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BaLLatris [955]
3 years ago
12

When Joseph first starts working at a grocery store, his hourly rate is \$10$10dollar sign, 10. For each year he works at the gr

ocery store, his hourly rate increases by \$0.50$0.50dollar sign, 0, point, 50. Joseph's hourly rate RRR, in dollars, is a function of ttt, the number of years he works at the grocery store. Write the function's formula.
Mathematics
1 answer:
morpeh [17]3 years ago
3 0

Answer:

R(t)=10+0.50t

Step-by-step explanation:

Let t represent the number of years.

We have been given that When Joseph first starts working at a grocery store, his hourly rate is $10.

For each year he works at the grocery store, his hourly rate increases by $0.50. Increase in hourly rates after t years would be 0.50t

The hourly rates after t years will be 10 plus 0.50t.

We can represent this information in an equation as:

R(t)=10+0.50t

Therefore, the function R(t)=10+0.50t represents Joseph's hourly rates after t years.

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Calculate out how many times the denominator goes into the numerator. To do that, divide 385 by 6 and keep only what is to the left of the decimal point:

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The probability that a student has a Visa card (event V) is .73. The probability that a student has a MasterCard (event M) is .1
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We assumed in this answer that the question b is, Are the events V and M independent?

Answer:

(a). The probability that a student has either a Visa card or a MasterCard is<em> </em>\\ P(V \cup M) = 0.88. (b). The events V and M are not independent.

Step-by-step explanation:

The key factor to solve these questions is to know that:

\\ P(V \cup M) = P(V) + P(M) - P(V \cap M)

We already know from the question the following probabilities:

\\ P(V) = 0.73

\\ P(M) = 0.18

The probability that a student has both cards is 0.03. It means that the events V AND M occur at the same time. So

\\ P(V \cap M) = 0.03

The probability that a student has either a Visa card or a MasterCard

We can interpret this probability as \\ P(V \cup M) or the sum of both events; that is, the probability that one event occurs OR the other.

Thus, having all this information, we can conclude that

\\ P(V \cup M) = P(V) + P(M) - P(V \cap M)

\\ P(V \cup M) = 0.73 + 0.18 - 0.03

\\ P(V \cup M) = 0.88

Then, <em>the probability that a student has either a Visa card </em><em>or</em><em> a MasterCard is </em>\\ P(V \cup M) = 0.88.<em> </em>

Are the events V and M independent?

A way to solve this question is by using the concept of <em>conditional probabilities</em>.

In Probability, two events are <em>independent</em> when we conclude that

\\ P(A|B) = P(A) [1]

The general formula for a <em>conditional probability</em> or the probability that event A given (or assuming) the event B is as follows:

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If we use the previous formula to find conditional probabilities of event M given event V or vice-versa, we can conclude that

\\ P(M|V) = \frac{P(M \cap V)}{P(V)}

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If M were independent from V (according to [1]), we have

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Which is different from we obtained previously;

That is,

\\ P(M|V) \approx 0.041

So, the events V and M are not independent.

We can conclude the same if we calculate the probability

\\ P(V|M), as follows:

\\ P(V|M) = \frac{P(V \cap M)}{P(M)}

\\ P(V|M) = \frac{0.03}{0.18}

\\ P(V|M) = 0.1666.....\approx 0.17

Which is different from

\\ P(V|M) = P(V) = 0.73

In the case that both events <em>were independent</em>.

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\\ P(V|M)*P(M) = P(M|V)*P(V) = P(V \cap M) = P(M \cap V)

\\ \frac{0.03}{0.18}*0.18 = \frac{0.03}{0.73}*0.73 = 0.03 = 0.03

\\ 0.03 = 0.03 = 0.03 = 0.03

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