Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624. Find the amount of his tax.

The explicit formula for the given sequence is a(n) = 2 . (0.5)ⁿ and the first five terms are: 1, 0.5, 0.25, 0.125, 0.0625

Given the parameters:

First term, a(1) = 1, and

common ratio, r = 0.5

We are ask to find the explicit formula for the geometric sequence and generate the first five terms.

Recall that in a geometric sequence:

a(n) = a(1) . rⁿ⁻¹

Where a(n) is the nth term.

Substituting a(1) = 1 and r = 0.5:

a(n) = 1 . (0.5)ⁿ⁻¹

       = (0.5)⁻¹. (0.5)ⁿ

       = 2 . (0.5)ⁿ

To generate the first five terms, we can use the above explicit formula for n = 1, 2, ..., 5  or we can use a recursive procedure. Remember that in a geometric sequence:

a(n) = a(n-1) . r

Therefore,

a(1) = 1  (given)

a(2) = 1 . (0.5) = 0.5

a(3) = 0.5 . (0.5) = 0.25

a(4) = 0.25 . (0.5) = 0.125

a(5) = 0.125 . (0.5) = 0.0625

Thus, the first five terms are: 1, 0.5, 0.25, 0.125, 0.0625

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From the calculation carried out below, the number of children admitted was 1,400 and the number of adults admitted was 700.

How do we calculate the different numbers of people admitted?

This question can be solved using the substitution method as follows:

x = Number of children admitted

y = Number of adults admitted

x + y = 2,100 ............................................. (1)

1.50x + 4y = 4,900 ................................ (2)

From equation (1), we have:

x = 2,100 - y ................................................. (3)

Substituting x = 2,100 - y into equation (2) and solving for y, we have:

1.50(2,100 - y) + 4y = 4,900

3,150 - 1.50y + 4y = 4,900

2.50y = 4,900 - 3,150

2.50y = 1,750

y = 1,750 / 2.50

y = 700

Substituting y = 700 into equation (3), we have:

x = 2,100 - 700

x = 1,400

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Answer:

Since the final answer has a factor of 4, it is a multiple of 4.

Step-by-step explanation:

Let the smaller even number be 2n.

The next greater even number is 2n + 2.

(2n)² + (2n + 2)² = 4n² + 4n² + 8n + 4 = 8n² + 8n + 4 = 4(2n² + 2n + 1)

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

Triangles are polygons with three sides and three perpendicular bisectors, whose equations need the informations of slopes and midpoints of each side. Bisectors are lines that partitions line segments in two parts of equal length.

First, determine the midpoints of each side:

Side AB

M₁(x, y) = 0.5 · (- 3, 0) + 0.5 · (0, 6)

M₁(x, y) = (- 1.5, 0) + (0, 3)

M₁(x, y) = (- 1.5, 3)

Side BC

M₂(x, y) = 0.5 · (0, 6) + 0.5 · (4, 6)

M₂(x, y) = (0, 3) + (2, 3)

M₂(x, y) = (2, 6)

Side AC

M₃(x, y) = 0.5 · (- 3, 0) + 0.5 · (4, 6)

M₃(x, y) = (- 1.5, 0) + (2, 3)

M₃(x, y) = (0.5, 3)

Second, determine the slope of the perpendicular bisectors:

Side AB

m = (6 - 0) / [0 - (- 3)]

m = 2

m' = - 1 / m

m' = - 1 / 2

Side BC

m = (6 - 6) / (4 - 0)

m = 0

m' = - 1 / m

m' = NaN  (Vertical line)

Side AC

m = [4 - (-3)] / (6 - 0)

m = 7 / 6

m' = - 1 / (7 / 6)

m' = - 6 / 7

Third, derive the equations of the bisectors:

Side AB

b = 3 - (- 1 / 2) · (- 1.5)

b = 9 / 4

y = - (1 / 2) · x + 9 / 4

Side BC

x = 2

Side AC

b = 3 - (- 6 / 7) · (0.5)

b = 24 / 7

y = - (6 / 7) · x + 24 / 7

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

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The next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].

