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.
Answer:
Step-by-step explanation:
As we know that,
<em>'Horizontal stretch, stretches the function left or right on the x-axis'. </em>
The general form of horizontal stretch is given by 'f(kx)', where 0<k<1 is the factor by which function is stretched horizontally.
Since, the function which is stretched by a factor of
.
The new function is i.e.
.
<em>Further, the function is reflected over y-axis.</em>
That is, the reflected function is i.e.
.
Hence, the required function is .
Answer: 20 $
divide 30 by
30 / = 20
she has saved 20 $ so far
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 = = 13.016
Reject H₀ Since > 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:
Conclusion:
We reject H₀
Since > 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.