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2 years ago

When expressing sets, you may write "inf" for infinity and "U" for union.

Mathematics

1 answer:

GarryVolchara [31]2 years ago

3 0

Answer:

The complement of the given set in interval notation is $(-\infty,-5]\cup(6,\infty)$ . It can we written as (-inf,5]U(6,inf).

Step-by-step explanation:

The given set in interval notation is

(−5,6]

It means the set is defined as

$A=\{x|x\in R,-5$

If B is a set and U is a universal set, then complement of set B contains the elements of universal set but not the elements of set B.

Here, universal set is R, the set set of all real numbers.

$U=\{x|x\in R\}$

The complement of the given set is

$A^c=U-A$

$A^c=\{x|x\in R,-\infty$

Complement of the given set in interval notation is

$A^c=(-\infty,-5]\cup(6,\infty)$

Therefore the complement of the given set in interval notation is $(-\infty,-5]\cup(6,\infty)$ . It can we written as (-inf,5]U(6,inf).

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Jeanne wants to start collecting coins and orders a coin collection starter kit. The kit comes with three coins chosen at random

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Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes $P_B(A)$ .

The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by
$P(A|B)= \frac{P(A \cap B)}{P(B)}$

In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.

The probability of selecting one coin is $\frac{1}{3}$

Part A:
To find the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.

P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.

Thus $P(A)= \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}$

P(B) means that the first envelope contains a quarter AND the second envelope contains a quarter

Thus $P(B)= \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Therefore, $P(A|B)=\left( \frac{ \frac{1}{27} }{ \frac{1}{9} } \right)= \frac{1}{3}$

Part B:
To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.

$P(C)= \frac{3}{3} \times \frac{2}{3} \times \frac{1}{3} = \frac{6}{27} = \frac{2}{9}$

 $P(D)= \frac{1}{3}$ 

Therefore, $P(C|D)=\left( \frac{ \frac{2}{9} }{ \frac{1}{3} } \right)= \frac{2}{3}$

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

We draw the right triangle as shown in the image attached.

Δ QRS

Where R is the right angle

Given

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Now, using Pythagorean Theorem, we can find RS:

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Opposite side is RS (which is 15)

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So,

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This is the value of SinQ.

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