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Igoryamba
3 years ago
15

A pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. If the area of the pool and the path combined

is 1440 square meters, what is the width of the path?
Mathematics
1 answer:
suter [353]3 years ago
5 0

Answer: the width of the uniform path is 9 meters.

Step-by-step explanation:

Let x represent the width of the uniform path.

A pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. It means that the combined length of the pool and the uniform path is (18 + 2x) meters and the combined width of the pool and the uniform path is (22 + 2x) meters.

If the area of the pool and the path combined is 1440 square meters, it means that

(18 + 2x)(22 + 2x) = 1440

396 + 36x + 44x + 4x² = 1440

4x² + 80x + 396 - 1440 = 0

4x² + 80x - 1044 = 0

Dividing both sides of the equation by 4, it becomes

x² + 20x - 261 = 0

x² + 29x - 9x - 261 = 0

x(x + 29) - 9(x + 29) = 0

x - 9 = 0 or x + 29 = 0

x = 9 or x = 29

Since the width cannot be negative, then x = 9 meters

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3 years ago
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Step-by-step explanation:

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2 years ago
When Ryan is serving at a restaurant, there is a 0.75 probability that each party will order drinks with their meal. During one
Triss [41]

Answer:

0.82 = 82% probability that at least one party will not order drinks

Step-by-step explanation:

For each party, there are only two possible outcomes. Either they will order drinks with their meal, or they will not. The probability of a party ordering drinks with their meal is independent of other parties. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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And p is the probability of X happening.

When Ryan is serving at a restaurant, there is a 0.75 probability that each party will order drinks with their meal.

This means that p = 0.75

During one hour, Ryan served 6 parties. Assuming that each party is equally likely to order drinks, what is the probability that at least one party will not order drinks?

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Either all parties will order drinks, or at least one will not. The sum of the probabilities of these events is decimal 1. So

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We want P(X < 6). So

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P(X = 6) = C_{6,6}.(0.75)^{6}.(0.25)^{0} = 0.18

P(X < 6) = 1 - P(X = 6) = 1 - 0.18 = 0.82

0.82 = 82% probability that at least one party will not order drinks

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3 years ago
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Answer:

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