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3 years ago

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) Probability of distance at most 100m, with λ = 0.0143:

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

F(100) = 0.76

Probability of distance at most 200:

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

F(200) = 0.94

Probability of distance between 100 and 200:

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

Distance exceeds the mean distance by more than 2σ:

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

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

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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.

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2 years ago

Select the correct answer.

Ronch [10]

It's the answer is C. (t2-p)(t4+pt2+p2)

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