A bag contains 3 gold marbles, 8 silver marbles, and 30 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.

What is your expected value if you play this game?

The measure of the angles are;

<1 = 109 degrees

<2 = 39 degrees

<3 = 71 degrees

We need to know the following about triangles, we have that;

From the information given, we have that;

For triangle UVT, we get;

35 + 36 + <1 = 180

add the like terms, we have;

<1 = 180 -71

<1 = 109 degrees

<2 + 80 + 71 = 180

collect terms

<2 = 180 - 151

<2 = 39 degrees

<3 = 71 degrees

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Explanation:

The standard form for linear equations is Ax+By = C. Anything perpendicular to this would be of the form Bx-Ay = D.

The equation 2x+3y = 9 gives

The perpendicular template goes from Bx-Ay = D to 3x-2y = D.

Plug in the coordinates of (1,-2) to compute D.

3x-2y = D

D = 3x-2y

D = 3*1 - 2*(-2)

D = 7

Therefore, the perpendicular equation is 3x-2y = 7

-----------------------

We need to solve this system

[tex]\begin{cases}2x+3y = 9\\3x - 2y = 7\end{cases}[/tex]

to locate point M.

There are a few methods. I'll use substitution.

Solve the 1st equation for x.

2x+3y = 9

2x = -3y+9

x = (-3y+9)/2

x = -1.5y + 4.5

Then substitute this into the other equation to solve for y.

3x - 2y = 7

3( x ) - 2y = 7

3( -1.5y+4.5 ) - 2y = 7

-4.5y + 13.5 - 2y = 7

-6.5y + 13.5 = 7

-6.5y = 7-13.5

-6.5y = -6.5

y = -6.5/(-6.5)

y = 1

Use that to determine x.

x = -1.5y + 4.5

x = -1.5*1 + 4.5

x = 3

Point M is located at (x,y) = (3, 1)

------------------------

Use the distance formula to find the distance from A(1,-2) to M(3,1)

[tex]A = (x_1,y_1) = (1,-2) \text{ and } M = (x_2, y_2) = (3,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-3)^2 + (-2-1)^2}\\\\d = \sqrt{(-2)^2 + (-3)^2}\\\\d = \sqrt{4 + 9}\\\\d = \sqrt{13}\\\\d \approx 3.605551\\\\[/tex]

Segment AM is exactly [tex]\sqrt{13}[/tex] units long.

That is approximately 3.605551 units.

You can use a tool like GeoGebra to confirm the answers are correct.

The equation that satisfies the data in the table is: A. y = 2/15(x) + 2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 - 0)/(0 + 15)

Slope (m) = 2/15

At data point (0, 2) and a slope of 2/15, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 2/15(x - 0)  

y = 2/15(x) + 2.

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The total surface area required to wrap the 15 cubed-shaped gift boxes is 3.6 square meters.

To calculate the total surface area of 15 cubed-shaped gift boxes, we need to find the surface area of one gift box and then multiply it by the total number of boxes.

The surface area of a cube can be calculated using the formula:

Surface Area = 6 * [tex](side length)^2[/tex]

Given that the length of each side of the cube-shaped gift box is 20 cm, we can substitute this value into the formula:

Surface Area of one gift box = 6 * (20 cm)^2

= 6 * [tex](400 cm^2)[/tex]

= 2400 [tex]cm^2[/tex]

Since we have 15 gift boxes, we multiply the surface area of one gift box by 15:

Total Surface Area = Surface Area of one gift box * Number of gift boxes

= 2400 [tex]cm^2 * 15[/tex]

= 36000 [tex]cm^2[/tex]

Now, we need to convert the area from square centimeters [tex](cm^2[/tex]) to square meters [tex](m^2).[/tex] There are 10000 square centimeters in a square meter:

Total Surface Area in square meters = Total Surface Area in square centimeters / 10000

= 36000 [tex]cm^2[/tex] / 10000

= 3.6[tex]m^2[/tex]

Therefore, the total surface area required to wrap the 15 cubed-shaped gift boxes is 3.6 square meters.

