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2 years ago

A circle has a radius of 6 inches and a central angle of 60°. What is the measure of the arc length associated with this angle?

Mathematics

1 answer:

Readme [11.4K]2 years ago

6 0

Answer:

$2\pi$

Step-by-step explanation:

first you take 60°/360°= 1/6 then you take 1/6 and multiple it by $2\pi$ and that equals $\frac{\pi }{3}$ finally take $\frac{\pi }{3}$ times the radius (6) and that should equal $2\pi$

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Calculate the sample standard deviation and sample variance for the following frequency distribution of hourly wages for a sampl

lidiya [134]

Answer:

(a) The sample variance is 16.51

(a) The sample standard deviation is 4.06

Step-by-step explanation:

Given

$\begin{array}{cc}{Class} & {Frequency} & 8.26 - 10.00 & 20 &10.01-11.75 & 38 &11.76 - 13.50& 36 & 13.51-15.25 &25&15.26-17.00 &27 &\ \end{array}$

Solving (a); The sample variance.

First, calculate the class midpoints.

This is the mean of the intervals.

i.e.

$x_1 = \frac{8.26+10.00}{2} = \frac{18.26}{2} = 9.13$

$x_2 = \frac{10.01+11.75}{2} = \frac{21.76}{2} = 10.88$

$x_3 = \frac{11.76+13.50}{2} = \frac{25.26}{2} = 12.63$

$x_4 = \frac{13.51+15.25}{2} = \frac{28.76}{2} = 14.38$

$x_5 = \frac{15.26+17.00}{2} = \frac{32.26}{2} = 16.13$

So, the table becomes:

$\begin{array}{ccc}{Class} & {Frequency} & {x} & 8.26 - 10.00 & 20&9.13 &10.01-11.75 & 38 &10.88&11.76 - 13.50& 36 &12.63& 13.51-15.25 &25&14.38&15.26-17.00 &27 &16.13\ \end{array}$

Next, calculate the mean

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

$\bar x = \frac{20*9.13 + 38 * 10.88+36*12.63+25*14.38+27*16.13}{20+38+36+25+27}$

$\bar x = \frac{1845.73}{146}$

$\bar x = 12.64$

Next, the sample variance is:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}$

So, we have:

$\sigma^2 = \frac{20*(9.13-12.63)^2 + 38 * (10.88-12.63)^2 +...........+27 * (16.13 -12.63)^2}{20+38+36+25+27-1}$

$\sigma^2 = \frac{2393.6875}{145}$

$\sigma^2 = 16.51$

The sample standard deviation is:

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

$\sigma = \sqrt{16.51}$

$\sigma = 4.06$

6 0

2 years ago

11/n=8/5 solve for n

mezya [45]

Answer:

n = 55/8

Step-by-step explanation:

$\frac{11}{n} = \frac{8}{5}\\\\cross \ multiply :\\ 8 \times n = 11 \times 5\\\\n = \frac{11 \times 5}{8} = \frac{55}{8}$

6 0

2 years ago

Read 2 more answers

Please help me with these 19 and 20 and tell me what you use to get the answer

ss7ja [257]

36 + h = 75...subtract 36 from both sides
h = 75 - 36
h = 39

-176 = h + (-219)
-176 = h - 219....add 219 to both sides
219 - 176 = h
43 = h

6 0

2 years ago

Read 2 more answers

Solve for the equation below<br><br> 4x^n + x^4n = ?

slavikrds [6]

4x + 6 = -10<span>Simplifying 4x + 6 = -10 Reorder the terms: 6 + 4x = -10 Solving 6 + 4x = -10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 4x = -10 + -6 Combine like terms: 6 + -6 = 0 0 + 4x = -10 + -6 4x = -10 + -6 Combine like terms: -10 + -6 = -16 4x = -16 Divide each side by '4'. x = -4 Simplifying x = -4</span>

7 0

2 years ago

Helga is ordering five pounds of mixed nuts for a graduation party. The party budget allows $18 for the nuts. If peanuts are $2.

aksik [14]

Answer:

6 pounds of peanuts 1 pound of almonds

Step-by-step explanation:

6 pounds of peanuts at $2 a pound is $12 and that leaves $6 for a pound of almonds totaling out to $18

6 0

3 years ago