Set A= 1, 3, 4, 5, 9, 10, 11
Set B= 2, 4, 6, 7, 11, 12
What is the union of sets A and B?

Part 1

V = pi*r^2*h .... volume of a cylinder

250 = pi*r^2*h

h = 250/(pi*r^2)

Plug this into the surface area of a cylinder equation

SA = 2*pi*r^2 + 2*pi*r*h

SA = 2*pi*r^2 + 2*pi*r*( 250/(pi*r^2) )

SA = 2*pi*r^2 + 500/r

Now replace every copy of r with x to get this function

f(x) = 2*pi*x^2 + 500/x

x = radius

y = f(x) = surface area

Next we'll use Desmos to graph this function. See the screenshot below. It produces some kind of curve that has two pieces to it. We'll only focus on the curve where x > 0 and y > 0. It makes no sense to have a negative radius, and we cannot have a negative surface area either.

Click on the lowest point of the parabolic looking shaped piece (it's not really a parabola, but we'll imagine that it is for the sake of simplicity).

The coordinates of that local min point will show up and they are (3.414, 219.689)

We have (x,y) = (3.414, 219.689) lead to r = 3.414 and SA = 219.689

This means that a radius of approximately r = 3.414 cm leads to the smallest surface area of approximately 219.689 square cm. This is when the amount of material is minimized.

Use this value of r to find h

h = 250/(pi*r^2)

h = 250/(pi*3.414^2)

h = 6.828

Desmos not only graphs, but it is also a standard calculator. The calculation is also shown in the screenshot.

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Part 2

Answer:

30%

Step-by-step explanation:

First subtract: 1 - .70 = .30

Then move decimal over to the right 2 times and add percentage sign instead of the decimal: 30%

Area of sector

option B

Answer:

b

Step-by-step explanation:

The area of a sector is (the angle) over 360 multiplied by pi (radius) squared

This would be 45/360 pi (4.5) squared, resulting in option b.

Answer:

b. x = 123

Step-by-step explanation:

Answer:

45m

Step-by-step explanation:

4m+19m+14m+8m=45m

The expected number of adults that believe ufos are watching earth is 4

The given parameters are:

p = 48%

Sample size, n = 8

The expected number of adults that believe ufos are watching earth is calculated as:

E(x) = np

This gives

E(x) = 8 * 48%

Evaluate

E(x) = 3.84

Approximate

E(x) = 4

Hence, the expected number of adults that believe ufos are watching earth is 4

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Answer:

D) None of the choices are correct.

Explanation:

Given triangles AHL and NKG

Sides which are congruent:

So, AHL ≅ NKG. There are no such options.

Explanation:

The value of 'a' out front in y = a sin(bx) determines the amplitude.

The b term helps us compute the period, which is 2pi/b for sine, cosine, secant, and cosecant functions.

For example, y = 2sin(3x) has an amplitude of 2 and period of 2pi/3

For tangent and cotangent functions, the period would be pi/b.

Answer:

y = [tex]\frac{1}{2}[/tex] x

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (6, 3) ← 2 points on the line

m = [tex]\frac{3-0}{6-0}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x ← equation of line

Answer:

311.0

Step-by-step explanation:

pi3^2(11)

pi r^2 (h)

Answer:

8

Step-by-step explanation:

Answer:

  A. one solution; lines intersect at one point

  B. (x, y) = (3, 4)

Step-by-step explanation:

A linear equation will be represented on a graph by a straight line. A pair of equations will graph as a pair of lines. If the lines are not coincident or parallel, they will intersect at exactly one point. That point is the solution to the pair of equations.

__

A graph of the given points quickly shows the lines are not parallel or coincident. Each point on line A satisfies the equation that describes the line. Each point on line B satisfies the equation that describes line B. The point of intersection is a point that satisfies both equations.

A pair of distinct non-parallel lines can have at most one point of intersection. Hence there can only be one solution to the pair of equations.

__

The graph shows the solution to the equations for lines A and B is ...

  (x, y) = (3, 4)

Answer:

27.5%

Step-by-step explanation:

Given:

Review:

Concepts:

Formula:

Now we must convert 275 milliliters to liters.

1. Divide the volume by 1,000.

275 ÷ 1000 = 0.275

2. Add the Unit Symbol for Liter.

0.275 ⇒ 0.275 L

Now we have to find how much of 1 liter- 0.275 liters as a percentage is.

To convert 0.275 to percent multiply 0.275 by 100. The result is 27.5 percent, or, using the percent sign, 27.5 %.

It will take 32 minutes for the population to grow from 1,000 to 32,000.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

If the population of an alien race doubles every two minutes,

1,000 x 32 = 32,000

Hence, It would take 32 minutes.

