A paper bag has six colored marbles. The marbles are red, green, blue, purple, yellow, and orange. List the sample space when choosing one marble.

S = {1, 2, 3, 4, 5, 6}
S = {red, blue, green, orange, yellow}
S = {g, r, b, y, o}
S = {green, blue, yellow, orange, purple, red}

Answer:

686 cm^2

Step-by-step explanation:

First find the sides

7f = 49

4f = 28

To find a triangle area (right triangle), multiply each side like a rectangle, but divide it by two.

(49*28)/2 = 686

Answer:

67

Step-by-step explanation:

When P₁ >3P₂ she must consume only tomatoes.

What are indifference curves ?

An indifference curve is a graph that illustrates numerous pairings of two goods or commodities that leave the customer equally well off or satisfied—hence indifferent—when it comes to owning any pairing of the two items that is represented along the curve.

Mary do trading 3 tomatoes for 1 nectarine.

So, MRS=3

P₁ >3P₂

P₁/P₂ > 3

P₁/P₂ < -3

This satisfies  MRS=3

P₁ >3P₂ shows budget constraint

consumer specializes in tomatoes consumption.

if  P₂ > 4 P₁ , consumer specializes in nectarine consumption. option is not there.

So, When P₁ >3P₂ she must consume only tomatoes.

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Use the distributive property to multiply 2 times 4−2w.

Subtract 8 from 8 to get 0.

Divide both sides by −4.

Divide −4 by −4 to get 1.

Answer:

w = 1

Step-by-step explanation:

2(4 - 2w) - 8 = -4

(2*4 + 2*-2w) - 8 = -4

(8 - 4w) - 8 = -4

-4w + 8 - 8 = -4

-4w = -4

w = -4/-4

w = 1

Check:

2(4 - 2*1) - 8 = -4

2(4-2) -8 = -4

2(2) - 8 = -4

4 - 8 = -4

The radius of the cone is 10√(3/πh) inches when the volume of the cone is 100 cubic inches.

According to the question,

We have the following information:

Volume of cone = 100 cubic inches

We know that the following formula is used to find the volume of cone:

Volume of cone = π[tex]r^{2}h/3[/tex] where r is the radius of the cone and h is the height of the cone

π[tex]r^{2}h/3[/tex] = 100

Now, using the cross multiplication method:

π[tex]r^{2}[/tex]h = 100*3

Dividing both sides of the equation by πh:

[tex]r^{2}[/tex] = 300/πh

r = 10√(3/πh) inches

We can also solve it further by putting the value of π.

Hence, the radius of the cone is 10√(3/πh) inches when the volume of the cone is 100 cubic inches.

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The one time joining fee found from the linear relationship between total cost and the number of months of membership is $250

A linear relationship is a relationship between two variables that has a straight line when graphed.

The total cost of the gym membership = C

The number of months of membership = t

The table in the question is presented as follows;

t (Time in months)     [tex]{}[/tex]                 C (Total cost)

2      [tex]{}[/tex]                                            200

4     [tex]{}[/tex]                                             250

9     [tex]{}[/tex]                                             375

The linear equation that represents the value in the table is found as follows;

Slope of the line, m = (375 - 250)/(9 - 4) = 25

The equation of the line in point and slope form is therefore;

(C - 375) = 25·(t - 9)

C = 25·(t - 9) + 375

C = 25·t - 225 + 375 = 25·t + 250

C = 25·t + 250

The joining fee is the amount paid at the start when t = 0, therefore;

Joining fee = 25 × 0 + 250 = 250

The one time joining fee is $250

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Answer:

density = 1.43 × 10⁻³ g/cm³

Step-by-step explanation:

We are told that oxygen gas of mass 2.23 kg has a volume of 1.56 × 10⁶ cm³, and we are told to find its density in g/cm³.