According to the given question.

We have a sequence 3, 6, 12, 24, 48, ..

Since, the first term of the sequence is 3.

The second term of the sequence is 6.

The third term of the sequence is 12.

Here, we can say that the next term is twice the previous term.

So, the next two terms of the given sequence, i.e.

Sixth term = 48 × 2 = 96

Seventh term  = 96 × 192

Therefore, the formula for the nth term of the sequence is given by

[tex]T_{n+1} = 2T_{n}[/tex].

Hence, the next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].

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The solution of the given system of equations is (3//2, -3/8)

We can solve a system of equations using:

- graphical method

- elimination method

- substitution method

The given system of equations:

(1/2)x + (2/3)y= 1  ......... (1)

(3/4)x - (1/3)y = 2  ..........(2)

Multiply equation (1) by 6

3x + 4y = 6   ..... (3)

Multiply equation (2) by 12

9x - 4y = 24  ...... (4)

Add equation (3) and (4)

3x + 4y = 6  

9x - 4y = 24  +

12x      = 30

   x      = 30/12 = 5/2

Substitute x = 5/2 into equation (3)

3x + 4y = 6  

3. (5/2) + 4y = 6

15/2 +4y = 6

4y = (12 - 15)/2 = -3/2

 y = -3/8

The solution is (3/2, -3/8)

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The markup percent of the water blaster in the store is 30%

The store sells a water blaster for $26
They bought it for $20

New price is $26

Original price is $20

The markup percent can be calculated as follows

26-20/20 × 100

= 6/20 × 100

= 0.3 × 100

= 30%

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Refer to the image attached.

Parametric equation uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables. When necessary, more than one parameter can be used.

Now,

In order to plot the graphs of the given parametric equations, we will be sketching a table, in which, the values of the equations will be found at various values of the parameter.

=> Refer to the table in the image attached.

For the values so found of the parametric equations for the respective parameter, a graph will be plotted for both the equations:

Refer to the graph in the image attached.

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Answer:

4784.

Step-by-step explanation:

8 * 598 = 8(600- _2_)

=

8 (600) - 8(_2_)

= 4800 - _16_

= 4784__

[tex]-3s\textless11s+1\\\\\\\\-3s-11s < 1\\\\\\-14s < 1\\\\\\-s < \frac{1}{14} \\\\s > -\frac{1}{14}[/tex]

===========================

[tex]\textcopyright ELIZA[/tex]

Answer:

70

Step-by-step explanation:

21 is 30 % so multiply 21 by 3 which is 63 and then divide 21 by 3 which is 7 and add the 7 to 63

Answer:

a=7

b=8

c=12

d=33

find e by adding up all numbers in the Venn diagram then subtract the total amount of people by total from the Venn diagram to find e

Answer:

y = 2x - 3

Step-by-step explanation:

1) Find the slope

The slope of any function, if given the coordinates of at least two of the points it crosses, is given by the formula  [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].

We are given the points (4, 5) and (-1, -5), therefore, we can substitute their values:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-5)}{4 - (-1)} = \frac{10}5 = 2[/tex]

2) Find the line's equation
We can find the line's equation by substituting one of the given points and the slope we just found into the formula [tex]y - y_1 = m(x - x_1)[/tex]:

[tex]y - 5 = 2(x - 4) \\ \to y - 5 = 2x - 8 \\ \to y = 2x - 3[/tex]

Answer: 2x - 3.

Step-by-step explanation: I took the test.

Answer:

= (3 + -10 + -2 + 13 + 11) / 5

= 15/5

Step-by-step explanation:

3

Hey there!

Your mean simply means, your average….

To find it you have to ADD all of your numbers and DIVIDE it by the total number you have in your data plot.

3 + -10 + -2 + 13 + 11 / 5

= 3 - 10 - 2 + 13 + 11 / 5

= -7 - 2 + 13 + 11 / 5

= -9 + 13 + 11 / 5

= 4 + 11 / 5

= 15 / 5

= 3

Therefore, your answer should be: 3

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The slope of the line passing through the pair of points, (1 , 3) and (4 , 9), is 2.

