There are some 1-dollar bills, some 5-dollar bills, and a 20-dollar bill in an envelope. The number of 1-dollar bills is five times the number of the 5-dollar bills. We randomly pull a bill from the envelope. How many 1-dollar bills are in this envelope if the expected value of the bill pulled is $2.00?

The reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.

For any function f(x), the reflection across the line y = x, gives the inverse of the function f(x).

In the question, we are asked for the equation, representing the reflection of f(x) = x⁴, across the line y = x.

The function can be shown as:

y = f(x) = x⁴,

or, x⁴ = y,

or, [tex]x = \pm\sqrt[4]{y}[/tex]

Changing the variables to general form, that is, y as the dependent variable and x as the independent variable, we get the inverse function as, [tex]y = F(x) = \pm \sqrt[4]x[/tex].

Thus, the reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.

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The complete question is:

"Which of the following equations represents F(x) = x⁴ reflected across the line y = x?

A. [tex]F(x)= \pm\sqrt[4]{x}[/tex]

B. [tex]F(x)= \sqrt[4]{x}[/tex]

C. [tex]F(x)= \pm x^4[/tex]

D. [tex]F(x)=- \sqrt[4]{x}[/tex] "

Answer:

f(x)⁻¹ = (x - 11)²

Step-by-step explanation:

To find the inverse of the function, you need to (1) swap the places of the "x" and "y" variables and then (2) solve for "y". Remember, f(x) is another way of writing "y".

y = √x + 11                                        <----- Original equation

x = √y + 11                                        <----- Swap variables

x - 11 = √y                                         <----- Subtract 11 from both sides

(x - 11)² = (√y)²                                  <----- Square both sides

(x - 11)² = y                                        <----- Simplify

Another way of writing the output of an inverse function is with f(x)⁻¹.

Answer:

C

Step-by-step explanation:

The first part of this is to represent the center.

It sits at (1,-1), so the left hand part of the equation is

(x - 1)^2 + (y + 1) = r^2

That means the answer has to be either B or C. D gets knocked out of the running because of the minus sign in the middle. D does not give a circle.

B is wrong because the y value should be plus. So the answer is C. Notice because the question is multiple choice you don't need to solve for r since all answers give r^2 = 36

Using the interpretation of the confidence interval, it is found that:

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

Considering the mean and the standard error, the bounds of the interval are:

Hence:

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Given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i

The given complex number is z = -1 - i

[tex]z^3[/tex] means to raise z to the power of 3

[tex]z^3=(-1-i)^3[/tex]

Expand and simplify the expression:

[tex]z^3=(-1)^3+3(-1)^2(-i)+3(-1)(-i)^2+(-i)^3\\\\z^3=-1-3i-3i^2-i^3[/tex]

Note that:

[tex]i^2=-1\\\\i^3=-i[/tex]

Substitute these into the resulting expression

[tex]z^3=-1-3i-3(-1)-(-i)\\\\z^3=-1+3-3i+i\\\\z^3=2-2i[/tex]

Therefore, given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i

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Answer: -5

Step-by-step explanation:

[tex]h(4)=\frac{1}{2}(4)-5=-3\\\\f(4)=3h(4)+4=3(-3)+4=-5[/tex]

Based on the width of the aluminum sheets and the angle of the edges, the depth that allows maximum cross-sectional area is 4 inches.

Assuming that the depth is x, the area would be:

= x (16 - 2x)

= 16x - 2x²

The maximum of the parabola is:

x = -b / 2a

= - 16 / (2 x -2)

= -16 / -4

= 4 inches

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The general-form equation of the circle is:

A. [tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

This circle has center at (4,4), hence:

[tex]x_0 = 4, y_0 = 4[/tex]

The radius is of 3 units(distance of A and B from the center), hence the equation is:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 4)^2 + (y - 4)^2 = 3^2[/tex]

We expand the equation to find the general form, hence:

[tex]x^2 - 8x + 16 + y^2 - 8y + 16 = 9[/tex]

[tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]

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Answer:

6

Step-by-step explanation:

Absolute value is a number's distance from 0, another way to think of it is that it makes any number positive, so |-6|, the absolute value of -6 would be 6.

