A coffee company surveyed 40 potential customers to see where they would like the company's new organic coffee sold. Respondents were given the following four locations and asked to choose as many as they liked: grocery stores, drugstores, health food stores, and big box stores. The results are summarized in the bar graph below, with the number of times each location was chosen noted above the corresponding bar.​

The fractional part vanishes when the argument is an integer; in this case, for

[tex]\left\{\dfrac1{1-xy}\right\} = 0 \iff \dfrac1{1-xy} = n \iff xy = \dfrac{n-1}n[/tex]

which are hyperbolas in the [tex](x,y)[/tex]-plane.

Observe that between neighboring hyperbolas, we have

[tex]\dfrac{n-1}n < xy < \dfrac n{n+1} \\\\ ~~~~ \implies \dfrac1{n+1} < 1-xy < \dfrac1n \\\\ ~~~~ \implies n < \dfrac1{1-xy} < n+1 \\\\ ~~~~ \implies \left\{\dfrac1{1-xy}\right\} = \dfrac1{1-xy} - \left\lfloor\dfrac1{1-xy}\right\rfloor = \dfrac1{1-xy} - n[/tex]

Split up the integral over [tex][0,1)^2[/tex] along the curves [tex]xy=\frac{n-1}n[/tex]. The subregions somewhat resemble the layers or scales of an onion (see attached plot with the first 5 "scales").

Let [tex]S_n[/tex] denote the [tex]n[/tex]-th ([tex]n\in\Bbb N[/tex]) "scale", starting from the blue region closest to the origin and counting diagonally upward in the direction of (1, 1).

In Cartesian coordinates, the integral over [tex]n[/tex]-th "scale" is

[tex]\displaystyle \iint_{S_n} x \left(\frac1{1-xy} - n\right) \, dy \, dx \\\\\\ ~~~~~~~~= \int_{(n-1)/n}^{n/(n+1)} \int_{(n-1)/(nx)}^1 x \left(\frac1{1-xy} - n\right) \, dy dx \\\\\\ ~~~~~~~~~~~~~ + \int_{n/(n+1)}^1 \int_{(n-1)/(nx)}^{n/((n+1)x)} x \left(\frac1{1-xy} - n\right) \, dx[/tex]

(see attached plot of the 2nd "scale" for reference)

The integral is trivial, so I'll leave it to you to confirm that it drastically reduces to

[tex]\displaystyle \iint_{S_n} x \left(\frac1{1-xy} - n\right) \, dy \, dx = \frac1{2n (n+1)^2} = \frac12 \left(\frac1n - \frac1{n+1} - \frac1{(n+1)^2}\right)[/tex]

Now we recover the original integral by summing over [tex]\Bbb N[/tex].

[tex]\displaystyle \int_0^1 \int_0^1 x \left\{\frac1{1-xy}\right\} \, dy \, dx = \frac12 \sum_{n=1}^\infty \left(\frac1n - \frac1{n+1} - \frac1{(n+1)^2}\right) \\\\ ~~~~~~~~ = \frac12 \left(\left(1-\frac12\right)+\left(\frac12-\frac13\right)+\left(\frac13-\frac14\right)+\cdots\right) - \frac12 \sum_{n=2}^\infty \frac1{n^2} \\\\ ~~~~~~~~ = \frac12 - \frac12 \left(\sum_{n=1}^\infty \frac1{n^2} - 1\right) \\\\ ~~~~~~~~ = \frac12 - \frac12 \left(\frac{\pi^2}6 - 1\right) = \boxed{1 - \frac{\pi^2}{12}}[/tex]

Answer:

-7 i + 16

Step-by-step explanation:

Simplify the following:

(-2 i + 1) (5 i + 6)

(1 - 2 i) (6 + 5 i) = (1) (6) + (1) (5 i) + (-2 i) (6) + (-2 i) (5 i):

6 + 5 i - 2 i×6 - 2 i×5 i

-2×6 = -12:

6 + 5 i + -12 i - 2 i×5 i

-2 i×5 i = -2 i^2 5:

