Work out the size of angle x

What is 85 percent as a decimal and fraction

Nesterboy [21]

To convert to decimal divide by 100. 85/100=0.85. You may want to simplify the fraction which is 17/20

8 0

3 years ago

Read 2 more answers

Evaluate the line integral c y3 ds,<br> c.x = t3, y = t, 0 â‰¤ t â‰¤ 3

Temka [501]

$\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\int_{t=0}^{t=3}t^3\sqrt{1^2+(3t^2)^2}\,\mathrm dt=\int_0^3t^3\sqrt{1+9t^4}\,\mathrm dt$

Take $u=1+9t^4$ so that $\mathrm du=36t^3\,\mathrm dt$ . Then

$\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\frac1{36}\int_{u=1}^{u=730}\sqrt u\,\mathrm du=\frac{730^{3/2}-1}{54}$

7 0

3 years ago

At first it decreased by 60 percent and it increased by 80 percent

storchak [24]

The quantity reported an <em>equivalent net</em> percentage change of 28 percent.

<h3>How to calculate the net change of a quantity in percentages</h3>

In this problem we must determine the <em>simple</em> percentage change equivalent to two <em>consecutive</em> percentual changes. The formula that describes the situation is:

1 + r/100 = (1 - 60/100) · (1 + 80/100)

1 + r/100 = 72/100

r/100 = - 28/100

r = - 28

The quantity reported an <em>equivalent net</em> percentage change of 28 percent.

<h3>Remark</h3>

The statement is incomplete. Complete form is presented below:

A quantity is changing. At first it descreased by 60 percent and it increased by 80 percent. What is net change of the quantity in percentage?

To learn more on percentages: brainly.com/question/13450942

#SPJ1

5 0

1 year ago

I need help on this one, I’ll really appreciate your hard work! :)

Y_Kistochka [10]

I believe it’s 1 lol

5 0

2 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

Ket [755]

Answer:

$\sigma = 11.28$ --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

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

<u>Start by calculating the mean</u>

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

<em>Hence, the standard deviation is approximately 11.28</em>

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.

8 0

2 years ago