
Taking logs of both sides gives:
which can be rearranged to get:
So it will take about 5.864 years for the amount to reach $4550.
Just divide the number of remaining pies by 3, and you will have the answer.
