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ira [324]
3 years ago
12

Tom is deciding whether or not he should become a member gym to use their basketball courts. The membership cost is $135. Member

s pay $2 to rent out the basketball courts. Non-members can rent the court also, but they have to pay $11 each time. how many times would Tom need to rent the court in order for it be cheaper to be a member than a non member?
Mathematics
1 answer:
Kisachek [45]3 years ago
6 0
135 + 2x
11x

135 + 30 (or 2 x 15) = 165
11 x 15 = 165

16 times.
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a)P=0.42

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Step-by-step explanation:

We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:

P=\begin{pmatrix}n\\ k\end{pmatrix} p^k(1-p)^{n-k}=\frac{n!}{k!(n!-k!)}p^k(1-p)^{n-k}

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P=\frac{10!}{2!(10!-2!)}0.01^2(1-0.01)^{10-2}\\P=\frac{10!}{2!*8!}0.01^2(0.99)^{8}\\P=45*0.01^2(0.99)^8=0.42

b) We have, 1-(1-p)^n=P, Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.

1-0.99^n\geq 0.95\\0.99^n\leq 1-0.95\\0.99^n\leq 0.05\\n\geq 297

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2. Now, you must solve for x, as following:

2x-x=10-6\\ x=4


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