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Akimi4 [234]
3 years ago
5

Find the next term of the arithmetic sequence. 8, –9, –26, –43...

Mathematics
1 answer:
ioda3 years ago
8 0

Answer:

The answer is - 60

Step-by-step explanation:

8 - ( - 9) =  17 \\  - 9 - ( - 26) = 17 \\  - 26 - ( - 43) = 17 \\  - 43 - ( - 60) = 17

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Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose t
andrezito [222]

Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:

f(x) = λ.e^{-\lambda.x}

and the cumulative distribution function, which describes the probability distribution of a random variable X, is:

F(x) = 1 - e^{-\lambda.x}

(a) <u>Probability</u> of distance at most <u>100m</u>, with λ = 0.0143:

F(100) = 1 - e^{-0.0143.100}

F(100) = 0.76

<u>Probability</u> of distance at most <u>200</u>:

F(200) = 1 - e^{-0.0143.200}

F(200) = 0.94

<u>Probability</u> of distance between <u>100 and 200</u>:

F(100≤X≤200) = F(200) - F(100)

F(100≤X≤200) = 0.94 - 0.76

F(100≤X≤200) = 0.18

(b) The mean, E(X), of a probability distribution is calculated by:

E(X) = \frac{1}{\lambda}

E(X) = \frac{1}{0.0143}

E(X) = 69.93

The standard deviation is the square root of variance,V(X), which is calculated by:

σ = \sqrt{\frac{1}{\lambda^{2}} }

σ = \sqrt{\frac{1}{0.0143^{2}} }

σ = 69.93

<u>Distance exceeds the mean distance by more than 2σ</u>:

P(X > 69.93+2.69.93) = P(X > 209.79)

P(X > 209.79) = 1 - P(X≤209.79)

P(X > 209.79) = 1 - F(209.79)

P(X > 209.79) = 1 - (1 - e^{-0.0143*209.79})

P(X > 209.79) = 0.0503

(c) Median is a point that divides the value in half. For a probability distribution:

P(X≤m) = 0.5

\int\limits^m_0 f({x}) \, dx = 0.5

\int\limits^m_0 {\lambda.e^{-\lambda.x}} \, dx = 0.5

\lambda.\frac{e^{-\lambda.x}}{-\lambda} = -e^{-\lambda.x} + e^{0}

1 - e^{-\lambda.m} = 0.5

-e^{-\lambda.m} = - 0.5

ln(e^{-0.0143.m}) = ln(0.5)

-0.0143.m = - 0.0693

m = 48.46

6 0
3 years ago
The volume of a cylinder is pi times the radius r squared multiplied by the height h. Write an expression for the volume.
Paul [167]
V= Area of the circle at the base • height =
Pi•r^2 •h
7 0
3 years ago
Olivia needs 54 licks for every3 lollipops she eats. Use the table using equivalent ratios
postnew [5]

Answer:

1:18

Step-by-step explanation:

54/3 = 18 3/3 = 1

18 to 1

18:1

1:18

3 0
3 years ago
You start at (6, 10). You move down 9 units. Where do you end?
Andrew [12]

Answer:

(6,1)

Step-by-step explanation:

You know that to move up or down means to change the y- coordinate. So for this on you do 10-9. This is 1. So the new y- coordinate is 1.

5 0
2 years ago
Select the correct answer.
Ronch [10]
It's the answer is C. (t2-p)(t4+pt2+p2)
4 0
3 years ago
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