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Vladimir [108]
3 years ago
8

What is the formula to find the length of an arc when given the central angle and radius?

Mathematics
1 answer:
vazorg [7]3 years ago
3 0
s = \dfrac{n}{360^\circ}2 \pi r

where
s = arc length
n = measure of central angle
r = radius

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A financial analyst wanted to estimate the mean annual return on mutual funds. A random sample of funds' returns shows an averag
Feliz [49]

A financial analyst wanted to estimate the mean annual return on mutual funds. A random sample of 60 funds' returns shows an average rate of 12%. If the population standard deviation is assumed to be 4%, the 95% confidence interval estimate for the annual return on all mutual funds is

A. 0.037773 to 0.202227

B. 3.7773% to 20.2227%

C. 59.98786% to 61.01214%

D. 51.7773% to 68.2227%

E. 10.988% to 13.012%

Answer: E. 10.988% to 13.012%

Step-by-step explanation:

Given;

Mean x= 12%

Standard deviation r = 4%

Number of samples tested n = 60

Confidence interval is 95%

Z' = t(0.025)= 1.96

Confidence interval = x +/- Z'(r/√n)

= 12% +/- 1.96(4%/√60)

= 12% +/- 0.01214%

Confidence interval= (10.988% to 13.012%)

3 0
3 years ago
A business executive bought 40 stamps for
alekssr [168]

Answer:

32 33-cent stamps, 8 23-cent stamps

Step-by-step explanation:

In order to solve this question, we need to set up a system of equations. Also known as solving for two variables (the number of each stamp).

Let's set x to be the number of 33-cent stamps. Similarly, let's set y to be the number of 23-cent stamps.

To make our first equation, let's think about the number of stamps total we have. We can say:

x + y =40

<em>(AKA - The number of 33-cent stamps, plus the number of 23-cent stamps, equals 40 stamps.)</em>

Now, let's make an equation for the cost of these stamps.

0.33x + 0.23y = 12.40

<em>(AKA - The cost of the stamps in total, should equal $12.40).</em>

So now, we have our two equations:

x + y =40\\0.33x+0.23y=12.40

If you have a TI-84 graphing calculator, you can go to apps -> polysmlt2 -> simultaneous eqn solver, and then input these equations into the menu. This will solve the problem for you.

If you need to do this manually, let's use substitution. Condense our first equation to make it more substitutable.

x+y=40\\x=40-y

Now, let's put this into our second equation.

0.33x+0.23y=12.40\\0.33(40-y)+0.23y=12.40

Distribute, and solve for y.

13.2-0.33y +0.23y =12.40\\13.2-0.1y=12.40\\-0.1y=-0.8\\y=8

Now, we plug this into one of our equations.

x+y=40\\x+8=40\\x=32

In the end, we have thirty-two 33-cent stamps, and eight 23-cent stamps.

3 0
1 year ago
Find the area and perimeter of each composite figure use 3.14 for pi round your answer to the nearest 10th
Ad libitum [116K]

1. Perimeter is 3 + 3 +3 +4 +5 = 18 feet

  Area = 3*3 = 9, 1/2*3*4 = 6, 9 + 6 =15 square feet

2. perimeter = 2.5 +2.5+ 2.5+2.5+0.5+0.5 = 11 meters

   Area = 3*.5 = 1.5, 3*2=6,  6+1.5 = 7.5 square meters

3. perimeter = 3.14*2*3 = 18.84 +8 = 26.8 inches

   Area = 6*4 = 24 + 3.14*3^2 = 28.26 = 28.26 +24 = 52.3 inches

4. surface area = 2*π*6*20+2*π*6^2= 980.2 yards

Volume = π*6^2*20 = 2261.9 cubic yards

5.surface area = 2*(9*7+2*2+2*9) = 190 cm

 Volume = 2*7*9 = 126 cubic cm

6. surface area = <span>2*(11*11+11*11+11*11) = 726 mm</span>

<span>  Volume = 11 *11*11 = 1331 cubic cm</span>


7 0
3 years ago
When juggling a ball travels in a complete circle every 10 seconds how many circle does it make in a minute.Please Help and expl
WITCHER [35]

Answer:

It make 6 circles in a minute.

Step-by-step explanation:

Given:

a ball travels in a complete circle every 10 seconds

i.e

one complete circle = time taken 10 seconds.

Two complete circle = time taken 20 seconds.

Three complete circle = time taken 30 seconds.

Four complete circle = time taken 40 seconds.

Five complete circle = time taken 50 seconds.

Six complete circle = time taken 60 seconds.

60 seconds =  one minute.

∴ Six complete circle  in one minute.

8 0
3 years ago
The table shows the ratio of caramel corn to cheddar cornvin a bag. What is the constant propotionality?
zvonat [6]
Since we know is a proportionality, namely a multiplier on "x", we can simply use any of those points, say hmmm let's use 10, 15,

\bf \qquad \qquad \textit{direct proportional variation}\\\\&#10;\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad  y=kx\impliedby &#10;\begin{array}{llll}&#10;k=constant\ of\\&#10;\qquad  variation&#10;\end{array}\\\\&#10;-------------------------------\\\\&#10;\textit{we know that }&#10;\begin{cases}&#10;x=10\\&#10;y=15&#10;\end{cases}\implies 15=k10\implies \cfrac{15}{10}=k\implies \cfrac{3}{2}=k
8 0
3 years ago
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