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vladimir1956 [14]
2 years ago
10

Mr. Hammond is the volunteer coordinator for a company that puts on running races. Last year, the company organized 7 short race

s and 8 long races, which required a total of 804 volunteers. This year, the company organized 11 short races and 5 long races, which required 688 volunteers in total. How many volunteers does each type of race require?
Mathematics
1 answer:
worty [1.4K]2 years ago
4 0

Answer:

28 short race volunteers

76 long race volunteers

Step-by-step explanation:

Let :

Short races = a

Long races = b

LAST YEAR:

7a + 8b = 804 - - - - (1)

THIS YEAR:

11a + 5b = 688 - - - (2)

Multiply (1) by 5 and (2) by 8

35a + 40b = 4020

88a + 40b = 5504

Subtract

-53a = - 1484

a = 1484 / 53

a = 28

Put a = 28 in equation (1)

7(28) + 8b = 804

196 + 8b = 804

8b = 804 - 196

8b = 608

b = 76

28 short race volunteers

76 long race volunteers

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Part b: <em>The probability of three or fewer passengers arrive in a one-minute period is 0.0103.</em>

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P\left( {X = x} \right) = \frac{{{e^{ - \lambda }}{{\left( {10} \right)}^x}}}{{x!}}

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<em>The probability of no arrivals in a one-minute period is 0.000045.</em>

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The probability mass function of X can be written as,

P\left( {X = x} \right) = \frac{{{e^{ - \lambda }}{\lambda ^x}}}{{x!}};x = 0,1,2, \ldots

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Part c:

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<em>The probability of no arrivals in a 15-second is 0.0821.</em>

Part d:  

The probability that there is at least one arrival in a 15-second period is calculated as,

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<em>The probability of at least one arrival in a 15-second period​ is 0.9179.</em>

​

​

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3 years ago
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