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3 years ago

Find the circumference of this figure. Show your calculations.

Mathematics

1 answer:

solong [7]3 years ago

5 0

Answer:

Circumference of circle= 37.68 units

Circumference of sector= 6.28 units

Step-by-step explanation:

The given figure is a circle with given radius OB= 6 units.

The circumference of a circle is the total length of its boundary.

For the complete circle its circumference can be calculated by;

Circumference= $2\pi r$

$=2*3.14*6\\=37.68$ units

For the circumference of the Sector with 60° in the figure, the circumference can be calculate by:

$=\frac{60}{360}* 2*\pi*6\\\\=\frac{1}{6}*12*3.14\\\\ =2*3.14\\\\=6.28$ units

So, the circumference of the full circle is 37.68 units and the circumference of the sector is 6.28 units.

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(a^2-b^2) (c^2-d^2) +4abcd

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The mean of five numbers is 8. If one of the five numbers is removed, the mean becomes 9. What is the value of the number that w

mestny [16]

Using the mean concept, it is found that the value of the number that was removed was of 4.

The mean of a data-set is given by the <u>sum of all observations in the data-set divided by the number of observations</u>.

The mean of five numbers is 8, hence, the sum of the numbers is given by:

S = 5 x 8 = 40.

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S = 4 x 9 = 36.

The difference is:

40 - 36 = 4.

Hence, the value of the number that was removed was of 4.

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2 years ago

The ratio of bleach to water in a cleaning solution is 2:18. For every 1 liter of bleach, how many liters of water are in the so

Paha777 [63]

Answer:

For every 1 liter of bleach there are 9 liters of water in the solution

Step-by-step explanation:

∵ The ratio of bleach to water in a cleaning solution is 2 : 18

- That means for every 2 liters of bleach there is 18 liters of water

∵ There is 1 liter of bleach

- Let us use the ratio method

→ bleach : water

→ 2 : 18

→ 1 : x

- By using cross multiplication

∴ x × 2 = 1 × 18

∴ 2 x = 18

- Divide both sides by 2

∴ x = 9

∵ x represents the number of liters of the water in the solution

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For every 1 liter of bleach there are 9 liters of water in the solution

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3 years ago

A sample was taken of the salaries of four employees from a large company. the following are their salaries, in thousands of dol

Free_Kalibri [48]

For given sample of salaries of four employees, the variance of their salaries is: 26 thousands of dollars

The formula for the variance is,

$S^2=\frac{\sum (x_i - \bar{x})^2}{n-1}$

where,

$S^2$ = sample variance

$x_i$ = the value of the one observation

$\bar{x}$ = the mean value of all observations

n = the number of observations

For given question,

n = 4

First we find the mean of their salaries.

(33 + 31 + 24 + 36 ) / 4 = 31

So, $\bar{x}=31$

Using the formula for variance ,

$S^2=\frac{(33-31)^2}{4-1}+\frac{(31-31)^2}{4-1}+\frac{(24-31)^2}{4-1}+\frac{(36-31)^2}{4-1}\\\\ S^2=\frac{4}{3} + \frac{0}{3} + \frac{49}{3} + \frac{25}{3} \\\\S^2= \frac{4+49+25}{3}\\\\S^2=\frac{78}{3} \\\\S^2=26$

Therefore, for given sample of salaries of four employees, the variance of their salaries is: 26 thousands of dollars

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2 years ago