6 + 5 i - 12 i + -2 i^2×5

i^2 = -1:

6 + 5 i - 12 i - 2-1×5

-2 (-5) = 10:

6 + 5 i - 12 i + 10

6 + 5 i - 12 i + 10 = (6 + 10) + (5 i - 12 i) = 16 - 7 i:

Answer:  -7 i + 16

Answer: your answer to this question would be 16-7i

Step-by-step explanation:

Considering the expression of a line, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing the value of slope m, substituting this value and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

In this case, you know:

Substituting the value of the slope m:

y= 1/3x +b

Substituting the point to calculate the value of b:

-1= 1/3×(-1) + b

-1= -1/3 + b

-1 + 1/3= b

-2/3= b

Finally, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.

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Answer: the better option would be to fill your tank up 15 gallons for $53.08

If you were to multiply 3.60 by 15, you would get 54.

53.08 < 54, therefore 53.08 is the better option.

Hope this helps!

Answer:

diameter is 24 inches

Step-by-step explanation:

diameter is basically two times the radius

The amount Logan should charge for each cupcake is $1.60 based on the markup of 35%

What is equivalent inputs for 60 cupcakes?

The equivalent inputs for 60 cupcakes, means the number of cupcakes that the materials used would have yielded in cupcakes if there was no wastage, hence, the cost per unit needs to be expressed to include 20% wastage

equivalent cost per unit=$0.95/(1-20%)=$1.1875

The 35% markup needs to be added to the equivalent cost per unit since markup is the profit as a percentage of cost

selling price=$1.1875*(1+35%)

selling price=$1.60

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Answer:

Step-by-step explanation:

E - 4,-2

F - 6, -3

G - 1, -4

Answer:

5,11 , 17, 23, 29, 35

Step-by-step explanation:

Answer:

5, 11, 17, 23, 29, 36

Step-by-step explanation:

To get from 5 to 11, we add 6. Similarly, to get from 11 to _, we add 6, and get 17. This also works with 29 to _. We get 36.

Answer:

6 7/8

Step-by-step explanation:

First we would need to turn the 5 1/2 into a improper fraction. Then, do the same for the 1 1/4 as well. To do this, multiply the denominator by the whole number and then add the numerator. Once you get those values, you simply multiply across, meaning the numerators get multiplied together and the denominators get multiplied together. The value you get is the improper fraction form of the simplest form. Then you can convert it back to a mixed fraction if that is the form you need. To do this divide the numerator by the denominator. Now we have a value of 11/2 x 5/4 = 55/8. So divide 55 by 8 and leave the remainder in fraction form. Therefore the answer should be 6 7/8, after it is reduced.

I hope this helps, have a blessed day! :)

Answer: m=2

Step-by-step explanation:

Highlighted points: (0, 4) and (-4, -4)

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

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

m=(-8)/(-4)

m=2

Answer:

w = 3, x = -35/2, y = 8, z = -1

Step-by-step explanation:

Solve the following system:

{-3 w - 2 x - 4 y - z = -5

{2 w + y + 6 z = 8

{4 z + 4 w = 8

{-4 w = -12

In the fourth equation, look to solve for w:

{-3 w - 2 x - 4 y - z = -5

{2 w + y + 6 z = 8

{4 z + 4 w = 8

{-4 w = -12

Divide both sides by -4:

{-3 w - 2 x - 4 y - z = -5

{2 w + y + 6 z = 8

{4 z + 4 w = 8

{w = 3

Substitute w = 3 into the first, second, and third equations:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{4 z + 12 = 8

{w = 3

In the third equation, look to solve for z:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{4 z + 12 = 8

{w = 3

Subtract 12 from both sides:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{4 z = -4

{w = 3

Divide both sides by 4:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{z = -1

{w = 3

Substitute z = -1 into the first and second equations:

{-4 y - 2 x - 8 = -5

{y = 8

{z = -1

{w = 3

Substitute y = 8 into the first equation:

{-2 x - 40 = -5

{y = 8

{z = -1

{w = 3

In the first equation, look to solve for x:

{-2 x - 40 = -5

{y = 8

{z = -1

{w = 3

Add 40 to both sides:

{-2 x = 35

{y = 8

{z = -1

{w = 3

Divide both sides by -2:

{x = -35/2

{y = 8

{z = -1

{w = 3

Collect results in alphabetical order:

Answer: {w = 3, x = -35/2, y = 8, z = -1

Answer:

14

Step-by-step explanation:

I think the question is whether: "a plumber has a 20-foot piece of PVC pipe. how many 7/5 foot pieces can be cut from the 20-foot piece?"

