The larger of two numbers is 10 less than twice the smaller number. If the sum of the two numbers is 38, find the two numbers.

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UNO [17]

Answer:

4.93827 x 10^19

Step-by-step explanation:

hope it helped

5 0

3 years ago

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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

The vector v⃗ in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis.

allsm [11]

The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis is: (0, -1/2, √3/2).

<h3>Vector</h3>

a. Vector (v)

Vector (v)=v (cos Ф, sin Ф)

V=1 while the counterclockwise angle that is measured from positive x=Ф=π/4

Hence:

Vector=3(cos π/4, sinπ/4)

Vector=(3/√2, 3√2)

b. Vector w:

Vector w=1(0, cos 2π/3, sin2π/3)

Vector w=(0, -1/2, √3/2)

Therefore the vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector ws: (0, -1/2, √3/2).

The complete question is:

Resolve the following vectors into components:

a. The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis.

(b) The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis.

Learn more about vector here:brainly.com/question/25705666

#SPJ1

5 0

2 years ago

Which equations below represent lines that are perpendicular to the line that contains (1, - 2) and (3,4)^ Select all that apply

Nady [450]

Answer:

Select all the lines with slope $-\frac{1}{3}$ .

Step-by-step explanation:

Use the slopes to help you answer this kind of questions.

The slope of the line going through: (1, - 2) and (3,4) is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

We plug in the coordinates to get:

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

All lines that are perpendicular to this line has slope $-\frac{1}{3}$ .

3 0

3 years ago

Lebron keeps track of his life relative to the year he was born . Relative to when he was born ,his brother was born in year -3

elena-s [515]

Answer:

A, because -3 is a negative integer it is to the left of zero, 7 is a positive integer is it to the right of zero.

Hope this helps <3

5 0

3 years ago