Sets A, B, and C are subsets of the universal set U. These sets are defined as follows.
U= {f,g,h,p,q,r,x,y,z}
A={f,g,p,q}
B={g,h,q,x,y}
C={p.q.x.y.z}

Find (C ∪ B) ∩ A'.
Write your answer in roster form or as Ø.

Volume of a cylinder: PI x radius^2 x height

= 3.14 x 5^2 x 10 = 785 m^3

Volume of a cone: pi x radius^2 x height/3

= 3.14 x 5^2 x 4/3 = 104.67 m^3

Total volume  = 785 + 104.67 = 889.67 M63

Answer: C. 889.67 M^3

Answer:

[tex]\textsf{C)}\quad \sf 889.67\: m^3[/tex]

Step-by-step explanation:

The given composite solid is made up of a cylinder and a cone.

To find the volume of the composite solid, find the volume of the cylinder and the volume of the cone, then add them together.

Volume of a cylinder:

[tex]\sf V=\pi r^2 h[/tex]

(where r is the radius and h is the height)

Given:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cylinder & = \sf \pi (5)^2(10)\\ & = \sf 250 \pi \:\:m^3 \end{aligned}[/tex]

Volume of a cone:

[tex]\sf V=\dfrac{1}{3} \pi r^2 h[/tex]

(where r is the radius and h is the height)

Given:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cone & = \sf \dfrac{1}{3} \pi (5)^2(4)\\ & = \sf \dfrac{100}{3}\pi \:\:m^3 \end{aligned}[/tex]

Therefore, the volume of the composite solid is:

[tex]\begin{aligned}\implies \sf Volume\:of\:composite\:solid & = \sf Cylinder\:volume+Cone\:volume\\ & = \sf 250\pi + \dfrac{100}{3}\pi \\ & = \sf \dfrac{850}{3} \pi \\ & = \sf \dfrac{850}{3} \times 3.14 \\ & = \sf 889.67\:m^3\:(2\:d.p.)\end{aligned}[/tex]

Answer:

y = -2x + 4

Step-by-step explanation:

The x-intercept would be the point (2,0) and the y intercept would have the point (0,4).  Once we know two points we can write the equation in the line intercept for of y = mx + b.  

We need to find the slope and the y intercept.  The slope is the steepness of the line and it is the change in y over the change in x.

The ordered pairs are written in  the form of (x, y).  From our two points, we will subtract the y's to find the top number of our fraction.

0 - 4 = -4 that is the numerator (top number) of our slope.  We do the same with the two x numbers that we have been given.

2 - 0 = 2  This is our numerator (or bottom number of our slope)

Our slope is -4 /2 to simplify, we divide the top and bottom number by 2 to get -2 / or just -2

Now that we have the slope we need to find the y-intercept.  We can use either of our original two points and our slope to determine the y-intercept.  It does not matter if you use the point (2,0) or (0,4).  I will use (2,0) and the slope of -2

y = mx + b

0 = -2(2) + b  

0 = -4 + b   add 4 to both sides of the equation

4 = b

Now that we have the slope and the y-intercept, we can write the equation

y = mx + b

y = -2x + 4

Answer: A and H

Step-by-step explanation:

y=x+1 is shaded below and dotted, so [tex]y < x+1 \implies x-y > -1[/tex].

Also, y=-2 is dotted and shaded above, so it represents [tex]y > -2[/tex]

Based on the amounts that Janet Lopez has to invest in stocks and bonds, the linear programming model would be:

The return on stocks (x) is 18% and the return on bonds (y) is 6%, The objective function:

= 0.18x + 0.06y

There are constraints to watch out for:

Maximum to lose on stocks is 22% and on bonds is 5% but these are to be less than the total amount of $100,000.

0.22x + 0.05y ≤ 100,000

The total amount to invest is $72,000 which means that both bonds and stocks need to be less than this amount:

x + y ≤ 720,000

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Answer:

A = -5

B = 1

Step-by-step explanation:

Hello!

You simply plug in the given x-value into the equation to find the missing y-value.

Plug in -1 for x into y = 2x - 3.

Plug in 2 for x into y = 2x - 3.

A. The formula (mathematical function) for the monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.

B.  Using the formula above, the value of R(10, 3) is $197.

A function is an expression, rule, or law defining the relationship between an independent variable and a dependent variable.

Functions are used to define physical relationships between variables.

