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My name is Ann [436]
3 years ago
9

A square building with an area of 225 m2 has a garden surrounding it that has an equal width on all sides. The area of the garde

n is 1/3 of the area of the building. What is the width of the garden?

Mathematics
1 answer:
xenn [34]3 years ago
8 0

Answer:

The width of the garden is 1.16 m

Step-by-step explanation:

step 1

<em>Find the area of the garden</em>

To find out the area of the garden multiply by 1/3 the area of the building

225(\frac{1}{3})=75\ m^2

step 2

Find the length side of the square building

The area of a square is

A=b^2

where

b is the length side of the square

we have

A=225\ m^2

so

b^2=225\\b=15\ m

step 3

Find the width of the garden

Let

x ----> the width of the garden

we know that

The area of the building plus the area of the garden is equal to

(15+2x)^2=225+75

solve for x

225+60x+4x^2=225+75\\4x^2+60x-75=0

Solve the quadratic equation by graphing

using a graphing tool

The  solution is x=1.16 m

see the attached figure

therefore

The width of the garden is 1.16 m

Find the exact value

The formula to solve a quadratic equation of the form ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

4x^2+60x-75=0  

so

a=4\\b=60\\c=-75

substitute in the formula

x=\frac{-60\pm\sqrt{60^{2}-4(4)(-75)}} {2(4)}

x=\frac{-60\pm\sqrt{4,800}} {8}

x=\frac{-60\pm40\sqrt{3}} {8}

x=\frac{-60+40\sqrt{3}} {8}\ m  ----> exact value

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Answer:

z= \frac{3.44-2.54}{0.45}=2

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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Solution to the problem

Let X the random variable that represent the grade points avergae of a population, and for this case we know the following properties

Where \mu=2.54 and \sigma=0.45

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

So we can find the z score for the value of X=3.44 in order to see how many deviations above or belowe we are from the mean like this:

z= \frac{3.44-2.54}{0.45}=2

So the value of 3.44 is 2 deviations above from the mean, so then we know that the percentage between two deviations from the mean is 95% and on each tail we need to have (100-95)/2 = 2.5% , because the distribution is symmetrical, so based on this we can conclude that:

P(X>3.44) = P(Z>2) = 0.025

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leva [86]

Answer:

x  ≤ – 3 or x ≥ 9.

Step-by-step explanation:

Given  : 9x ≤ –27 or 4x ≥ 36.

To find : Solve the compound inequality.

Solution : We have given  9x ≤ –27 or 4x ≥ 36.

For 9x ≤ –27 .

On dividing both sides by 9.

x  ≤ – 3.

For ,  4x ≥ 36.

On dividing both sides by 4.

x ≥ 9.

We can write x  ≤ – 3 or x ≥ 9.

Therefore,  x  ≤ – 3 or x ≥ 9.

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Two ships leave a harbor at the same time. One ship travels on a bearing Upper S 14 degrees Upper W at 15 miles per hour. The ot
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Answer:

69.94 miles

Step-by-step explanation:

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The angle the first ship's direction makes in the North-East direction is 90° - 75° = 15°

The angle the second ship's direction makes in the South-West direction  = 14°

The distance moved by the two ships form the side of a triangle. The angle,  θ between the two ship directions is 14° + 90° + 15° = 119°

Using the cosine rule, we find the distance d between the two ships

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= √(3321 + 1570.78)

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Answer:

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Step-by-step explanation:

We want to simplify

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