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3 years ago

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Net income is equal to the total revenue from selling an item minus the cost of producing the item. Determine the net income if

the revenue from a business is $400,000 and the cost is $156,800. Use 4072-01-01-03-00_files/i0330000.jpg where I = net income, R = revenue, C = cost

1 answer:

Travka [436]3 years ago

3 0

C-Cost because it the most reasonableness one

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The sum of the first n terms of an arithmetic series is n/2(3n-5). If the second and fourth terms of the arithmetic series are t

sergiy2304 [10]

Let <em>a</em> be the first term in the arithmetic sequence. Since it's arithmetic, consecutive terms in the sequence differ by a constant <em>d</em>, so the sequence is

<em>a</em>, <em>a</em> + <em>d</em>, <em>a</em> + 2<em>d</em>, <em>a</em> + 3<em>d</em>, …

with the <em>n</em>-th term, <em>a</em> + (<em>n</em> - 1)<em>d</em>.

The sum of the first <em>n</em> terms of this sequence is given:

$a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n(3n-5)}2$

We can simplify the left side as

$\displaystyle \sum_{i=1}^n (a+(i-1)d) = (a-d)\sum_{i=1}^n1 + d\sum_{i=1}^ni = an+\dfrac{dn(n-1)}2$

so that

$an+\dfrac{dn(n-1)}2 = \dfrac{n(3n-5)}2$

or

$a+\dfrac{d(n-1)}2 = \dfrac{3n-5}2$

Let <em>b</em> be the first term in the geometric sequence. Consecutive terms in this sequence are scaled by a fixed factor <em>r</em>, so the sequence is

<em>b</em>, <em>br</em>, <em>br</em> ², <em>br</em> ³, …

with <em>n</em>-th term <em>br</em> ⁿ⁻¹.

The second arithmetic term is equal to the second geometric term, and the fourth arithmetic term is equal to the third geometric term, so

$\begin{cases}a+d = br \\\\ a+3d = br^2\end{cases}$

and it follows that

$\dfrac{br^2}{br} = r = \dfrac{a+3d}{a+d}$

From the earlier result, we then have

$n=7 \implies a+\dfrac{d(7-1)}2 = a+3d = \dfrac{3\cdot7-5}2 = 8$

and

$n=2 \implies a+\dfrac{d(2-1)}2 = a+d = \dfrac{3\cdot2-5}2 = \dfrac12$

so that

$r = \dfrac8{\frac12} = 16$

and since the second arithmetic and geometric terms are both 1/2, this means that

$br=16b=\dfrac12 \implies b = \dfrac1{32}$

The sum of the first 11 terms of the geometric sequence is

<em>S</em> = <em>b</em> + <em>br</em> + <em>br</em> ² + … + <em>br</em> ¹⁰

Multiply both sides by <em>r</em> :

<em>rS</em> = <em>br</em> + <em>br</em> ² + <em>br</em> ³ + … + <em>br</em> ¹¹

Subtract this from <em>S</em>, then solve for <em>S</em> :

<em>S</em> - <em>rS</em> = <em>b</em> - <em>br</em> ¹¹

(1 - <em>r</em> ) <em>S</em> = <em>b</em> (1 - <em>r</em> ¹¹)

<em>S</em> = <em>b</em> (1 - <em>r</em> ¹¹) / (1 - <em>r</em> )

Plug in <em>b</em> = 1/32 and <em>r</em> = 1/2 to get the sum :

$S = \dfrac1{32}\cdot\dfrac{1-\dfrac1{2^{11}}}{1-\dfrac12} = \boxed{\dfrac{2047}{32768}}$

6 0

3 years ago

Two six-sided number cubes are rolled. What is the probability that a product of 12 is rolled? Express your answer as a decimal.

Aleksandr-060686 [28]

Answer:

1/9

Or .11 repeating (~.11)

Step-by-step explanation:

36 ways, because of 6 * 6.

Now, let's analyze 12.

2 * 6,

6 * 2,

3 * 4,

4 * 3.

That's 4/36 ways. Also simplified to 1/9

7 0

3 years ago

Kim bought 12 boxes of drinks He paid $15 for each box. There were 12 drinks in each box. Kim sold 3/4 of the drinks for $1.50 e

ella [17]

Answer:

what's the question ?

Step-by-step explanation:

6 0

3 years ago

303 is 93% of what? 3.26 32.58 325.81 3,258.06

emmasim [6.3K]

325.81
It is correct im sure of it

5 0

3 years ago

Answer question 11 and 12

Darya [45]

Answer:

11. y = -2x - 4.

12. y = x - 5

Step-by-step explanation:

11. the given points on the line are ((-2, 0) and (0, -4)

The slope of the line

= difference in y values / corresponding difference in x values

= ( - 4 - 0) / 0 - (-2))

= -4 / 2

= -2.

The general form of a straight line is y = mx + c where m = the slope and c = y value of the intercept on the y-axis.

So the equation is:

y = -2x - 4.

12.

The points are (1, -4) and (3, -2).

The slope is (-2 - (-4)) / (3 - 1)

= 2/2

= 1.

So the equation is

y = 1x + c

We find c by plugging in the point (1, -4):

-4 = 1 + c

c = -4 - 1

c = -5.

The equation is y = x - 5.

5 0

3 years ago