If an author can type 2500 words in 5 minutes, how many words can he type in 210 minutes?

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponenti

melomori [17]

Answer:

a) 0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

b) Capacity of 252.6 cubic feet per second

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

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

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).

This means that $m = 100, \mu = \frac{1}{100} = 0.01$

(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

We have that:

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

This is P(X > 190). So

$P(X > 190) = e^{-0.01*190} = 0.1496$

0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

(b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08?

This is x for which:

$P(X > x) = 0.08$

So

$e^{-0.01x} = 0.08$

$\ln{e^{-0.01x}} = \ln{0.08}$

$-0.01x = \ln{0.08}$

$x = -\frac{\ln{0.08}}{0.01}$

$x = 252.6$

Capacity of 252.6 cubic feet per second

5 0

3 years ago

Melissa made a total of 14 baskets during her last basketball game. She made a number of 2-point baskets and a number of 3-point

OLga [1]

Answer:

Melissa made 11 3 point baskets in her last basket ball game.

Step-by-step explanation:

because three multiplied by ten equals thirty so therefore if you multiply three by 11 you get thirty three points

5 0

3 years ago

Read 2 more answers

ASAPPP HURRY 25 POINTS!!!

puteri [66]

Answer:

They are equal to each other, because one vertical angle is a reflection of the other. True

They are not equal to each other, because one vertical angle is not a reflection of the other. False

They are equal to each other, because one vertical angle is supplementary to the other. False

They are not equal to each other, because one vertical angle is not supplementary to the other. False

8 0

2 years ago

Read 2 more answers

Write the equation in slope-intercept form for the line that passes through the points (-6, -4) and (-3, 1).

ozzi

Answer:

y = 5/3x+6

Step-by-step explanation:

4 0

2 years ago

A bag contains a total of 60 marbles. A marble is to be chosen at random from the bag. If the probability that a blue marble wil

valkas [14]

Answer:

There are 21 blue marbles

Step-by-step explanation:

In this question, we are asked to calculate the number of blue marbles in a bag that contains a total of 60 marbles, given the probability of choosing a blue marble.

Mathematically, the probability of choosing a blue marble can be represented as:

P(B) = number of blue marbles/ Total number of marbles

From the question, we can identify that P(B) is 0.35, number of Marbles is unknown while the total number of marbles is 60.

We insert these values in the equation;

0.35 = number of blue marbles/60

Hence, number of blue marbles = 60 * 0.35 = 21

4 0

3 years ago