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VladimirAG [237]
3 years ago
9

Need help on geometry Please

Mathematics
1 answer:
juin [17]3 years ago
5 0
1. To find this we are going to use the converse of the Pythagorean theorem: if the square of the longest side of a triangle is equal to the sum of the squares of its smaller side, the triangle is a right one.
We know from our picture that the longer side of the triangle is 36 and its shorter sides are 24 and 15.
36^2=24^2+15^2
1296=576+225
1296 \neq 801
The converse also says that if the square of the longest side is greater than the sum of the squares of the shorter sides, the triangle is obtuse, and if the square of the longest side less than the sum of the squares of the shorter sides, the triangle is acute.
1296\ \textgreater \ 801 

We can conclude that our triangle is an obtuse one; the correct answer is the third one: obtuse

2. Here we have a right triangle with longer side 80 feet and one of the shorter sides 65 feet. Lest x be the distance from the base to the guy wire attached point.
Using the Pythagorean theorem:
80^2=65^2+x^2
x^2=80^2-65^2
x= \sqrt{80^2-65^2}
x=46.64

We can conclude that the correct answer is fourth choice: 46.64

3. Here we are going to use the Pythagorean theorem. We know that the longest side of our triangle is 40 and its shorter sides are 9 and x. Using the Pythagorean theorem:
40^2=9^2+x^2
x^2=40^2-9^2
x= \sqrt{40^2-9^2}
x=38.97

We can conclude that the correct answer is the fourth option: 38.97

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An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservation
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Answer:

a) 0.109375 = 0.109 to 3 d.p

b) 1.00 to 3 d.p

Step-by-step explanation:

Probability of someone that made a reservation not showing up = 50% = 0.5

Probability of someone that made a reservation showing up = 1 - 0.5 = 0.5

a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?

For this to happen, 5 or 6 people have to show up since the limousine can accommodate a maximum of 4 people

Let P(X=x) represent x people showing up

probability that at least one individual with a reservation cannot be accommodated on the trip = P(X = 5) + P(X = 6)

P(X = x) can be evaluated using binomial distribution formula

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 6

x = Number of successes required = 5 or 6

p = probability of success = 0.5

q = probability of failure = 0.5

P(X = 5) = ⁶C₅ (0.5)⁵ (0.5)⁶⁻⁵ = 6(0.5)⁶ = 0.09375

P(X = 6) = ⁶C₆ (0.5)⁶ (0.5)⁶⁻⁶ = 1(0.5)⁶ = 0.015625

P(X=5) + P(X=6) = 0.09375 + 0.015625 = 0.109375

b) If six reservations are made, what is the expected number of available places when the limousine departs?

Probability of one person not showing up after reservation of a seat = 0.5

Expected number of people that do not show up = E(X) = Σ xᵢpᵢ

where xᵢ = each independent person,

pᵢ = probability of each independent person not showing up.

E(X) = 6(1×0.5) = 3

If 3 people do not show up, it means 3 people show up and the number of unoccupied seats in a 4-seater limousine = 4 - 3 = 1

So, expected number of unoccupied seats = 1

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