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vitfil [10]
2 years ago
11

A pole 5 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After pl

acing the pole, Zachary measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.

Mathematics
1 answer:
sammy [17]2 years ago
4 0

The length of the guy's wire to the nearest foot is 89 feet.

The situation forms a right-angled triangle.

<h3>Properties of a right angle triangle:</h3>
  • A right-angle triangle has one angle of 90 degrees.
  • The sides can be found using the Pythagoras theorem.
  • The angles can be found using trigonometric ratios.

The hypotenuse of the triangle is the length of the wire.

let's use the smaller triangle to find the angle opposite the tower. Therefore,

tan ∅ = opposite / adjacent

tan ∅ =  5 / 2

∅ = tan⁻¹ 2.5

∅ = 68.1985905136

∅ = 68.20°

Therefore,

cos 68.20 = adjacent / hypotenuse

cos 68.20 = 33 / hypotenuse

hypotenuse = 33 / cos 68.20

hypotenuse = 88.8606843161

Therefore,

length of wire ≈ 89 feet.

learn more on triangles here; brainly.com/question/25762788?referrer=searchResults

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An urn contains 5 red balls and 2 green balls. Two balls are drawn one after the other. What is the probability that the second
AleksAgata [21]

Answer:

<em>The probability that the second ball is red is 71%</em>

Step-by-step explanation:

<u>Probabilities</u>

We know there are 5 red balls and 2 green balls. Let's analyze what can happen when two balls are drawn in sequence (no reposition).

The first ball can be red (R) or green (G). The probability that it's red is computed by

\displaystyle P(R)=\frac{5}{7}

The probability is's green is computed by

\displaystyle P(G)=\frac{2}{7}

If we have drawn a red ball, there are only 4 of them out of 6 in the urn, so the probability to draw a second red ball is

\displaystyle P(RR)=\frac{5}{7}\cdot \frac{4}{6}=\frac{10}{21}

If we have drawn a green ball, there are still 5 red balls out of 6 in the urn, so the probability to draw a red ball now is

\displaystyle P(GR)=\frac{2}{7}\cdot \frac{5}{6}=\frac{5}{21}

The total probability of the second ball being red is

\displaystyle P(XR)=\frac{10}{21}+\frac{5}{21}=\frac{5}{7}=0.71

The probability that the second ball is red is 71%

7 0
3 years ago
You are president of the high school band booster club. You have arranged for the school’s jazz band to perform at a local coffe
vazorg [7]
Booster's share =y =0.75x
gross receipts=x=700
plug x=700 in y=0.75x
y=0.75*700
y=525
3 0
3 years ago
Read 2 more answers
In an examination 80% students passed. if 15 less have appeared and 10 less have passed, the ratio of passers to failures would
Nina [5.8K]

Answer:

60 students passed, and 75 appeared in examination.

Step-by-step explanation:

Let's say s is the total number of students and p is the number of students who passed.

80% of the students passed, so:

0.8 s = p

If there were 10 less passers, and 15 less students (5 less failures), then the ratio of passers to failures would be 5/1.

(p − 10) / (s − p − 5) = 5 / 1

Simplify the second equation:

p − 10 = 5 (s − p − 5)

p − 10 = 5s − 5p − 25

6p = 5s − 15

Substitute the first equation.

6 (0.8 s) = 5s − 15

4.8 s = 5s − 15

0.2 s = 15

s = 75

p = 0.8 s

p = 60

60 students passed, and 75 appeared in examination.

5 0
3 years ago
What is the sum of (q+r)-(r+10)
KATRIN_1 [288]

Answer:

q+10 is the answer

6 0
3 years ago
Nick and Monica are paid $41.25 for their work. Nick worked 2.5 hours, and Monica worked 3 hours. They split the money according
vlada-n [284]

Answer:

BRIANLIEST PLZ

N = 18.75

M = 22.5

Step-by-step explanation:

Need the ratio of money paid to each. We know how the ratio of time is divided so we can use this ratio to find the amount paid.

T = t1 + t2 = 2.5 + 3 = 5.5

r1 =2.5/5.5

r2 = 3/5.5

Nick = r1 * 41.25 = 18.75

Monica = r2 * 41.25 = 22.5

7 0
3 years ago
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