Answer:

6

Step-by-step explanation:

The absolute value is always positive, since it's the number's distance from zero.

Thus, the absolute value of -6 is 6.

Done !!

Answer:

Step-by-step explanation:

hello : y = -2x - 5

          y = 2/3x + 3

means :  -2x-5 = 2/3 x+3

-6x-15 = 2x +9

-8x=24   so : x = -3

put the value for : x in the first equation :y = -2(-3)-5  =1

the  ordered pair (-3;1) is solution

Answer:

y = (-3/4)x + 2

Step-by-step explanation:

y = m * x + b   where m is the slope and b is the y-intercept

y = (-3/4)x + b       substituting the slope

4 = 6 + b     =>         b = 2        substituting the point given

y = (-3/4)x + 2

The value of the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex] after substituting y = 7 is 108

The given expression is:

[tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex]

Simplifying the expression, we have:

[tex]2+4+y^2+4+y^2\\\\2y^2+10[/tex]

Substitute y = 7 into the simplified expression

[tex]2(7)^2+10\\\\=2(49)+10\\\\=98+10\\\\=108[/tex]

Therefore, after substituting y = 7, into the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex], the resulting value is 108

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Answer: -1

Step-by-step explanation: khan academy

The equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

[tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex]

Evaluate the product

[tex]7 * 6x^2 \sqrt{2x^4*2x^{12 }[/tex]

This gives

[tex]42x^2 \sqrt{4x^{16}[/tex]

Take the square root of 4

[tex]2*42x^2 \sqrt{x^{16}[/tex]

Take the square root of x^16

[tex]2*42x^2 *x^8[/tex]

So, we have:

[tex]84x^{10[/tex]

Hence, the equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

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Answer:

Step-by-step explanation:

The equivalent expression of  is

How to determine the equivalent expression?

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

Evaluate the product

This gives

Take the square root of 4

Take the square root of x^16

So, we have:

Hence, the equivalent expression of is

The line segment in the figure can be named as: IYM and MYI.

If we have three points on a line segment, the point on the middle will be the alphabet in the center when naming the line, while the alphabets of both endpoints can be written either at the beginning or ending.

Given the figure above, Y will be at the center. The endpoints are I and M. Therefore, the line segment can be named as: IYM and MYI.

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[tex]f(x) = \sqrt{1 - 4{ x}^{2} } [/tex]

[tex]1 - 4x {}^{2} \geqslant 0[/tex]

[tex] - \infty \: \: \: \: \: \: \: \: - 0.5 \: \: \: \: \: \: \: \: \: 0.5 \: \: \: \: \: \: \: \: \infty \\ - \: \: \: \: \: \: \: \: \: \: \: \: \: \:0 \: \: \: \: \: + \: \: \: \:0 \: \: \: \: \: - [/tex]

[tex]domain \\ [ \: -0.5 \: , \: 0.5 \: ][/tex]

[tex]g(x) = 1 - 4x {}^{2} \\ g'(x) = - 8x \\ g'(x) = 0 \\ x = 0 \\ g(0) = 1 - 4(0) = 1 \\ maximum \: = 1[/tex]

[tex]range \\ [ \: 0 \: , \: 1 \: ][/tex]

Answer:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

[tex]\textsf{Range}: \quad [0, 1][/tex]

Step-by-step explanation:

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

Given function:

[tex]f(x)=\sqrt{1-4x^2}[/tex]

As negative numbers don't have real square roots:

[tex]\implies 1-4x^2\geq 0[/tex]

Therefore, to find the domain, solve the inequality.

