a certain type of aluminum screen 2 feet in width has, on the average, three flaws in a 100-foot roll. we assume flaws occur randomly so the number of flaws follow some poisson distribution. what is the probability that the first 40 feet in a roll contain no flaws?

The solution of the polynomial division 12x³ + 5x² - 27x + 13 is divided by 3x - 1 is; 4x² + 3x - 8 + (5/(3x - 1))

We want to use long division method to solve the polynomial division when 12x³ + 5x² - 27x + 13 is divided by 3x - 1.

             4x² + 3x - 8

          -------------------------

3x - 1  | 12x³ + 5x² - 27x + 13

         -  12x³ - 4x²        

          -----------------------------

                     9x² - 27x  

                 -   9x² - 3x

          -----------------------------

                            -24x + 13

                        -    -2x + 8

          -----------------------------

                                      5

          -----------------------------

Expressing the solution of the polynomial division in the given quotient and remainder form gives us;   4x² + 3x - 8 + (5/(3x - 1))

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Answer:

The range is the allowed values of y.

Set notation: { y | -9 [tex]\leq[/tex] y [tex]\leq[/tex] 0, y ∈ R}

Interval notation: [-9,0]

Hope that helps

For the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.

As given in the question,

For the saving account,

Amount deposited is directly proportional to the number of weeks

Let y be the amount deposited and x be the number of weeks

y ∝ x

y = kx

'k' is the constant of proportionality

As per data unit rate is measured in dollars per week

For y = $14 then x = 2 weeks

14 = 2k

⇒ k = $7

For y = $35 then x = 5weeks

35 =5k

⇒ k = $7

Therefore, for the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.

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The coordinates of the endpoint G is (0, 7).

The midpoint of the coordinate is the centre point which can be calculated by finding the average. So, the relation representing the endpoints and midpoint is as follows -

Midpoint (x, y) = ([tex] x_{1}[/tex] + [tex] x_{2}[/tex]/2), ([tex] y_{1}[/tex] + [tex] y_{2}[/tex]/2)

Keep the value in mentioned formula to find the endpoint G, represented as [tex] x_{1}[/tex] and [tex] y_{1}[/tex].

(3, 6) = ([tex] x_{1}[/tex] + 6/2) ([tex] y_{1}[/tex] + 5/2)

Relating the x and y values -

x value :

3 = [tex] x_{1}[/tex] + 6/2

[tex] x_{1}[/tex] + 6 = 3×2

[tex] x_{1}[/tex] + 6 = 6

[tex] x_{1}[/tex] = 6 - 6

[tex] x_{1}[/tex] = 0

y value :

6 = [tex] y_{1}[/tex] + 5/2

[tex] y_{1}[/tex] + 5 = 6×2

[tex] y_{1}[/tex] + 5 = 12

[tex] y_{1}[/tex] = 12 - 5

[tex] y_{1}[/tex] = 7

Thus, the coordinates of point G from the line GH is (0, 7).

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The number of game disks that must be produced for the average cost to be $4.70 is 2600.

Given:

The average cost of producing x game disks for a computer is given by the function C(x) = 2.6+5460/x

To determine the number of game disks that must be produced for the average cost to be $4.70.

Substitute the average cost in the equation and solve to find the value of x i.e. number of disks,

4.70 = 2.6 + 5460/x

4.70 - 2.6 = 5460/x

2.1x = 5460

x = 5460/2.1

x = 2600

Therefore, the number of game disks that must be produced for the average cost to be $4.70 is 2600.

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The solution of the given linear equation is x = -9.53

Here we have the linear equation:

-0.24*x - 16.4 = 1.48*x

To solve this, first we need to move all the terms with x to the left and the terms without x to the right.

-0.24*x - 1.48*x = 16.4

(-0.24 - 1.48)*x = 16.4

-1.72*x = 16.4

Now we can divide both sides by -1.72 to get:

x = 16.4/-1.72 = -9.53

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Answer: c) (is it c?)

Step-by-step explanation: c) x= - 74.5

0.24x+16.4=-1.48 step 1- subtract: -1.48- 16.4

0.24x= -17.88    (divide)

x= −74.5

there

i hope this helps!!

Answer: x = -33

Explanation:

Given the following question:

x - 11 = -44

Step 1: collect the like terms

x = -44 + 11

x = -33

Therefore, x = -33

The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7,negative 0.5,0.9 and 1.9 are plotted."

Here the values are

-0.5,-2.8,1.9,0.9 and -1.7

The number line a graphical representation that a line on which numbers are marked at intervals, used to represents the simple numerical operations.
Here there are three negative numbers -0.5,-2.8 and -1.7

The positive numbers are 1.9 and 0.9

The statement "A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5,0.9 and 1.9 are plotted" is suited of all the given conditions

Hence, The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted."

