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2 years ago

Triangle ABC is similar to triangle QRS by the AA Similarity Postulate. Also, m∠A = 32° and m∠S = 102°. What is m∠B?

1 answer:

5 0

The sum of interior angles of any polygon is:

s=180(n-2)

Since we are dealing with a triangle:

s=180(3-2)

s=180°

That is, the sum of angles of any triangle is 180°.

In this case we are given two angles with measures of 32° and 102° so

a+b+c=180

32+b+102=180 combine like terms on left

b+134=180 subtract 134 from both sides

b=46°

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Can anybody help me with this ?

BabaBlast [244]

Answer:

1st scenario: 163.3°

2nd scenario: 125.2°

3rd scenario: 142.3°

Step-by-step explanation:

1st scenario: angles 1 and 2 form a linear pair and add up to 180

2nd scenario: angles 1 and 4 are same-side interior and add up to 180

3rd scenario: angles 1 and 8 are corresponding and equal; if angle 7 is 37.7 then angle 8 is 142.3 (they form a linear pair). Since angles 1 and 8 are equal then angle 1 is also 142.3

6 0

2 years ago

In the year 2007, a person bought a new car for $23500. For each consecutive year after that, the value of the car depreciated b

Alexandra [31]

Answer:

17155

Step-by-step explanation:

23500-27%-17155

To the nearest hundred: 17200.

8 0

2 years ago

Identify the scale factor Photograph: height 3 in. Painting: height 24 in.

Finger [1]

Answer:

Step-by-step explanation:

The new height is 24

The original height is 3

24/3 is 8

The scale factor is 8

6 0

3 years ago

In 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alc

Fynjy0 [20]

Answer:

We conclude that the proportion of adults who totally abstain from alcohol has changed.

Step-by-step explanation:

We are given that in 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?"

Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 in

Let p = proportion of adults who totally abstain from alcohol.

where, p = $\frac{429}{1100}$ = 0.39

So, Null Hypothesis, $H_0$ : p = 39% {means that the proportion of adults who totally abstain from alcohol has not changed}

Alternate Hypothesis, $H_A$ : p $\neq$ 39% {means that the proportion of adults who totally abstain from alcohol has changed}

The test statistics that would be used here One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who totally abstain from alcohol = $\frac{352}{1100}$ = 0.32

n = sample of adults surveyed = 1100

So, test statistics = $\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }$

= -4.976

The value of z test statistics is -4.976.

Now, at 0.10 significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of adults who totally abstain from alcohol has changed.

4 0

2 years ago

6.75 + StartFraction 3 Over 8 EndFraction x = 13 and one-fourth

amid [387]

Easy the answer is B: 17 and one-third

3 0

3 years ago

Read 2 more answers