Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

JT has two jobs: mowing yards and washing cars. Let [tex]\( X \)[/tex] represent the weekly earnings for mowing yards, and [tex]\( Y \)[/tex] represent the weekly earnings for washing cars. The mean of [tex]\( X \)[/tex] is \[tex]$60, and the mean of \( Y \) is \$[/tex]35.

Which answer choice correctly calculates and interprets the mean of the sum, [tex]\( S = X + Y \)[/tex]?

A. [tex]\( \mu_S = 47.5 \)[/tex]; next week, JT will earn \[tex]$47.5.
B. \( \mu_S = 47.5 \); JT can expect to earn \$[/tex]47.5, on average, in a typical week.
C. [tex]\( \mu_S = 95 \)[/tex]; next week, JT will earn \[tex]$95.
D. \( \mu_S = 95 \); JT can expect to earn \$[/tex]95, on average, in a typical week.

Sagot :

GinnyAnswer
To solve this problem, we need to find the mean of the sum of JT's weekly earnings from both jobs. Let's denote:

- [tex]\( \mu_X \)[/tex] as the mean of JT's weekly earnings for mowing yards.
- [tex]\( \mu_Y \)[/tex] as the mean of JT's weekly earnings for washing cars.
- [tex]\( \mu_S \)[/tex] as the mean of the total weekly earnings, where [tex]\( S = X + Y \)[/tex].

We are given:
- [tex]\( \mu_X = \$60 \)[/tex]
- [tex]\( \mu_Y = \$35 \)[/tex]

The mean of the sum [tex]\( S = X + Y \)[/tex] can be calculated by summing the individual means:
[tex]\[ \mu_S = \mu_X + \mu_Y \][/tex]

Substituting the given values:
[tex]\[ \mu_S = 60 + 35 \][/tex]
[tex]\[ \mu_S = 95 \][/tex]

Therefore, the mean of JT's total weekly earnings from both jobs is \[tex]$95. Next, we interpret this result in the context of the problem. Among the given options, the correct interpretation of the mean is: \[ \mu_5 = 95; JT can expect to earn \$[/tex] 95, on average, in a typical week. \]

This interpretation correctly describes the mean as an expected average earnings per week, rather than a guaranteed amount for a specific upcoming week.

So, the correct answer choice is:
[tex]\[ \mu_5=95; JT can expect to earn \$ 95, on average, in a typical week. \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.