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Pachacha [2.7K]
2 years ago
6

You and another person are sunbathing on the beach near a lifeguard station. The other person chooses a spot that is the same di

stance from the shoreline but 11 feet closer to the station than you. The angles of elevation from you and the other person to the top of the lifeguard station are 36 degrees and 46 degrees, respectively. Estimate the height of the lifeguard station to the nearest tenth of a foot.

Mathematics
1 answer:
Schach [20]2 years ago
7 0

Answer: 26.8 feet

Step-by-step explanation:

In the figure attached you can see two right triangles  triangle ABD and a triangle ACD.

You are located at point B and the other person at point C.

The approximate height of the lifeguard station is <em>x</em>.

Keep on mind that:

tan\alpha=\frac{opposite}{adjacent}

Therefore:

<em>For the triangle ABD</em>:

tan(36\°)=\frac{x}{DC+11}    [EQUATION 1]

<em>For the triangle ACD:</em>

tan(46\°)=\frac{x}{DC}    [EQUATION 2]

Solve from DC from [EQUATION 2]:

DC=\frac{x}{tan(46\°)}

Substitute into [EQUATION 1] and solve for x:

tan(36\°)=\frac{x}{(\frac{x}{tan(46\°)}+11)}\\tan(36\°)(\frac{x}{tan(46\°)}+11)=x\\11*tan(36\°)=x-\frac{xtan(36\°)}{tan(46\°)}\\7.991=0.298x

x=26.81ft≈26.8ft

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Olive is allowed to bring one friend on a trip with her.
san4es73 [151]

Answer:

Process of elimination

Step-by-step explanation:

If Olive wants to choose a friend while not playing favorites, while also not being random, she has to eliminate the ones she knows she will NOT take on the trip. She can choose this by selecting the one she knows that will be best on the trip with her, depending on the situation.

Or, if Olive only has one friend, then it wouldn't be surprising that she would take that one friend on the trip, since she has no one else to choose. This way, it is not playing favorites, nor is it random. Hope this helps you!

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2 years ago
Samantha is making soup. To make the broth, she combines 2/5 cup of veg stock and 2/3 cup of chicken stock. Boiling the broth ca
nlexa [21]
Okay so.
2/5=24/60 (multiply 2/5 by 12)
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Add 24/60 with 40/60 which is 64/60 after you get that you subtract by 15/60 and you get 49/60.
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2 years ago
NEED HELP FINDING SLOPE OF THE LINE
mamaluj [8]

Answer:

slope = - \frac{2}{3}

Step-by-step explanation:

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with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (2, - 2) ← 2 points on the line

m = \frac{-2-2}{2-(-4)} = \frac{-4}{2+4} = \frac{-4}{6} = - \frac{2}{3}

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tiny-mole [99]

Ok, so the question is based on geometric progression. Remember, the formula for calculating the nth-term of a geometric progression is: a*r^{n-1}. The a in the expression stands for the 1st term of the sequence, and r is the common ratio of the elements of the sequence. Now let's take a look at the problem.

"A ping pong ball has a 75% rebound ration". We can infer that our common ratio, r, is 75% which is 0.75.

"When you drop it from a height of k feet...", this means the first height you drop it from, a.k.a, the first term.

Now going back to the expression, the nth-term = a*r^{n-1}, we can substitute our common ration, 0.75 with r, and our 1st term, k, with a. This becomes: k * 0.75^{n-1}. This becomes our expression.

a. The highest height achieved by the ball after six bounces. Our nth-term here is 6, so let's use our expression to find the 6th term. n_{6} = 235 * 0.75^{6-1} = 235*0.75^{5} = 235*0.2373 = 55.7655ft

b. The total distance travelled by the ball when it strikes the ground for the 12th time. This involves the use of the sum of elements in the geometric progression. The formula for that is \frac{a(1 - r^{n})}{1-r}, provided that r is less than 1, which it is in this case, since 0.75 is less than one. Our nth-term here is 12, so we substitute.

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Step 2:

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Alternate hypothesis: u ≠ 4

Population mean: u ≠ 4

Step 3 and step 4 are attached.

Step 5: Based on the calculation, the calculated value of t is less than the t critical value, therefore, the null hypothesis will be failed to be rejected.

2. Sketch the distributions involved

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