Cost monthly subscription = $28.20 per box

Number of normal potatoes in each box = 16

Cost of additional luxury potatoes = $5 per potato

If the monthly revenue function, R, is given as R(s, n) where:

s = number of monthly subscribers

n = total number of luxury potatoes ordered

The monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.

The value of R(10, 3) is $197 ($18.20 x 10 + $5 x 3)

Thus, using the formula above, the value of R(10, 3) is $197.

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Answer:

First  angle:

x =32

Second angle:

3x

3(32) = 96

Third angle:

2x - 12

2(32) -12 =52

Step-by-step explanation:

x + 3x + 2x - 12 = 180  The sum of the interior angles of a triangle is 180

6x -12 = 180  Combine the x terms

6x = 192  add 12 to both sides

x = 32

Check: 52 + 96 + 32 = 180

The equation of a hyperbola is  [tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1

What are the steps to Hyperbola equation ?

To find the equation of hyperbola, the following steps must be taken. You need to identify;

The general equation of a hyperbola can be expressed as

[tex]x^{2}[/tex]/[tex]a^{2}[/tex] - [tex]y^{2}[/tex]/[tex]b^{2}[/tex] = 1

From the graph, we have the following parameters

a = 3

[tex]a^{2}[/tex] = [tex]3^{2}[/tex] = 9

b = 2

[tex]b^{2}[/tex] = [tex]2^{2}[/tex] = 4

The equation of a hyperbola can be expressed as

[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1

The vertices = V(+/-a,0) = (+/-3,0)

The center = C(0,0)

The focus = F(+/-C, 0)

Where [tex]C^{2}[/tex] = [tex]a^{2}[/tex]  + [tex]b^{2}[/tex]

C = [tex]\sqrt{9 + 4}[/tex]

C = [tex]\sqrt{13}[/tex]

Focus = F(+/- [tex]\sqrt{13}[/tex], 0)

The general equation for asymptote = +/- b/a X

= +/-2/3X

Therefore, the equation of a hyperbola can be expressed as

[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1

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Answer:

B. More than 90

Step-by-step explanation:

Hope this helps!

Answer:

A = 55

Step-by-step explanation:

take the two identical triangles and join them so that you get a rectangle wih sides 5 and 11. now multiply them togeter to get the are of the polynom

The area of triangle is 55 square centimeters.

Area is the amount of space occupied by a two-dimensional figure.

The formula for the area of triangle is

[tex]Area = \frac{1}{2} \times base\times height[/tex]

According to the given question.

We have a figure of a quadrilateral which is made up of four right angled tringles.

Now,

The area of a triangle with base 5cm and height 7 cm

= [tex]\frac{1}{2} \times 5\times 7[/tex]

[tex]=\frac{35}{2}[/tex]

[tex]= 17.5[/tex] square centimeters

And, the area of triangle with base 4cm and height 5cm

= [tex]\frac{1}{2} \times 4\times 5[/tex]

[tex]= 10[/tex] square centimeters

Since, the quadrilateral is made up of 2 right angled triangle with base 5cm and height 7cm and 2 right angled triangle with base 4cm and height 5cm.

Therefore, the area of quadrilateral or the given fiure

= 2( area of triangle with height 7cm and base 5cm + area of triangle with base 4cm and height 5cm )

= 2(17.5 + 10) square centimeter

= 2 × 27.5

= 55 square centimeters

Hence, the area of triangle is 55 square centimeters.

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Using a system of equations, it is found that her normal week is of €285.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The first equation, considering the first sentence, is given by:

x + 8y = 375.

The second equation, considering the second sentence, is given by:

x + 4y = 330.

Then the system is:

Multiplying the second equation by -2, the system is:

Adding the equations, we have that her normal week is given by:

x = 660 - 375 = €285.

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The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.

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

Let x represent the first car consumption and y represent the second car consumption, hence:

x + y = 55   (1)

Also:

15x + 20y = 975   (2)

From both equations:

x = 25, y = 30

The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.

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Answer:

x^4-3x+2

Step-by-step explanation:

There are several different ways to divide algebraic expressions. Here the most simple way to do it (and good idea to try first) is to FACTOR and CANCEL.

see image.

Factor an x from the top. Cancel that x with the bottom x. See image.

