Evan wants to make an array of 32 miniature cars What are all the different ways Evan can place the cars? ​

Answer:

[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........[/tex]

The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]

Step-by-step explanation:

Given

[tex]f(x)= \frac{9}{3x+ 2}[/tex]

[tex]c = 6[/tex]

The geometric series centered at c is of the form:

[tex]\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.[/tex]

Where:

[tex]a \to[/tex] first term

[tex]r - c \to[/tex] common ratio

We have to write

[tex]f(x)= \frac{9}{3x+ 2}[/tex]

In the following form:

[tex]\frac{a}{1 - r}[/tex]

So, we have:

[tex]f(x)= \frac{9}{3x+ 2}[/tex]

Rewrite as:

[tex]f(x) = \frac{9}{3x - 18 + 18 +2}[/tex]

[tex]f(x) = \frac{9}{3x - 18 + 20}[/tex]

Factorize

[tex]f(x) = \frac{1}{\frac{1}{9}(3x + 2)}[/tex]

Open bracket

[tex]f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}[/tex]

Rewrite as:

[tex]f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}[/tex]

Collect like terms

[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}[/tex]

Take LCM

[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}[/tex]

[tex]f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}[/tex]

So, we have:

[tex]f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}[/tex]

By comparison with: [tex]\frac{a}{1 - r}[/tex]

[tex]a = 1[/tex]

[tex]r = -\frac{1}{3}x + \frac{7}{9}[/tex]

[tex]r = -\frac{1}{3}(x - \frac{7}{3})[/tex]

At c = 6, we have:

[tex]r = -\frac{1}{3}(x - \frac{7}{3}+6-6)[/tex]

Take LCM

[tex]r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)[/tex]

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)

So, the power series becomes:

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}ar^n[/tex]

Substitute 1 for a

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}1*r^n[/tex]

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}r^n[/tex]

Substitute the expression for r

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n[/tex]

Expand

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n][/tex]

Further expand:

[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................[/tex]

The power series converges when:

[tex]\frac{1}{3}|x - \frac{7}{3}| < 1[/tex]

Multiply both sides by 3

[tex]|x - \frac{7}{3}| <3[/tex]

Expand the absolute inequality

[tex]-3 < x - \frac{7}{3} <3[/tex]

Solve for x

[tex]\frac{7}{3} -3 < x <3+\frac{7}{3}[/tex]

Take LCM

[tex]\frac{7-9}{3} < x <\frac{9+7}{3}[/tex]

[tex]-\frac{2}{3} < x <\frac{16}{3}[/tex]

The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]

Write z in polar form:

z = 1 + √3 i = 2 exp(i π/3)

Taking the square root gives two possible complex numbers,

√z = √2 exp(i (π/3 + 2kπ)/2)

with k = 0 and k = 1, so that

√z = √2 exp(i π/6) = √(3/2) + √(1/2) i

and

√z = √2 exp(i 7π/6) = -√(3/2) - √(1/2) i

Answer:

Subtraction, and then division.

Step-by-step explanation:

We would subtract 3 on each side to undo the '3', and then divide by 6 on both sides to isolate 'x'.

[tex]6x+3 = 9\\\\6x + 3 - 3 = 9 - 3\\\\ 6x = 6\\\\\frac{6x=6}{6}\\\\\boxed{x=1}[/tex]

Hope this helps.

To solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.

A linear equation in one variable has the standard form Px + Q = 0. In this equation, x is a variable, P is a coefficient, and Q is constant.

Given that 6x + 3 = 9.

First, we have to separate variable and constants. So, we have to subtract 3 from both sides.

6x + 3 - 3 = 9 - 3

i.e. 6x = 6

Now, to solve this equation, we use division.

x = 6/6 = 1

i.e. x = 1

Therefore, to solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.

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x = 30

y = 2

Get the explanation from the image I have shared.

Hope it helps you

Answer:

A statement that shows current balance of an account and all transactions that occurred on that account since the last statement.

Transactions such as deposits, withdrawals, checks written, debt card uses...

There are other examples of bank statements for things like home loans, business loans, and investments.

Answer:

Kindly check explanation

Step-by-step explanation:

H0 : quality does not vary among shift

H1 : quality varies among shift

The expected values :

(Row * column) / grand total

Given the data:

Observed values :

_________________total

_______467 191 42 __700

_______445 171 34 __650

_______254 129 17 _ 400

Total __ 1166 491 93 _ 1750

Expected value count using the formula :.

Expected Values:

466.4 ____196.4 ______37.2

433.086 _182.371___ 34.5429

266.514_ 112.229____ 21.2571

The Chisquare statistic (χ²) :

χ² = (observed - Expected)²/ observed

χ² = 5.76045

The degree of freedom = (row - 1) * (column - 1)

Degree of freedom = (3-1)*(3-1) = 2*2 = 4

Pvalue = 0.2178

Pvalue > α ; We foal to reject H0 ; Hence, we conclude that quality does not vary among shift

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A graphing calculator does a nice job of graphing these equations.

