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labwork [276]
2 years ago
6

The perimeter of a flower garden with three sides is 46 feet. One side of the garden is 11 feet long. Another side of the garden

is 13 feet long. What is the length of the third side? Enter your answer in the box. feet
Mathematics
1 answer:
saul85 [17]2 years ago
7 0

Answer:

<h2>22ft</h2>

Step-by-step explanation:

Step one:

given that the orientation of the garden is a triangular shape(it has three sides)

the perimeter is given as=46ft

one side y=11ft

the second side z= 13ft

let the third side be xft

Step two:

the expression for the perimeter = z+y+x

46=11+13+x

46=24+x

solve for x

x=46-24

x=22ft

Therefore the third side is 22ft long

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Answer:

Ratio = \frac{R^2 - r^2 }{ r^2}

Step-by-step explanation:

Given

See attachment for circles

Required

Ratio of the outer sector to inner sector

The area of a sector is:

Area = \frac{\theta}{360}\pi r^2

For the inner circle

r \to radius

The sector of the inner circle has the following area

A_1 = \frac{\theta}{360}\pi r^2

For the whole circle

R \to Radius

The sector of the outer sector has the following area

A_2 = \frac{\theta}{360}\pi (R^2 - r^2)

So, the ratio of the outer sector to the inner sector is:

Ratio = A_2 : A_1

Ratio = \frac{\theta}{360}\pi (R^2 - r^2) : \frac{\theta}{360}\pi r^2

Cancel out common factor

Ratio = R^2 - r^2 : r^2

Express as fraction

Ratio = \frac{R^2 - r^2 }{ r^2}

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Solve the inequality 5u≤8u−21 and write the solution in interval notation
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Step-by-step explanation:

5u\leq 8u-21

Subtract 8u from both sides

-3u\leq -21

Divide by -3 on both sides

u\geq 7

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[7,∞)

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Dillion divided a 3 1/3 pound bag of pears among his 5 friends. How many pounds of pears does did each friend revive?
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The pesticide diazinon is in common use to treat infestations of the German cockroach, Blattella germanica. A study investigated
cluponka [151]

Answer:

We conclude that there is no difference in the proportion of cockroaches that died on each surface.

Step-by-step explanation:

We are given that a study investigated the persistence of this pesticide on various types of surfaces.

After 14 days, they randomly assigned 72 cockroaches to two groups of 36, placed one group on each surface, and recorded the number that died within 48 hours. On the glass, 18 cockroaches died, while on plasterboard, 25 died.

<em>Let </em>p_1<em> = proportion of cockroaches that died on glass surface.</em>

<em />p_2<em> = proportion of cockroaches that died on plasterboard surface.</em>

So, Null Hypothesis, H_0 : p_1-p_2 = 0      {means that there is no difference in the proportion of cockroaches that died on each surface}

Alternate Hypothesis, H_A : p_1-p_2\neq 0      {means that there is a significant difference in the proportion of cockroaches that died on each surface}

The test statistics that would be used here <u>Two-sample z proportion</u> <u>statistics</u>;

                       T.S. =  \frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}  } }  ~ N(0,1)

where, \hat p_1 = sample proportion of cockroaches that died on glass surface = \frac{18}{36} = 0.50

\hat p_2 = sample proportion of cockroaches that died on plasterboard surface = \frac{25}{36} = 0.694

n_1 = sample of cockroaches on glass surface = 36

n_2 = sample of cockroaches on plasterboard surface = 36

So, <u><em>test statistics</em></u>  =  \frac{(0.50-0.694)-(0)}{\sqrt{\frac{0.50(1-0.50)}{36}+\frac{0.694(1-0.694)}{36}  } }

                               =  -1.712

The value of z test statistics is -1.712.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that there is no difference in the proportion of cockroaches that died on each surface.

8 0
3 years ago
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