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3 years ago

Please someone help me to prove this.

Mathematics

2 answers:

kodGreya [7K]3 years ago

5 0

Hope this can help.

KengaRu [80]3 years ago

4 0

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the following Sum Identity:

$\tan (A + B) =\dfrac{\tan A+\tan B}{1-\tan A\cdot \tan B}$

Given: A + B + C = 180° → A + B + C = π

<u>Proof LHS → RHS</u>

Given: A + B + C = π

Multiply by 2: 2(A + B + C = π)

→ 2A + 2B + 2C = 2π

→ 2A + 2B = 2π - 2C

Apply tan: tan(2A + 2B = 2π - 2C)

→ tan (2A + 2B) = tan(2π - 2C)

→ tan (2A + 2B) = - tan 2C

$\text{Sum Identity:}\qquad \qquad \dfrac{\tan 2A+\tan 2B}{1-\tan 2A\cdot \tan 2B}=-\tan 2C$

Simplify: tan 2A + tan 2B = -tan 2C (1 - tan 2A · tan 2B)

Distribute: tan 2A + tan 2B = -tan 2C + tan 2A · tan 2B · tan 2C

Add tan 2C: tan 2A + tan 2B + tan 2C = tan 2A · tan 2B · tan 2C

LHS = RHS is proven

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What graph represents the piecewise function?

adoni [48]

Answer: Lower left corner

A piecewise function is basically a combination of other functions to make one single function. We can break up the given piecewise function into two parts:

f(x) = x-4

f(x) = -2x

The f(x) will change depending on what x happens to be. If x is 0 or smaller, then we go with f(x) = x-4. Otherwise, if x is larger than 0, then we opt for f(x) = -2x.

To graph this, we basically graph y = x-4 and y = -2x together on the same coordinate system. We only graph y = x-4 if x is 0 or smaller. Likewise, we graph y = -2x when x > 0. This results in the graph shown in the lower left corner of your four answer choices.

Note: the closed circle means "include this point as part of the graph". The open circle means "exclude this point as part of the graph". So this is why the upper right corner is very close but not quite the answer we want.

5 0

3 years ago

A flatbed truck is being loaded with steel girders weighing 1825 lbs each. How much will 15 of these girders weigh, combined?

saw5 [17]

I think I know how it's done!

You need to multiply 1825 by 15. You may want to show the work in this one.

1825•15 = 27,375

Thus, the truck will be loaded with 27,375 lbs of steel girders.

Hope this helps you succeed!

6 0

3 years ago

If flipping a coin gives you a 50/50 chance of it landing on heads or tails, does this mean a coin only has two sides? Who else

Pachacha [2.7K]

yesss bru im so bored

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3 years ago

Read 2 more answers

PLEASE HELP! (Sorry about the picture)

Ganezh [65]

I think the answer is the Last one

6 0

3 years ago

Life rating in Greece. Greece has faced a severe economic crisis since the end of 2009. A Gallup poll surveyed 1,000 randomly sa

elena-s [515]

Answer:

The population parameter of interest is the true proportion of Greek who are suffering

While the point estimate of this parameter is proportion of those that would rate their lives poorly enough to be considered "suffering". which is 25%

The condition is met

The 95% confidence interval is $0.223 < p < 0.277$

If the confidence level is increased which will in turn reduce the level of significance but increase the critical value( $Z_{\frac{\alpha }{2} }$ ) and this will increase the margin of error( deduced from the formula for margin of error i.e $E \ \alpha \ Z_{\frac{\alpha }{2} }$ ) which will make the confidence interval wider

Looking at the formula for margin of error if the we see that if the sample size is increased the margin of error will reduce making the confidence level narrower

Step-by-step explanation:

From the question we are told that

The sample size is n = 1000

The population proportion is $\r p = 0.25$

Considering question a

The population parameter of interest is the true proportion of Greek who are suffering

While the point estimate of this parameter is proportion of those that would rate their lives poorly enough to be considered "suffering". which is 25%

Considering question b

The condition for constructing a confidence interval is

$n * \r p > 5\ and \ n(1 - \r p ) >5$

$1000 * 0.25 > 5 \ and \ 1000 * (1-0.25 ) > 5$

$250 > 5 \ and \ 750> 5$

Hence the condition is met

Considering question c

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_\frac{ \alpha }{2} * \sqrt{ \frac{\r p (1 - \r p ) }{n} }$

substituting values

$E = 1.96 * \sqrt{ \frac{ 0.25 (1 - 0.25 ) }{ 1000} }$

$E = 0.027$

The 95% confidence interval is mathematically represented as

$\r p - E < p < \r p + E$

substituting values

$0.25 - 0.027 < p < 0.25 + 0.027$

substituting values

$0.223 < p < 0.277$

considering d

considering e

Looking at the formula for margin of error if the we see that if the sample size is increased the margin of error will reduce making the confidence level narrower

5 0

3 years ago

Please someone help me to prove this. ​

Please someone help me to prove this.