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Lelechka [254]
3 years ago
11

The table shows the amount of lemon juice needed to make lemonade. (Unit 9 Lesson 3) Lemon juice (cups) 5 10 20 Servings 35 70 1

40 Are the two quantities proportional? If so, what is the constant of proportionality?
Mathematics
1 answer:
Gwar [14]3 years ago
6 0
Lemon Juice (cups)    5    10    20
Servings                   35     70  140

The two quantities are proportional. Lemon Juice (cups) is the x-value ; while servings is the y-value.

  35 ÷   5 = 7
  70 ÷ 10 = 7
140 ÷ 20 = 7

The constant of proportionality is 7.

The equation would be: y = 7x
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A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 20 times, and the man is asked to predict
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P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}

Where n is the number of identical experiments and p is the probability of success. In this case n is 20.

Additionally, if he has no ESP the probability that he predict correctly is 0.5, because he is only guessing.

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P(x)=\frac{20!}{x!(20-x)!}*0.5^{x}*(1-0.5)^{20-x}

Therefore the probability that he would have done at least 17 out of 20 well if he had no ESP is:

P(x\geq 17)=P(17)+P(18)+P(19)+P(20)\\

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P(17)=\frac{20!}{17!(20-17)!}*0.5^{17}*(1-0.5)^{20-17}=0.00108719\\P(18)=\frac{20!}{18!(20-18)!}*0.5^{18}*(1-0.5)^{20-18}=0.00018119\\P(19)=\frac{20!}{19!(20-19)!}*0.5^{19}*(1-0.5)^{20-19}=0.00001907\\P(20)=\frac{20!}{20!(20-20)!}*0.5^{20}*(1-0.5)^{20-20}=0.00000095

So, P(x\geq 17) is equal to:

P(x\geq 17)=0.00108719+0.00018119+0.00001907+0.00000095\\P(x\geq 17)=0.00128

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