The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:

m = (y2 - y1)/(x2 - x1)

where m is the slope

x1 and y1 are the coordinates of one point

x2 and y2 are the coordinates of the 2nd point

Given two points in the line, (1 , 3) and (4 , 9), plug in the values to the formula for the slope.

m = (y2 - y1)/(x2 - x1)

m = (9 - 3)/(4 - 1)

m = 6/3

m = 2

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The point-slope form is y - 3 = 2(x - 2) and 2x - y = 1 be the standard form.

Given: (x1, y1) = (2, 3) and (x2, y2) = (3, 5)

The point-slope form is given by,

y - y1 = m(x - x1)

m = (y2 - y1)/(x2 - x1)

substitute the values in the above equation, we get

m = (5 - 3)/(3 - 2)

The value of m = 2.

Point-slope form is y - 3 = 2(x - 2)

Therefore, the point-slope form is y - 3 = 2(x - 2).

How to rewrite the equation in standard form?

The standard form is Ax + By = C

Since, slope-intercept form is y = 2x - 1

⇒ 2x - y = 1

Therefore, 2x - y = 1 is the standard form.

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The probability that the spinner will land on a number that is not a multiple of 11 is 73/80.

Multiples of 11 are 11,22,33,44,55,66,77.

That means there are 7 multiples of 11

80 -7 = 73

There are 73 non multiples of 11

P( non multiples of 8) = non multiples of 11 / total

                                  = 73/80

Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.

The likelihood that an event will occur is measured by probability. It is difficult to provide a complete prediction for many events. By employing it, we are only able to forecast the likelihood of an event, or how likely it is, to occur.

According to the probability formula, the likelihood of an event occurring, or P(E), is determined by the proportion of positive outcomes to all other outcomes.

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Answer: 2 2/3

Step-by-step explanation:

Answer:

You showed the right work and got the right answer!

x = 6

Step-by-step explanation:

Since B is in the middle of A and C, AB + BC = AC

So,

2x - 11 + 8 = x + 3

x - 3 = 3

x = 6

y(2.5) = 15.9389 is Use euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem.

What is euler's method?

First-order methods, such as the Euler method, have local errors that are proportional to the square of the step size and global errors that are proportional to the step size.

f(x,y) = 3y+2xy

So, starting at t0 = 2, repeat the above sequence until t0>2.5

a) m = f(2,1) = 3(1)+2(2)(1) = 7

b) y1 = y0 + hm = 1+0.1(7) = 1.7

c) t1 = t0 + h = 2.1

d) show t1 and y1

e) t0 = t1 = 2.1

f) y0 = y1 = 1.7

2nd iteration

a) m = f(2.1,1.7) = 3(1.7)+2(2.1)(1.7) = 5.1 + 7.14 = 12.24

b) y1 = y0 + hm = 1.7+0.1(12.24) = 1.7 + 1.224 = 2.924

c) t1 = t0 + h = 2.2

d) show t1 and y1

e) t0 = t1 = 2.2

f) y0 = y1 = 2.924

This is what I got for all iterations from a simple program x y

2.1 1.7

2.2 2.924

2.3 5.08776

2.4 8.9544576

2.5 15.938934528

y(2.5) = 15.9389

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The expression will give value 28

To evaluate the expression for the given value of variables, we will keep the value of each variable in the equation. The expression will be solved based on the arithmetic operators given in expression.

Rewriting the expression -

Value = 9t + 6 (2v - t) - 7v

Now keeping the value of v and t in expression to find the value.

Value = 9×1 + 6 (2×5 - 1) - 7×5

Firstly solving the bracket and performing multiplication of extreme left and right values of expression

Value = 9 + 6 (10 - 1) - 35

Value = 9 + 6 (9) - 35

Value = 9 + 54 - 35

Performing addition before subtracting the values

Value = 63 - 35

Performing subtraction

Value = 28

Hence, the expression according to given variables is equal to 28.