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The Shares for the other teams are indeed 12, 9, and 6, respectively,  confirms that the solution is correct,there were 8 red balls.

The problem step by step. We are given the following information:

1. The total number of balls is 35.

2. One team takes all the red balls.

3. The remainder (non-red balls) is shared among the other teams in the ratio 4:3:2.

4. The smallest share is 6 balls.

Let's assume the number of red balls is "r". Therefore, the number of non-red balls is 35 - r.

According to the ratio, the shares for the other teams are:

Team 1: (4/9) * (35 - r)

Team 2: (3/9) * (35 - r)

Team 3: (2/9) * (35 - r)

Given that the smallest share is 6 balls, we can set up the equation:

(2/9) * (35 - r) = 6

To solve this equation, we can simplify and solve for "r":

(35 - r) = (9/2) * 6

35 - r = 27

r = 35 - 27

r = 8

Therefore, there were 8 red balls.

To verify the solution, we can calculate the shares for the other teams:

Team 1: (4/9) * (35 - 8) = 4 * 27/9 = 12

Team 2: (3/9) * (35 - 8) = 3 * 27/9 = 9

Team 3: (2/9) * (35 - 8) = 2 * 27/9 = 6

The shares for the other teams are indeed 12, 9, and 6, respectively, which confirms that the solution is correct.

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Based on the image you provided, it appears to be a rectangular prism (a box) with given dimensions. To find the volume of the rectangular prism, we can use the formula:

Volume = Length × Width × Height

From the image, we can see the following dimensions:

Length = 6 cm

Width = K cm

Height = 22 cm

To find the volume, we need to know the value of K. Unfortunately, the value of K is not provided in the image or the previous conversation.

If you provide the value of K, I can calculate the volume of the rectangular prism for you.

Answer: The angulier expression

Step-by-step explanation:

The choice of the best Regression model depends on the specific characteristics of the data and the underlying theory or knowledge about the relationship between the variables.

The regression model best represents the relationship between the total number of bacterial clusters and the number of elapsed days, we need to examine the data and consider different regression models.

There are several types of regression models commonly used, including linear regression, polynomial regression, exponential regression, and logarithmic regression. Each model represents a different functional form and can capture different types of relationships between variables.

Without specific data or context provided, it is challenging to determine the exact regression model that best represents the relationship. However, I can briefly explain the characteristics and typical use cases for each regression model:

1. Linear Regression: This model assumes a linear relationship between the variables, where the dependent variable changes linearly with respect to the independent variable. It is suitable when the relationship appears to be a straight line on a scatter plot.

2. Polynomial Regression: This model captures non-linear relationships by including higher-order terms of the independent variable, such as quadratic (x^2), cubic (x^3), or higher-degree terms. It is suitable when the relationship seems to follow a curve rather than a straight line.

3. Exponential Regression: This model assumes an exponential relationship between the variables, where the dependent variable changes exponentially with respect to the independent variable. It is suitable when the data exhibits rapid growth or decay.

4. Logarithmic Regression: This model assumes a logarithmic relationship between the variables, where the dependent variable changes logarithmically with respect to the independent variable. It is suitable when the relationship shows diminishing returns or saturation.

the best regression model, it is important to visually analyze the data through a scatter plot and assess the linearity or curvature of the relationship. Additionally, statistical measures such as the coefficient of determination (R-squared) and residual analysis can help evaluate the goodness of fit for different models.

the choice of the best regression model depends on the specific characteristics of the data and the underlying theory or knowledge about the relationship between the variables.

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The equivalent fraction for 1, using the number line and dividing it into four equal parts, is 1/4.

To find an equivalent fraction using a number line, we need to determine a fraction that represents the same value as the given fraction.

