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3 years ago

The composite figure is made up of a rectangle and two pentagons. Find the

Mathematics

1 answer:

NARA [144]3 years ago

4 0

Given:

A composite figure made up of a rectangle and two pentagons.

To find:

The area of the composite shape.

Solution:

If a pentagon has a side length of s and an apothem of a, the area of the pentagon is given by

$A=\frac{5}{2} (a)(s).$

In the given diagram, the pentagons have side lengths of 8 units and an apothem of 5.5 units.

The area of a pentagon $= \frac{5}{2} (5.5)(8) = 110$ sq units.

The area of 2 such pentagons $= 2(110)= 220$ square units.

The rectangle has a length of 14 units and a width of 8 units.

The area of a rectangle $= (l)(w).$

The area of the rectangle $= (14)(8)=112$ square units.

The area of the composite shape is the sum of the individual areas of the different shapes.

The area of the composite shape $=220+112=332$ sq units.

The area of the composite shape is option A. 332 sq units.

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4 years ago

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earnstyle [38]

Answer:

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{1.307 -0}{\frac{7.798}{\sqrt{14}}}=0.6271$

df=n-1=14-1=13

$p_v =P(t_{(13)}>0.6271) =0.2707$

Step-by-step explanation:

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.

Let put some notation

x=test value CL , y = test value CO

x: 57.8 35.7 54.5 56.8 51.1 70.8 77.3 51.6 54.7 63.6 59.2 59.2 55.8 38.5

y: 44.7 52.1 60.2 52.7 47.2 65.6 71.4 48.8 53.1 66.3 59.8 47.5 64.5 34.4

The system of hypothesis for this case are:

Null hypothesis: $\mu_x- \mu_y \leq 0$

Alternative hypothesis: $\mu_x -\mu_y >0$

The first step is calculate the difference $d_i=x_i-y_i$ and we obtain this:

d: 13.1, -16.4,-5.7,4.1,3.9,5.2,5.9,2.8,1.6,-2.7,-0.6,11.7,-8.7,4.1

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{29}{8}=1.307$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =7.798$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{1.307 -0}{\frac{7.798}{\sqrt{14}}}=0.6271$

The next step is calculate the degrees of freedom given by:

$df=n-1=14-1=13$

Now we can calculate the p value, since we have a right tailed test the p value is given by:

$p_v =P(t_{(13)}>0.6271) =0.2707$

So the p value is higher than the significance level provided of 0.01, so then we can conclude that we FAIL to reject the null hypothesis that the difference mean between after and before is higher or equal than 0. So we can't conclude that the mean neck rotation is greater in the clockwise direction than in the counterclockwise direction at 1% of significance.

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4 years ago

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3 years ago