(***Also, note: never "cancel" anything connected by a + or a - )

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{x^{5}+(3\times x^{2}) +(2\times x) }{x}} \end{gathered}$}[/tex]

Takes into account expressions that have not yet been taken into account.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{\red{\not{x}}(x-1)(x^{3}+x^{2} +x-2) }{\red{\not{x}} } } \end{gathered}$}[/tex]

Cancel x in both the  numerator and the denominator.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{(x-1)(x^{3}+x^{2} +x-2) } \end{gathered}$}[/tex]

The expression expands

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x^{4}-3x+2 } \end{gathered}$} }[/tex]

The geometric center of the graph under the function is 5/3

The equation of the function is given as:

f(x) = 3 - |x - 2|

The interval is given as:

x ∈ [0, 3]

The geometric center (gc) of the graph under the function is calculated using

gc = ∫x f(x) dx/∫f(x) dx

Substitute the known values in the above equation

gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx

Integrate the numerator and the denominator of the above equation

gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]

Recall that the interval is given as x ∈ [0, 3]

Substitute the interval values in the above equation.

The equation is then simplified using a graphing calculator.

So, we have

gc = (65/6)/(13/2)

Express the quotient expression as a product

gc = (65/6) * (2/13)

Divide 65 by 13

gc = 5/6 * 2

Divide 2 by 6

gc = 5/3

Hence, the geometric center of the graph under the function is 5/3

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Answer:

D

Step-by-step explanation:

It pass the vertical line test.

Hope this helps <3

As per the given graph, the graph fails the vertical line test. The correct option is B.

A graph is a visual representation of data that uses lines, bars, or other symbols to show how different values are related to each other.

Graphs are often used to display information in a way that is easy to understand and interpret.

The vertical line test is a way to determine whether a given graph represents a function.

According to this test, if any vertical line intersects the graph at more than one point, then the graph does not represent a function.

In the given graph, we can see that there are some vertical lines that intersect the graph at more than one point, such as the vertical line passing through x = 2.

Therefore, the graph does not pass the vertical line test and does not represent a function.

Thus, the correct answer is B.

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The percentage of students age 15 and above travel to school by bus is 47%

The table of values is given as:

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15                            18                 165

Age 15 and above    65                                 195

Column totals          152          110        98      360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above  = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15           87              18      60        165

Age 15 and above    65          92        38        195

Column totals          152          110        98      360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%

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Answer:

Step-by-step explanation:

The volume of the glasses is as follows;

The volume of cylinder glass 1 = πr²h

The volume of cylinder glass 1 = 3.14 × 3² × 6

The volume of cylinder glass 1 = 3.14 × 9 × 6

The volume of cylinder glass 1 = 169.56 cm³ = 170 cm³

The volume of the glass 2 = 2 / 3 π r³ + πr²h

The volume of the glass 2 = 2 / 3 × 3.14 × 3³ + 3.14 × 3² × 3

The volume of the glass 2 = 56.52 + 84.78

The volume of the glass 2 = 141.3 cm³ = 141 cm³

The volume of conical glass 3 = 1 / 3 πr²h

The volume of conical glass 3 = 1 / 3 × 3.14 × 3² × (√7² - 3² = √40)

The volume of conical glass 3 = 9.42 × √40

The volume of conical glass 3 = 59.5773111176

The volume of conical glass 3 = 60 cm³

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The radius of the circle exists approximately 4.95 feet.

Given the area of the square as A = 98 ft²

The side length of the square choice is equivalent to the diameter of the circle.

First, we must obtain the length of the square.

Area of a square [tex]= L^2[/tex]

98 = L²

L = √98

L = 9.89 ft

Thus the diameter of the circle exists at 9.89 ft

radius = diameter/2

radius = 9.89/2

radius ≈ 4.95 feet

Therefore the radius of the circle exists approximately 4.95 feet.

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I assume you meant [tex]f(x)=8^x[/tex].

Reflecting across the x-axis would give [tex]y=-8^x[/tex].

Reflecting across the y-axis would give [tex]y=8^{-x}[/tex].

The box plot that represents the data is a box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.(second option)

A box plot is used to study the distribution and level of a set of scores. The whiskers represent the minimum and maximum values.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.

The data arranged in ascending order : 11, 13, 23, 24, 24, 27, 31

Median = 24

First quartile = 1/4 x (7 + 1) = 2nd term =13

Third quartile = 3/4 x (7 + 1) = 6th term = 27

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Answer:

all real values of x where x < -1

The correct statement is all real values of x where x < -1.

Option A is the correct answer.

