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3 years ago

Which of the following is the measure of one of the central angles of a regular octagon?

Mathematics

2 answers:

Lena [83]3 years ago

5 0

General Idea:

The measure of one of the central angles of a regular Polygon ( $\theta$ ) can be used using the below formula:

$\theta= \frac{360^{\circ}}{n} \\\\Where: \\\; n\; is\; number\; of\; sides\; of\; regular\; polygon$

Applying the concept:

The measure of one of the central angles of a regular octagon.

The octagon have 8 sides, using the above formula we get...

$\theta= \frac{360}{n} \\\\\theta = \frac{360}{8} = 45^{\circ}$

Conclusion:

The correct option is <em><u>A) 45 degrees</u></em>

vekshin13 years ago

5 0

A. 45 degrees. Smsmsnsmms

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Let X denote the total snowfall in the Twin Cities in December of a given year, measured in centimeters. The five-number summary

Gre4nikov [31]

Answer:

Concept: Caclulating Standard Variables

We have a five number summary which is more than enough information to calculate our mean.
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3 years ago

What is always true about vertical lines

natta225 [31]

Answer:

Vertical lines have undefined (or no) slope always, so this is a true statement. To see why, look at a horizontal line (which is perpendicular). They have zero slope. That comes from the y = mx + b slope intercept form and their equation being y = b, and b is some number.

Step-by-step explanation:

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2 years ago

Read 2 more answers

A local car dealer claims that 25% of all cars in San Francisco are blue. You take a random sample of 600 cars in San Francisco

Delvig [45]

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test.

For the null hypothesis,

p = 0.25

For the alternative hypothesis,

p ≠ 0.25

b) The test statistic to be used is the z test. The formula is

z = (P - p)/√pq/n

c) Considering the population proportion, probability of success, p = 0.25

q = probability of failure = 1 - p

q = 1 - 0.25 = 0.75

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 141

n = number of samples = 600

P = 141/600 = 0.235

Therefore

z = (0.235 - 0.25)/√(0.25 × 0.75)/600 = - 0.85

d) Recall, population proportion, p = 0.25

The difference between sample proportion and population proportion is 0.25 - 0235. = 0.015

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.25 - 0.015 = 0.235

the p for the right tail is 0.25 + 0.015 = 0.265

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail 0.198

We would double this area to include the area in the right tail of z = 0.85. Thus

p = 0.198 × 2 = 0.396

e) Since alpha, 0.01 < than the p value, 0.396, then we would fail to reject the null hypothesis.

f) In a sample of 600 cars, we would observe a sample proportion of 0.015 or more away from 0.25 about 39.6% of the time by chance alone. Therefore, the sample result is not statistically significant because it could occur in 39.6% of the time by chance alone.

8 0

3 years ago

Joy Co. allocates overhead expenses to all departments on the basis of floor space (sq. ft.) occupied by each department. This y

salantis [7]

The ratio between the departments is

A: B: C
15000 : 18000 : 9000
15 : 18 : 9
5 : 6 : 3

The budget needs to be divided into 5+6+3 = 14 parts
The budget for one part is 22000/14

The budget for department B is $\frac{22000}{14}*6=9428.571428$
Rounded to the nearest dollar, the budget is $9429

7 0

3 years ago

The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginnin

vazorg [7]

Answer:

$z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784$

$p_v =2*P(Z>1.784) =0.074$

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the two proportions differes at 10% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=42$ represent the number of infested vines for Pernod5

$X_{2}=22$ represent the number of infested vines for Action

$n_{1}=440$ sample of Pernod5

$n_{2}=360$ sample of Action

$\hat p_{1}=\frac{42}{440}=0.0955$ represent the proportion of residents of infested vines for Pernod5

$\hat p_{2}=\frac{22}{360}=0.0611$ represent the proportion of infested vines for Action

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.1$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between thw two population proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} - p_{2}=0$

Alternative hypothesis: $p_{1} - p_{2} \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{1}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{42+22}{440+360}=0.08$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>1.784) =0.074$

4 0

3 years ago