To do this we have to first convert the mass, which is given in kg, to g:

mass = 2.23 kg = 2.23 kg × 1000 [tex]\mathrm{_\frac{g}{kg}}[/tex]

                          = 2230 g

Next, we can find the density of the gas using the following formula:

[tex]\boxed{density = \frac{mass}{volume}}[/tex]

⇒ density = [tex]\mathrm{\frac{2230 \ g}{1.56 \times 10^{6} \ cm^3}}[/tex]

                 = 1.43 × 10⁻³ g/cm³

Therefore, the density of the oxygen gas is 1.43 × 10⁻³ g/cm³.

By solving a linear equation, it is obtained that Warren has drawn 30 pictures of animals

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let Warren has drawn 5x pictures of animals and 2x pictures of people

Warren has drawn 18 more pictures of animals than people in his notepad

By the problem,

5x - 2x = 18

3x = 18

x = [tex]\frac{18}{3}[/tex]

x = 6

Number of pictures of animals Warren has drawn = [tex]5 \times 6 = 30[/tex]

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The x and y table of all 5 points in this graph include the following:

x                   y

1                   1

2                  2

3                  3

4                  4

5                  5

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Additionally, the graph of any proportional relationship is always modeled by a straight line with the data points passing through the origin (0, 0).

In this scenario, we can reasonably and logically deduce that all of the data points in this graph are represented by the red symbols.

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The ball was in the air for 1.5 seconds. The answer is true.

The equation of the form ax² + bx +c is known as a quadratic equation.

The given equation is h(t) = -16t² + 20t + 6.

To find the time for which the ball was in the air, substitute h(t) =0.

0 = -16t² + 20t + 6

Use the quadratic formula to solve the equation:

[tex]t= \frac{- 20 \pm\sqrt{20^2 - 4(-16)(6)}}{2(-16)}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{784}}{-32}\\\\t= \frac{- 20 \pm28}{-32}[/tex]

t = (-20 + 28)/(-32) or t = (-20-28)/(-32)

t = -0.25 or t = 1.5

Since time cannot be negative, discard the negative value.

Hence, the ball was in the air for 1.5 seconds. The answer is true.

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Giving every student in the experiment the same final exam is an example of A. Randomization.

The process of conducting research in an objective and controlled manner in order to maximize precision and draw specific conclusions about a hypothesis statement is known as experimental design.

The process in which participants in clinical trials are randomly assigned to separate groups that receive different treatments or other interventions. Neither the researcher nor the participant has any say in which treatment or intervention the participant receives.

A random process is a sequence of random variables that describe a process whose outcomes follow an evolution described by probability distributions. This was illustrated in the examination.

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Complete options

A. Randomization

B. Blocking

C. Direct control

D. Replication

Derek's hourly rate is $10 and Charlie's hourly rate is $10.45, Charlie's earns $0.45 more per hour than Derek.

A unit rate means a rate for one of something.

Given that, a graph which shows Derek's earning hourly, and Charlie earns $52.25 in 5 hours of work,

Derek's earns $10 for an hour

Charlie's earning for an hour = 52.25/ 5 = $10.45

Hence, Charlie's hourly rate is $10.45, and he earns $0.45 more per hour than Derek.

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Answer:1341

Step-by-step explanation:

1342123

The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:

                                         FIFO          LIFO

Ending inventory          $10,250     $12,800

Cost of goods sold       $17,000     $14,450

FIFO (First-in, First-out) assumes that the physical flow of goods sold depends on the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

Date       Description                      Units   Unit Costs      Total Cost

April 1     Beginning inventory       220          $50             $11,000

April 5    Purchases                        100          $60                6,000

April 10   Purchases                         50          $45                2,250

April 16   Sales                              -300          $80

April 25  Sales                                -20          $95

April 30  Purchases                      200          $40                8,000

Total                                               570                             $27,250

Units sold                                      320

Ending inventory                          250

FIFO:

Ending Inventory = $10,250 (200 x $40 + 50 x $45)

Cost of goods sold = $17,000 ($27,250 - $10,250)

LIFO:

Ending Inventory = $12,800 (220 x $50 + 30 x $60)

Cost of goods sold = $14,450 ($27,250 - $12,800)

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Calculate Ending Inventory And COGS Using FIFO And LIFO Methods For ABC Inc.

