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4 years ago

Solve 2(L) + 3(4L) = 990.50

Mathematics

2 answers:

snow_lady [41]4 years ago

6 0

2(L) is 2L and 3(4L) is 12L
SO 12+2(L)= 14(L)
990.50 divided by 14 (L) is 70.75
Therefore L=70.75

Alika [10]4 years ago

5 0

Answer:

L = 70.75

Step-by-step explanation:

2(L) + 3(4L) = 990.50

Distribute, combine like terms,

2L + 12L = 14L = 990.50

Divide both sides by 14.

L = 70.75

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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

worty [1.4K]

Answer:

a) $P(X \leq 100) = 1- e^{-0.01342*100} =0.7387$

$P(X \leq 200) = 1- e^{-0.01342*200} =0.9317$

$P(100\leq X \leq 200) = [1- e^{-0.01342*200}]-[1- e^{-0.01342*100}] =0.1930$

b) $P(X>223.547) = 1-P(X\leq 223.547) = 1-[1- e^{-0.01342*223.547}]=0.0498$

c) $m = \frac{ln(0.5)}{-0.01342}=51.65$

d) $a = \frac{ln(0.05)}{-0.01342}=223.23$

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}$

Solution to the problem

For this case we have that X is represented by the following distribution:

$X\sim Exp (\lambda=0.01342)$

Is important to remember that th cumulative distribution for X is given by:

$F(X) =P(X \leq x) = 1-e^{-\lambda x}$

Part a

For this case we want this probability:

$P(X \leq 100)$

And using the cumulative distribution function we have this:

$P(X \leq 100) = 1- e^{-0.01342*100} =0.7387$

$P(X \leq 200) = 1- e^{-0.01342*200} =0.9317$

$P(100\leq X \leq 200) = [1- e^{-0.01342*200}]-[1- e^{-0.01342*100}] =0.1930$

Part b

Since we want the probability that the man exceeds the mean by more than 2 deviations

For this case the mean is given by:

$\mu = \frac{1}{\lambda}=\frac{1}{0.01342}= 74.516$

And by properties the deviation is the same value $\sigma = 74.516$

So then 2 deviations correspond to 2*74.516=149.03

And the want this probability:

$P(X > 74.516+149.03) = P(X>223.547)$

And we can find this probability using the complement rule:

$P(X>223.547) = 1-P(X\leq 223.547) = 1-[1- e^{-0.01342*223.547}]=0.0498$

Part c

For the median we need to find a value of m such that:

$P(X \leq m) = 0.5$

If we use the cumulative distribution function we got:

$1-e^{-0.01342 m} =0.5$

And if we solve for m we got this:

$0.5 = e^{-0.01342 m}$

If we apply natural log on both sides we got:

$ln(0.5) = -0.01342 m$

$m = \frac{ln(0.5)}{-0.01342}=51.65$

Part d

For this case we have this equation:

$P(X\leq a) = 0.95$

If we apply the cumulative distribution function we got:

$1-e^{-0.01342*a} =0.95$

If w solve for a we can do this:

$0.05= e^{-0.01342 a}$

Using natural log on btoh sides we got:

$ln(0.05) = -0.01342 a$

$a = \frac{ln(0.05)}{-0.01342}=223.23$

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Answer: The average number of miles she would have to ride each day to meet her goal = 3.2 miles.

Step-by-step explanation:

Given: Elizabeth wants to ride her bicycle 28.6 miles this week.

She already ridden 19 miles.

Number of days she will ride more =3

Let m = average number of miles ridden in a day.

Then,

Total distance = initial distance + (m) (Number of days)

i.e. 28.6 = 19+3m (Required equation)

Subtract 19 from both sides , we get

$9.6=3m\\\\\Rightarrow\ m=\dfrac{9.6}{3}\\\\\Rightarrow\ m=3.2\ miles$

Hence, the average number of miles she would have to ride each day to meet her goal = 3.2 miles.

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Angelina_Jolie [31]

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Answer:

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Step-by-step explanation:

When you double the speed, the time needed to finish the lap would halve.

6 *2 =12

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Please help ASAP 26 pts + brainliest to right/best answer

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Answer:

d power property

Step-by-step explanation:

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log (5^3x^3) ^ 1/12

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