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dusya [7]
3 years ago
9

1. Is a rotation of 180° the same as a reflection over the y-axis? Please justify your answer in complete sentences.

Mathematics
1 answer:
sp2606 [1]3 years ago
5 0

Answer:

Not the same.

Step-by-step explanation:

Given that there is a rotation of 180 degrees .  To check whether this is a reflection over the y axis.

Reflection over the y axis make the coordinates (x,y) as (-x,y)

i.e. this means rotation of 180 degrees about the origin anticlockwise.

Hence just rotation of 180 degrees is not the same as a reflection over y axis.

The conditions are:

i) 180 degree to be rotated anticlockwise

ii) Rotation is about the origin

Hence a rotation of 180 degrees need not always be the same as reflection over y axis.

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A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise
DiKsa [7]

Answer:

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, we failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.

Step-by-step explanation:

Refer to the attached data.

The Null and Alternate hypothesis is given by

Null hypotheses = H₀: μ₁ = μ₂

Alternate hypotheses = H₁: μ₁ ≠ μ₂

The test statistic is given by

$ t = \frac{\bar{x}_1  - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }  $

Where \bar{x}_1 is the sample mean of people who do not exercise regularly.

Where \bar{x}_2 is the sample mean of people who do exercise regularly.

Where s_1 is the sample standard deviation of people who do not exercise regularly.

Where s_2 is the sample standard deviation of people who do exercise regularly.

Where n_1 is the sample size of people who do not exercise regularly.

Where n_2 is the sample size of people who do exercise regularly.

$ t = \frac{72.7  - 69.7}{\sqrt{\frac{10.9^2}{16} + \frac{8.2^2}{12} } }  $

t = 0.83

The given level of significance is

1 - 0.95 = 0.05

The degree of freedom is

df = 16 + 12 - 2 = 26

From the t-table, df = 26 and significance level 0.05,

t = 2.056 (two-tailed)

Conclusion:

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, We failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.

4 0
3 years ago
Find two numbers that round to 387.4 when rounded to the nearest ten
maria [59]

Answer:

39

Step-by-step explanation:

4 is once 7 is more than 5 so u have to add 1 number to the 8 so 8 will become 9

6 0
3 years ago
In a right triangle, the measure of one acute angle is twice the sum of the measure of the other acute angle and 30. Find the me
Alja [10]

Answer:

Step-by-step explanation:

if we have a right triangle,

one angle=90

180-90=90

let x be one angle, and y another angle

the other is 2x+30

x+2x+30=90

3x=60

x=20

y=70

5 0
3 years ago
Read 2 more answers
You gave the server at a restaurant a 22% tip and ended up paying $41.48. What was the price of your meal before you applied the
const2013 [10]

Answer: The price of meal before the tip = $34.

Step-by-step explanation:

Given : The percentage of tip = 22% = 0.22 ( we divide a percentage by 100 to convert it into decimal)

Total amount paid ( including tip) =  $41.48

Formula for Total bill = Price of meal + Tip amount , where Tip amount= 22% of Price of meal.

Let x be the price of meal, then

Total bill =x + 0.22 x (x )

⇒ $41.48= x(1+0.22)  [ By distributive property]

⇒ $41.48 = x (1.22)

⇒ x= ($41.48) ÷ 1.22

⇒ x= 34

Hence, the price of your meal before you applied the tip = $34.

7 0
3 years ago
A student finished 72 of her homework problems in class. If the ratio of problems she finished to problems she still had left wa
kramer


Finished:Left

8:1

8/1 = 72/x

Cross Multiply

8x=72

divide each side by 8

x=9

She already finished 72 and has 9 remaining

Total = Finished + Remaining = 72 + 9 = 81

4 0
3 years ago
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