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2 years ago

Triangle \triangle A'B'C'△A

1 answer:

6 0

From the information given, the rotated triangle is same as the original triangle. This is because, vertices of the rotation remain at the origin - (0,0).

<h3>What is the proof the above?</h3>

Notice that the question states: △A'B'C' is the image of △ABC. Given that the △ without primes is the original and the one with primes depict the rotated triangle,

under a rotation about the origin, (0,0) (0,0) (0, 0), indicating no movement,

△A'B'C' is in the same position with △ABC.

Learn more about rotation at:
brainly.com/question/27915888
#SPJ1

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A mammoth bone is found to contain roughly 5% of the isotope C-14. Living elephant bones commonly contain about 40% C-14. Given

Elina [12.6K]

Answer:

The mammoth died 17.190 years ago.

Step-by-step explanation:

Given information:

Half-life of C-14 is 5.700 years.

Living elephant bones commonly contain about 40% C-14.

For every 5700 years, the elephant's bones losses a half-life of C-14. And supposing that the living mammoth bones had the same percentage of C-14.

If the mammoth when living has 40%, then:

After 5.730 years, the mammoth bones will contain 20%.
After 11.460 years(2 half-lives), the mammoth bones will contain 10%.
After 17.190 years(3 half-lives), the mammoth bones will contain 5%.

6 0

3 years ago

Read 2 more answers

List 3 equivalent ratios of 5/2

jek_recluse [69]

3 equivalent ratios or 5/2
10 /4
20/8
30/12

6 0

3 years ago

Read 2 more answers

Solve for x <br><br><br> Question: 2x/3 -x/5 =7

iris [78.8K]

Answer:

$(2x \times 5 - x \times 3 ) \\ \div 15 = 7 \\ \\ 10x - 3x = 7 \times 15 \\ 7x = 105 \\ x = 105 \div 7 \\ x = 15$

8 0

4 years ago

The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of cos

madreJ [45]

Answer:

$F=\frac{s^2_2}{s^2_1}=\frac{5.4}{2.3}=2.348$

$p_v =2*P(F_{15,15}>2.348)=0.109$

And we can use the following excel code to find the p value:"=2*(1-F.DIST(2.348,15,15,TRUE))"

Since the $p_v > \alpha$ we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation is different between the two groups at 10% of significance.

Step-by-step explanation:

Assuming the following question :"The accounting department analyzes the variance of the weekly unit costs reported by two production departments. Asample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use α= .10."

Data given and notation

$n_1 = 16$ represent the sampe size for sample 1

$n_2 =16$ represent the sample size for sample 2

$s^2_1 = 2.3$ represent the sample variance for sample 1

$s^2_2 = 5.4$ represent the sample variance for sample 2

$\alpha=0.1$ represent the significance level provided

Confidence =0.9 or 9%

F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:

$F=\frac{s^2_2}{s^2_1}$

Solution to the problem

System of hypothesis

We want to test if the variation is equal for both groups or no, so the system of hypothesis are:

H0: $\sigma^2_1 = \sigma^2_2$

H1: $\sigma^2_1 \neq \sigma^2_2$

Calculate the statistic

Now we can calculate the statistic like this:

$F=\frac{s^2_2}{s^2_1}=\frac{5.4}{2.3}=2.348$

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have $n_2 -1 =16-1=15$ and for the denominator we have $n_1 -1 =16-1=15$ and the F statistic have 15 degrees of freedom for the numerator and 15 for the denominator. And the P value is given by:

P value

Since is a bilateral test the p value is given by

$p_v =2*P(F_{15,15}>2.348)=0.109$

And we can use the following excel code to find the p value:"=2*(1-F.DIST(2.348,15,15,TRUE))"

Conclusion

4 0

4 years ago

Your plumber charged a fee of $60 and an additional $21.50 per hour for a repair visit. Your bill was $124.50. How long was the

vodomira [7]

First, subtract the fee to the final bill amount.

124.50 - 60 = $64.50 (amount paid for the total visit hourly without fee)

Second, divide to find how many hours the plumber took to repair.

64.50 / 21.50 = <u>3 hours</u>

______

Best of Luck,

Wolfyy :)

8 0

3 years ago