Find the area of the shaded region if the dimensions of the unshaded region are 12ft x 20ft . use 3.14 for π as necessary.

Answer:

[tex]4x^{6} y^{10}[/tex]  A.

The mean of the given data is 206.5.

To find the mean of the given data:

Sum of values = 211 + 226 + 186 + 221 + 181 + 228 + 207 + 215 + 203 + 203 + 204 + 196 + 226 + 212 + 212 + 201 + 219 + 191 + 191 + 185 + 193 + 231 = 4,542

Number of values = 22

Mean = 4,542 ÷ 22 = 206.5

Therefore, the mean of the given data is 206.5.

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Answer:

Step-by-step explanation:

Answer:

Neither

Step-by-step explanation:

This function isn't even, because

[tex]f(x) = f( - x)[/tex]

Basically this mean for every x opposites the y value should be the same.

Here, 6 and -6 doesn't share the same y value, nor as -3,and 3.

This function isn't odd because

[tex]f( - x) = - f(x)[/tex]

Basically, this means our y values should be reflected about the orgin,

here, the y values does not switch signs for every x value and it's opposite itself , so this function isn't odd.

So The answer is neither

Answer:

[tex] {x}^{x} (1 + log(x)) [/tex]

I hope this helps you.

Answer: equation y= 3/2x+ 4/3

Step-by-step explanation:

To find the Tth term of an arithmetic progression, you should use the formula: Tn: a + (n-1)d, whereby 'a' is the first term, you have to find 'n' and 'd' is the difference between the first 2 numbers to find out by how much the arithmetic progression is increasing or decreasing. Hence, 29/30 minus 4/5 equals to 1/6. 'a' is 4/5 and 'd' is 1/6.

Use the above formula by replace a and d then you'll get the answer. Hope this helps.

[tex]2 \sqrt{5} \: + \: 7 \sqrt{5} \\ \sqrt{5} \: ( \: 2 + \: 7 \: ) \\ \sqrt{5} \: ( \: 9 \: ) \\ 9 \sqrt{5} [/tex]

The simplification of the expression 2√5 + 7√5 is: 9√5.

So, Option A. is correct.

To simplify the expression 2√5 + 7√5, we can combine the like terms.

Both terms have the same radical expression, which is √5, so we can add their coefficients together.

2√5 + 7√5 = (2 + 7)√5

Now, simplify the coefficients:

2 + 7 = 9

Therefore, the simplified expression is:

2√5 + 7√5 = 9√5

So, the final answer is 9√5.

So, Option A. is correct.

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Answer:

I hope I've finally done justice to it.

Step-by-step explanation:

[tex]y=-5x^2 \sqrt{x}[/tex]

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

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

[tex] \frac{dy}{dx} = - 5( \frac{5}{2}) {x}^{ \frac{5}{2} - 1 } [/tex]

[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) {x}^{ \frac{3}{2} } [/tex]

[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) \sqrt[3]{ {x}^{2} } [/tex]

Answer:

a) 52  

b)115

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:h(x) = - \cfrac{1}{3} x + 2[/tex]

we need to find -4 h(9) :

[tex]\qquad❖ \: \sf \: - 4 \: h(9)[/tex]

[tex]\qquad❖ \: \sf \: - 4 \bigg(- \dfrac{1}{3} \times 9 + 2 \bigg)[/tex]

[tex]\qquad❖ \: \sf \: - 4( - 3 + 2)[/tex]

[tex]\qquad❖ \: \sf \: - 4( - 1)[/tex]

[tex]\qquad❖ \: \sf \:4[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]

Answer:

1) x=4, y=7

2) x=1, y=2

3) x=-3, y=2

4) x=1, y=1

word problem) 5g of nutmeg and 20g of cinnamon

Step-by-step explanation:

1)

2x-9y=-55

2(x+2y) = 2x+4y = 36

(2x+4y)-(2x-9y)=36-(-55)

13y = 91

y = 7 so x = 4

2)

2(3x+2y) = 6x+4y = 14

6x-6y=-6

(6x+4y)-(6x-6y) = 14-(-6)

10y = 20

y = 2 so x = 1

3)

2(6x+10y) = 12x+20y = 4

5(7x+4y) = 35x+20y = -65

(35x+20y) - (12x+20y) = -65-4

23x = -69

x = -3 so y = 2

4)

just add them

(3x+2y)+(x-2y) = 5+(-1)

4x = 4

x = 1 so y= 1

last)

c+n = 25

9c + 12.5n = 25*9.7 = 242.5

9(c+n) = 9*25

9c+9n=225

9c+12.5n - 9c-9n = 242.5-225

3.5n = 17.5

n = 5 so c = 20

5g of nutmeg and 20g of cinnamon

The surface area of the larger sphere is equal to 636.365 square centimeters.

