Which is the approximate solution to the system y = 0.5x + 3.5 and y = −A system of equations. y equals 0.5 x plus 3.5. y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction.x + shown on the graph?

Horizontal asymptote of c(x) is 450.

A horizontal asymptote is a line that guides the graph of a function for x-values but is not itself a part of the graph. "far," either "far" to the right or "far" to the left. Eventually, whether the graph is large enough or little, it may intersect.

Since we have given that

Cost to produce one refrigerator = $450

Fixed monthly cost = $200,000

Thus, the following formula represents the average cost to produce x refrigerators:

C(x) = (200000 + 450x)/x

Horizontal asymptote of c(x) would be

= 450x/x

= 450

Hence, Horizontal asymptote of c(x) is 450

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The mean in minutes of the length of time given= 9.1

The formula used for the determination of mean when a frequency table is given is

= total/n

Where total = frequency×midpoint

n = 42

To calculate the total, the mid point of each length of time is determined as follows;

1+4/2 = 2.5 × 4 = 10

4+7/2= 5.5 × 8 = 44

7+10/2 = 8.5 × 14= 119

10+13/2 = 11.5× 9 = 103.5

13+16/2= 14.5×5 = 72.5

16+19/2= 17.5× 2= 35

Total= 10+44+119+103.5+72.5+35 = 384

Therefore mean = 384/42= 9.1

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Answer:

He is 2 years old.

Step-by-step explanation:

She is 22, in 8 years she will be 30. 30 is 3×10. At that time, her brother will be 10; that is 8 years from now. So now, the little brother is 10-8 = 2 years old.

If you must show algebra work:

x = brother's age now.

x+8=brother's age in 8 years.

YingYu's age in 8 years = 3 × brother's age in 8 years

22+8 = 3(x+8)

30 = 3x +24

6 = 3x

2 = x

Answer:

∠S = 66°

Step-by-step explanation:

A parallelogram's 4 angles always add up to 360°, and opposite angles are the same. (∠S = ∠U; ∠T = ∠V)

So, ∠S + ∠T = 180°.

180° = (2x + 4x + 12 + 6)°

180° = (6x + 18)°

162° = (6x)°

27° = x°

(2x + 12)° = ∠S

(2(27) + 12)° = ∠S

(54 + 12)° = ∠S

66° = ∠S

Answer:

  x = 10.67

Step-by-step explanation:

The triangles shown are similar, so corresponding sides are proportional. This lets us write a relation that can be solved for x.

For the given figure, we can write the proportion ...

  AB/CA = DB/ED . . . . . . where DB = ED +BE

  (3x-4)/12 = (24 +3x)/24 . . . . . . substitute given values

Multiplying by 24 gives ...

  2(3x -4) = 3x +24

  6x -8 = 3x +24 . . . . . eliminate parentheses

  3x = 32 . . . . . . . . add 8-3x

  x = 32/3 = 10 2/3 ≈ 10.67 . . . . . divide by 3 and convert to decimal

The value of x to the nearest hundredth is 10.67.

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{2a} + \cfrac{9}{10} = \cfrac{5}{12a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{2a} - \cfrac{5}{12a} = - \cfrac{9}{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7(6) - 5}{12a} = - \cfrac{9}{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{42 - 5}{12a} = - \cfrac{9}{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 37(10) = - 9(12a)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 370 = - 108a[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = - \cfrac{370}{108} [/tex]

[tex]\qquad \sf  \dashrightarrow \: a = - \dfrac{185}{54} [/tex]

There will be 60 residuals for simple bivariate regression's  60 observations.

According to the statement

We have given that the there is 60 observations and we have to find the number of simple bivariate regression for these observations.

So, For the solution of this problem,

We know that the

A simple linear regression (also known as a bivariate regression) is a linear equation describing the relationship between an explanatory variable and an outcome variable, specifically with the assumption that the explanatory variable influences the outcome variable, and not vice-versa.

And we know that the it is always same for the number as the number of given observations.

That's why there is 60 residuals.

So, There will be 60 residuals for simple bivariate regression's  60 observations.

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The correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.

Given a function f(x) and other function 4f(x+2).

We are required to choose a transformation that will give 4f(x+2) from a function f(x).

Function is like a relationship between two or more variables that are expressed in equal to form. The values which we enter in a function is known as domain and the value that we get as a result are known as range.

So, we have to reach 4f(x+2) from f(x).