Answer:

  (e)  b h a k

Step-by-step explanation:

You want the order of operations involved in the transformation ...

  g(x) = a(bx -h) +k

The Order of Operations tells you that multiplication takes precedence over addition, and expressions inside parentheses are evaluated first.

We note there is an expression in parentheses here: (bx -h). In that expression is a multiplication operation (bx) and an addition operation (_-h).

The multiplication is done first, so evaluating this expression in parentheses, we ...

Once the parenthetical expression is evaluated, we proceed to the main event. Again, multiplication and addition are required. That means the next two steps are ...

In summary, the operations we perform during evaluation of the transformation successively apply the parameters ...

  b h a k

The equation and solution representing the total interest, T, earned by Kalia when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10, is D. T = 100 • 0.01 • 10; $10.

Simple interest is interest that does not compound.

Simple interest does not accumulate interest, unlike compound interest, which is added to the principal for subsequent interest.

Principal = $100

Simple interest rate = 1%

Period of savings = 10 years

The simple interest in dollars = T

T = 100 x 0.01 x 10

T = $10

Thus, Option D correctly represents the total interest earned by Kalia.

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The coordinates M along the directed line segment is (-12, -2)

The points are given as:

K  = (-16, 10)

L = (-9, -11)

The ratio on the segment can be represented as;

KM : LM, m : n = 4 : 3

So, we have the coordinates of the point M that lies along the directed line segment to be

M = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

So, we have:

M = 1/(4 + 3) * (4 * -9 + 3 * -16, 4 * -11 + 3 * 10)

Evaluate

M = 1/7 * (-84, -14)

Evaluate

M = (-12, -2)

Hence, the coordinates of the point M is (-12, -2)

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The equation of the line is y = x -3. The graph of the line is attached below.

What is a line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.

Given that the slope of the line is 1.

Assume that the equation of the line is y = mx +c, where m is the slope of the line and c is y-intercepts.

Putting m = 1 in y = mx +c:

y = 1 × x +c

y = x +c

Since the line passes through the point (-2, -5), thus the point satisfies  the given equation of line.

Putting x = -2 and y = -5 in y = x +c

-5 = -2 + c

c = -3

The equation of line is y = x - 3.

The points on the line are

(-2, -5), (0, -3), (3, 0).

Plot the points and join them:

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The equation formed when x is the subject of the function f(x) = x² - 9, has two values of output for each input value to the function, therefore;

f(x) = x² - 9 does not have an inverse.

An inverse of a function is an anti function that reverses the values in the output into the input values thereby undoing the operations performed by the function.

A function f has an inverse if and only if it is bijective, such that there is a one to one correspondence between the set of the input elements and the set of the output elements

A function that has an inverse is said to be a bijective or invertible function or a function with one-to-one correspondence

The function in the question f(x) = x² - 9

Making x the subject of the function to verify if it has an inverse gives;

x² = f(x) + 9

[tex]x = \pm\sqrt{f(x) +9}[/tex]

Putting x = f⁻¹(x) gives;

[tex]f^{-1}(x) = \pm\sqrt{x +9}[/tex]

Therefore, each value of x gives two values of f⁻¹(x), such that the set of the output of inverse function, f⁻¹(x) does not have a one-to-one correspondence with the set of values of x.

The function f(x) = x² - 9 is not invertible and therefore does not have an inverse function.

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Answer:

Step-by-step explanation:

A is a point

AB is a line

ABC is a plane

Therefore,  ABC is a plane.

__________________

Hope this helps!

Have a great day!

For the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of sec∅= ( - √106/ 9 ) in simplest radical form.

As given in the question,

For the given angle ∅ (theta) in standard position:

Terminal side of ∅ is passes through the point ( -9, 5 )

( -9 , 5 ) represents ∅ is in the second quadrant.

