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3 years ago

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The midpoint of a segment is ( 6, -6) and one endpoint is (13,-1). Find the coordinates of the other endpoint

1 answer:

3241004551 [841]3 years ago

3 0

So, the formula for finding the midpoint of a segment given the coordinates of its endpoints is:

((x1+ x2)/2, (y1 + y2)/2 {Average of the x coordinates, average of the y coordinates}.

For this problem we know the coordinates of the midpoint along with one of the endpoints.

So the x coordinate of the midpoint (9) must equal (12 + x2)/2.

That is: 9 = (12 + x2)/2 Solve for x2. Follow a similar pattern to find the y coordinate of the unknown endpoint.

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In a proper fraction, is the numerator less than or greater than the denominator?

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Answer:

In a proper fraction, the numerator is less than the denominator.

Step-by-step explanation:

For example, 3/4. It is a proper fraction because the numerator is not greater than the denominator.

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3 years ago

What is the measure of the unknown angle?

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A pair of fair dice is cast. Let Edenote the event that the number landing uppermost on the first die is a 1 and let Fdenote the

iris [78.8K]

Answer:

They are not independent

Step-by-step explanation:

Given

E = Occurrence of 1 on first die

F = Sum of the uppermost occurrence in both die is 5

Required

Are E and F independent

First, we need to list the sample space of a roll of a die

$Event\ 1 = \{1,2,3,4,5,6\}$

Next, we list out the sample space of F

$Event\ 2 = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,\$

$6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}$

In (1): the sample space of E is:

$E = \{1\}$

So:

$P(E) = \frac{n(E)}{n(Event\ 1)}$

$P(E) = \frac{1}{6}$

In (2): the sample space of F is:

$F = \{5,5,5,5\}$

So:

$P(F) = \frac{n(F)}{n(Event\ 2)}$

$P(F) =\frac{4}{36}$

$P(F) =\frac{1}{9}$

For E and F to be independent:

$P(E\ and\ F) = P(E) * P(F)$

Substitute values for P(E) and P(F)

This gives:

$P(E\ and\ F) = \frac{1}{6} * \frac{1}{9}$

$P(E\ and\ F) = \frac{1}{54}$

However, the actual value of P(E and F) is 0.

This is so because $E = \{1\}$ and $F = \{5,5,5,5\}$ have 0 common elements:

So:

$P(E\ and\ F) = 0$

Compare $P(E\ and\ F) = \frac{1}{54}$ and $P(E\ and\ F) = 0$ .

These values are not equal.

Hence: the two events are not independent

6 0

3 years ago