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2 years ago

What is the slope of the line

Mathematics

1 answer:

kicyunya [14]2 years ago

5 0

Answer:

-3

Step-by-step explanation:

Slope is rise over run or the change in y over change in x. So to find the slope count the difference from one point to the next, for example (0,4) and (1,1). In this case, the y-value decreases by 3, so -3, and the x-value increases by 1, so +1. Which would be -3/1 or just -3. One way to visually check is to remember that slopes less than -1 or greater than 1 make the line steeper and negative slopes make the graph decrease from left to right.

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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

2 years ago

in the function y= -1/2(x-1)^2+3, what effect does the negative sign have on the graph, as compared to the graph of y=x^2?

Karo-lina-s [1.5K]

The negative sign will have an effect in terms of which way the graph opens up. Since the function starts off negatively the graph will open down, like an upside down U. Rather if the function started off positive I.e Y=x^2 the graph will open upwards like a upright U.

3 0

2 years ago

Do the ratios 6/1 and 18/3 forma proportion yes or no?

andrezito [222]

I'm pretty sure it's no...

4 0

2 years ago

suppose that the height of a candle is a linear function of the amount of time it has been burning. after 14 hours of burning a

prisoha [69]

Answer:

13.0

idk I just just guessing

6 0

2 years ago

Read 2 more answers

Need help with number 1 and explain

dexar [7]

Answer:

Step-by-step explanation:

If the answer is between 0 to 0.49, the best estimate is 0.

If the answer is between 0.5-1.49, the best estimate is 1.

If the answer is 1.5 or greater, the best estimate is 2.

Without giving the fractions 1/10 and 1/12 a common denominator, we know the answer is between 2/12 and 2/10.

2/12 is less than 2/10. 2/10 is 0.2, which is less than 0.5.

Since the final answer is less than 0.5, the best estimate is 0.

6 0

2 years ago