In this question we must estimate the surface area of the smaller sphere. By geometry we know that the volume of a sphere is directly proportional to the cube of its radius and the surface area is directly proportional to the square of radius, then the volume to surface area ratio is equal to:

V/A = k · r      (1)

Where:

Then, we can derive the following relationship between the two spheres by eliminating the proportionality constant:

V/(A · r) = V'/(A' · R)     (2)

Where:

First, we need to determine the radii of the spheres:

Larger radius

R = ∛(3 · V' / 4π)

R = ∛(3 · 647 / 4π)

R ≈ 5.365 cm

Smaller sphere

r = ∛(3 · V / 4π)

r = ∛(3 · 87 / 4π)

r ≈ 2.749 cm

Lastly, we find the surface area of the larger sphere:

A · r · V' = A' · R · V

A' = (A · r · V') / (R · V)

A' = (167 · 2.749 · 647) / (5.365 · 87)

A' = 636.365 cm²

The surface area of the larger sphere is equal to 636.365 square centimeters.

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Answer:

Step-by-step explanation:

i doont know

This system of equations have infinite solution.

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

Given that,

The system is 2x + y = 1 and 4x + 2y = 2. It is graphed below.

Solutions to a system are the intersection points. Since these two lines are the same line they intersect everywhere. There are infinitely many solutions.

2x+y = 1   ...........(1)

4x+2y = 2  .......(2)

Then from equation (2) dividing by 2 on both side

2x+y = 1

since both lines are same. They overlap to each other.it means the equation have many solution.

Hence,This system of equations have infinite solution.

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The above question is not complete.

How many solutions does this system of equations have?

(a) none

(b) exactly two

(c) infinitely many

(d) exactly one

Graph of a system of linear equations. Equation 1 is 2x plus y equals 1.. Equation 2 is 4x plus 2y equals 2. The graphs are the same line.

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.

Answer:

if X is the angle degree like I think it is, then X = 56 degrees

Step-by-step explanation:

isosceles triangles will have 2 equal base angles.

90 degree angle - 28 = 62°

62 is now each base angle.

62 times 2 angles equals 124

the final angle, x, is 180 - 124 = 56°

In order to solve a problem that begins with a negative number and is divided by a positive number, the answer must also be negative.

Divide 21 ÷ 7

we get = 3

Mark it as negative number = -3

Hope this helps :)

Answer:

  a.  1080

  b.  405

Step-by-step explanation:

Function evaluation is often conveniently done using a calculator. Many calculators know about the order of operations, so can be used without fear of an incorrect evaluation.

Put the value where the variable is and do the arithmetic.

  f(x) = 40(3^x)

  f(3) = 40(3^3) = 40(27) = 1080

  g(x) = 5(3^(x+1))

  g(3) = 5(3^(3+1)) = 5(3^4) = 5(81) = 405

The length of rectangle is 25 feet and the width  of rectangle is 135 feet.

According to the question,

The perimeter of a rectangle is 320 feet. The length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.

Odd integers that follow each other and they differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers. The perimeter of a rectangle is 320 feet. Let the length of a rectangle is x. The next consecutive odd integer is x+2.width = 5(x+2)

    =5x+10.

Let, Length - l:Width - w; l = 5w and the perimeter of a rectangle is 320 feet. Formula for perimeter of rectangle is 2(Length + Breadth). Perimeter of a rectangle is the sum of the length of all sides of the rectangle. The perimeter of a rectangle formula is,

P = 2(l + b)

In words, it is equal to the sum of two times the length and two times the breadth of the rectangle. Perimeter for any figure is defined as the length of its boundary.

2(length + width) = 320

Length+ width=160

x+5x+10=160

6x=150

x=25

Length = 25 feet

width = 5(25+2)=135 feet.

Hence, the length of rectangle is 25 feet and the width of rectangle is 135 feet..

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The value of the firm is $50 million

The given parameters are:

EBIT = $10 million

Tax Rate, Tc = 40%

Unlevered cost of capital, RU = 12%

The value of the firm is calculated as:

Value = EBIT*(1 - Tc)/Ru

This gives

Value = 10 million *(1 - 40%)/12%

Evaluate the expression

Value = 50 million

Hence, the value of the firm is $50 million

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The area under the curve y = x² + 4 on the interval [-3, 2] exists [tex]$\frac{95}{3}[/tex].

The area under a curve between two points exists seen by accomplishing a definite integral between the two points. To estimate the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. This area can be estimated by utilizing integration with given limits.

The equation that represents the curve exists

y = x² + 4

To estimate the area under the curve in the interval of [-3, 2] will be

[tex]$&\text { area }=\int_{-3}^{2} x^{2}+4 d x \\[/tex]

[tex]$&=\left[\frac{x^{3}}{3}+4 x\right]_{-3}^{2} \\[/tex]

[tex]$&=\frac{1}{3}\left[x^{3}\right]_{-3}^{2}+4[x]_{-}^{2} _{3} \\[/tex]

simplifying the above equation, we get

[tex]$&=\frac{1}{3}\left[(2)^{3}(-3)^{3}\right]+4[(2)-(-3)] \\[/tex]

[tex]$&=\frac{1}{3}[8+27]+4[2+3] \\[/tex]

[tex]$&=\frac{1}{3}(35)+20 \\[/tex]

[tex]$&=\left(\frac{95}{3}\right)[/tex]

Therefore, the area under the curve y = x² + 4 on the interval [-3, 2] exists [tex]$\frac{95}{3}[/tex].