Let's assume the given fraction is 1. On a number line, the fraction 1 can be represented as the distance between 0 and 1. Now, we want to find an equivalent fraction, so let's choose a different representation on the number line.

To find an equivalent fraction that represents the same value, we can divide the number line segment between 0 and 1 into equal parts. Let's say we divide it into 4 equal parts.

Now, we need to determine which of the four equal parts represents the fraction 1. Since we divided the segment into four equal parts, each part represents 1/4 (one-fourth) of the whole segment.

Therefore, the equivalent fraction for 1, using the number line and dividing it into four equal parts, is 1/4.

So, the equivalent fraction for 1 is 1/4.

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Answer:

50:1

Step-by-step explanation:

There are 50 goats and 1 chicken

The GCD of 50 and 1 is 1 so you can't simplify

Answer:

10 years old

Step-by-step explanation:

lets break it down:

6 more means +6

four times means *4

so if her son is x years old, she is 4x+6

since we know she's 46, we know that 4x+6=46

now we just solve the equation

4x+6=46

-6 on both sides

4x=40

/4 on both sides

x=10

The parametric equations representing the same path as the given equations are: x = 1

y = 4sin(1)

To identify the parametric equations that represent the same path as the given equations x = 2 + 1 and y = 4 sin(theta), we can eliminate the parameter theta to express x and y in terms of a new parameter, let's call it t.

We know that [tex]cos^2(theta) + sin^2(theta)[/tex] = 1 (from the Pythagorean identity). Rearranging this equation, we have:

[tex]sin^2(theta) = 1 - cos^2(theta)[/tex]

Now, let's substitute the given equations into this identity:

[tex]sin^2(theta) = 1 - (2 + cos(theta))^2[/tex]

[tex]sin^2(theta) = 1 - (4 + 4cos(theta) + cos^2(theta))[/tex]

[tex]sin^2(theta) = 1 - 4 - 4cos(theta) - cos^2(theta)[/tex]

[tex]sin^2(theta) = -3 - 4cos(theta) - cos^2(theta)[/tex]

Next, let's substitute [tex]sin^2(theta) with (1 - cos^2(theta))[/tex]in the y equation:

[tex](1 - cos^2(theta)) = -3 - 4cos(theta) - cos^2(theta)[/tex]

Simplifying the equation, we get:

[tex]2cos^2(theta) + 4cos(theta)[/tex]+ 2 = 0

Dividing the equation by 2, we have:

[tex]cos^2(theta) + 2cos(theta[/tex]) + 1 = 0

This equation can be factored as:

[tex](cos(theta) + 1)^2[/tex]= 0

Taking the square root of both sides, we get:

cos(theta) + 1 = 0

cos(theta) = -1

Therefore, the value of cos(theta) is fixed at -1 for all values of theta.

Substituting cos(theta) = -1 into the given equations, we have:

x = 2 + (-1) = 1

y = 4sin(1)

Hence, the parametric equations representing the same path as the given equations are:

x = 1

y = 4sin(1)

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The missing numbers in the sequences are:

Sequence 1: 3.50

Sequence 2: 3.50

Sequence 3: 2

Sequence 4: 8.00

Sequence 5: 25

Let's analyze the given sequences to find the missing numbers:

Sequence 1:

0.5, 1.25, 2.0, 2.75, ?

Observing the pattern, it appears that each term is obtained by adding 0.75 to the previous term.

Applying this pattern, the missing number would be 2.75 + 0.75 = 3.50.

Sequence 2:

4.25, ?

Looking at the sequence, it seems to be decreasing by 0.75 between each term.

Applying this pattern, the missing number would be 4.25 - 0.75 = 3.50.

Sequence 3:

512, 256, 128, 64, 32, 16, 8, 4, ?

Here, each term is obtained by dividing the previous term by 2.

Applying this pattern, the missing number would be 4 / 2 = 2.

Sequence 4:

5.75, 6.50, 7.25, ?

