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Gnom [1K]
2 years ago
5

A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between

the landmarks in degrees.
What is the distance, x, between the two landmarks? Round the answer to the nearest tenth.

A. 32.5 m
B. 42.1 m
C. 85.1 m
D. 98.5 m

Mathematics
2 answers:
LenKa [72]2 years ago
8 0

Answer:

The correct answer is 98.5 m, or D.

I just took the test and got it correct.

KonstantinChe [14]2 years ago
4 0
X² = Side1² + Side2² - 2[(Side1)(Side2)] cos(Toby's Angle)x² = 55² + 65² - 2[(55)(65)] cos(110°)x² = 3025 + 4225 -7150[cos(110°)]x² = 7250 - 2445.44x = √4804.56x = 69.31m
∴The distance, x, between two landmarks is 69.31m

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Ierofanga [76]
The correct answer is 40 bars. 

In order to find this amount we have to find when the y values are worth the same. Since both equations are equal to y, we can set them equal to each other to find a time when the y values are the same. 

Company A = Company B
.75x = 10 + .50x ---> Now subtract .50x from both sides. 
.25x = 10 ---> Now divide both sides by .25
x = 40

When x = 40 it will cost $30 from both companies. 

3 0
2 years ago
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The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the
navik [9.2K]

Answer:

a) 0.019

b) 0.563

c) x = 1.966 hours

Step-by-step explanation:

E(X) = 1

Exponential random variable's probability function is given as

P(X=x) = λ e^(-λ.x)

The cumulative distribution function is given as

P(X ≤ x) = 1 - e^(-λ.x)

a) The time between the arrivals of small aircraft at a county airport that is exponentially distributed.

But the number of planes that land every hour will be obtained using the Poisson distribution formula.

It is the best for discrete systems.

Poisson distribution formula is given as

P(X = x) = (e^-λ)(λˣ)/x!

λ = 1 aircraft per hour.

The probability that more than three aircraft arrive within an hour = P(X > 3)

P(X > 3) = 1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

P(X > 3) = 1 - 0.98101 = 0.01899 = 0.019 to 3 d.p

b) If 30 separate one-hour intervals are chosen, what Is the probability that no interval contains more than three arrivals

Probability of one 1-hour interval not containing more than 3 arrivals = 1 - P(X > 3)

= 1 - 0.01899 = 0.98101

Probability that thirty 1-hour intervals will not contain more than 3 arrivals = (0.98101)³⁰ = 0.5626 = 0.563 to 3 d.p

c) Determine the length of an interval of time (In hours) such that the probability that no arrivals occur during the interval is 0.14

We can now use the cumulative distribution function for exponential random variable for this

P(X ≤ x) = 1 - e^(-λ.x)

P(X > x) = 1 - P(X ≤ x)

P(X > x) = e^(-λ.x)

λ = 1, x = ?,

0.14 = e⁻ˣ

e⁻ˣ = 0.14

In e⁻ˣ = In 0.14 = -1.966

-x = -1.966

x = 1.966 hours

Hope this Helps!!!

4 0
2 years ago
Mr. Jones waffle recipe uses 3/4 cups of milk to make 8 waffles how many cups of milk should be used to make 24 waffles?
ella [17]

Answer:

9/4

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5 0
2 years ago
The answer for Mixed Degree Systems 
Setler79 [48]

Answer:

We have to find the maximum number of solutions of each of the following system:

1)

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That means they will never intersect each other at any point.

Ans hence we will get zero solutions.

2)

Two distinct parabolas:

Two parabolas can maximum intersect at 2 points this could be seen by the diagrams.

3)

A line and a circle.

A line and a circle can maximum have 2 solutions.

4)

A parabola and a circle.

It can have maximum two solutions it can be seen from the diagram.

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