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svetoff [14.1K]
3 years ago
10

Daryl measures the angle of elevation to be 62 degrees. Frances measures the angle of elevation to be 54 degrees. if the two ent

husiasts are 28m apart, how far off the ground is the helicopter.

Mathematics
1 answer:
Leya [2.2K]3 years ago
5 0

Answer:

<em>The helicopter is 27.38 m far off the ground</em>

Step-by-step explanation:

The drawing shown in the image below has all the measures and variables needed to solve the problem.

We need to find R, the height of the helicopter. We'll use the law of sines to find the length of side a.

\displaystyle \frac{28}{\sin X}=\frac{a}{\sin 54^\circ}

The angle X is the measure needed to complete 180°:

X = 180° - 54° - 62° = 64°

Solving for a:

\displaystyle a=\frac{28}{\sin 64^\circ}\cdot \sin 54^\circ

Calculating:

a = 31.11 m

Now using the sine ratio in the right triangle to the left side:

\displaystyle \sin 62^\circ=\frac{R}{a}

Solving for R:

R=a\sin 62^\circ

R=31.11*0.88

R = 27.38 m

The helicopter is 27.38 m far off the ground

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After painting the fence steve and janet realize that their house also needs painting. But steve will have to do the painting hi
gladu [14]

Answer:

Therefore, Steve will paint house for 20.6 days.

Step-by-step explanation:

We know that Steve determines that it would take them 9 days to paint the house together (if they were both healthy) and that it would take Janet (when healthy) 16 days to paint the house alone.

We conclude that in 1 day Janet painted 1/16 of the house. In nine days, Janet painted 9/16 of house.

So, 7/16 of house paint Steve in nine days.

We have the following proportion:

\frac{7}{16}:9=1:x\\\\\frac{7}{16}x=9\\\\x=9\cdot \frac{16}{7}\\\\x=20.6

Therefore, Steve will paint house for 20.6 days.

4 0
3 years ago
The graph represents this system of equations:
Kipish [7]

Answer:

(2.5, - 2)

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is

(2.5, - 2 ) ← point of intersection

3 0
3 years ago
Read 2 more answers
Several years​ ago, 38​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students r
Colt1911 [192]

Answer:

0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995

0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564

We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

For this case we are interesting in the parameter of the true proportion of people satisfied with the quality of education the students receive

The confidence level is given 95%, the significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical values are:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The estimated proportion of people satisfied with the quality of education the students receive is given by:

\hat p =\frac{499}{1165}= 0.428

The confidence interval for the proportion if interest is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And replacing the info given we got:

0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995

0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564

We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.

8 0
3 years ago
In a group of 60 workers they get paid an average of 80$ a day per person.
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Answer:

48 workers earn $75 a day.

Step-by-step explanation:

Let x people earn 75 a day then 60-x earn 100 dollars a day.

Average is $80 a day so total paid out to the 60 workers

= 60*80 = $4800.

So  75x + 100(60-x) = 4800

75x + 6000 - 100x = 4800

6000 - 4800 = 100x - 75x

1200 = 25x

x = 48.

6 0
2 years ago
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