In this sequence, each term is obtained by adding 0.75 to the previous term.

Applying this pattern, the missing number would be 7.25 + 0.75 = 8.00.

Sequence 5:

1, ?, 25, 125

Observing the pattern, it seems that each term is obtained by multiplying the previous term by 25.

Applying this pattern, the missing number would be 1 x 25 = 25.

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Answer: 0.14 cubic meters

To cover the rectangular yard with a concrete layer one tenth of a meter thick, we need to find the volume of concrete required, which can be calculated as:

Volume = area * thickness

The area is the product of the length and width of the rectangular yard, and the thickness is one tenth of a meter.

The length of the rectangular yard is given as 0.2 meters, the width is given as 7 meters, and the thickness is 0.1 meters.

So, the volume of concrete is:

Volume = 0.2 meters * 7 meters * 0.1 meters = 0.14 cubic meters

Hope this helps!

Step-by-step explanation:

For angles outside circle    angle = 1/2 ( large arc - small arc)

46 = 1/2 [  21x-5  - (x + blank) ]

92 =   21x -5 - x -blank

97 = 20x - blank

97 = 20x - 23

120 = 20 x

x = 6

The reasoning for the third step of the proof would be "Corresponding parts of congruent triangles are congruent." Let's go through the explanation:

1. Given: Quadrilateral ABCD is a rectangle.

2. Given: AB & CD (Opposite sides of a rectangle are equal).

3. To prove: AC & BD.

To prove that AC is equal to BD, we can utilize the property that opposite sides of a rectangle are equal (step 2). In a rectangle, opposite sides are parallel and congruent. Therefore, we have AB || CD and AB = CD.

Now, we need to show that the triangles ABAD and ACDA are congruent, specifically using the SAS (Side-Angle-Side) congruence theorem. The congruence of these triangles will allow us to establish the equality of their corresponding parts, including AC and BD.

4. Given: AD = AD (Reflexive Property of Equality).

5. By step 2, we know AB = CD. Additionally, AD = AD is given (Reflexive Property of Equality).

6. By step 3, ZBAD = ZCDA.

7. Using SAS triangle congruence theorem, we can conclude that triangles ABAD and ACDA are congruent.

Finally, according to the "Corresponding parts of congruent triangles are congruent" property, we can state that AC = BD. This establishes the equality of the diagonals of the rectangle.

Therefore, the correct reasoning for step 3 is "Corresponding parts of congruent triangles are congruent."

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The solution is: we can say that we would need to include all of this information on a W-4 form except for information that is not related to your tax situation or employment, such as your favorite color or hobbies.

Here, we have,

W-4 form is a tax form that employees in the United States use to provide their employers with information about their tax situation.

The form includes information such as the employee's name, address, social security number, number of dependents, and filing status.

Therefore, we can say that we would need to include all of this information on a W-4 form except for information that is not related to your tax situation or employment, such as your favorite color or hobbies.

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Answer:

9

Step-by-step explanation:

3x^2 + 3x - 9

Substitute x = 2 into the equation.

3(2)^2 + 3(2) - 9

3(4) + 6 - 9

12 + 6 - 9

18 - 9 =

9

The Sample space, a clear set of possible outcomes for choosing one card from the set.

The sample space for choosing one card from a set of 10 labeled cards, where each card is labeled with an expression, would consist of all the possible outcomes of this selection process.

Since there are 10 cards in the set, the sample space would consist of the individual expressions labeled on each card. Let's assume the expressions on the cards are labeled as follows:

Card 1: Expression 1

Card 2: Expression 2

Card 3: Expression 3

...

Card 10: Expression 10

{Expression 1, Expression 2, Expression 3, ..., Expression 10}

This sample space represents all the possible outcomes when selecting one card from the set. Each outcome corresponds to one specific expression labeled on a card.

the sample space only includes the individual expressions and not any particular order or arrangement of the cards. The order of the expressions does not matter in this case, as the focus is solely on the expressions themselves.

the sample space, we establish a clear set of possible outcomes for choosing one card from the set.

