The product of 0.6 and a number is 31.8 more than the number . Find the number

What is 90 divided by 5 in distributive property

zaharov [31]

18 is the answer //////////////////

3 0

4 years ago

The angle of the elevation from the top of a 95 Todd building into a hot air balloon in the sky and 76° if the horizontal distan

AnnZ [28]

Answer:

The height of the hot air balloon is 1514.54 feet approximately.

Step-by-step explanation:

Consider the provided information.

The angle of elevation from the top of a 95-foot tall building to a hot air balloon in the sky is 76. If the horizontal distance between the building and the hot air balloon is 354 feet, find the height of the hot air balloon

The figure is shown below:

Let the height of the balloon is AD, the height of the building is BC.

Draw a line BE parallel to CD.

Therefore, AD=x+95, BC=95 and BE=CD=354 ft

Now in triangle $ABE$ .

$\tan\theta=\dfrac{\text{Opp}}{\text{Adj}}$

$\tan76^{\circ}=\dfrac{AE}{BE}$

$AE\approx 4.01\times 354$

$AE\approx 1419.54$

The height air balloon is 1419.54+95 =1514.54 ft

Hence, the height of the hot air balloon is 1514.54 feet approximately.

7 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:

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

A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?

kolezko [41]

(x-center)^2+(y-center)^2=r^2
x^2+y^2=r^2
(5)^2+(-12)^2=r^2
25+144=r^2
169=r^2
r=13

5 0

3 years ago

Read 2 more answers

How does a 180 degree rotation about the origin change the coordinates of a shape

notsponge [240]

Answer:

According to the 180°-rotation rule, you take the OPPOSITE of both the x-coordinate and y-coordinate:

180°: [x, y] → [-x, -y]

I am joyous to assist you anytime.

6 0

3 years ago