The value of function is usually expressed on y axis and variable x on x axis.

To increase the value of x by 2 we have to stretch it in x direction.To find the 4 times value of function we have to stretch the y axis to 4 units.

Hence the correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.

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Answer:

x = 7; y = 4 1/3

Step-by-step explanation:

The solution is the point of intersection of the lines.

Read the point of intersection.

You can also solve the system using algebra.

y = 1/3 x + 2

y = 4/3 x - 5

1/3 x + 2 = 4/3 x - 5

x + 6 = 4x - 15

-3x = -21

x = 7

y = 1/3 x + 2

y = 1/3 × 7 + 2

y = 2 1/3 + 2

y = 4 1/3

Answer: x = 7; y = 4 1/3

Answer:

True

Step-by-step explanation:

All faces of a cube are the same.

Step-by-step explanation:

Reduce 13/100 to lowest terms

13

100

is already in the simplest form. It can be written as 0.13 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 13 and 100 is 1

Divide both the numerator and denominator by the GCD

13 ÷ 1

100 ÷ 1

Reduced fraction:

13

100

Therefore, 13/100 simplified to lowest terms is 13/100.

The mixed number [tex]7\dfrac{13}{100}[/tex] is [tex]\dfrac{713}{100}[/tex] on simplification.

A mixed number is a mathematical representation of a number that consists of a whole number and a fraction. It's called a "mixed number" because it combines both a whole number and a proper fraction. The whole number part represents a whole quantity, while the fractional proportion represents a proportion of a whole.

Mixed numbers are generally employed to represent measures that aren't whole numbers but are still greater than 1. They're particularly useful when dealing with magnitudes, such as lengths or quantities of things, that concern both whole units and fractional parts.

Given that

[tex]7\dfrac{13}{100}[/tex] [tex]= 7 + \dfrac{13}{100}[/tex]

       [tex]= \dfrac{700}{100}+ \dfrac{13}{100}\\= \dfrac{700+13}{100} \\= \dfrac{713}{100}[/tex]

Hence, The mixed number [tex]7\dfrac{13}{100}[/tex] can be simplified as [tex]\dfrac{713}{100}[/tex].

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Step-by-step explanation:

4)

the surface area is

top and bottom : 2× pentagon (5 sides)

sides : 5× rectangle 14×8 ft²

let's start with the easiest : the rectangles.

5 × 14×8 = 560 ft²

the area of a pentagon is similar to any regular polygon :

n × triangle of side×height (to middle of pentagon) / 2

n = number of sides (5 in our case).

the middle or center of the pentagon is the top vertex of each triangle.

so,

5 × 14×9.63 / 2 = 5 × 7 × 9.63 = 337.05 ft²

and we have 2 of them (top and bottom), so

2×337.05 = 674.1 ft³

in total the surface area is

560 + 674.1 = 1,234.1 ft²

5)

6 sides :

top and bottom : 7×14 rectangle

left and right : 7×8 rectangle

front and back : 8×14 rectangle

so, we have

2× 7×14 = 196 mm²

2× 7×8 = 112 mm²

2× 8×14 = 224 mm²

in total that is : 532 mm²

Answer:

D. 195

Step-by-step explanation:

The y-intercept of the equation  g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation  g(x) = 3^x - 5 is y = -5

The equation of the function g(x) is given as:

g(x) = 3^x - 5

The y-intercept is a point on the graph where the value of x is 0

This is represented by x= 0 or (0, y)

This means that we substitute 0 for x in the above equation

So, we have:

g(0) = 3^0 - 5

Evaluate the exponent 3^0

g(0) = 1 - 5

Evaluate the difference of 1 and 5

g(0)  = -4

Rewrite this point as

(0, -4)

This means that the y-intercept of the equation  g(x) = 3^x - 5 is (0, -4)

The equation of the function g(x) is given as:

g(x) = 3^x - 5

The asymptote is a point on the graph where that is parallel to the graph

In the above equation, we have:

g(x) = 3^x - 5

Express the radical as 0

y = 0 - 5

Evaluate the difference of 0 and 5

y  = -5

This means that the asymptote of the equation  g(x) = 3^x - 5 is y = -5

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The conic section will form an Ellipse.

The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the center at all angles.

A conic section is a curve formed when the surface of a cone and a plane connect. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, though historically it was occasionally referred to as a fourth type.