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Answer: 59/16 or 3 11/16

Step-by-step explanation:

11 4/5 ÷ 3 1/5

= 59/5  ÷ 16/5

= 59/5 x 5/16

= 59 x 5/ 5 x 16

= 295/80

= 295 ÷ 5/ 80 ÷ 5

= 59/16

= 3 11/16

The artist should buy the canvas with dimensions [tex]$10" \times 16"$[/tex]. This canvas has an aspect ratio of [tex]1.6[/tex], which is the closest among the available options to the Golden Ratio of [tex]1.618[/tex].

To determine which canvas size most closely matches the Golden Rectangle, we need to calculate the aspect ratio for each canvas and compare it to the Golden Ratio.

The Golden Ratio, also known as Phi [tex]($\varphi$)[/tex], is approximately [tex]1.618[/tex].

Let's calculate the aspect ratios for each canvas:

Canvas 1: [tex]$24" \times 36"$[/tex]

Aspect ratio = [tex]$\frac{36}{24} = 1.5$[/tex]

Canvas 2: [tex]$24" \times 40"$[/tex]

Aspect ratio = [tex]$\frac{40}{24} \approx 1.667$[/tex]

Canvas 3: [tex]$10" \times 16"$[/tex]

Aspect ratio = [tex]$\frac{16}{10} = 1.6$[/tex]

Canvas 4: [tex]$26" \times 16"$[/tex]

Aspect ratio = [tex]$\frac{16}{26} \approx 0.615$[/tex]

Canvas 5: [tex]$20" \times 12"$[/tex]

Aspect ratio = [tex]$\frac{12}{20} = 0.6$[/tex]

To find the canvas that most closely matches the Golden Ratio, we need to choose the canvas with an aspect ratio closest to [tex]1.618[/tex].

Calculating the differences between the aspect ratios and the Golden Ratio:

Canvas 1: [tex]$|1.5 - 1.618| \approx 0.118$[/tex]

Canvas 2: [tex]$|1.667 - 1.618| \approx 0.049$[/tex]

Canvas 3: [tex]$|1.6 - 1.618| \approx 0.018$[/tex]

Canvas 4: [tex]$|0.615 - 1.618| \approx 1.003$[/tex]

Canvas 5: [tex]$|0.6 - 1.618| \approx 1.018$[/tex]

The canvas with the aspect ratio closest to the Golden Ratio is Canvas 3: [tex]$10" \times 16"$[/tex], as it has the smallest difference of approximately [tex]0.018[/tex].

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The area of the triangle with side lengths 5, 6, and 7 is approximately 14.6969 square units.

To find the area of a triangle when the lengths of its three sides are given (5, 6, and 7), we can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c can be calculated as:

Area = √(s(s - a)(s - b)(s - c))

where s is the semi perimeter of the triangle, given by:

s = (a + b + c) / 2

Let's calculate the area step by step:

Determine the lengths of the sides.

a = 5

b = 6

c = 7

Calculate the semi perimeter.

s = (a + b + c) / 2

s = (5 + 6 + 7) / 2

s = 18 / 2

s = 9

Apply Heron's formula to find the area.

Area = √(s(s - a)(s - b)(s - c))

Area = √(9(9 - 5)(9 - 6)(9 - 7))

Area = √(9(4)(3)(2))

Area = √(216)

Area = 14.6969 (rounded to four decimal places)

Therefore, the area of the triangle with side lengths 5, 6, and 7 is approximately 14.6969 square units.

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Party A received the most votes with a total of 47 votes, while Party B received 38 votes.

To determine which party received the most votes, we need to calculate the number of votes for each party based on the given percentages and population distribution.

Let's assume the total population is 100 for easier calculations.

