4log(2) x + log(2)5 = log(2)405

Charlie is late for the hot-air balloon rally. He stops his car 65 meters from a hot-air balloon already in flight. While Charli

aalyn [17]

Answer: 111.4m

Explanation:

1) Trigonometric ratios

You only need to use tangent ratio.

tangent ratio = opposite-leg / adjacent-leg = balloon height / horizontal distance

2) First, find the height of the ballon when he is watching at an angle of elevation of 28°

tangent ratio = opposite-leg / adjacent-leg = balloon height / horizontal distance

tan(28°) = balloon height/65m ⇒balloon height = tan(28°)×65m

balloon height = 34.56m

3) Second, find the height of the balloon,when he is watching at an angle of elevation of 66°

tan(66°) = height of the balloon / 65m ⇒ height of the balloon = tan(66°)×65m

height of the balloon = 145.99m

4) Vertical distance the balloon ascended while Charlie watched.

Subtract the final initial height from the final height:

145.99m - 34.56m = 111.43m

4) Round to the nearest tenth: 111.4 m

6 0

3 years ago

Can someone break this down for me?!

Anna [14]

Answer:

The answers are in the question.

Step-by-step explanation:

The wording can be off-putting but the answers are mostly there for you. It says that when the wind was at the tail of the plane, the travel was hastened to 5 hours instead of six. Is the rate of speed with the wind in favor of the plane is r+21, then it stands to reason that traveling AGAINST the wind will cause the rate to drop to r-21. Taking the average of the two travel times (5 and 6 hours each), we get 5.5 hours. Since speed is distance divided by time, the speed of the plane in still air will be <em>d</em> / 5.5

Be sure to label the speed as mph.

5 0

3 years ago

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,91

Maurinko [17]

Answer:

a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

b) Wider

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.

This means that $n = 3900, \pi = \frac{1911}{3900} = 0.49$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.4768$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.5032$

The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

Question b:

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.

3 0

2 years ago

Find the vertex of the given function.<br> f(x) = |x – 5| + 10<br> The vertex is at (, ).

sammy [17]

5,10 is the answer ........

6 0

3 years ago

Read 2 more answers

Rico bought 3 adult tickets and 5 child tickets for a total of $50.

aliina [53]

Step-by-step explanation:

3x + 5y = 50

x + 5y = 31

use substitution

x = 31-5y

3(31-5y) +5y = 50

93 -15y + 5y = 50

93 - 10y = 50

--10y = -43

y = 43/10 = $4.30 for kids

now solve for x

x + 5(4.30) = 31

x + 21.5 = 31

x = $9.5 for adults

4 0

3 years ago