In a US presidential election of the 227 million eligible voters, 51.5 percent voted in the election. Let A and B be the number of people who voted for candidates Alpha and Beta, respectively.

How many people voted in the election?

Assume all voters voted for candidate Alpha or candidate Beta. Write an equation for A in terms of B

Candidate Alpha won the popular vote by 4.8 million votes. Write an equation for A in terms of B

Assuming b. and c., how many people voted for candidate Beta?

Assuming b. and c., how many people voted for candidate Alpha?

Decompose each given F(s) into partial fractions.

[tex]F(s) = \dfrac{s+1}{s(s-1)(s-3)}[/tex]

has partial fraction decomposition

[tex]\dfrac{s+1}{s(s-1)(s-3)} = \dfrac as + \dfrac b{s-1} + \dfrac c{s-3}[/tex]

Combine the rational terms on the right and solve for the coefficients:

[tex]\dfrac{s+1}{s(s-1)(s-3)} = \dfrac{a(s-1)(s-3) + b s(s-3) + c s(s-1)}{s (s-1) (s-3)}[/tex]

[tex]1 = a(s-1)(s-3) + bs(s-3) + c s(s-1)[/tex]

[tex]1 = 3 a + (-4 a - 3 b - c) s + (a + b + c) s^2[/tex]

[tex]\begin{cases}3a=1 \\ -4a-3b-c = 0 \\ a+b+c=0 \end{cases} \implies a=\dfrac13, b=-\dfrac12, c=\dfrac16[/tex]

Then

[tex]F(s) = \dfrac13 \times \dfrac1s - \dfrac12 \times \dfrac1{s-1} + \dfrac16 \times \dfrac1{s-3}[/tex]

Using the frequency-shifting property, the inverse transform is

[tex]\boxed{f(t) = \dfrac13 - \dfrac{e^t}2 + \dfrac{e^{3t}}6}[/tex]

The other transform can be dealt with in the same manner.

[tex]F(s) = \dfrac1{(s-1)(s-2)(s-3)} = \dfrac a{s-1} + \dfrac b{s-2} + \dfrac c{s-3}[/tex]

[tex]\implies 1 = a(s-2)(s-3) + b(s-1)(s-3) + c(s-1)(s-2)[/tex]

[tex]\implies 1 = 6 a + 3 b + 2 c + (-5 a - 4 b - 3 c) s + (a + b + c) s^2[/tex]

[tex]\implies \begin{cases}6 a + 3 b + 2 c=1 \\ -5a-4b-3c = 0 \\ a+b+c=0\end{cases} \implies a=\dfrac12, b=-1, c=\dfrac12[/tex]

[tex]\implies F(s) = \dfrac12 \times \dfrac1{s-1} - \dfrac1{s-2} + \dfrac12 \times \dfrac1{s-3}[/tex]

[tex]\implies \boxed{f(t) = \dfrac{e^t}2 - e^{2t} + \dfrac{e^{3t}}2}[/tex]

In hexadecimal/base-16, we have B₁₆ = 11, C₁₆ = 12, and D₁₆ = 13, so

4D₁₆ = 4 × 16¹ + 13 × 16⁰ = 77

and

BC2₁₆ = 11 × 16² + 12 × 16¹ + 2 × 16⁰ = 3010

Answer:

300

Step-by-step explanation:

60 * 5 = 300

heres a link hope it help you

https://www.journaldespalaces.com/carriere/offre-118597-Officier-de-restauration-Cafetier.html

Translation involves moving a function along its coordinates

The image of the function is [tex]g(x) = (x + 2)^2 - 6[/tex]

The parent function is given as:

[tex]f(x) = x^2[/tex]

When the function is translated 2 units left, we have:

[tex]f'(x) = (x + 2)^2[/tex]

When the function is translated 6 units down, we have:

[tex]f"(x) = (x + 2)^2 - 6[/tex]

Rewrite as:

[tex]g(x) = (x + 2)^2 - 6[/tex]

Hence, the image of the function is [tex]g(x) = (x + 2)^2 - 6[/tex]

Read more about translation at:

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Answer:

If he earns (e) $7.75 per hour, this implies e = 7.75h.

Step-by-step explanation:

If you wanted to solve that-

e = 7.75h

193.75 = 7.75h

Divide both sides by 7.25  

h = 25

Answer: proportional

Step-by-step explanation: just took the quiz

Answer:

T = 31

Step-by-step explanation:

(T + 8) + T = 70

subtract 8 from both sides

T+T = 62

Rewrite

2T = 62

divide both sides by 2

T = 31

Answer:

Step-by-step explanation:

The factored form of a quadratic function is f (x) = a (x - p) (x - q) where p and q are the zeros of f (x).

