Answer and explanation:
<h2>X</h2>3x + 6y = 180 <em>Use the original expression to find x</em>
3x = 180 - 6y <em>Subtract 6y by both sides</em>
<em>Divide by 3 to get x</em>
x = 60 - 3y
<h2>Y</h2>x = 60 - 3y <em>Use the new expression to find y</em>
x - 60 = - 3y <em>Subtract 60 by both sides</em>
<em>Divide by -3 to get y</em>
Image of answer
I hope that helps
- 4018669
Answer:
The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we select appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sum of values of <em>X</em>, i.e ∑<em>X</em>, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
And the standard deviation of the distribution of the sum of values of X is given by,
The information provided is:
<em>μ</em> = $970
<em>σ</em> = $129
<em>n</em> = 102
Since the sample size is quite large, i.e. <em>n</em> = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.
Then,
Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.