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3 years ago

Za and Z6 are complementary angles. Za measures 78°. What is the measure of Zb?

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

5 0

Answer:

$\boxed{\angle b = 12 \degree}$

Given:

$\angle a \: and \: \angle b \: are \: complementary \: angles\\ \\ \angle a = 78 \degree$

Step-by-step explanation:

Two Angles are Complementary when they add up to 90° (a Right Angle).

$= > \angle a + \angle b = 90 \degree \\ \\ = > 78 \degree + \angle b = 90\degree \\ \\ = > \angle b = 90 \degree - 78 \degree \\ \\ = > \angle b = 12 \degree$

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Write the product in its simplest form:

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Step-by-step explanation:

84 = 2 * 2 *3 * 7

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3 years ago

Lena purchased a prepaid phone card for $20. Long distance calls cost 21 cents a minute using this card, Lena used her card only

slega [8]

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Step-by-step explanation:

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3 years ago

2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviati

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Answer:

$\sigma = 11.28$ --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Explain how the standard deviation is calculated.

Start by calculating the mean

To do this, we divide the sum of the products of grade and number of students by the total number of students;

i.e.

$\bar x = \frac{\sum fx}{\sum f}$

So, we have:

$\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}$

$\bar x = \frac{7531}{91}$

$\bar x = 82.76$

Next, calculate the variance using the following formula:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}$

i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset

So, we have:

$\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}$

$\sigma^2 = \frac{11580.6816}{91}$

$\sigma^2 = 127.26$

Lastly, take the square root of the variance to get the standard deviation

$\sigma = \sqrt{\sigma^2}$

$\sigma = \sqrt{127.26}$

$\sigma = 11.28$ --- approximated

Hence, the standard deviation is approximately 11.28

Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.