Solve Z=x+y/5 for y

Find the measure of the missing angles in the triangle below round your answer to the nearest degree

navik [9.2K]

Answer:

a. 40°

b. 21°

Step-by-step explanation:

a. Reference angle = θ

Opposite = 5

Adjacent = 6

Apply TOA:

$Tan (\theta) = \frac{Opp}{Adj}$

$Tan (\theta) = \frac{5}{6}$

$\theta = Tan^{-1}(\frac{5}{6})$

$\theta = 40$ (nearest degree)

b. Reference angle = x

Opposite = 5

Hypotenuse = 14

Apply SOH:

$Sin (x) = \frac{Opp}{Hyp}$

$Sin (x) = \frac{5}{14}$

$x = Sin^{-1}(\frac{5}{14})$

$x = 21$ (nearest degree)

3 0

3 years ago

If 20 is decreased to 18.6, the decrease is what percent of the original number?

Lady bird [3.3K]

Answer:

1.4

Step-by-step explanation:

10 decreased by 1.4 is 18.6

5 0

3 years ago

A bird is flying 10 feet above sea level, while a shark swims 15ft below sea level. How far is the bird from the shark?

kondaur [170]

Answer:

25 ft

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Find the point-slope form. Then use that to find the slope-intercept form

umka2103 [35]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 5 &,& 10~) 
% (c,d)
&&(~ 8 &,& 16~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{16-10}{8-5}\implies \cfrac{6}{3}\implies 2
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-10=2(x-5)\implies y-10=2x-10
\\\\\\
y-=2x-10+10\implies y=2x$

4 0

4 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:

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%

b

The condition is met

c

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

d

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

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

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

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

So

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

$250 > 5 \ and \ 750> 5$

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

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

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