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The coordinates of the 3 respective points from the given parameters are; (6, -2); (-1, 1); (2, 6)

1) The coordinates of the point located 5/6 of the way from A to B is;

x = ⁵/₆(7 - 1) + 1

x = 6

y = ⁵/₆(-4 - 8) + 8

y = -2

x, y = (6, -2)

2) The coordinates of the point located ¹/₄ of the way from A to B is;

x = -3 + ¹/₄(5 - (-3))

x = -1

y = 0 + ¹/₄(4 - 0)

y = 1

x, y = (-1, 1)

3) The coordinates of the point located ¹/₆ of the way from A to B is;

x = ¹/₆(7 - 1) + 1

x = 2

y = ¹/₆(-4 - 8) + 8

y = 6

x, y = (2, 6)

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The original cost was it before the sale will be £ 26.4.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio.

In a sale is 25% off all prices but cost £33 in the sale.

Then the original cost was it before the sale will be

Let x be the original cost.

Then we have

1.25x = £33

      x = £26.4

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1 year = 12 months

Pages to write in 12 months = 1260

Pages to write in 1 month = 1260/12

= 105 pages per month

The coterminal angle to -ㅠ/2 in the range between 0 and 2ㅠ radians is 3ㅠ/2.

For any angle A, all the coterminal angles are of the form:

B = A + n*(2ㅠ).

Where n is an integer different than zero.

In this case, the angle is A = -ㅠ/2

So the coterminal angles are of the form:

B = -ㅠ/2 + n*(2ㅠ)

We want it to be between 0 and 2ㅠ, so we can define n = 1, then we get:

B = -ㅠ/2 + (2ㅠ) = -ㅠ/2 + ((4/2)ㅠ) = 3ㅠ/2

Then we can conclude that the correct option is b.

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Answer:

1

Step-by-step explanation:

[tex]\text{Given that,}~ (x_1,y_1) = (-2,4)~ \text{and}~ \text{slope,}~ m = -\dfrac 32\\ \\\text{Equation of line,}~\\\\~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -4 =-\dfrac 32(x+2)\\\\\implies y-4 =-\dfrac 32x - 3\\\\\implies y = -\dfrac 32x -3 +4\\\\\implies y = -\dfrac 32x +1[/tex]

The current equation of the perpendicular line;

 ⇒ is the slope-intercept form: [tex]y= mx + b[/tex]

Now for the point-slope form, we need a point on the line and the slope of the line:

⇒ we have

Since this is the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex]

 ⇒ where the (x₁,y₁) is the point on the line and m is the slope

    [tex]= > Equation: (y-4)=-\frac{3}{2}(x+2)[/tex]

To convert the equation to slope-intercept form:

  ⇒ must isolate 'y' to one side and everything to the other side

      [tex]y= -\frac{3}{2}(x+2)+4\\ y=-\frac{3}{2} x-3+4\\y=-\frac{3}{2}x+1[/tex]

Answer: [tex]y = -\frac{3}{2}x+1[/tex]

Hope that helps!

Answer:

Berries with any blush of red are not ripe, yet may ripen further once picked if kept at room temperature. That said though, you really want to ...

Step-by-step explanation:

oksosjaoqkqeand

[tex]66 \sqrt[3x9 \frac{ \sqrt[xx. \sqrt[36 \sqrt[3136(2 > kaki \: kwl{]{?} ]{?} ]{?} }{?} ]{?} [/tex]

Answer:

She is wrong.

Step-by-step explanation:

The mean score is

7 + 8 + 3 + 0 + 2= 20

We then divide it by the number which is 5

20/5= 4.

Therefore, Maria is wrong.

This is because she divided by 4 instead of 5, as she didn't include the rational number 0.

Answer:

Range = 1 1/4

Step-by-step explanation:

Range = Maximum - Minimum

Arranging the data in ascending order :

Solving for range :

Measurement is the area of the number sense that has a relationship with the quantity of ingredients used in recipes.

The measures of recipes are determined by:

So measure recipes, one can either measure them using artefacts such as cups, spoons, or other kind of containers.

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The store must sell 60 of each set each to obtain the biggest possible income

The given parameters can be represented using the following table:

                        Set 1        Set 2     Available

Notebook         2                3         300

Pen                   1                  1          120

Selling price     8               11.5

Using the above data values, we have:

Objective function: Max P = 8x + 11.5y

Subject to:

2x + 3y ≤ 300

x + y ≤ 120

Next, we plot the graph of the above inequalities (see attachment)

From the attached graph, we have:

(x,y) = (60,60)

Hence, the store must sell 60 of each set each to obtain the biggest possible income

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b²-4ac is the discriminant (D)!

you use it when you have a second degree function and want to find the x. If:

D<0 -> no x that we can find

D=0 -> 1 answer for x

D>0 -> 2 answers for x

when your D is = or > 0 then you use these formulas to find the x:

x1= (-b-VD)/2a

x2= (-b+VD)/2a

example1:

f(x)=2x²+3x+4=0

D= b²-4ac

= 3²-4×2×4

=9- 32

=-23

-> no answers for x

example2:

f(x)=2x²+5x+2=0

D= 4²-4×2×2

= 25-16

=9

x1= (-b-VD)/2a

= (-5-3)/4

= -8/4

=-2

x2= (-b+VD)/2a

= (-5+3)/4

=-2/4

=-1/2