Answer:
2
Step-by-step explanation:
Given
See attachment for chart
Required
Number of off days
To do this, we simply calculate the expected value of the chart.
This is calculated as:

Where
x = days
f = chances
So, we have:



You just flip each of the numbers spots - the x and y
Answer:
B
Step-by-step explanation:
Answer:

Step-by-step explanation:
Given expression is:
![(\sqrt[8]{x^7} )^{6}](https://tex.z-dn.net/?f=%28%5Csqrt%5B8%5D%7Bx%5E7%7D%20%29%5E%7B6%7D)
First we will use the rule:
![\sqrt[n]{x} = x^{\frac{1}{n} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%7D)
So for the given expression:
![\sqrt[8]{x^{7}}=(x^{7} )^{\frac{1}{8} }](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bx%5E%7B7%7D%7D%3D%28x%5E%7B7%7D%20%29%5E%7B%5Cfrac%7B1%7D%7B8%7D%20%7D)
We will use tha property of multiplication on powers:


Applying the outer exponent now


Let x be the number of weeks; therefore, the two linear equations are

Where T stands for the punches on the tea punch card and C for the punches on the coffee punch card.
Solving by substitution. Set T=C, then

Thus, substitute the value of x=3 into the first equation,

Thus, after 3 weeks, Josiah will have the same number of punches on each card, and he will have 23 punches on each card.