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Answer:

7.52 m^3

Step-by-step explanation:

This is like compound interest in a banking calculation

Future volume = 5 (1 + .06)^7 = 7.52 m^3

Based on the given parameters, the number of filet mignon the restaurant served is 14

From the question, the given parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

This means that the proportion of filet mignon is

filet mignon = 100%- Salmon filets

This gives

filet mignon = 100%- 80%

Evaluate the difference

filet mignon = 20%

The number of filet mignon is calculated as:

filet mignon = 20% * Dinner specials

Substitute the known values in the above equation

filet mignon = 20% * 70

Express 20% as decimal

filet mignon = 0.20 * 70

Evaluate the product

filet mignon = 14

Hence, the number of filet mignon the restaurant served is 14

So, the complete parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

filet mignon = 14

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Answer:

The file contains the solution to the question

The limit does not exist.

In order for such a limit to occur, the fraction [tex]\frac{x^{2} }{x^{2} +y^{2} }[/tex] must be comparable to the same value [tex]L[/tex], regardless of the way we take to get there [tex](0,0)[/tex].

Try approaching [tex](0,0)[/tex] along the x-axis.

This means setting [tex]y=0[/tex] and finding the limit [tex]lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].

We obtain:

[tex]lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1[/tex]

Now evaluate approaching [tex](0,0)[/tex] along the y-axis.

This means setting [tex]x=0[/tex] and finding the limit [tex]lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].

[tex]lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0[/tex]

Approaching the origin via these two methods results in distinct limits.

[tex]lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex] ≠ [tex]lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }[/tex]

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

[tex]lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }[/tex]

The intersection of the sets has the following properties: Commutative law – A ∩ B = B∩ A. Associative law – (A ∩ B)∩ C = A ∩ (B∩ C) φ ∩ A = φ

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The time that the ball is in the air if the player lets the ball drop is 2.145 sec

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

-16t²+32t+5

by comparing this equation to the standard form of the quadratic equation we get

a=-16 b=32 c=5

the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:

the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)

t = -32/2×-16

t=1sec

by putting h(t) to zero and determining the time (t) when the ball hits the ground:

-16t²+32t+5=0

-16(t²+2t+5/16)=0

t²-2t-5/16=0

(t)²-2×1×t+(1)²-5/16=1

(t-1)²=21/16

t-1=√21/√16

t=1+4.58/4

t=1+1.145

t=2.245sec

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Answer:

Akua now -- x

Ama now -- 4x

Akua in 10 years ---- x+10

Ama in 10 years ---- 4x+10

4x+10 = 2(x+10)

solve for x

let Ama's age be X and Akua's age be Y

X=4Y.......

X+10=(Y+10)2......

4Y+10=2Y+20

4Y-2Y=20-10

2Y=10 divide both side by 2

2Y/2=10/2

Y=5

X=4x5

X=20

therefore Ama =20years and Akua=5years

hope it helps..

The value of the mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is  16.94%

The equation is given as

∝At + (1-∝) Ft

The value for Alpha = 0.7

1 - ∝ = 1 - 0.7

= 0.3

Forecast in match = 62

Ft = 51. 5

the difference = 62 - 51.5

= 10.5

The error = 10.5/62 * 100

= 16.94%

Hence the value of the  mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is  16.94%

The past demand data shown below can be regarded as stationary.

Month Demand

January

50

February

55

March

62

April

45

What is the mean absolute percentage error of the forecast for March found by the exponential smoothing method with a smoothing constant of 0.3?

O a. 14.68%

Ob. 16.94%

O c. 12.57%

Od. 11.33%

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Answer:

The club leader needs $73 for pizzas for 9 students.

Step-by-step explanation:

p(x) = 2x +1

r(x) = 4x − 3

r(p(x)) = 4(2x +1) − 3

r(p(x)) = 8x +4 − 3

r(p(x)) = 8x +1

r(p(9)) = 8(9) +4 − 3

r(p(9)) = 72 +1

r(p(9)) = $73

First symmetrically cut the pentagon to get 5 pieces. (So that you will get the idea that this polygon is divided into 5 triangles)

Then find the area of one of the triangles:

Area of Triangle = [tex]\frac{1}{2} bh[/tex]

A = [tex]\frac{1}{2}[/tex] × 4 × 10

A = 20 m²

To find the area of the whole pentagon shape:

A = 20 × 5 = 100 m²

Hope it helps!