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3 years ago

Find the area of the shape shown below.

Mathematics

1 answer:

Sveta_85 [38]3 years ago

4 0

Answer:

<em>32 units² </em>

Step-by-step explanation:

$A_{1}$ = 4(2 + 2 + 6) ÷ 2 = 20

$A_{2}$ = (2 × 2) ÷ 2 = 2

$A_{3}$ = 2² = 4

$A_{4}$ = 2 × 6 ÷ 2 = 6

A = $A_{1}$ + $A_{2}$ + $A_{3}$ + $A_{4}$ = <em>32 units²</em>

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Many elementary school students in a school district currently have ear infections. A random sample of children in two different

Marta_Voda [28]

Answer:

Step-by-step explanation:

The summary of the given data includes;

sample size for the first school $n_1$ = 42

sample size for the second school $n_2$ = 34

so 16 out of 42 i.e $x_1$ = 16 and 18 out of 34 i.e $x_2$ = 18 have ear infection.

the proportion of students with ear infection Is as follows:

$\hat p_1 = \dfrac{16}{42}$ = 0.38095

$\hat p_2 = \dfrac{18}{34}$ = 0.5294

Since this is a two tailed test , the null and the alternative hypothesis can be computed as :

$H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0$

level of significance ∝ = 0.05,

Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.

The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.

$\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}$

$\bar p = \dfrac{16 +18}{42 +34}$

$\bar p = \dfrac{34}{76}$

$\bar p = 0.447368$

$\bar p + \bar q = 1 \\ \\ \bar q = 1 -\bar p \\ \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632$

The pooled standard error can be computed by using the formula:

$S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} + \dfrac{\bar p \bar p}{n_2} }$

$S.E = \sqrt{ \dfrac{ 0.447368 * 0.552632}{ 42} + \dfrac{ 0.447368 * 0.447368}{34} }$

$S.E = \sqrt{ \dfrac{ 0.2472298726}{ 42} + \dfrac{ 0.2001381274}{34} }$

$S.E = \sqrt{ 0.01177284105}$

$S.E = 0.1085$

The test statistics is ;

$z = \dfrac{\hat p_1 - \hat p_2}{S.E}$

$z = \dfrac{0.38095- 0.5294}{0.1085}$

$z = \dfrac{-0.14845}{0.1085}$

z = - 1.368

Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools

5 0

3 years ago

Solve for x. (TYPE ONLY THE NUMBER FOR YOUR ANSWER).

scoray [572]

9514 1404 393

Answer:

x = 7

Step-by-step explanation:

The sum of angle measures in a quadrilateral is 360°.

(8x-5)° +107° +83° +119° = 360°

8x = 56 . . . . . . . divide by °, subtract 304

x = 7 . . . . . . . . . . divide by 8

3 0

3 years ago

Question 5 of 20

Cerrena [4.2K]

Answer:

it is d i am 20 percent postive

6 0

3 years ago

Which of the following functions is graphed below?

Butoxors [25]

Answer:

Option (B)

Step-by-step explanation:

Given question is not complete; find the complete question in the attachment.

In the graph attached,

Parent function is an absolute value function,

f(x) = |x|

When this graph is shifted 4 units left, rule for the translation will be,

f(x) → f(x + 4)

Therefore, the new function of above translation will be,

g(x) = f(x + 4) = |x + 4|

Now the graph is shifted 2 units down so the translated function will be,

h(x) = g(x) - 2

h(x) = |x + 4| - 2

If we rewrite the function in the form of an equation, graph will be represented by

⇒ y = |x + 4| - 2

Therefore, Option (B) will be the answer.

8 0

3 years ago

Explain the effect level of significance and sample size have on hypothesis testing results. Provide an example and explain how

Scorpion4ik [409]

Solution :

The level of significance refers to the probability of the null hypothesis that may be rejected in the study by the observer. As the sample size increases, the p value also increases but the significance remains same. When the sample size increase and becomes large, the null hypothesis can be rejected more easily.

The business decisions are taken defending the significance level of the statistical validation in cases of uncertainty. Suppose the null hypothesis is the sales after the marketing campaigning remains same. The company will launch the marketing campaign when the confidence level is 95% so that after the campaign the sales will increase. It means that the significance level must be high enough for rejecting null hypothesis of sales post of the marketing campaign that remains same.

When the sample size increases, the sensitivity of hypothesis increases, and for a large sample, the hypothesis may be rejected even though it is true.

4 0

3 years ago