Answer:

Step-by-step explanation:

x-axis and y-axis meet at (0, 0), that is the origin

Answer:

$9,360

Explanation:

so for 1040 hours, he earned:

$9 * 1,040

$9,360

The required equation that can be used to figure out how many miles Hugh and his brothers have traveled based on the number of miles they have driven is y = 65x

Given the following variables

Time taken to travel is x

Mils traveled is y

Using the coordinate points (2, 130) and (4, 260)

The standard linear equation is y = mx + b

slope m = 260-130/4-2
m = 130/2

m = 65

For the intercept

130 = 65(2) + b

b = 0

The required equation that can be used to figure out how many miles Hugh and his brothers have traveled based on the number of miles they have driven is y = 65x

Learn more on linear functions here; https://brainly.com/question/14323743

Answer:

Option A

Step-by-step explanation:

Both fractions have common denominators (x - 4). So, we can add the numerators.

[tex]\dfrac{x-9}{x-4}+\dfrac{x^{2}-x+5}{x-4}=\dfrac{x-9 +x^{2}-x +5}{x-4}\\\\\\=\dfrac{x -x +x^{2}-9+5}{x-4}\\\\\\=\dfrac{x^{2}-4}{x-4}[/tex]

Answer:

10/11

Step-by-step explanation:

Answer:

where is the table?

Step-by-step explanation:

._.

Given :

⠀

To Find :

⠀

Solution :

We know that,

[tex]\qquad { \pmb{ \bf{Length \times Width = Area_{(rectangle)}}}}\:[/tex]

⠀

Now substituting the values :

[tex]\qquad {\dashrightarrow{ \sf{214 \: in\times 234 \: in = Area_{(rectangle)}}}}\:[/tex]

[tex]\qquad {\dashrightarrow \: { { \sf{50,076 \: {in}^{2} = Area_{(rectangle)}}}}\:}

[/tex]

⠀

Hence, The area of the rectangle is 50,076 in² .

The area of a rectangle with a length of 2 1/4 inches and a width of 2 3/4 inches is 6 3/16 in². Option C is correct.

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

[tex]A=a\times b[/tex]

Here, (a)is the length of the rectangle and (b) is the width of the rectangle.

The rectangle given in the problem has,

Thus, the area of the rectangle is,

[tex]A=2\dfrac{1}{4}\times2\dfrac{3}{4}\\A=\dfrac{8+1}{4}\times\dfrac{8+3}{4}\\A=\dfrac{9}{4}\times\dfrac{11}{4}\\A=\dfrac{99}{16}\\\A=\dfrac{96+3}{16}\\A=6\dfrac{3}{16}[/tex]

Thus, the area of a rectangle with a length of 2 1/4 inches and a width of 2 3/4 inches is 6 3/16 in². Option C is correct.

Learn more about the area of rectangle here;

https://brainly.com/question/11202023

Answer:

you would have to separate the shapes and find out what the area  of them both and add them together

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 3 5 are all odd numbers.

There are 6 numbers all together on a die. 1 2 3 4 5 6

That means that 3/6 times, he should roll an odd number

3/6 * 78 = 39

He should get 39 rolls which are an odd number.

Answer:

You find the range by subtracting the smallest value from the highest in the set. So in this case, it would be 5-0=0

Step-by-step explanation:

Hope This Helps

Have A Great Day

~Zero~

Answer:

[tex]\huge\boxed{\sf{b=55\:(b=y-intercept\:;)}}[/tex]

Step-by-step explanation:

Hello.

The y-intercept of a line is a point where the graph touches the y-axis.

Y-intercepts always have an x-coordinate of 0.

Now, what is the y-intercept?

If we have a point (0, b) then b is the y-intercept.

This is just a formula, so don't think that the y-intercept is b, okay?

The y-intercept is b, but only in formulae. :)

Using the formula, we can deduce that

the y-intercept is 55.

I hope it helps.

Have a great day.

[tex]\boxed{imperturbability}[/tex]

Answer:

The answer is B 80.00 hope this helps

have a nice day

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answered here: https://brainly.com/question/26774005

Answer:

i'm not sure but here's some encouragement- YOU CAN DO IT

Step-by-step explanation:

[tex]f(x)=cos(x)x^{-2}\implies f(x)=\cfrac{cos(x)}{x^2}\implies \cfrac{df}{dx}=\stackrel{\textit{quotient rule}}{\cfrac{-sin(x)\cdot x^2-cos(x)\cdot 2x}{(x^2)^2}} \\\\\\ \cfrac{df}{dx}=\cfrac{-x[x\cdot sin(x)+2cos(x)]}{x^4}\implies \cfrac{df}{dx}=\cfrac{-[xsin(x)+2cos(x)]}{x^3}[/tex]

We need slope

[tex]\\ \rm\Rrightarrow m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \rm\Rrightarrow m=\dfrac{2-1}{6-3}[/tex]

[tex]\\ \rm\Rrightarrow m=\dfrac{1}{3}[/tex]

This can be solved using two methods:

Method #1:

The slope is 1/3.

Method #2:

The slope is 1/3.

Looking at the two methods, we can conclude that:

The slope of the line is 1/3.

Answer:

<

Step-by-step explanation:

Answer:

The y-intercept is the point at which the graph crosses the y-axis. At this point, the x-coordinate is zero. To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y.

Step-by-step explanation:

hope it helps