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3 years ago

Explain why the function y=1-cosx is an even function

Mathematics

1 answer:

Oksanka [162]3 years ago

8 0

A function is said to even if it returns the same output when given two opposite inputs:

$f(x) = f(-x)$

In your case, you have

$f(x) = 1-\cos(x), \quad f(-x) = 1-\cos(-x)$

And since $\cos(x) = \cos(-x)$ , the proof is concluded.

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Dairy cows at large commercial farms often receive

IrinaK [193]

Answer:

a) The 99% confidence interval for the true mean milk production is (26.35 kg/d, 29.65 kg/d).

b) They would need to use a confidence level of 94.52%.

Step-by-step explanation:

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

$\alpha = \frac{1-0.99}{2} = 0.005$

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

So it is z with a pvalue of $1-0.005 = 0.995$ , so $z = 2.575$

Now, find 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. So

$M = 2.575*\frac{2.25}{\sqrt{12}} = 1.65$

The lower end of the interval is the mean subtracted by M. So it is 28-1.65 = 26.35 kg/d

The upper end of the interval is the mean added to M. So it is 28 + 1.65 = 29.65 kg/d.

The 99% confidence interval for the true mean milk production is (26.35 kg/d, 29.65 kg/d).

(b) If the farms want the confidence interval to be no wider than 1.25 kg/d, what level of confidence would they need to use?

Now we want to find the value of z when M = 1.25. So:

$1.25 = z*\frac{2.25}{\sqrt{12}}$

$0.6495z = 1.25$

$z = 1.92$ , that has a pvalue of 0.9726.

So the confidence level should be 1 - 2*(1-0.9726) = 0.9452

They would need to use a confidence level of 94.52%.

3 0

3 years ago

Alexandria wants to go hiking on Saturday. She will consider these conditions when she chooses which of several parks to visit:

kkurt [141]

The answer would be 200 miles. I just took the test and got it right.

7 0

3 years ago

Read 2 more answers

Without solving, identify whether each of the following equations has a unique solution, no solution, or infinitely many solutio

Aleksandr [31]

Answer:

yes it gas a unique solution

Step-by-step explanation:

8x+3=8x+7

6 0

3 years ago

I have no idea what I'm doing can you help me please?

8_murik_8 [283]

Answer:

i dont know use cat

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

If <img src="https://tex.z-dn.net/?f=f%28x%29%3D3%5Ex" id="TexFormula1" title="f(x)=3^x" alt="f(x)=3^x" align="absmiddle" class=

SOVA2 [1]

$$f(x)+f(x+1) \stackrel{1}{=} 3^x+3^{x+1} \stackrel{2}{=} 3^x+3^x\cdot3^1\stackrel{3}{=}3^x+3\cdot3^x\stackrel{4}{=}4\cdot3^x\stackrel{5}{=}4\cdot f(x)$

1) Substitution from definition.

2) We use $$x^{a+b}=x^a\cdot x^b$

3) We are changing the order of 3 and $3^x$ .

4) We add 1 and 3 $3^x$ and we get $4\cdot 3^x$

5) Substitution from definition (but the other way than at the beginning).

8 0

3 years ago