All categories

3 years ago

The measure of ADB is 162 . what is the measure of EAB?

Mathematics

2 answers:

Xelga [282]3 years ago

6 0

An angle formed by a chord and a tangent line is half the measure of the intercepted arc.

The intercepted arc is ADB, which is given as 162 degrees.

Angle EAB = 1/2 of 162

The answer is 81 degrees.

inessss [21]3 years ago

3 0

Answer:

∠EAB = 81°

Step-by-step explanation:

Given : $\widehat{ADB} =162^{\circ}$

Tangent = EF

Chord = AB

To Find: ∠EAB

Solution :

We will use Tangent-Chord Angle Theorem

Tangent-Chord Angle Theorem : An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc

Angle formed by a chord and a tangent that intersect on a circle =∠EAB

Intercepted arc = $\widehat{ADB} =162^{\circ}$

So, by theorem

$\angle {EAB} = \frac{1}{2}\widehat{ADB}$

$\angle {EAB} = \frac{1}{2}\times 162^{\circ}$

$\angle {EAB} = 81^{\circ}$

Hence the measure of ∠EAB is 81°

You might be interested in

Sarah has 25 coins that are dimes and nickels. Together they total $2.00. How many of each type does she have?

Ivanshal [37]

Answer:

15 dimes and 10 nickels

Step-by-step explanation:

15 dimes because 15 multiplied by 10 cents is $1.50

10 nickels because 10 multiplied by 5 cents is $0.50

15 x 0.10 = 1.50 10 x 0.50 = 0.50

0.50 + 1.50 = 2.00

8 0

3 years ago

Read 2 more answers

△ABC has interior angles with measures x°, 90°, and 70°, and △DEF has interior angles with measures y°, 70°, and 20°. Using the

DerKrebs [107]

The letter answer is d

4 0

3 years ago

A triangular lot has sides of 215m, 185m, and 125m. Find the measures of the angles at its corners

Vlada [557]

Answer:

The measures of the angles at its corners are $59.1\°,35.4\°,85.5\°$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle A

Applying the law of cosines

$185^{2}= 215^{2}+125^{2}-2(215)(125)cos(A)$

$2(215)(125)cos(A)= 215^{2}+125^{2}-185^{2}$

$cos(A)= [215^{2}+125^{2}-185^{2}]/(2(215)(125))$ $cos(A)=0.513953$

$A=arccos(0.513953)=59.1\°$

step 2

Find the measure of angle B

Applying the law of cosines

$125^{2}= 215^{2}+185^{2}-2(215)(185)cos(B)$

$2(215)(185)cos(B)= 215^{2}+185^{2}-125^{2}$

$cos(B)= [215^{2}+185^{2}-125^{2}]/(2(215)(185))$ $cos(B)=0.81489$

$B=arccos(0.81489)=35.4\°$

step 3

Find the measure of angle C

Applying the law of cosines

$215^{2}= 125^{2}+185^{2}-2(125)(185)cos(C)$

$2(125)(185)cos(C)= 125^{2}+185^{2}-215^{2}$

$cos(C)= [125^{2}+185^{2}-215^{2}]/(2(125)(185))$ $cos(C)=0.0784$

$C=arccos(0.0784)=85.5\°$

3 0

3 years ago

A genetic experiment involving peas yielded one sample of offspring consisting of 437437 green peas and 129129 yellow peas. Use

navik [9.2K]

Answer:

The null hypothesis: $\mathbf{H_o: p=0.27}$

The alternative hypothesis: $\mathbf{H_1: p \neq 0.27}$

Test statistics : z = −2.30

P-value: = 0.02144

Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.

Conclusion: We accept the alternative hypothesis and conclude that under the same circumstances the proportion of offspring peas will be yellow is not equal to 0.27

Step-by-step explanation:

From the given information:

Let's state the null and the alternative hypothesis;

Since The claim is that 27% of the offspring peas will be yellow.

The null hypothesis state that the proportion of offspring peas will be yellow is equal to 0.27.

i.e

$\mathbf{H_o: p=0.27}$

The alternative hypothesis state that the proportion of offspring peas will be yellow is not equal to 0.27

$\mathbf{H_1: p \neq 0.27}$

<u>The test statistics:</u>

we are given 437 green peas and 129 yellow apples;

Hence;

$\hat p = \dfrac{x}{n}$

where ;

$\hat p$ = sample proportion

x = number of success

n = total number of the sample size

$\hat p = \dfrac{129}{437+129}$

$\hat p = \dfrac{129}{566}$

$\mathbf{\hat p = 0.2279}$

Now; the test statistics can be computed as :

$z = \dfrac { \hat p -p }{\sqrt {\dfrac{p(1-p)}{n} } }$

$z = \dfrac {0.2279 -0.27 }{\sqrt {\dfrac{0.27(1-0.27)}{566} } }$

$z = \dfrac {-0.043 }{\sqrt {\dfrac{0.27(0.73)}{566} } }$

$z = \dfrac {-0.043 }{\sqrt {\dfrac{0.1971}{566} } }$

$z = \dfrac {-0.043 }{\sqrt {3.48233216*10^{-4} } }$

$z = \dfrac {-0.043 }{0.01866} }$

z = −2.30

C. P-value

P-value = P(Z < z)

P-value = P(Z< -2.30)

By using the P-value method and the normal distribution as an approximation to the binomial distribution.

from the table of standard normal distribution

move left until the first column is reached. Note the value as –2.0

move upward until the top row is reached. Note the value as 0.30

find the probability value as 0.010724 by the intersection of the row and column values gives the area to the left of

z = -2.30

P- value = 2P(z ≤ -2.30)

P-value = 2 × 0.01072

P - value = 0.02144

Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.

Conclusion: We accept the alternative hypothesis and conclude that under the same circumstances the proportion of offspring peas will be yellow is not equal to 0.27

8 0

3 years ago

The yearbook club has 5 members returning from last year. They set up a booth in the cafeteria to recruit more members, and an a

boyakko [2]

The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups. So the last answer choice is the right one

6 0

3 years ago

Read 2 more answers