The cost of buying lemons to make two 9-inch lemon pies is $5.20.

The first step is to convert cup to tablespoons

1 cup = 16 tablespoons

one 9-inch lemon pie would require 8 tablespoons (16 /2)

two  9-inch lemon pie would require 16 tablespoons (8 x 2)

The second step is to determine how much lemons would be needed.

Lemons needed = table spoons needed / table spoon one lemon would yield

16 / 2 = 8 lemons

The total cost of lemons needs to make the pies = cost of one lemon x number of lemons needed

8 x 0.65 = $5.20

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Answer:

$32.07

Step-by-step explanation:

Just add them together.

For the given distributions, we have that:

a) The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.

b) The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.

The range of a distribution is given by the difference between the greatest value and the smallest value.

Hence, for the Traditional classroom, the range is given by:

86.4 - 56.6 = 29.8.

For the Flipped classroom, the range is given by:

92.6 - 64.4 = 28.2.

Hence:

The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.

Using a calculator, following the described procedure, the standard deviations are given as follows:

Hence:

The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.

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The speed of plane in still air is 715 MPH and the speed of the wind is 65 MPH

Distance travelled by airplane = 3900 miles

Time taken by the plane to travel the distance with the wind = 5 hours

Time taken by the plane to travel the distance against the wind = 6 hours

Let the speed of the plane in still air be x

Let the speed of the wind be y

Finding the speed of the air and airplane when distance is covered with the wind using the formula:

Speed of airplane + Speed of wind = Distance/Time

x + y= 3900/5

x + y = 780------(1)

Finding the speed of the air and airplane when distance is covered against the wind using the formula:

Speed of airplane - Speed of wind = Distance/Time

x - y = 3900/6

x - y = 650------(2)

Equating (1) and (2) we get:

2x = 1430

x = 715

Putting x = 715 in (1) we get:

y = 65

So, Speed of airplane in still air is 715 MPH and Speed of wind is 65 MPH  

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Answer:

3.75

Step-by-step explanation:

15/4=3.75

Answer:

12 1/3

Step-by-step explanation:

because when you find the total cost plus divide it gives u the answer

Using the concepts of asymptotes and inverse function, we have that:

a) For f, the vertical asymptote is x = -2/3 and the horizontal asymptote is y = 1/6.

b) The inverse function is: [tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]

c) For the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.

For this problem, the function is given by:

[tex]f(x) = \frac{x + 10}{6x + 4}[/tex]

The zero of the denominator is:

6x + 4 = 0

6x = -4

x = -4/6 = -2/3.

Hence the vertical asymptote is x = -2/3.

The horizontal asymptote is given as follows:

[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{x + 10}{6x + 4} = \lim_{x \rightarrow \infty} \frac{x}{6x} = \lim_{x \rightarrow \infty} \frac{1}{6} = \frac{1}{6}[/tex]

To find the inverse function of a function y = f(x), we exchange x and y then isolate y.

Exchanging x and y, we have that:

[tex]x = \frac{y + 10}{6y + 4}[/tex]

Applying cross multiplication:

x(6y + 4) = y + 10

6xy - y = 10 - 4x

y - 6xy = 4x - 10

y(1 - 6x) = 4x - 10

[tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]

Applying the same procedure, for the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.

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The new images has vertices Q´(-1, 0), R´(-1, 2), T´(4/3, 2), U´(4/3, 0) and the type of dilation is contraction.

When we dilate the points of a given figure, we simply multiply each x-coordinate and y-coordinate by the scale factor.