We have,

To determine the values for which the graph of the function

f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.

Let's consider the factors individually:

(x - 3): This factor is positive for x > 3 and negative for x < 3.

(x + 1): This factor is positive for x > -1 and negative for x < -1.

To determine the overall sign of the function, we need to consider the signs of both factors together.

When both factors are positive or both factors are negative, the function is positive.

When the factors have opposite signs, the function is negative.

From the above analysis, we can conclude the following:

When x > 3, both factors are positive, so the function is positive.

When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.

When x < -1, both factors are negative, so the function is positive again.

Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).

Thus,

The correct statement is all real values of x where x < -1.

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Firstly changing mixed fraction.

[tex] \frac{3}{2} - \frac{5}{4} + \frac{23}{4} [/tex]

By taking the LCM

[tex] \frac{6 - 5 + 23}{4} [/tex]

-5 + 23 (-) (+) = (-)

[tex] \frac{6 + 18}{4} [/tex]

[tex] \frac{24}{4} [/tex]

[tex]6[/tex]

Hope it helps you, any confusions you may ask!

Answer:

6 (work below)

Step-by-step explanation:

1 1/2 = 3/2

1 1/4 = 5/4

5 3/4 = 23/4

The least common multiple of the denominators is 4, so 3/2 will become 6/4.

6/4 - 5/4 = 1/4 + 23/4 = 24/4 = 6

Brainliest, please :)

The dimensions of the length and width are 25 meters and 12. 5 meters respectively.

Area of a rectangle

area of rectangle = l × w

where

l = length

w = width

Note that,

Perimeter = 2w+ l

50 = 2w + l

l = 50  - 2w

Hence,

area = w(50 - 2w)

288 = 50w - 2w²

-2w² + 50w - 288 = 0

-w² + 25w - 144 = 0

The dimension w can be found as follows;

w = - b / 2a

where

a = -1

b = 25

w = - 25 / 2 ×  -1

w = 12.5 meters

Then, we have that

l = 50  - 2w

Substitute the value of w

l = 50 - 2(12.5)

l = 50 - 25

I = 25 meters

Thus, the dimensions of the length and width are 25 meters and 12. 5 meters respectively.

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The number of new cases be on Thursday after all of this growth and falling is 956.

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

There are initially 800 cases, hence:

Number of cases on Monday = 1.15 * 800 = 920

Number of cases on Tuesday = 1.05 * 920 = 966

Number of cases on Wednesday = 0.9 * 966 = 869.4

Number of cases on Thursday = 1.1 * 869.4 = 956.34

The number of new cases be on Thursday after all of this growth and falling is 956.

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Answer:

12 years old

Step-by-step explanation:

Set up the following equation:

x + 2 = 2(x - 5) (distribute the 2)

x + 2 = 2x - 10 (subtract 2 from both sides)

x = 2x - 12 (subtract 2x from both sides)

-x = -12 (multiply both sides by negative 1)

x = 12

Brainliest, please :)

Answer: 12

Step-by-step explanation:

Let's algebraically represent this situation. Say his current age is x. We can rephrase the sentence to say that in two years, his age is the same as twice his age 5 years ago.

The phrase "in two years" means when his age is 2 more than his current age, or x + 2.

The phrase "same as" represents equality. The expressions on both sides have the same value.

The phrase "twice his age 5 years ago" is his age minus 5, multiplied by 2. We can write this as 2*(x-5).

Now that we have "translated" the equation from words to numbers, let's put it all in one equation and solve:

[tex]x+2=2(x-5)[/tex]

[tex]x+2=2x-10[/tex] [Distributive Property]

[tex]x+2-2x-2=2x-10-2x-2[/tex] [Adding -2x-2 to both sides]

[tex]-x=-12[/tex] [Combining like terms and simplifying]

[tex]x=12[/tex] [Multiplying both sides by -1 to remove the negative]

Hence, Billy's age is 12.

Answer:

Step-by-step explanation:

no idea tbh

x is 40 degrees

y is 40 degrees

Hope this helps!

Answer:

58

Step-by-step explanation:

[tex]x = \frac{141 - 25}{2} = 58[/tex]

The sum of the exponential expression is e^8x + e^2x

Exponential functions are inverse of logarithmic function

Given the exponential function below;

(e^4x)² + e^2x

Expand

e^8x + e^2x

Hence the sum of the exponential expression is e^8x + e^2x

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