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3 years ago

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Write an equation of the trend line rounding to two decimal places needed for this problem choose the points (1990, 253) and (20

02,323) choose the correct answer below.
A) y=-5.83x+11,355.33
B) y=5.83x+514.14
C) y=5.83x-11,355.33
D) y=-5.83x-514.17

1 answer:

solniwko [45]3 years ago

6 0

Answer:The answer is C

Step-by-step explanation:

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Answer:

$y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}$

Step-by-step explanation:

Given

$y=c_1e^x +c_2e^{-x$

$y(1) = 0$

$y'(1) =e$

Required

The solution

Differentiate $y=c_1e^x +c_2e^{-x$

$y' = c_1e^x - c_2e^{-x}$

Next, we solve for c1 and c2

$y(1) = 0$ implies that; x = 1 and y = 0

So, we have:

$y=c_1e^x +c_2e^{-x$

$0 = c_1 * e^1 + c_2 * e^{-1}$

$0 = c_1 e + \frac{1}{e}c_2$ --- (1)

$y'(1) =e$ implies that: x = 1 and y' = e

So, we have:

$y' = c_1e^x - c_2e^{-x}$

$e = c_1 * e^1 - c_2 * e^{-1}$

$e = c_1 e - \frac{1}{e}c_2$ --- (2)

Add (1) and (2)

$0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2$

$e = 2c_1e$

Divide both sided by e

$1 = 2c_1$

Divide both sides by 2

$c_1 = \frac{1}{2}$

Substitute $c_1 = \frac{1}{2}$ in $0 = c_1 e + \frac{1}{e}c_2$

$0 = \frac{1}{2} e+ \frac{1}{e}c_2$

Rewrite as:

$\frac{1}{e}c_2 = -\frac{1}{2} e$

Multiply both sides by e

$c_2 = -\frac{1}{2} e^2$

So, we have:

$y=c_1e^x +c_2e^{-x$

$y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}$

$y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}$

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3 years ago

Complete the table of values for..

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Answer:

Step-by-step explanation:

y = x² + x - 3

x = - 3

y = ( - 3 )² + ( - 3 ) - 3 = 3

( - 3 , <em>3</em> )

x = 0 ⇒ y = - 3

( 0 , <em>- 3</em> )

x = 1

y = ( 1 )² + ( 1 ) - 3 = - 1

( 1 , <em>- 1 </em>)

<em>(b).</em> Coordinate x of the vertex of quadratic equation y = ax² + bx + c is

- $\frac{b}{2a}$

x = - $\frac{1}{2(1)}$ = - $\frac{1}{2}$ = - 0.5

y = ( - 0.5 )² + ( - 0.5 ) - 3 = - 3.25 = - 3 $\frac{1}{4}$

( - $\frac{1}{2}$ , - 3 $\frac{1}{4}$ )

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3 years ago

Tania, a long distance runner, runs at an average speed of 5 mph. Five hours after tanning leaves your house, you leave in your

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It would take me Approximately 55 minutes to catch up with her and we would be 50 miles from my home

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Acceptance Sampling Random sampling from a large lot of manufactured items yields a number of defective items X with an approxim

AfilCa [17]

Answer:

Step-by-step explanation

Let β = np, n= 5 and p= 0, 0.1, 0.3, 0.5, 0.9 and 1

x > a, a= 0

The probability of an item inspected, P(x) = β∧x*e∧-β/x!

a) For x= 1: β = 5 X 0 = 0

P(x=1) = 0

For x = 2: β = 5 X 0.1 = 0.5

P(x=2) = 0.5²*e∧-0.5/2!

For x = 3: β = 5 X 0.3 = 1.5

P(x=3) = 1.5³*e∧-1.5/3!

For x =4: β = 5 X 0.5 = 2.5

P(x=4) = 2.5∧4*e∧-2.5/4!

For x = 5: β = 5 X 0.9 = 4.5

P(x=5) = 4.5∧5*e∧-4.5/5!

For x= 6: β = 5 X 1 = 5

P(x= 6) = 5∧6*e∧-5/6!

b) For plan1, x = 1: β + 10 X 0.1 = 1

P(x=1) = e∧-1/1! = 1/e = 1/2.718 = 0.368

For plan2, x=20: β = 100 X 0.1 = 10

P(x=20) = 10∧20*e∧-10/20!

Plan 2 is preferable because the probability of success is very small and the number of trial is comparatively large, hence, the poisson distribution will be suitable probability model.

d) Plan 1 is prefered instead, because the probability of success is larger and more profit is made.

e) Plen 2 is prefered, because it will be cheaper to afford.

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3 years ago

F(x)=x^2+9x-16<br><br><br> What is vertex <br><br> Axis of semetry

UNO [17]

Answer:

axis of symmetry is $x=\frac{-9}{2}$ .

The ordered pair of the vertex is $(\frac{-9}{2},\frac{-145}{4})$ .

Step-by-step explanation:

Your function is a quadratic.

Compare $x^2+9x-16$ to $ax^2+bx+c$ .

You should see that $a=1,b=9,c=-16$ .

The x-coordinate of the vertex or the axis of symmetry since the axis symmetry goes through the vertex can be found by computing $\frac{-b}{2a}$ .

So here we go!

The axis of symmetry is $x=\frac{-9}{2(1)}=\frac{-9}{2}$ .

When you write your axis of symmetry be sure to write it as an equation.

That is the axis of symmetry is $x=\frac{-9}{2}$ .

Now that was also the x-coordinate of your vertex. To find the corresponding y-coordinate of the vertex, plug your value for $x$ into

$y=x^2+9x-16$ .

$y=(\frac{-9}{2})^2+9(\frac{-9}{2})-16$

Put into calculator:

$y=\frac{-145}{4}$ when $x=\frac{-9}{2}$

The ordered pair of the vertex is $(\frac{-9}{2},\frac{-145}{4})$ .

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