In second quadrant sine in positive and cosine is negative.

Base is negative and altitude is positive.

Base = -9

Altitude = 5

Using Pythagoras theorem,

Hypotenuse² = (-9)² + (5)²

⇒ Hypotenuse = √106

cos ∅ = -9 / √106

sec ∅ = 1/ cos ∅

         = - √106/9 ( simplest radical form )

Therefore, for the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of

sec∅= ( - √106/ 9 )  in simplest radical form.

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The division that can match the model is that 6 ÷ 1/5 = 30.

Division is one of the four fundamental mathematical operations, along with addition, subtraction, and multiplication. It is defined as the splitting of a large group into smaller groups so that each group has an equal number of items. In mathematics, it is an operation used for equal grouping and equal sharing.

It is a process of repeated subtraction. It is the inverse operation of multiplication. It is defined as the formation of equal groups. When we divide numbers, we break them down into smaller numbers so that the multiplication of those smaller numbers equals the larger number taken.

In this case, the division will be:

= 6 ÷ 1/5

= 6 × 5

= 30

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Using the multiplication operation, the greatest number of people who could be in the 380 rooms with space for 6 persons at the same time is 2,280.

Multiplication operation is one of the basic mathematical operations, including subtraction, addition, and division.

A multiplication operation involves applying the multiplier to the multiplicand to result in a product.

The total number of rooms in the resort = 380

The number of people per room = 6

380 x 6 = 2,280

Thus, by multiplication, if 6 persons occupy each of the 380 rooms, the resort will have 2,280 persons at a time.

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The width across Keala book cover is 40cm

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees

From the question,

The length of the cover

= 22 1/4

= 89/4

The area of the cover

=890 cm²

From the formula

Area of a Rectangle = Length x Breadth

890=89/4×Breadth

Breadth = 890×4/89

Breadth=40cm

Hence, the width of the book cover is 40cm

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The theorem that will prove similarity of triangle ΔGHS and ΔFES is AAA ( angle angle angle) theorem. The value of FE is 45m.

AAA theorem states that if two triangles have all three corresponding angles equal then they are similar triangles.

In the given figure FE║GE means FE is parallel to GE.

so ∠EFS = ∠HGS

and ∠FES = ∠GHS

also ∠S is common for both.

If two triangles are similar then ratio of corresponding sides are also same.

So, by applying this

[tex]\frac{FS}{GS}[/tex] = [tex]\frac{FE}{GH}[/tex]

54/24 = FE/20

( 54*20 ) / 24 = FE

FE = 45m.

Therefore the triangles will be similar by theorem AAA and the value of FE will be 45m.

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The end of the graph is

As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity

The end behavior of function typically says the characteristics of the function at the ends

This is determined by examining the graph and the coordinates.

The end behavior is can be written as

x ⇒ ∞ f(x) ⇒ -∞

x ⇒ -∞ f(x) ⇒ ∞

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Answer:

5

Step-by-step explanation:

:)

Answer:5

Step-by-step explanation:|-10|-|-5|

                                             10-5

                                              5

Answer:

x = 11

Step-by-step explanation:

(7x - 4) and 73 are alternate exterior angles and are congruent , then

7x - 4 = 73 ( add 4 to both sides )

7x = 77 ( divide both sides by 7 )

x = 11

Answer:

[tex]x = 11[/tex]

Step-by-step explanation:

two angles are congruent for the parallelism of the two horizontal lines (external alternates). thus

[tex]7x - 4 = 73 \\ 7x = 77 \rightarrow x = 11[/tex]

Answer:5/6

Step-by-step explanation:

There are 9 numbers from the range with the difference of 4 in the digits

The properties of the numbers are given as

Difference: Largest - Smallest = 4

Range: 10 to 99

The numbers with above properties are as follows

15, 26, 37, 48, 59, 62, 73, 84 and 95

When these numbers are counted, we have

Frequency = 9

This means that there are 9 of such numbers from 10 to 99

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