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Elden [556K]
3 years ago
5

Mathematical connections

Mathematics
1 answer:
Anna71 [15]3 years ago
8 0
RS + ST = RT

a.
2x + 10 + x - 4 = 21
3x + 6 = 21
3x = 21 - 6
3x = 15
x = 15/3
x = 5
RS = 2x + 10 = 2*5 + 10 = 10 + 10 = 20
ST = x - 4 = 5 - 4 = 1

b.
3x - 16 + 4x - 8 = 60
7x - 24 = 60
7x = 60 + 24
7x = 84
x = 84/7
x = 12
RS = 3x - 16 = 3*12 - 16 = 36 - 16 = 20
ST = 4x - 8 = 4*12 - 8 = 48 - 8 = 40

c.
2x - 8 + 11 = x + 10
2x + 3 = x + 10
2x - x = 10 - 3
x = 7
RS = 2x - 8 = 2*7 - 8 = 14 - 8 = 6
RT = x + 10 = 7 + 10 = 17

d.
4x - 9 + 19 = 8x - 14
4x + 10 = 8x - 14
10 + 14 = 8x - 4x
24 = 4x
x = 24/4
x = 6 
RS = 4x - 9 = 4*6 - 9 = 24 - 9 = 15
RT = 8x - 14 = 8*6 - 14 = 34
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The arrivals of clients at a service firm in Santa Clara is a random variable from Poisson distribution with rate 2 arrivals per
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Answer:

1.76% probability that in one hour more than 5 clients arrive

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

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The arrivals of clients at a service firm in Santa Clara is a random variable from Poisson distribution with rate 2 arrivals per hour.

This means that \mu = 2

What is the probability that in one hour more than 5 clients arrive

Either 5 or less clients arrive, or more than 5 do. The sum of the probabilities of these events is decimal 1. So

P(X \leq 5) + P(X > 5) = 1

We want P(X > 5). So

P(X > 5) = 1 - P(X \leq 5)

In which

P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353

P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707

P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707

P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1804

P(X = 4) = \frac{e^{-2}*2^{4}}{(4)!} = 0.0902

P(X = 5) = \frac{e^{-2}*2^{5}}{(5)!} = 0.0361

P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.1353 + 0.2702 + 0.2702 + 0.1804 + 0.0902 + 0.0361 = 0.9824

P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9824 = 0.0176

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