Based on the given information:

33% of the population (33 out of 100) said they would vote for Party A.

10% of the population (10 out of 100) said they would vote for Party B.

15% of the population (15 out of 100) said they would not vote.

So far, we have accounted for 33 + 10 + 15 = 58 people.

The remaining population is 100 - 58 = 42 people.

In the rest of the population:

1/3 (1/3 × 42) = 14 people voted for Party A.

2/3 (2/3 × 42) = 28 people voted for Party B.

Now let's calculate the total votes for each party:

Party A received 33 (from initial survey) + 14 (from the rest of the population) = 47 votes.

Party B received 10 (from initial survey) + 28 (from the rest of the population) = 38 votes.

Therefore, Party A received the most votes with a total of 47 votes, while Party B received 38 votes.

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The volume of the hemisphere with a diameter of 60.9 inches rounded to the nearest tenth is 59131.7 inches³.

Given that,

Diameter of a hemisphere = 60.9 inches

We have to find the volume of the hemisphere.

We know that, radius is half the measure of the diameter.

Radius of the hemisphere = 60.9 / 2 = 30.45 inches

Volume of a hemisphere is,

Volume = 2/3 π r³

Here r is the radius

Substituting,

Volume = 2/3 π (30.45)³

             = 59131.7 inches³

Hence the volume is 59131.7 inches³.

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Answer:

4 pounds

Step-by-step explanation:

First, we can calculate how much money Ivanna spent by subtracting her remaining balance after buying the coffee from the original amount on the gift card.

amount spent = $80 - $47.88 = $32.12

Now, we can calculate how many pounds of coffee she bought by dividing the amount she spent by the price rate of coffee by pound.

[tex]\$32.12 \div \dfrac{\$8.03}{1 \text{ lb}}[/tex]

[tex]= \$32.12 \times \dfrac{1 \text{ lb}}{\$8.03}[/tex]

[tex]= \dfrac{32.12}{8.03} \text{ lb}[/tex]

[tex]= \boxed{4 \text{ lb}}[/tex]

So, Ivanna bought 4 pounds of coffee.

Answer:  Ivanna bought 4 pounds of coffee for an amount of$32.12.

Step-by-step explanation:

According to the question,

Money with Ivanna initially: $80

Money with Ivanna later: $47.88

step 1: here we need to find the difference between the amount initially and later,

Difference between the amount initially and later: $80 - $47.88 = $32.12

Given,

Price of coffee per pound:  $8.03

Step 2: now we divide the amount spent by the price per unit of coffee,

that is: $32.12/$8.03 = 4

so the answer is Ivanna bought 4 pounds of coffee for an amount of$32.12

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The value of probability P (A or B) is,

⇒ P (A or B) = 48

We have to given that,

The Venn diagram of the probability is shown in image.

Now, By given diagram,

⇒ P (A) = 24 + 14

⇒ P (A) = 38

⇒ P (B) = 24 + 10

⇒ P (B) = 34

⇒ P (A and B) = 24

We have to given that,

The expression is,

P (A or B) = P (A) + P (B) - P (A and B)

Substitute all the values, we get;

P (A or B) = 38 + 34 - 24

P (A or B) = 48

Thus, The value of probability P (A or B) is,

⇒ P (A or B) = 48

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Answer: B. t= 15; s=5

Step-by-step explanation:

We will create a system of equations.

    8t + 12s = 180

    t = 3s

Next, we will substitute this value of t into the first equation and solve for s.

    8t + 12s = 180

    8(3s) + 12s = 180

    24s + 12s = 180

    36s = 180

    s = 5 shirts

Lastly, we will substitute this value of s back into t = 3s and solve for t.

    t = 3s

    t = 3(5)

    t = 15 shirts

Based on the given information, the fair conclusion would be:

C. The current stock price is up for the day by 0.38%.

The statement mentions that the stock price is up for the day, which is indicated by the positive change of 0.27 (+0.38%).