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The number of homes in 2011 is 44,313

Given that 57 homes are built each year, in 2002, there were 43,800 homes, then the next years have the number of homes as follows:

2003: 43,800 + 57

2004: 43,800 + 57 + 57

2005: 43,800 + 57 + 57 + 57

This goes on until 43,800 + 57n

where n is the number of years after 2002.

2011 is 9 years after 2002, so the number of homes will be:

43,800 + 57(9)

= 43,800 + 513

= 44,313

Hello!

Let's take this problem step by-step:

What is the formula for the circumference of a circle:

 [tex]\text{Circumference} = 2\pi *\text{radius}[/tex]

Since the circumference is 25 cm

  [tex]25 = 2\pi *\text{radius}\\\\\text{radius} = \dfrac{25}{2\pi }[/tex]

Answer: [tex]\text{radius} = \dfrac{25}{2\pi }[/tex]

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Answer:

113.85

Step-by-step explanation:

230*55% because 100%-45%=55% is 126.5

Then 126.5*90% because 100%-10%=90% which is 113.85

The values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13  .

In the question ,

the equation is given as

(x+yi)+(4+9i)=9-4i

to find the value of x and y , we solve LHS and RHS of the equation separately

So LHS =

(x+yi)+(4+9i)

x+yi+4+9i

Adding the real and imaginary terms , we get

(x+4)+(y+9)i which is equal to RHS that is 9-4i

So , on comparing , we get

x+4 = 9    and      y+9 = -4

x= 9-4      and      y = -4-9

x = 5       and       y = -13

Therefore , the values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .

The given question is incomplete , the complete question is

What are the The values of X and Y that satisfy this equation (x+yi)+(4+9i)=9-4i  ?

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The number of pounds of pork he bought in decimal is 12.21 lb

Decimal:

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

For example 12.34 is a decimal.

Given,

At a butcher​ shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat.

Here we need to find the number of pounds of pork he bought using a decimal.

First, we have to convert the given fractions into decimal then we get,

Amount of beef = 2 7/20

Which is equal to,

=> 2 + 7/20

=> 2 + 0.35 = 2.35 lb

Similarly,  total amount of meat = 14 14/25

=> 14 + 14/25

=> 14 + 0.56 = 14.56

Therefore, the amount of pork is,

=> total amount of meat - the amount of beef

=> 14.56 - 2.35

=> 12.21.

Therefore, the the number pounds of pork in decimal is 12.21 lb.

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Answer:

a) do the first three terms

Answer: a) -4, -2, 0      b) 14

Step-by-step explanation:

To find any term, we plug the number into the equation for n.

a)

1st term => 2(1) - 6 = 2 - 6 = -4

2nd term => 2(2) - 6 = 4 - 6 = -2

3rd term => 2(3) - 6 = 6 - 6 = 0

b)

10th term => 2(10) - 6 = 20 - 6 = 14

Answer:

its 12

Step-by-step explanation:

17j+7 is the algebraic expression for Seven more than the product of 17 and Julie's savings.

Expression is a combination of variables, operators and numbers.

The given phrase is

"Seven more than the product of 17 and Julie's savings"

and j is variable to represent Julie's savings.

In the phrase we have Seven more than, it means we are adding 7 to something.

According to problem we are adding 7 to "product of 17 and Julie's savings"

Product means multiplying a number with another factor. Here the factor is julies saving j.

17j+7 is the translated algebraic expression.

Hence 17j+7 is the translation of  Seven more than the product of 17 and Julie's savings.

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We know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.

So, let 'D' be the diameter and 'C' be the circumference.

Calculate C as:

(A) D = 5 m and C = 22 m

So, C = 15.7 m does not approximate 22 m.

(B) D = 19 in and C = 60 in

So, C = 59.66 approximates 60 in.

(C) D = 33 cm and D = 80 cm

So, C = 103.62cm does not approximate 80cm.

Therefore, we know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.

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The correct question is given below:
Select all the pairs that could be reasonable approximations for the diameter and circumference of a circle. * 1 point A. 5 meters and 22 meters. B. 19 inches and 60 inches. C. 33 centimeters and 80 centimeters.

We can multiply each side by 14ft yo find the value on feet and late calculate the area

tha area formula is

where b=84ft and h=112ft

the area is 4,704ft2

we have the following:

in this case we must find the largest divisor between the numbers 12 and 20, this number is 4:

Therefore 3 flyers for the science club and 5 flyers for the music club. And it would be 4 places

Answer:

[tex](y+2)=\frac{2}{3} (x-5)[/tex]

Step-by-step explanation:

Point slope form is shown below:

[tex](y-y_1)=m(x-x_1)[/tex]

We are given the slope m = 2/3 and the point x1 = 5, y1 = -2

Simply plug in these numbers into the above equation.

[tex](y--2)=\frac{2}{3} (x-5)[/tex]

Simplify:

[tex](y+2)=\frac{2}{3} (x-5)[/tex]

Answer:

Undefined slope

Step-by-step explanation:

Slope , m is equal to rise/run    Or   ( y1-y2) / ( x1 -x2)

              This line is a vertical line at x = -8    And thus has undefined slope

              (Because you cannot divide by zero)

Answer:

Undefined

Step-by-step explanation:

Hey! Let's help you with your question here! I am unsure if the points are correct cause you've written each one down twice. If it does change, I will change my answer accordingly.

