Ask question

Ask question

All categories

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?

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

You might be interested in

Which polynomials are listed with their correct additive inverse? Check all that apply.

mote1985 [20]

Answer:

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

Step-by-step explanation:

Im sure this is correct its been a year since ive learned this i tried my best to remember <3

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

*the reason it is 2x-15 and not 15+2x is because "more than" is considered a "turn around word" meaning it is the opposite

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:

The associative property states that you can add or multiply regardless of how the numbers are grouped.

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