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brilliants [131]
3 years ago
12

I need the answer to be proper in simple steps​

Mathematics
1 answer:
Stella [2.4K]3 years ago
6 0

Answer:

  a) φ = 4/7

  b) φ = 4

Step-by-step explanation:

The relationship between radius, angle, and arc length is ...

  a = r·φ . . . . . φ in radians

You want to find the angle φ, so you can divide this equation by r:

  φ = a/r

__

a) φ = a/r = (8 cm)/(14 cm) = 8/14

  φ = 4/7 radians

__

b) φ = a/r = (16 cm)/(4 cm) = 16/4

  φ = 4 radians

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Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a
rusak2 [61]

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.025 = 0.975, so Z = 1.96.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that \sigma = 2

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when M = 0.5. So

M = z\frac{\sigma}{\sqrt{n}}

0.5 = 1.96\frac{2}{\sqrt{n}}

0.5\sqrt{n} = 2*1.96

Dividing both sides by 0.5

\sqrt{n} = 4*1.96

(\sqrt{n})^2 = (4*1.96)^2

n = 61.5

Rounding up

We would have to take a sample of 62 to achieve this result.

8 0
3 years ago
If , n^-3 = 1/8 then n would be which of the following? -1/2 -2 2 1/2
lions [1.4K]

Answer:

2

Step-by-step explanation:

{n}^{ - 3}  =  \frac{1}{8}  \\  \\  {n}^{ - 3}  =  \frac{1}{ {2}^{3} }  \\  \\  {n}^{ - 3}  = {2}^{ - 3}.. (\because \frac{1}{a^n} = a^{-n}) \\  \\ n = 2 \\(\because exponents \: are \: same\: hence\: \\bases\: will \: also\: be\: equal)

4 0
3 years ago
Read 2 more answers
There are 20 students in the classroom. 5 of these students are selected to go to an assembly. how many such selections are poss
Ksju [112]
Order of the people does not affect the total number of ways. Thus, we use combinations.

Total combinations: 20C5 = 15,504 ways.
4 0
3 years ago
The graph of a function is shown below. find the following, g(10), g(-3)
Rzqust [24]

Answer:

g(5x)=0

Step-by-step explanation:

Given that g(x)=4

From the graph when x=-2 then g(x)=4

Hence 5x=-10

Now from the graph

g(-10)=0

4 0
2 years ago
WORTH 20 POINTS PLEASE HELP
Dmitriy789 [7]
The answer is d its decreasing
8 0
3 years ago
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