We're looking for a slope of the line that passes through 2 points I see! Alright, so as you would recall, most equations of a linear line are described in the form of slope-intercept form. And that being this:

[tex]y=mx+b[/tex]

When we're finding for slope of the line, we're essentially just look for m. But how can we find m with only just 2 points? Well, we can! Using a formula that helps us find the slope using exactly 2 points! And that is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, all we have to do is plug in the values as such and solve:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-11-(-1)}{-8-(-8)}[/tex]

From here, we come to a problem. If we were to solve this equation to find the slope, we will get an undefined value mainly because the denominator will equal 0 and we can't have it equal 0. So therefore, it is undefined.

Answer:

price for one ribbon =19 cents

she got $20

20- 16.77 the rest from the money = 3.23

so she spends 3.23 from buying the ribbon

how much ribbon does she buy

3.23 ÷ 0.19= 17 ribbons

Answer:

DF = 13

Step-by-step explanation:

Congruent triangles:

        In ΔABC & ΔDEF,

                     ∠A = ∠D

                     ∠C = ∠F

                      CB = FE

            ΔABC ≅ ΔDEF   {Angle Angle Side congruency}

              DF = AC = 13

From the list given, the line that is perpendicular to 3x – y = 10 is x + 3y = 27. (Option C)

It is to be noted that lines that intersect at a right angle (90 degrees) are considered perpendicular lines.

To justify the above results, we recall that when two lines are perpendicular then the product of their slope is -1.

The slope is given by y = mx + c  where m is the slope.

Hence, the slope of the given equation 3x -y = 10 is  arrived at by re-writing the expression as follows:

Y = 3x -10 where

slope m₁ = 3

given Lets attempt to derive the slope of the options given:

1) y = 3x + 5

m₂ = 3
The product of the slopes are:
= m₁ x m₂

=  3 x 3

⇒ 9 ≠ -1

Therefore, this is not a perpendicular line.

2) y = -13x + 17 our new m₂ = -13
m₁ x m₂
⇒ 3 x -13
⇒ -39 ≠ -1

Again, this is not the required line.

3) x + 3y = 27 [divide all sides by 3]
y = -1/3(x) + 9
The new m₂ = -1/3

Compute for slope:

= 3 x - (1/3)
= -3/3
= -1

Hence,  x + 3y = 27 is the perpendicular line.

4) y -2 = 13(3x + 36)
y = 39x + 468 +2
y = 39x + 470
New Slope (m₂) = 39

Solving to check the slope, we have:
m₁ x m₂ = 3 x 39
⇒ 117 ≠ -1.

Thus, we have our final answer as option C.

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The required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.

The slope of the perpendicular lines is equal to the inverse and of the opposite sign.

Here,
Standard equation of the line,
y = mx + c
The property of the perpendicular line states that the product of their slopes is equal to -1.
So the slope of the given line is m = 3,

Let the slope of the perpendicular line that we have to determine, be x
According to the property,
The slope of line × slope of perpendicular line = -1
3 × x = -1
x = -1/3
So looking forward to the option, the line that has a slope of -1/3 is x + 3y = 27. because
x + 3y = 23
Transform the above equation to standard form,
y = -1/3x + 23
From the above equation, the slope of the above line is m = -1/3,

Thus, the required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.

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The equation represent the number of gallons of water remaining in the tank is y = 28 - 2t

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The water remaining is illustrated as y.

The time taken is t.

The appropriate equation will be:

y = 28 - (2 × t)

y = 28 - 2t

This illustrates the water remaining in the tank.

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This is because

distance = rate*time

Rate is another term for speed.

Answer:

c) f = 28

Step-by-step explanation:

Given problem,

→ f³ = 21952

Now the value of f will be,

→ f³ = 21952

→ f = ³√21952

→ [ f = 28 ]

Let's check the following,

→ 28³

→ (28 × 28) × 28

→ 784 × 28 = 21952

Hence, option (c) is correct.

The value of  Q(x) =   x² - 1  

R(x) = 4

What is Long Division?

Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.

By long Division method:

                        x² - 1            

                     _______________________________

         (3x - 4) | 3x³ - 4x² - 3x

                       3x³ - 4x²

                       _________________

                            0 - 0   - 3x      

                                       - 3x + 4  

                                ___________________

                                          0  + 4

Q(x) =   x² - 1  

R(x) = 4

Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1  ) + 4

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Correct answer is A, the rule for translating ABC to A'B'C' is left 2, up 9.

An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. are frequently called slides. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."

A translation in geometry is a type of transformation that shifts a geometric figure in a certain direction without altering its size or orientation. The figures are congruent before and after the transformation since it is a type of stiff transformation.

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