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krek1111 [17]
3 years ago
15

The amount of blueberries picked, in pounds, varies directly as the number of hours worked. After

Mathematics
2 answers:
Alekssandra [29.7K]3 years ago
8 0

Answer: Hello there!

We know that the number of blueberries picked varies directly as the number of hours worked.

Direct variation means that: b = kh

where b is the number of blueberries, k is a constant of proportionality and h is the number of hours worked.

we know that in 10 hours there are 30 pounds of blueberries collected, then we can replace these numbers in the equation and solve it for k. And you want that I don't include units in the answer, so I will not include them.

30 = k*10

k = 30/10 = 3

Then the constant of proportionality is 3, whit is the amount of punds of blueberrys collected in one hour.

OverLord2011 [107]3 years ago
4 0

Answer:

3

Step-by-step explanation:

3 pounds were picked per hour

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(b)\dfrac{8}{39}

(c)\dfrac{25}{117}

Step-by-step explanation:

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Number of Women, n(W)=3

Total Sample, n(S)=24+3=27

Since you cannot appoint the same person twice, the probabilities are <u>without replacement.</u>

(a)Probability that both appointees are men.

P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}

(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

  • A man is appointed first and a woman is appointed next.
  • A woman is appointed first and a man is appointed next.

P(One man and one woman are appointed)=P(MW)+P(WM)

=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}

(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

  • A man is appointed first and a woman is appointed next.
  • A woman is appointed first and a man is appointed next.
  • Two women are appointed

P(at least one woman is appointed)=P(MW)+P(WM)+P(WW)

P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}

In Part B, P(MW)+P(WM)=\frac{8}{39}

Therefore:

P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}

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3 years ago
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