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3 years ago

A swimming pool at a park measures 9.75 meters by 7.2 meters.

Mathematics

1 answer:

neonofarm [45]3 years ago

6 0

Answer:

Part a) The area of the swimming pool is $70.2\ m^2$

Part b) The total area of the swimming pool and the playground is $105.3\ m^2$

Step-by-step explanation:

Part a) Find the area of the swimming pool

we know that

The area of the swimming pool is

$A=LW$

where

L is the length side

W is the width side

we have

$L=9.75\ m\\W=7.2\ m$

substitute the values

$A=(9.75)(7.2)$

$A=70.2\ m^2$

therefore

The area of the swimming pool is $70.2\ m^2$

Part b) The area of the playground is one and a half times that of the swimming pool. Find the total area of the swimming pool and the playground

we know that

To obtain the area of the playground multiply the area of the swimming pool by one and a half

$\frac{1}{2}(70.2)=35.1\ m^2$

To obtain the total area of the swimming pool and the playground, adds the area of the swimming pool and the area of the playground

$70.2\ m^2+35.1\ m^2=105.3\ m^2$

therefore

The total area of the swimming pool and the playground is $105.3\ m^2$

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The mean number of words per minute (WPM) read by sixth graders is 97 with a standard deviation of 19 WPM. If 75 sixth graders a

andrey2020 [161]

Answer:

0.0174 = 1.74% probability that the sample mean would be greater than 101.63 WPM

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this problem, we have that:

$\mu = 97, \sigma = 19, n = 75, s = \frac{19}{\sqrt{75}} = 2.1939$

What is the probability that the sample mean would be greater than 101.63 WPM?

This is 1 subtracted by the pvalue of Z when X = 101.63. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{101.63 - 97}{2.1939}$

$Z = 2.11$

$Z = 2.11$ has a pvalue of 0.9826.

1 - 0.9826 = 0.0174

0.0174 = 1.74% probability that the sample mean would be greater than 101.63 WPM

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3 years ago

What is the approximate circumference of a circle with a diameter of 500 kilometers? Use π ≈ 3.14.. . A.. 785 kilometers. . B..

Anestetic [448]

3.14×500= 1570 kilometers

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4 years ago

Read 2 more answers

BRAINLIESTTTTTT ASAPPPP<br> PLEASE ANSWER MY QUESTION

yawa3891 [41]

The red line is represented by y ≥ -3x + 3.

The blue line is represented by y < 3/2x - 6.

A) In this system of inequalities, there is one solid line and one dashed line.

The solid line is the inequality y ≥ -3x + 3 because it has the symbol greater than or equal to. The "equal to" part of the symbol is important because it means that any coordinate located on the solid line is a solution.

However, the inequality y < 3/2x - 6 is a dashed line because it does not have "equal to." This makes the inequality a dashed line which means that all coordinates on it will not be a solution to the inequality.

In the inequality y ≥ -3x + 3, the shading is above the line. This means that all coordinates within the line and shaded area above the line will be a solution to the inequality.

In the inequality y < 3/2x - 6, the shading is below the line. This means that all coordinates within the shared area of the line will be a solution to the inequality. However, since y is not less than or EQUAL TO, all coordinates within the dashed line is not a solution to the inequality.

The solution area, where a coordinate is a solution to
both inequalities, is where the shaded areas of both inequalities overlap.

B) The point (-6, 3) is a not solution to both of the inequalities because it is not within the shared areas of the two inequalities.

Substitute the coordinate (-6, 3) in the inequality y < 3/2x - 6.

y < 3/2x - 6

3 < 3/2(-6) - 6

3 < -9 - 6

3 < -15

This is not true because a negative number cannot be greater than a positive number. Therefore, this proves that the coordinate (-6, 3) is not a solution for the inequality y < 3/2x - 6.

Check if the coordinate fits for the other inequality.

y ≥ -3x + 3

3 ≥ -3(-6) + 3

3 ≥ 18 + 3

3 ≥ 21

This is also not true because 3 is not greater than or equal to 21. Therefore, this coordinate is not a solution to the inequality y ≥ -3x + 3.

The coordinate (-6, 3) is not a solution for the system of inequalities because it is not a solution for both inequalities.

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4 years ago

8p + 2q = -16<br> 2p - q=2

yKpoI14uk [10]

Answer:

p = -1 q = -4

Step-by-step explanation:

a system of eq and solve for p and q ??? can do :)

Eq. 1) 8p + 2q = - 16

Eq. 2) 2p - q = 2

use Eq .2 and solve for q

2p - 2 = q

plug into Eq.1 with q

8p +2(2p - 2) = - 16

8p +4p -4 = -16

12p = - 12

p = -1

plug -1 into Eq. 1 for p and solve for q

8(-1) + 2q = - 16

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2q = -8

q = -4

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3 years ago

What is the measure ?

Ivenika [448]

Check the picture below.

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3 years ago