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Answer:

83in²

Step-by-step explanation:

This can also be expressed as;

Area of polygon=Area of ∆ABF +Area of rectangle BCDF + Area 0f ∆DEF

For ∆ABF;

Area of ∆ABO=∆AOF

Area of ∆ABF=2×Area of ∆ABO

Area of ∆ABO=1/2×Length×height

=1×4×7/2=28/2=14in

But area of ∆ABF=2×Area of ∆ABO

Area=2×14in=28in.

Area of rectangle;

Area=length×breadth

Area=5in×8in=40in.

Area of ∆DEF=2×Area of ∆EFG

Area=1/2× base× height

Area=1×2.5×6/2

Area=15/2=7.5in.

But area of ∆EFG=2×7.5in

=15in.

Area of polygon=28in+40in+15in=83in

The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.

In this question we must find the vertex coefficient of the equation of the parabola, which is the vertex form of the quadratic equation:

y - k = C · (x - h)²

If we know that (h, k) = (- 5, - 2) and (x, y) = (- 4, 2), then the vertex coefficient is:

2 - (- 2) = C · [- 4 - (- 2)]²

4 = C · (- 2)²

C = 1

The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.

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The equation 2^x = 128 as a logarithmic equation is log₂(128) = x

The equation is given as:

2^x = 128

Take the logarithm of both sides

log(2^x) = log(128)

Rewrite as:

x * log(2) = log(128)

Divide both sides of the equation by log(2)

x = log(128)/log(2)

Apply the change of base rule

x = log₂(128)

Hence, the equation 2^x = 128 as a logarithmic equation is log₂(128) = x

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Answer:

  b.  18

Step-by-step explanation:

The perpendicular bisector of a chord is a diameter of the circle. Conversely, if the diameter is perpendicular to a chord, it also bisects it.

  BC = BP +PC

  BC = 2×BP . . . . . . . BP = PC

  BP = BC/2 = 36/2 = 18 . . . . . . . divide by 2; substitute given values

The length of segment BP is 18 units.

The value of f(3) is 147.3306

The function is given as:

[tex]f(x)=147+2e^{-0.6x[/tex]

Substitute 3 for x

[tex]f(3)=147+2e^{-0.6*3[/tex]

Evaluate the product

[tex]f(3)=147+2e^{-1.8[/tex]

Evaluate the exponent

f(3)=147 + 2* 0.1653

Evaluate the sum

f(3) = 147.3306

Hence, the value of f(3) is 147.3306

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Answer:

6

Step-by-step explanation:

Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.

[tex]x+4=3x-8\\x=3x-12\\-2x=-12\\x=6[/tex]

The length of AC is simply x, therefore 6

Answer:

37 child tickets / 74 adult tickets

Step-by-step explanation:

I randomly picked a number and increased or decreased whether the solution was too high or low (guess and check)

The number of child tickets sold that day is 37.

We have,

Let's assume the number of child tickets sold is "C" and the number of adult tickets sold is "A."

The cost of a child ticket: $6.80

The cost of an adult ticket: $9.90

The total sales for the day: $984.20

The number of adult tickets sold is twice the number of child tickets sold:

A = 2C

To find the number of child tickets sold, set up an equation based on the total sales:

6.80C + 9.90A = 984.20

Substituting the value of A from equation 4:

6.80C + 9.90(2C) = 984.20

Simplifying the equation:

6.80C + 19.80C = 984.20

26.60C = 984.20

C = 984.20 / 26.60

C ≈ 37

Therefore,

37 child tickets were sold that day.

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Answer:

a

Step-by-step explanation:

given y varies directly as x² and inversely as z³ then the equation relating them is

y = [tex]\frac{kx^2}{z^3}[/tex] ← k is the constant of variation

to find k use the condition y = 12 when x = 4 and z = 2 , then

12 = [tex]\frac{k(4)^2}{2^3}[/tex] = [tex]\frac{16k}{8}[/tex] ( multiply both sides by 8 )

96 = 16k ( divide both sides by 16 )

6 = k

y = [tex]\frac{6x^2}{z^3}[/tex] ← equation of variation

when y = 1.728 and z = 5 , then

1.728 = [tex]\frac{6x^2}{5^3}[/tex] = [tex]\frac{6x^2}{125}[/tex] ( multiply both sides by 125 )

216 = 6x² ( divide both sides by 6 )

36 = x² ( take square root of both sides )

[tex]\sqrt{36}[/tex] = x , that is

x = 6

Answer:

d - 18

Step-by-step explanation:

The question said to use d as the variable. We do not know the number of dollars Paul owes. So we put d for that amount.

Then "minus" means to subtract 18.

Writing the expression is all that is being asked for. Translating the words into algebra. We aren't solving anything. Not even writing an entire equation, just an expression, so it has no equals sign.

Answer:

Since <ABC ~= <DBE and <BAC ~= <BDE, the triangle s are similar by angle-angle.