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olchik [2.2K]
3 years ago
15

Which function has the same domain as y = 2 StartRoot x EndRoot

Mathematics
1 answer:
snow_lady [41]3 years ago
4 0
The answer is A. Y=square root of 2x
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1. The table shows the probabilities of a response chocolate or vanilla when asking a child or adult. Use the formula for condit
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\begin{matrix}&\text{chocolate}&\text{vanilla}&\text{total}\\\text{children}&0.14&0.26&0.40\\\text{adults}&0.21&0.39&0.60\\\text{total}&0.35&0.65&1.00\end{matrix}

a. "Chocolate" and "Adults" (whatever those mean) will be independent as long as

P(\text{chocolate}\cap\text{adults})=P(\text{chocolate})\cdot P(\text{adults})

"Chocolate" has the marginal distribution given by the second column, with a total probability of P(\text{chocolate})=0.35. Similarly, "Adults" has the marginal distribution described by the third row, so that P(\text{adults})=0.60. Then

P(\text{chocolate})\cdot P(\text{adults})=0.35\cdot0.60=0.21

Meanwhile, the joint probability of "Chocolate" and "Adults" is given by the cell in the corresponding row/column, with P(\text{chocolate}\cap\text{adults})=0.21.

The probabilities match, so these events are indeed independent.

Parts (b) and (c) are checked similarly.

b. Yes;


P(\text{children})\cdot P(\text{chocolate})=0.40\cdot0.35=0.14
P(\text{children}\cap\text{chocolate})=0.14

c. Yes;

P(\text{vanilla})\cdot P(\text{children})=0.65\cdot0.40=0.26
P(\text{vanilla}\cap\text{children})=0.26
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3 years ago
5a+2a(5-b)= <br><br> Simplify the expression
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5a+2a(5−b)

Distribute:

=5a+(2a)(5)+(2a)(−b)

=5a+10a+−2ab

Combine Like Terms:

=5a+10a+−2ab

=(−2ab)+(5a+10a)

=−2ab+15a

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3 years ago
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