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Furkat [3]
3 years ago
15

1. Find the area of parallelogram ABCD.

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
5 0

Answer:

1: C =69.3 m2

2: F = ll units

3. C:  3 in.

4. G =65 units

Step-by-step explanation:

1: C =69.3 m2

We see from the figure that height of the parallelogram ABCD is not known and the base is 10 m

Taking the right angled triangle the height is given by

Sine theta= height/hypotenuse

height = hypotenuse* sine theta

         = 8* sine 60

         = 8* 0.866= 6.928

Area of parallelogram= base * height

                   = 10 * 6.928

                   = 69.28

                  =69.3 m²

2: F = ll units

We see from the figure that height of the parallelogram DEFG is not known and the base is 13 cm

Area of parallelogram= base * height

                  143 = 13 * height

           Height = 143/13= 11 units

3. C:  3 in.

The area of the triangle = 1/2 * base * height

Let the height be x then the base is 3x

54= 1/2*x*3x

54= 3x²/2

27= 3x²

x²=27/3

x²= 9

x= 3

The height is 3 inches

4. G =65 units

Area of the quadrilateral = 1/2 *PR*QO + 1/2 *PR*OS

                                      = 1/2*13*4+ 1/2*13*6

                                        =26+ 39

                                        = 65 units

These measurements are given in the diagram .

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bagirrra123 [75]
It’s B



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Answer:

a) 29.4-1.96\frac{7}{\sqrt{10}}=25.06  

29.4+1.96\frac{7}{\sqrt{10}}=33.74  

So on this case the 95% confidence interval would be given by (25.06;33.74)  

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p_v =P(z>1.988)=0.0234    

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\mu population mean (variable of interest)  

\sigma=7 represent the population standard deviation  

n=10 represent the sample size  

95% confidence interval  

The confidence interval for the mean is given by the following formula:  

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96  

Now we have everything in order to replace into formula (1):  

29.4-1.96\frac{7}{\sqrt{10}}=25.06  

29.4+1.96\frac{7}{\sqrt{10}}=33.74  

So on this case the 95% confidence interval would be given by (25.06;33.74)  

Part b

What are H0 and Ha for this study?  

Null hypothesis:  \mu \leq 25  

Alternative hypothesis :\mu>25  

Compute the test statistic

The statistic for this case is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

We can replace in formula (1) the info given like this:  

z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988  

Give the appropriate conclusion for the test

Since is a one side right tailed test the p value would be:  

p_v =P(z>1.988)=0.0234  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis.    

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800,00 rounded to the nearest hundred thousand
lisov135 [29]

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Answer:

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Step-by-step explanation:

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