__

The very steep slope suggests the graph will need somewhat different vertical and horizontal scales in order to show anything useful.

Answer:

B for first one.

75 for second.

Hope this helps !

Step-by-step explanation:

Answer:

Step-by-step explanation:

I=∫e^2x dx

put 2x=t

2dx=dt

dx=dt/2

I=1/2∫e^t dt

=1/2 e^t+c

=1/2 e^{2x}+c

Answer:

The average rate of change in the number of public library visits from 1993 to 1997 was of 0.1 billion an year.

Step-by-step explanation:

Average rate of change:

Division of the subtraction of the final value by the initial value, divided by the length of time.

The number of visits to public libraries increased from 1.3 billion in 1993 to 1.7 billion in 1997.

Initial value: 1.3 billion

Final value: 1.7 billion

1997 - 1993 = 4 years.

Thus:

[tex]A = \frac{1.7 - 1.3}{4} = \frac{0.4}{4} = 0.1[/tex]

The average rate of change in the number of public library visits from 1993 to 1997 was of 0.1 billion an year.

9514 1404 393

Answer:

  $58,800

Step-by-step explanation:

Each year, the value is multiplied by 1-1/15 = 14/15. Then after 2 years, the initial value has been multiplied by (14/15)^2 = 196/225. The value after 2 years is ...

  $67,500×196/225 = $58,800

Answer:

X = 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

No

Answer:

[tex]The \ two \ numbers \ are \ \frac{1}{6} \ and \ \frac{5}{6}[/tex]

Step-by-step explanation:

Let the two numbers be = x , y

Given:

    One of the number is 5 times other number, that is y = 5x ----- ( 1 )

    The sum of their reciprocals is 36/5 , that is

                                                                    [tex]\frac{1}{x} + \frac{1}{y} = \frac{36}{5}[/tex]   ------ ( 2 )

  Substitute y in the second equation.

      [tex]\frac{1}{x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{1 \times 5}{5 \times x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{5}{5x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{5+1}{5x} = \frac{36}{5}\\\\\frac{6}{5x} =\frac{36}{5}\\\\36 \times 5x = 6 \times 5\\\\x = \frac{6 \times 5}{36 \times 5} = \frac{1}{6}[/tex]

  Substitute x in first equation.

   [tex]y = 5x\\\\y = 5 \times \frac{1}{6} \\\\y = \frac{5}{6}[/tex]

Answer:

B. The nominal level of measurement is most appropriate because data cannot be ordered.

Step-by-step explanation:

Nominal scale is used when there is no specific order scale and data can be arranged according to name. Ordinal scale requires variables to be arranged in specific order. For fast food restaurant the best scale used is nominal scale as variables can be arranged according to their name without specific order.

9514 1404 393

Answer:

  y = (1/3)√x

Step-by-step explanation:

Vertical scaling of a function is accomplished by multiplying the function by the scale factor. If you want to scale the square root function by a factor of 1/3, then the scaled function is ...

  y = (1/3)√x

The statement that correctly describes  the symmetry of the cubic parent function is 'It is symmetric about the origin.'

The correct answer is option (c)

"The graph of the function is said to be symmetric about X-axis if whenever (a, b) is on the graph then so is (a, -b) "

"The graph of the function is said to be symmetric about Y-axis if whenever (a, b) is on the graph then so is (-a, b) "

"The graph of the function is said to be symmetric about X-axis if whenever (a, b) is on the graph then so is (-a, -b) "

For given question,

The parent cubic function is [tex]f(x)=x^3[/tex]

The graph of the function  [tex]f(x)=x^3[/tex] is as shown below.

From graph we can observe that, point (x, y) as well as (-x, -y) is on the graph.

This means, the graph of  the function  [tex]f(x)=x^3[/tex] is symmetric about the origin.

Therefore, the statement that correctly describes  the symmetry of the cubic parent function is 'It is symmetric about the origin.'

The correct answer is option (c)

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The missing side 'a' of the triangle ABC is 96.80 units.

What is a triangle?

A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.

For the given situation,

Let ABC be the triangle and a,b,c be the respective sides of the triangle.

The diagram below shows that the triangle with their dimensions.

The dimensions are

A=60°, b=50, c=48.

The two sides and one angle of the triangle are given.

The missing side a can be found by using the law of cosines,

[tex]a=\sqrt{b^{2}+c^{2} -2abcosA }[/tex]

Substitute the above values,

⇒ [tex]a=\sqrt{50^{2}+48^{2} -2(50)(48)cos60 }[/tex]

⇒ [tex]a=\sqrt{2500+2304-4800(-0.9524)}[/tex]

⇒ [tex]a=\sqrt{2500+2304+4571.58}[/tex]

⇒ [tex]a=\sqrt{9375.58}[/tex]

⇒ [tex]a=96.82[/tex] ≈ [tex]96.80[/tex]

Hence we can conclude that the missing side 'a' of the triangle ABC is 96.80 units.