Here the points are Q (-3,0), R (-3,6), T (4,6), U (4,0) and the scale factor is

k = 1/3

Therefore,

⇒ Q (-3,0) → Q´ (-3 × 1/3,0 × 1/3) = (-1, 0)

⇒ R (-3,6) → R´  (-3 × 1/3, 6 × 1/3) = (-1, 2)

⇒ T (4,6) →  T´  (4 × 1/3, 6 × 1/3) = (4/3, 2)

⇒ U (4,0) → U´  (4 × 1/3, 0 × 1/3) = (4/3, 0)

Thus, the new images has vertices Q´(-1, 0), R´(-1, 2), T´(4/3, 2), U´(4/3, 0) and the type of dilation is contraction

Dilation is the process of modifying the dimensions of an object or shape by varying some scale variables. For instance, a circle with a radius of 10 units gets shrunk to a circle with a radius of 5 units. This technique is applied in photography, fine art, logo design, and other fields.

Four fundamental categories of transformations exist in geometry.

These are:

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nwm życzę powodzenia kolego drogi

Answer:

The room is 5 inches in the drawing.

Step-by-step explanation:

If the room is 20 feet and each inch in his drawing measures 4 feet what you need to do is see how many times 4 goes into 20.

4 times 5 = 20

So the answer would be 5

Hope it helps! =D

Answer:(7/9)^12

Step-by-step explanation:

Answer:

C. (7/9)^12

Step-by-step explanation:

(49/81)^6 = (7^2/9^2)^6 = (7/9)^(2x6) = (7/9)^12

The output values of ​g(​-6), ​g(1​), and ​g(8​) in the given piecewise function are -1, 6 and -6 respectively.

Given the piecewise function in the question;

                   x + 5, for x ≤ 1

                   2 - x, for x > 1

Determine the output value of g(-6), -6 falls in the domain of x ≤ 1,

Hence;

g(x) = x + 5

g(-6) = -6 + 5

g(-6) = -1

Determine the output value of g(1), 1 falls in the domain of x ≤ 1,

Hence;

g(x) = x + 5

g(1) = 1 + 5

g(1) = 6

Determine the output value of g(8), 8 falls in the domain of x > 1,

Hence;

g(x) = 2 - x

g(8) = 2 - 8

g(8) = -6

Therefore the output values of ​g(​-6), ​g(1​), and ​g(8​) in the given piecewise function are -1, 6 and -6 respectively.

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Answer:

57, 59 and 61

Step-by-step explanation:

Let the first odd number be n The next consecutive odd number is n + 2 and the next one after that is n + 4
(consecutive odd numbers have difference of 2 between them. For example if 7 is the first odd number next one is 9(7+2) and the next one is 11(7+4)

We are given that the sum of the numbers is 177. So we have the following equation:

n + (n + 2) + (n +4) = 177

Simplifying gives

n + n + 2 + n + 4  = 177

Collect like terms:

n + n + n + 2 + 4 = 177
3n + 6 = 177

Subtract 6 from both sides
==> 3n = 177 - 6
==> 3n = 171

Divide by 3 both sides
3n/3 = 171/3

n = 57 and this is the first of the odd numbers

The next odd number is 57+ 2 = 59

and the next one after that is 59 + 2 = 61 (same as 57 + 4)

Answer:

16 meters is the answer of this question

Answer:

x+4+2x-7=180

3x-3=180

3x=183

x=61

Answer: the answer is MO=5

Step-by-step explanation:

Answer:

(1, 1,-3)

Step-by-step explanation:

The linear system of equation has one solution as x = 16 and y = -12.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

The given system of equation are :

y=-x+4..........(1)

x + 2y = -8......(2)

Now, solving the above using substitution of y in equation (2) :

x + 2y = -8

x+2(-x+4) = -8

x-2x+8 = -8

-x = -16

x = 16

Now, substituting back x value in equation (1) we get :

y = -x+4

y = -16 +4

y = -12

Therefore, The linear system of equation has one solution as x = 16 and y = -12.

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