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3 years ago

Using the drawing, if the measure of angle 2 is 42° and the measure of angle 3 is 52°, what is the measure of angle 6?

Mathematics

2 answers:

photoshop1234 [79]3 years ago

7 0

Answer:

Option D is correct

94° is the measure of angle 6

Step-by-step explanation:

Exterior angle theorem states the sum of the measures of the two non-adjacent interior angles of the triangle.

As per the statement:

if the measure of angle 2 is 42° and the measure of angle 3 is 52°.

$\angle 2 = 42^{\circ}$

$\angle 3= 52^{\circ}$

By definition of exterior angle we have;

$\angle 6 = \angle 2 + \angel 3$

Substitute the given values we have;

$\angle 6 = 42^{\circ}+52^{\circ}$

Simplify:

$\angle 6 = 94^{\circ}$

Therefore, the measure of angle 6 is, 94 degree.

Anarel [89]3 years ago

5 0

The answer is D. 94°

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Write the number in scientific notation.<br> 1,920,000

LUCKY_DIMON [66]

The answer is 1.92 x 10^6

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3 years ago

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

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3 years ago

5.which of the following ordered pairs is a solution of the given system of linear equations

liq [111]

Answer:

the answer is d

Step-by-step explanation:

answers are shown