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Answer:

it's equal to 21 when I say it's equal to 21

D

Because slope of section D is greater than the others and hence speed is highest.

Answer:

The desired distance is √5

Step-by-step explanation:

Recall that the distance from a point to a line is measured along a path perpendicular to the line.  Thus, given the line y = -2x + 5, the slope of any line perpendicular to it is the negative reciprocal of -2:  +1/2.

The line perpendicular to y = -2x + 5 and passing through (4, 2) is

y - 2 = (1/2)(x - 4), or

2y - 4 = x - 4, or 2y = x, or y = (1/2)x.

Now our problem becomes "find the length of the line connecting (4, 2) and the intersection of y = -2x + 5 and y = (1/2)x."  

Equating these, we get (1/2)x = -2x + 5, which, if multiplied through by 2, becomes x = -4x + 10, or 5x = 10, or x = 2.  If x = 2, then y = (1/2)(2) = 1.

Finally, find the distance between (2, 1) and (4, 2):

Using the Pythagorean Theorem, d = √(2^2 + 1^2) = √5

The distance from (4, 2) to the line y = -2x + 5 is √5

Step-by-step explanation:

[tex] \sqrt{15} = 3.872983346 = 3.88[/tex]

Answer:

Contribution margin = Revenue − Variable costs

Step-by-Step Explanation

For example, if the price of your product is $20 and the unit variable cost is $4, then the unit contribution margin is $16.

The first step in doing the calculation is to take a traditional income statement and recategorize all costs as fixed or variable. This is not as straightforward as it sounds, because it’s not always clear which costs fall into each category.

Hope this helps and if it does, don't be afraid to rate my answer as well as maybe give it a "Thanks"? (Or even better a "Brainliest"). And if it’s not correct, I am sorry for wasting your time, and good luck finding the correct answer :)  

Answer:c>2

Step-by-step explanation:

-6c (divide) (-6) > -12 (divide) (-6)

c>-12 (divide) (-6)

c>12 (divide) 6

c> 2

Answer:

5.23%

Step-by-step explanation:

See Image below:)

Answer:2921

Step-by-step explanation: Add the two equations together to get (x+y)+(x-y)=3500+2342. Simplify and get 2x=5842. Divide 5842 by 2 and get 2921.

Answer:

(First of all its 20 points not 40 but any ways) A ferris wheel has a raidus of 20 m. Passengers get on halfway up on the right side. The direction of rotation is counter clockwise. The bottom of the ferris wheel is 2 m above ground. It rotates every 36 seconds. Determine height above the ground after 15 seconds algebraically. Determine seconds to the nearest tenth when height is 38 m above the ground algebraically.

**

let t=seconds after wheel starts to rotate.

let h=meters above ground after wheel starts to rotate

..

The formula I got: h(t)=20sin(πt/18)+22

This is close to the formula you got, except I left the negative sign out since passengers start to rise after the wheel starts going counter-clockwise.

..

After 15 seconds:

h=20sin(15π/18)+22

=20sin(5π/6)+22

=20*(1/2)+22

=32 m

..

When h=38 m

38=20sin(πt/18)+22

38-22=20sin(πt/18)

20sin(πt/18)=16

sin(πt/18)=16/20=4/5=.8

arcsin(.8)=0.927

πt/18=0.927 (radians)

t=(.927*18)/π≈5.31

..

height above the ground after 15 seconds≈38 m

seconds elapsed when height is 38 m above ground≈5.3 seconds

Answer:

Kindly check explanation

Step-by-step explanation:

Given :

Pool dimension :

rectangular floor that measures 22 feet by 13 feet and a flat ceiling that is 7 feet above the floor

Floor area = length * width

Floor area = 22 * 13 = 286 ft²

Volume of the pod :

Floor area * height = 286ft² * 7ft = 2002 ft³

2.)

Surface area = length * width

Surface area = 28 * 20 = 560 ft²

Volume of the pool :

Surface area * deptb = 560ft² * 7ft = 2002 ft³

3.)

Area of flower bed = length * width

Floor area = 30 * 5 = 150 ft²

Volume of the soil flowerbed holds :

Depth = 1.1 m

Area of flowerbed * depth =150ft² * 1.2ft = 180 ft³

Answer:

sin(C) = opposite side / hypotenuse

= 15/17

Answer:

[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]

Step-by-step explanation:

[tex] \small \sf \: Sin ( C ) = \frac {Opposite \: side }{Hypotenuse} \\ [/tex]

Where we have given :-

substitute the values, we get

[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]