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Nuetrik [128]
2 years ago
6

does somebody knows how to do this one?

Mathematics
1 answer:
vlada-n [284]2 years ago
6 0

Answer:

Step-by-step explanation:

To find the area subtract the area of the semicircle from the area of the rectangle.

Although the line isn’t there, if you imagine there is one, then you will see that you form a rectangle which is the same line as the semicircle’s diameter.

The area of rectangle is:

⇒ A = lw

⇒ A = (14)(8)

⇒ A = 112cm^{2}

The area of the semicircle;

⇒ A = \frac{1}{2}\pi r^{2}

⇒ A = \frac{1}{2}\pi (7)^{2}

*Note here that the radius is half the diameter, so it is 7cm, not 14cm

⇒ A = 76.97cm^{2}

Finally subtract the two areas;

⇒ A = 112 - 76.97

⇒ A = 35.03cm^{2}

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Read 2 more answers
In a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per
alexdok [17]

Answer:

The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.

Step-by-step explanation:

We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.

In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.

Let p_1 = <u><em>population proportion of cars driven at high altitudes who exceeded a standard of 10 grams</em></u>.

p_2 = <u><em>population proportion of cars driven at low altitudes who exceeded a standard of 10 grams</em></u>.

So, Null Hypothesis, H_0 : p_1\leq p_2      {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}

Alternate Hypothesis, H_A : p_1>p_2      {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}

The test statistics that will be used here is <u>Two-sample z-test statistics</u> for proportions;

                             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 cars driven at high altitudes who exceeded a standard of 10 grams = \frac{24}{90} = 0.27

\hat p_2 = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = \frac{42}{380} = 0.11

n_1 = sample of cars driven at high altitudes = 90

n_2 = sample of cars driven at low altitudes = 380

So, the test statistics =  \frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }      

                                   =  3.234

The value of z-test statistics is 3.234.

7 0
3 years ago
The sum of the measures of the angles of any triangle is 180 degrees. in triangle​ abc, angles a and b have the same​ measure, w
frutty [35]
<span>Its given that the sum of the values of total angles of a triangle is 180. It is also given that angles a and b are equal and that value of c is 72. Thus we get the following equation:
   
a + b + c = 180
   
a + a + 72 = 180 since a = b

2a = 108
   
a = b = 54 and c = 72</span>
7 0
3 years ago
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