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Sindrei [870]
2 years ago
6

Does the point (4, 0) satisfy the equation y = x2?

Mathematics
1 answer:
andre [41]2 years ago
8 0
Y=x^2
substitute the values into the original equation
0=4^2
0=16
No it does not satisfy the equation because 0 does not equal to 16
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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
snow_lady [41]

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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Stolb23 [73]
14753 is your answer

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Surface area of a sphere with a diameter of 17.5 inches
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Answer:

Ans is behind

Step-by-step explanation:

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This is a 30-60-90 triangle.
Triss [41]

Answer:

x = \frac{2\sqrt{21}}{3}

Step-by-step explanation:

For a 30-60-90 triangle:

  • Short leg = s
  • Long leg = s√3
  • Hypotenuse = 2s

Thus:

  • Short leg = √7/√3 = (√21)/3
  • Long leg = √7
  • Hypotenuse = x = 2(√21)/3
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2 years ago
What is the median of this set of data? 66, 51, 77, 68, 60, 75, 54, 80
labwork [276]
51, 54, 60, 66, 68, 75, 77, 80 The median is 67
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