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The dimensions of the rectangular playing field are:

length = 92 yards and

width = 24 yards.

Given, the perimeter of the rectangular field is : 232 yards.

From the given question, length of the field is 4 yards less than quadruple the width.

hence, let the width of the field be x yards.

Length of the field = 4x - 4 yards.

we know that perimeter of the rectangle = 2(l+w)

therefore, substitute the values in the above formula:

2(4x - 4 + x) = 232

2(5x - 4) = 232

multiply the terms.

10x - 8 = 232

arrange the constants on one side.

10x = 232 + 8

10x = 240

x = 240/10

x = 24

hence we get the width as x = 24 yards.

Now substitute the value of x to find out the value of the length.

therefore, l = 4x - 4

l = 4(24) - 4

l = 96 - 4

l = 92

Therefore length and width of the rectangular field is 92 and 24 yards respectively.

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The probability that the first chip is green and the second is brown is 1/20,

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Given that A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.

The probability of selecting the chip is green;

= 5/20

= 1/4

The probability of selecting the chip is brown;

= 4/20

= 1/5

Then the probability that the first chip is green and the second is brown

= 1/4 x 1/5

= 1/20

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The profession that is projected to have the greatest percent of increase in the number of jobs from 2006 to 2016 is B. sound engineer technician.

The increase in percentage for orthodontist will be:

= (10214 - 9206) / 9206 × 100

= 1008 / 9206 × 100

= 10.95%

The increase in percentage for sound engineer will be:

= (17864 - 16125) / 16125 × 100

= 1739/16125 × 100

= 10.79%

The increase in percentage for police officer will be:

= (719041 - 648982) / 719041 × 100

= 70059/719041 × 100

= 9.74%

The increase in percentage for editor will be:

= (124135 - 122273)/124135 × 100

= 1862/124135 × 100

= 1.5%

Therefore, the sound engineer has the greatest percentage increase.

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Answer:

sound engineer

Step-by-step explanation:

Answer:

[tex]y = -5x - 23[/tex]

Step-by-step explanation:

To write an equation in the slope-intercept form for a line, given the coordinates of a point on the line as well as the line's slope, we use the following formula:

[tex]\boxed{y - y_1 = m(x - x_1)}[/tex],

where [tex]m[/tex] is the slope of the line and [tex](x_1, y_1)[/tex] are the given coordinates of a point.

In this question, we are told that the slope is -5 and the coordinates of a point passing through the point are (-3, -8).

Therefore, using the above formula, we can write:

[tex]y - (-8) = -5(x - (-3))[/tex]

⇒ [tex]y + 8 = -5(x + 3)[/tex]

⇒ [tex]y + 8 = -5x - 15[/tex]           [Distributing -5 into the brackets]

⇒ [tex]y = -5x - 15 - 8[/tex]           [Subtracting 8 from both sides]

⇒ [tex]y = -5x - 23[/tex]

This means that the equation for the slope-intercept form of the line is  [tex]y = -5x - 23[/tex] .

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Answer:

-t*(t -16) ≥ 39

-t*(t -16)  = 39

t = 3 or 13 hours

Step-by-step explanation:

When number of people is at 39 or more means the number of people of greater than or equal to 39.

 So, the inequality is,

          -t*(t -16) ≥ 39

When the number of people is 39, the equation is,

     -t*(t - 16) = 39

     -t²+ 16t   = 39

0 = 39 + t² - 16t

t² - 16t + 39 = 0

Sum = -16

Product = 39

Factors = -3 , -13   [ (-3) * (-13) = 39  & (-3) +(-13) = -16 ]

Rewrite the middle term using the factors.

t² - 3t - 13t + 39 = 0

t(t -3) - 13(t - 3) = 0

(t -3)( t - 13)     = 0

     t -3 = 0     ; t- 13 = 0

          t = 3  or  t = 13

t = 3 hours or 13 hours.