Subtract 1 from both sides:

[tex]\implies -4x^2\geq -1[/tex]

Divide both sides by -1 (reverse the inequality):

[tex]\implies 4x^2 \leq 1[/tex]

Divide both sides by 4:

[tex]\implies x^2\leq \dfrac{1}{4}[/tex]

[tex]\textsf{For }\:a^n \leq b,\:\:\textsf{if }n\textsf{ is even then }-\sqrt[n]{b} \leq a \leq \sqrt[n]{b}:[/tex]

[tex]\implies -\sqrt[2]{\dfrac{1}{4}} \leq x \leq \sqrt[2]{\dfrac{1}{4}}[/tex]

[tex]\implies -\sqrt{\dfrac{1}{4}} \leq x \leq \sqrt{\dfrac{1}{4}}[/tex]

[tex]\implies -\dfrac{1}{2} \leq x \leq \dfrac{1}{2}[/tex]

Therefore:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

To find the range, input the endpoints of the domain into the function:

[tex]\implies f\left(-\dfrac{1}{2}\right)=\sqrt{1-4\left(-\dfrac{1}{2}\right)^2}=0[/tex]

[tex]\implies f\left(\dfrac{1}{2}\right)=\sqrt{1-4\left(\dfrac{1}{2}\right)^2}=0[/tex]

To find the limit of the range, find the extreme point(s) of the function by differentiating the function and setting it to zero.

[tex]\implies f(x)=(1-4x^2)^{\frac{1}{2}}[/tex]

[tex]\implies f'(x)=\dfrac{1}{2}(1-4x^2)^{-\frac{1}{2}} \cdot -8x[/tex]

[tex]\implies f'(x)=-\dfrac{4x}{\sqrt{1-4x^2}}[/tex]

Setting it to zero and solving for x:

[tex]\implies -\dfrac{4x}{\sqrt{1-4x^2}}=0[/tex]

[tex]\implies -4x=0[/tex]

[tex]\implies x=0[/tex]

Substitute x = 0 into the function:

[tex]\implies f(0)=\sqrt{1-4(0)^2}=1[/tex]

Therefore, the range is [0, 1]

The inequality graphed is the one in the first option.

On the graph we can see a solid parabola, the parabola opens downwards, and we can see that the vertex of the parabola is on the point (-1, 5).

And the shaded region is above the parabola.

Then the inequality is of the form:

y  ≥  parabola.

By knowing where is the vertex, we know that:

parabola = -a*(x + 1)^2 + 5

Then the correct option is the first one.

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Answer:

2-2 goes with 1 - 1

10 - 7 goes with 8 - 5

4 - 3 goes with 7 - 6

8 - 2 goes with 9 - 3

9 - 5 goes with 5 - 1

Have a nice day.

I am Clara btw.

Step-by-step explanation:

The solutions to the given quadratic equations are x = -25/16 and x = 1

From the question, we are to determine the solutions to the given quadratic equation

The given quadratic equation is

16x² + 9 = 25

The equation can be solved as follows

16x² + 9 = 25

16x² + 9 - 25 = 0

16x² -16x +25x -25 = 0

16x(x -1) +25(x -1) = 0

(16x +25)(x -1) = 0

16x + 25 = 0 OR x - 1 = 0

16x = -25 OR x = 1

x = -25/16 OR x = 1

Hence, the solutions to the given quadratic equations are x = -25/16 and x = 1

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Answer:

1: r^5, 2: st^2, 3: qr, 4: 1, 5: m, 6: x, 7: 1/z, 8: a, 9: d^4f^2 10: 1, 11: cd^2, 12: b, 13: 1, 14: st^2, 15: 1/mn.

Step-by-step explanation:

1 explanation: Cancel the common factor of r^6 and r.

2 explanation: Simplify the expression.

3 explanation: simplify the expression.

4 explanation: Simplify the expression.

5 explanation: simplify the expression.

6 explanation: Cancel the common factor of x^2 and x.

7 explanation: Cancel the common factor of z^4 and z^5.

8 explanation: Cancel the common factor of a^2 and a.

9 explanation: simplify the expression.

10 explanation: simplify the expression.

11 explanation: simplify the expression.

12 explanation: simplify the expression.

13 explanation: simplify the expression.

14 explanation: simplify the expression.

15: simplify the expression.

Answer:

Six Serving Men is a team exercise that examines an issue from twelve different viewpoints. It is based on the words of the poem by Rudyard Kipling: I keep six honest serving men, they taught me all I knew. Their names are What and Why and When and How and Where and Who. To use this technique in a meeting, provide 12 areas for answering questions related to the central topic

Step-by-step explanation:

The distribution is skewed because it's on the right side of the polygon and this illustrates that's it's positively skewed.

