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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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Answer:

The Numbers with no Variable (x,y) and an additive sign are the correct additive inverse

Step-by-step explanation:

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4 0
3 years ago
The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees ba
blsea [12.9K]

Answer:

The test statistic is z = -2.11.

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Group 1: Sample of 35, mean of 1276, standard deviation of 347.

This means that:

\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537

Group 2: Sample of 35, mean of 1439, standard deviation of 298.

This means that:

\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712

Test if there is a difference in productivity level.

At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So

H_0: \mu_1 - \mu_2 = 0

At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So

H_1: \mu_1 - \mu_2 \neq 0

The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

From the two samples:

X = \mu_1 - \mu_2 = 1276 - 1439 = -163

s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144

Test statistic:

z = \frac{X - \mu}{s}

z = \frac{-163 - 0}{77.3144}

z = -2.11

The test statistic is z = -2.11.

7 0
3 years ago
Fifteen more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by
lapo4ka [179]
2x-15=3(x-15) 
2x-15=3x-45
2x+30=3x
30=x

Let's check this work!

2(30)-15=3(30-15)
60-15=3(15)
45=45

She worked 45 hours each week

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3 0
3 years ago
Alondra says that (12 + 31) × 5 is equivalent to 12 + 31 × 5 because of the associative property.
Tju [1.3M]

Answer:

Step-by-step explanation:

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5 0
3 years ago
Read 2 more answers
Tickets to the zoo cost $12 for adults and $8 for children. The school has a budget of $240 for the field trip. An equation repr
Oxana [17]

Answer:

18 children

Step-by-step explanation:

Given

240 = 12x +8y

<em>Required (missing part of the question):</em>

<em>Number of children that will be able to go to the zoo if 8 adult tickets are purchased</em>

 

<em>The graph is missing. However, the question can be solved without the graph.</em>

<em />

From the question and equation, we can deduce the following:

  • x represents adults
  • y represents children

So, when 8 adult tickets were sold.

This means

x = 8

Substitute 8 for x in 240 = 12x +8y

240= 12 * 8 + 8y

240= 96+ 8y

Subtract 96 from both sides

240 - 96 = 96 - 96 + 8y

144 =  8y

8y = 144

Solve for y

y= \frac{144}{8}

y= 18

<em>This means that 18 children will be able to go</em>

5 0
3 years ago
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