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Cloud [144]
3 years ago
12

Kate wants to buy a bike that costs $250. She has $40 saved. She will also do 5 days of yard work earning $38 for each day. Will

Kate have enough money for the bike? I need a answer ASAP!!
Mathematics
2 answers:
Alex Ar [27]3 years ago
4 0
Unfortunately, Katie will be $20 short

She has $40
Plus the $38 x 5 she will be earning which is $190
$190+$40 is $230

Looks like Kate needs one more day of hard work to get her bike ; )
TEA [102]3 years ago
3 0
40 + 5(38) = 40 + 190 = 230....nope, she is short by 20 bucks
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Answer:

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The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponenti
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Answer:

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Step-by-step explanation:

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The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \mu e^{-\mu x}

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P(X \leq x) = 1 - e^{-\mu x}

The probability of finding a value higher than x is:

P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).

This means that m = 100, \mu = \frac{1}{100} = 0.01

(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

We have that:

P(X > x) = e^{-\mu x}

This is P(X > 190). So

P(X > 190) = e^{-0.01*190} = 0.1496

0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

(b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08?

This is x for which:

P(X > x) = 0.08

So

e^{-0.01x} = 0.08

\ln{e^{-0.01x}} = \ln{0.08}

-0.01x = \ln{0.08}

x = -\frac{\ln{0.08}}{0.01}

x = 252.6

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