. An oil refnery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refnery to storage tanks located on the south bank of the river 6 km east of the refnery. The cost of laying pipe is $400,000ykm over land to a point P on the north bank and $800,000ykm under the river to the tanks. To minimize the cost of the pipeline, where should P be located

Answers

Answer 1

Answer:

The point P should be located at 0,51 Km from point B, to minimize costs

Step-by-step explanation:

The oil refinery ( point A ) the opposite point ( B) in the south bank, and the storage tank (point C) these three points shape a right triangle. Let´s call x the distance between point A and point P ( the arriving point of the pipeline in the south bank ) then:

Cost = cost of pipeline in-ground* ( 6 - x ) + cost of pipeline in water* L

where L is the hypothenuse of the right triangle  ( A , B , P )

Cost ($) = 400000 * ( 6 - x ) + 800000 * √ 2² + x²

C (x) = 400000* ( 6 - x ) + 800000* √4 + x²

C(x) = 2400000 - 400000*x  + 800000* √4 + x²

Tacking derivatives on both sides of the equation

C´(x) = - 400000 + 800000* ( 2x)/√4 + x²

C´(x) = 0         - 400000 + 1600000*x / √4 + x²  = 0

- 400000* (√4 + x² )  + 1600000*x  = 0

- (√4 + x² ) + 4* x = 0

- (√4 + x² )  = - 4*x

Squaring both sides

4 + x²  = 16*x²

15*x² = 4

x² = 4/ 15

x = ± √0,27

x = ± 0,51

We should dismiss the negative solution

x = 0,51 Km

The point P should be located at 0,51 Km from point B


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Answers

2x +100=16+4x
-2x. -2x
100=16+2x
-16. -16
84=2x
divide both sides
x=42

Answer:

x=42

Step-by-step explanation:

Write the equation.

2(x+50)=16+4x

Spread the parentheses

2x+100=16+4x

Put variables on one side, numbers on the other.

2x-4x=16-100

Add/subtract/multiply/divide the variables with variables and numbers with numbers.

-2x=-84

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Flip sides to make x positive

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Answers

Answer:

[tex]Pr = 32.49\%[/tex]

Step-by-step explanation:

Given

Let E represents the event of wearing glasses or contacts.

So;

[tex]P(E) =57\%[/tex]

Required

The probability that selected 2 wears glasses

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[tex]Pr = 32.49\%[/tex]

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Answers

Answer:

1. wire is approx. 143.96 ft

2. pole is approx. 106.55 ft

Step-by-step explanation:

Mapping the information on the SOHCAHTOA picture below:

Φ = 46

wire = hypotenuse

adjacent side = 100

CAH is most suitable:

cos 46° = 100/wire => wire = 100/cos 46 ≈ 143.96

pole = opposite side + 3

TOA is most suitable:

tan 46° = (pole-3)/100 => pole = 3 + 100 * tan 46 ≈ 106.55

Question 7 (2 points)
Given the function rule y = 3x + 11, what is the value of x if y = 57
Hint: Make sure you are substituting for the correct variable!

Answers

Step-by-step explanation:

3x+11=57

subtract 11 from both sides and you will get this

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Answer:

15.333

Step-by-step explanation:

3x+11=57(y)

reverse the question

so:

57-11=46

46 divided by 3=15.333

so x=15.333

hope that helps

thank you

19NBoli

The lines shown below are parallel. If the green line has a slope of-4, what is
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10
A.
B. 4
- 10
-5
5
10
C. -4
O
-5
D.
4
10 -

Answers

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What is parallel lines?

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

The property of parallel lines states that slope of both lines will b same.

Therefore slope of red lines is -4

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Answer and working out attached. Hope this helps

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Answers

Answer:

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Step-by-step explanation:

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x = 9 + 12

x = 21

Answer:

21

Step-by-step explanation:

let X = ( )

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Answer:

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Step-by-step explanation:

#Eleventeen

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Answers

The probability of x<4 successes is P(X <4) = 0.01909.

How to find that a given condition can be modelled by binomial distribution?

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

In this question:

​n=10 p=0.15 x<4

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\\\\\\P(X < 4) = \: ^{10}C_40.15^4(1-0.15)^{10-4}\\\\\\P(X < 4) = \: ^{10}C_40.00050625(0.85)^{6}\\\\\\P(X < 4) = 0.01909[/tex]

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Step-by-step explanation:

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Abcdefghijklmnopqrstuvwxyz

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Answers

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Answers

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Step-by-step explanation:

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