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Ksenya-84 [330]
3 years ago
11

What is the sum of the first 200 natural numbers?

Mathematics
1 answer:
kow [346]3 years ago
6 0
The sum of the first natural numbers is 20100
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The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a
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Answer:

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Step-by-step explanation:

Let X be the commuting time for the student. We know that X\sim N(30, (5)^2). Then, the normal probability density function for the random variable X is given by

f(x) = \frac{1}{\sqrt{2\pi(5)^{2}}}\exp[-\frac{(x-\mu)^{2}}{2(5)^{2}}]. We are seeking the probability P(X>35) because the student leaves home at 8:25 A.M., we want to know the probability that the student will arrive at the college campus later than 9 A.M. and between 8:25 A.M. and 9 A.M. there are 35 minutes of difference. So,

 

P(X>35) = \int\limits_{35}^{\infty}f(x)dx = 0.1587

To find this probability you can use either a table from a book or a programming language. We have used the R statistical programming language an the instruction pnorm(35, mean = 30, sd = 5, lower.tail = F)

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4 years ago
What is the slope of the line through (3,2) and (-3,4)?
NISA [10]

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Step-by-step explanation:

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m = \frac{4-2}{-3-3} = \frac{2}{-6} = - \frac{1}{3}

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Answer: attached below

Step-by-step explanation:

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