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damaskus [11]
3 years ago
12

How many times does the image of the octagon coincide with the preimage during the rotation?

Mathematics
2 answers:
Delicious77 [7]3 years ago
7 0

The image would coincide with the pre-image during the rotation. Therefore, the octagon would coincide a total of 8 times as it rotates 360 degrees about its center.

Dennis_Churaev [7]3 years ago
4 0

An octagon has 8 sides, a rotation of 45° (360°/8) will map the octagon onto its preimage. Answer is 8.


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A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name br
natima [27]

Answer:

Step-by-step explanation:

Given that:

A study is conducted and the study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands.

a)

Thus; we formulate the null and the alternative hypotheses as follows:

The proportion is ; \frac{64}{100} = 0.64

Null hypothesis:    {H_0}:p = 0.64  

The Null hypothesis states that there is no evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

Alternative hypothesis: {H_a}:p \ne 0.64H

The Alternative hypothesis states that there is evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

b)

The proportion of the population = 0.64

The sample size n = 100

The number of shoppers = 52  stating that the supermarket brand was as good as the national brand

The sample proportion \hat  p = \frac{52}{100}

\hat  p = 0.52

The z - value is calculated by the formula:

z = \dfrac{\hat p-p}{\frac{\sqrt{ p(1-p)}}{100 }}

z = \dfrac{0.52-0.64}{\frac{\sqrt{ 0.64(1-0.64)}}{100 }}

z = \dfrac{-0.12}{0.048 }}

z = -2.50

Since z = -2.50

the p-value = 2P(Z ≤ -2.50)

p-value = 2 × 0.0062

The p-value = 0.0124

c)

At  significance level,  ∝ = 0.05 ; The p-value = 0.0124

According to  the rejection rule, if p-value is less than 0.05 then we will reject null hypothesis at ∝ = 0.05

Hence, the p-value =0.0124 < ∝ (=0.05)

According to the reject rule; reject null hypothesis.

Conclusion: There is no evidence at all that the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%.

d) we know that the significance level of ∝  = 0.05

The value{z__{0.05}}  is obtained as:

P\left( {\left| Z \right| \le z} \right) = 0.05

Now; to determine Z ; we locate the probability value of 0.05 form the table of standard normal distribution. Then we proceed to the left until the  first column is reached and  the value is 1.90. Also , we move upward until we reach the top and the value is 0.06. Now; the intersection of the row and column results the area  to the left of z

This implies that :P(Z \leq -1.96)=0.05

The critical value for left tail is -1.96 and the critical value for right tail is 1.96.

Conclusion:

The critical value is -1.96 and the value of test statistic is - 2.50.  Here, we can see that  the value of test statistic is lesser than the critical value. Hence, we can be concluded that there is evidence that reject the null hypothesis.

Therefore, Yes, the national brand ketchup manufacturer is pleased with the conclusion.

5 0
3 years ago
What would be the appropriate units and intervals to use along the x- and y-axes
Vika [28.1K]

X axes are supposed to be positive and the y is negative.

3 0
3 years ago
Please give the answer
dybincka [34]

Answer:

When N is an even number, use the first equation in the matrix. When N is negative use the second equation.

Step-by-step explanation:

n = 6 | 6/2 = 3

n=5 | 3(5)+1 = 16

5 0
3 years ago
Does the ordered pair, (1, 5/2) satisfies the given equation<br> 3x-3y=-3 ?
vampirchik [111]

Answer:

Ordered pair, (1, 5/2) does not satisfy the given equation  3x-3y=-3

Step-by-step explanation:

3x-3y=-3

Here (x, y) = (1, \frac{5}{2} )

3(1)-3(\frac{5}{2} )=-3

3- (\frac{15}{2} )=-3\\6-15=-6\\-9\neq -6

7 0
2 years ago
The table shows the results of a survey of 400 random people on whether they like liquid soap, bar soap, or both. A 4-column tab
In-s [12.5K]

Answer: 100/400

<u>Step-by-step explanation:</u>

\begin{array}{l|c|c|c}&Liquid&Not\ Liquid&Total\\ Bar&200&100&300\\Not\ Bar&80&20&100\\Total&280&120&400\end{array}

\dfrac{Not\ Bar:Total}{Total:Total}\quad =\dfrac{100}{400}

4 0
3 years ago
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