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kompoz [17]
3 years ago
6

ABCDEFGH is a regular octagon. The minimum degree of rotation by which this octagon can map onto itself is (30 ; 45 ; 90 ; 120 °

). It will take ( 2 ; 4 ; 6 ; 8 ) increments of that degree of clockwise rotation for A′ (the image of A) to coincide with C.

Mathematics
2 answers:
USPshnik [31]3 years ago
4 0

Answer:

45°

2 - Clockwise

Step-by-step explanation:

ABCDEFGH is a regular octagon.

The minimum degree of rotation by which this octagon can map onto itself.

For rotation we have to find the central angle of each side.

Complete angle = 360°

A regular octagon has 8 equal sides. All sides make same angle at center.

8Ф = 360°

Ф = 45°

If we rotate regular octagon by 45° then it map onto itself.

Hence, 45° correct answer.  

After 2 times clockwise rotation by 45° each time. We will get the image of A coincide with C as shown in attach figure.

C is second vertex of A.

eduard3 years ago
3 0
Since the center is 360 degrees, divide by 8 to find the measure of each angle formed by drawing a radius to each vertex. This gives you 45 degrees. To move A to C would take two rotations which is (45)*2= 90 degrees
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Step-by-step explanation:

As we know that,

<em>'Horizontal stretch, stretches the function left or right on the x-axis'. </em>

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Since, the function y=x^{3} which is stretched by a factor of \frac{1}{5}.

The new function is y=(\frac{x}{5})^{3} i.e. y=\frac{x^{3}}{125}.

<em>Further, the function is reflected over y-axis.</em>

That is, the reflected function is y=\frac{(-x)^{3}}{125} i.e. y=\frac{-x^{3}}{125}.

Hence, the required function is y=\frac{-x^{3}}{125}.

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3 years ago
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Answer:

a. it has rotational symmetry with an angle of rotation of 90°

Step-by-step explanation:

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3 years ago
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7 0
3 years ago
Read 2 more answers
Workers at a certain soda drink factory collected data on the volumes​ (in ounces) of a simple random sample of 1818 cans of the
ohaa [14]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Workers at a certain soda drink factory collected data on the volumes​ (in ounces) of a simple random sample of 18 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a normally distributed population.

If the workers want the filling process to work so that almost all cans have volumes between 12.02 oz and 12.66 ​oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.01 significance level. Complete parts​ (a) through​ (d) below.

a. Identify the null and alternative hypotheses.  

b. Compute the test statistic.

c. Find the p-value.

d. State the conclusion.

Answer:

Null hypotheses = H₀: σ = 0.16  oz

Alternate hypotheses = H₁: σ < 0.16  oz

Critical value = 6.408

Chi-square value = \chi^2 = 13.016

Reject H₀  Since \chi^2 > Critical value

Reject H₀ Since p-value ≤ α

We have significant evidence at given significance level that the population of volumes has a standard deviation of less than 0.16 oz.

Step-by-step explanation:

Set up hypotheses:

The null hypotheses is that the population of volumes has a standard deviation of 0.16 oz

Null hypotheses = H₀: σ = 0.16  oz

The claim to be tested is that the population of volumes has a standard deviation of less than 0.16 oz

Alternate hypotheses = H₁: σ < 0.16  oz

Determine type of test:

Since the alternate hypothesis states that the population of volumes has a standard deviation of less than 0.16 oz, therefore we will use a lower-tailed chi-square test.

Determine the Critical value:

Given level of significance = 0.01

Since it is a lower-tailed test, the areas given in the chi-square table are the areas to the right of the critical value. To get the areas on the left, subtract it from  one, and then look it up

α = 1 - 0.01 = 0.99

degree of freedom = df = n - 1 = 18 - 1 = 17

The critical value from the chi-square table at α = 0.99 and df = 17 is found to be

Critical value = 6.408

Using an online “chi-square p-value calculator”

The left tail p-value for df = 17 and Critical value = 6.408 is found to be

p-value = 0.01

Set up decision rule:

Reject H₀ If  > Critical value

We reject the Null hypothesis If the calculated chi-square value is more than the critical value.

OR

Reject H₀ If p-value ≤ α

Compute the test statistic:

$ \chi^2 = \frac{(n-1) s^2}{\sigma^2} } $

$ \chi^2 = \frac{(18-1) 0.14^2}{0.16^2} } $

\chi^2 = 13.016

Conclusion:

We reject H₀

Since \chi^2 > Critical value

13.016 > 6.408

Also

p-value ≤ α

0.01 ≤ 0.01

We have significant evidence at given significance level that the population of volumes has a standard deviation of less than 0.16 oz.

5 0
3 years ago
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