The sum of the measures of a pair of alternate angles of two parallel lines is 210°. What are the measures of these two angles?

1 answer:

3 0

The answer is 105 and 105 because they did not tell you that one had more than the other, so it's equal. Plus, it could not be 210 or over or 0 or less. It was spilt up equally between both alternate angles, and the lines are parallel, so the angles are equal. So just do 210/2 and get what one of the angles would be. Great question!

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45.67 × 32.58 but show your work

melisa1 [442]

Solution:

1. Set up the long multiplication.

2. Calculate 7 x 8, which is 56.
Since 56 is two-digit, we carry the first digit 5 to the next column.

3. Calculate 6 x 8, which is 48. Now add the carry digit of 5, which is 53.
Since 53 is two-digit, we carry the first digit 5 to the next column.

4. Calculate 5 x 8, which is 40. Now add the carry digit of 5, which is 45.
Since 45 is two-digit, we carry the first digit 4 to the next column.

5. Calculate 4 x 8, which is 32. Now add the carry digit of 4, which is 36.
Since 36 is two-digit, we carry the first digit 3 to the next column.

6. Bring down the carry digit of 3.

7. Calculate 7 x 5, which is 35.
Since 35 is two-digit, we carry the first digit 3 to the next column.

8. Calculate 6 x 5, which is 30. Now add the carry digit of 3, which is 33.
Since 33 is two-digit, we carry the first digit 3 to the next column.

9. Calculate 5 x 5, which is 25. Now add the carry digit of 3, which is 28.
Since 28 is two-digit, we carry the first digit 2 to the next column.

10. Calculate 4 x 5, which is 20. Now add the carry digit of 2, which is 22.
Since 22 is two-digit, we carry the first digit 2 to the next column.

11. Bring down the carry digit of 2.

12. Calculate 7 x 2, which is 14.
Since 14 is two-digit, we carry the first digit 1 to the next column.

13. Calculate 6 x 2, which is 12. Now add the carry digit of 1, which is 13.
Since 13 is two-digit, we carry the first digit 1 to the next column.

14. Calculate 5 x 2, which is 10. Now add the carry digit of 1, which is 11.
Since 11 is two-digit, we carry the first digit 1 to the next column.

15. Calculate 4 x 2, which is 8. Now add the carry digit of 1, which is 9.

16. Calculate 7 x 3, which is 21.
Since 21 is two-digit, we carry the first digit 2 to the next column.

17. Calculate 6 x 3, which is 18. Now add the carry digit of 2, which is 20.
Since 20 is two-digit, we carry the first digit 2 to the next column.

18. Calculate 5 x 3, which is 15. Now add the carry digit of 2, which is 17.
Since 17 is two-digit, we carry the first digit 1 to the next column.

19. Calculate 4 x 3, which is 12. Now add the carry digit of 1, which is 13.
Since 13 is two-digit, we carry the first digit 1 to the next column.

20. Bring down the carry digit of 1.

21. Calculate 36536 + 228350 + 913400 + 13701000, which is 14879286

22. Place the decimal.
45.67 has 2 decimal places, and 32.58 has 2 decimal places.
Therefore, the answer should have 2 + 2 = 4 decimal places.

23. Therefore, 45.67 x 32.58 = 1487.9286.
1487.92861487.9286

Done!

7 0

4 years ago

Write the sum as a product of 2 factors:

kotykmax [81]

36w+24m that one factor

8 0

3 years ago

An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance th

scZoUnD [109]

Answer:

a) 0.047

b) 50% probability that the sample proportion of smart phone users is greater than 0.33.

c) 33.39% probability that the sample proportion is between 0.19 and 0.31

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$