It should be noted that the polygon can be gotten by plotting the data.

After the analysis of the distribution, the distribution is skewed to the right.

This illustrates that it is skewed.

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The graph of function f is shifted right 3 units and up 4 units.

Let f(x) be the parent function

Now use the Rule : f(x)→f(x-b) to find the shifting of graph

The graph shifts right by b units

So, shift the graph by 3 unit

So, f(x)→f(x-3)

So, the graph shifted right by 3 units

2nd rule used is Rule : f(x)→f(x)+b to find the another shifting of graph

The graph shifts up by b units

Now shift the obtained graph up by 4 units

So,  f(x-3)→f(x-3)+4

So, the graph shifts up by 4 units

Thus, The graph of function f is shifted right 3 units and up 4 units.

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The four of them can get to the island if the two women begins the journey first. Detail below:

From the question given, we were told that:

With the above information in mind, we can determine how the four of them can get to the island by following the steps listed below:

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The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the number of hamburger sold and y represent the number of cheeseburgers sold, hence:

x + y = 460    (1)

Also:

y = 3x       (2)

From both equations:

x = 115, y = 345

The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.

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Answer:

18.75 percent

Step-by-step explanation:

150 / 800 x 100 = 18.75

The volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.

To find the volume of the solid generated, we use the shell method since the cross-sections are parallel to the axis of rotation.

So, [tex]V = 2\pi\int\limits^a_b {xy} \, dx[/tex]

Now given that  the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis.

So, we integrate from x = 0 to x = 2.

[tex]V = 2\pi\int\limits^a_b {xy} \, dx\\= 2\pi\int\limits^2_0 {x(x^{2} + x)} \, dx\\= 2\pi\int\limits^2_0 {(x^{3} + x^{2} )} \, dx\\= 2\pi\int\limits^2_0 {x^{3} + 2\pi\int\limits^2_0 x^{2} } \, dx\\= 2\pi[\frac{x^{4} }{4}]_{0}^{2} + 2\pi[\frac{x^{3} }{3}]_{0}^{2} \\= 2\pi[\frac{2^{4} - 0^{4} }{4}}]+ 2\pi[\frac{2^{3} - 0^{3} }{3}]\\= 2\pi[\frac{16 - 0}{4}}]+ 2\pi[\frac{8 - 0}{3}]\\= 2\pi[\frac{16}{4}}]+ 2\pi[\frac{8}{3}]\\= 2\pi (4)+ [\frac{16\pi}{3}]\\= 8\pi + [\frac{16\pi}{3}]\\[/tex]

[tex]= \frac{24\pi + 16\pi}{3} \\= \frac{40\pi}{3}[/tex]

So, the volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.

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The two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

Given the equation; 9x² + 4 = 0

First, we subtract 4 from both sides.

9x² + 4 = 0

9x² = -4

x² = -4/9

Take the square roots of both sides

x = ±√(-4/9)

Rewrite -4/9 as (2i/3)²

x = ±√(2i/3)²

x = ±(2i/3)

Hence,

x = 2i/3, -2i/3

Therefore the two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

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Answer:

but it says ill get 10 only

Step-by-step explanation:

The answer choice which sin(x + y) - sin(x - y) simplifies to is; 2(cos x)(sin y).

It follows from the task content that the expression given in the task content can be simplified by trigonometric identities as follows;

sin(x + y) - sin(x - y) = sinxcosy + cosxsiny - (sinxcosy -cosxsiny)

= 2cosxsiny.

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The list price of the house is $260,869.57

What is a list price?

This is the price the property is valued to sell at in an arm's length transaction in a transaction that occurs between independent parties.

In this case, the property was sold for 92% of its list price, which means the sales price is 92% multiplied by the list price.

sales price=92%* list price

sales price=$240,000

list price=unknown(assume it is X)

$240,000=92%*X

X=$240,000/92%

X=$260,869.57

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