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Allisa [31]
3 years ago
8

PLEASE HELP!!!!!!!

Mathematics
2 answers:
blagie [28]3 years ago
7 0

Answer:

Its 3

Step-by-step explanation:


il63 [147K]3 years ago
4 0
Well to solve for r, what you would need to do is make up an equation based on the expressions that represent the segments of the line in the image.

JK represents the first aspect of the line and is equal to 6r.

Likewise, KL represents the second component of the line and is equal to 3r.

We also know the total value from the first point to the last one, and that is 27.

Now simply add the first 2 expressions that represent the segments of the line and make it equal to the total length of the line, 27 and then solve for r.

6r + 3r = 27
9r = 27
r = 27/9
r = 3.

So now we know that JK is 6 • 3 = 18 and KL is 3 • 3 = 9, thus adding both together will give a value of 27, 18 + 9 = 27.

The solution is C.3
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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:

\\ P(A|B) = \frac{P(A \cap B)}{P(B)}

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)}

\\ P(M|V) = \frac{0.03}{0.73}

\\ P(M|V) \approx 0.041

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

\\ P(M|V) = P(M) = 0.18

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>.

Notice that  

\\ 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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Step-by-step explanation:

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