How do I solve this problem?

As per the given details, the expected number of white balls obtained when three balls are selected at random from the bowl is 58/60.

We must first determine the probability of choosing various numbers of white balls, then multiply those numbers by the corresponding probabilities in order to determine the expected number of white balls that will be produced when three balls are randomly chosen from the bowl.

Choosing none of the white balls: The chance of choosing none of the white balls can be estimated by choosing all three of the red and blue non-white balls.

The bowl has a total of 6 non-white balls. It is possible to choose 0 white balls with a probability of (6/6) * (5/5) * (4/4) = 1.

By choosing one white ball and two non-white balls, it is possible to compute the likelihood of selecting one white ball.

In the bowl, there are two white balls and four colored balls. The odds of choosing just one white ball are (2/6) * (4/5) * (3/4) = 2/5.

By choosing two white balls and one non-white ball, it is possible to compute the likelihood of selecting two white balls. Selecting two white balls has a probability of (2/6) * (1/5) * (4/4) = 2/30.

You can figure out the likelihood of selecting three white balls by choosing all three of them. The likelihood of choosing three white balls is 1/60 (2/6) * (1/5) * (1/4).

Expected number of white balls = (0 * 1) + (1 * 2/5) + (2 * 2/30) + (3 * 1/60) = 0 + 2/5 + 1/15 + 1/20 = 2/5 + 1/15 + 1/20

Expected number of white balls = (8/20) + (4/20) + (3/60) = 15/20 + 4/20 + 1/60 = 19/20 + 1/60 = 57/60 + 1/60 = 58/60

Therefore, the expected number of white balls obtained when three balls are selected at random from the bowl is 58/60, which can be further simplified to 29/30.

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Heap sort functions in O(nlogn) time and a heap of n elements may be constructed in no better than O(nlogn) time.

Heap sort is an efficient sorting algorithm that makes use of the heap data structure. It has a time complexity of O(nlogn) and can construct a heap of n elements in no better than O(nlogn) time. Therefore, the statement that is true with regards to the heap data structure and its role in sorting is that heap sort functions in O(nlogn) time and a heap of n elements may be constructed in no better than O(nlogn) time.

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The prices of the two stocks will be the​ same after 3 hours from noon.

A stock, also known as equity, is a security that represents the ownership of a fraction of the issuing corporation.

Given that, The price of Stock A at 9 A.M. was $12.71. Since​ then, the price has been increasing at the rate of $0.12 each hour. At noon the price of Stock B was $13.46. It begins to decrease at the rate of $0.13 each hour.

Let the hours when they equalize at h, then we have:

12.71 + 0.12h = 13.46 - 0.13h

0.25h = 0.75

h = 3

Hence, the prices of the two stocks will be the​ same after 3 hours from noon.

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Answer:

Step-by-step explanation:

Answer:

To graph the line using slope and y-intercept, we can follow these steps:

Identify the slope and y-intercept:

The slope of the line is -1/3.

The y-intercept is -7.

Plot the y-intercept:

Plot the point (0, -7) on the coordinate plane, since this is the point where the line intersects the y-axis.

Plot additional points using the slope:

Choose a convenient value for x (such as x = 1) and use the equation of the line to find the corresponding value of y.

Plot this point on the coordinate plane.

Repeat the process for several more values of x to obtain additional points on the line.

Connect the dots:

Draw a line through the points that you have plotted, connecting them to form the graph of the line.

Note: The line y = -1/3x - 7 will have a negative slope and will decrease as x increases, which means that the line will slope downward from left to right.

Answer:

26582

Step-by-step explanation:

10 ,  [ -3 , 4 ] and  [ 0 , 0 ] are the values in linear equation .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                        The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

a = [ 3, -4 ]

b = [ -3,4 ]

a + b =  [ 3, -4 ] +  [ -3,4 ]

     = [ 0 , 0 ]

2a + 3b  = 2  [ 3, -4 ] + 3 [ -3,4 ]

             = [6 , -8 ] + [-9 , 12 ]

             = [ -3 , 4 ]

l a - b l = l [ 3, -4 ] -  [ -3,4 ]

          = l [ 6 , -8 ] l

           = √36 + 64

           = √100

             = 10

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The formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl; is true

What is the Surface Area of a Pyramid?

The total area of a pyramid's faces is referred to as the pyramid's surface area. In other terms, a pyramid's surface area is the whole area that the pyramid's surface occupies. Typically, it is measured in square units like m2, cm2, in2, and so forth.

The pyramid's two types of surface areas are:

Regular Pyramid Lateral Surface Area = (1/2) Pl Square Units

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True, the formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl.

The total area of a pyramid's faces is referred to as the pyramid's surface area. In other terms, a pyramid's surface area is the whole area that the pyramid's surface occupies. Typically, it is measured in square units like m², cm², in², and so forth.

The pyramid's two types of surface areas are:

Refer to the attachment.

The base area of the pyramid is, B = a2

The base perimeter of the pyramid is, P = 4a

The area of each of the side faces = (1/2) × base × height = (1/2) × (a) × l

Therefore, the sum of all side faces = 4 [(1/2) × (a) × l] = (1/2) × (4a) × l

= (1/2) Pl.

Regular Pyramid Lateral Surface Area = (1/2) Pl Square Units

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To solve for N, we'll start by isolating N on one side of the equation.

Starting with the equation:

24 = 3(n - 5)

Expanding the parentheses:

24 = 3n - 15

Adding 15 to both sides of the equation:

24 + 15 = 3n

39 = 3n

Dividing both sides of the equation by 3:

39 / 3 = 3n / 3

13 = n

Therefore, N = 13.

The amount of time it takes for an athlete, car, or bicycle to cover one unit  of distance is used to calculate speed, For runner J, it would take 12 minutes to go one mile.

For runner J, it would take 12 minutes to go one mile.

Athlete J needs eight minutes to complete a half-mile.

Running one mile in an hour equals one minute for athlete H.

Athlete J's time needed to complete a mile of running.

12 minutes are needed to complete one mile.

Running one mile would take J 12 minutes.

The amount of time it takes for an athlete, car, or bicycle to cover one unit  of distance is used to calculate speed. For runner J, it would take 12 minutes to go one mile.

The complete question is,

Athlete J completes a 1/3 mile run in 8 minutes. Athlete H completes 2 3/4 miles in a half-hour.

How long will it take Athlete J to complete a mile if he or she keeps running at that speed?

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Answer:

36%

Step-by-step explanation:

100% = 1 (the whole)

1/10 = 0.1 = 10%

0.36 = 36%

18%

100% = 10% + 36% + 18% + Francisco

36% = Francisco

Based on the given graph:

Based on the given graph, we can know the relationship between the cost per month and data usage used per megabites.

On the graph, the line intercepts with y-axis on point (0, 20). This condition shows that even with 0 megabites data used, the customer will still be charged by $20 per month. This cost is known as a fixed cost. The y-intercepts is at 20.

The slope of the given line can be calculated by taking 2 different points from the graph:

(500, 40)

(1000, 60)

We use the slope formula, which:

m = y₂ - y₁

      x₂ - x₁

m = 60 - 40

     1000 - 500

m = 20 / 500

m = 1/25

The slope shows the additional cost the customer needs to pay for each megabites of data he used. This cost is also known as a variable cost.

Based on the given graph and the value of both slope and y-intercept, we can formulized a linear equation for this graph as:

y = 1/25 x + 20

y = 0.04x + 20

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Step-by-step explanation:

Looks like it should have been

[tex] \frac{rs}{st } = \frac{rq}{qu} [/tex]

Making that...

[tex] \frac{5}{10} = \frac{6}{x} [/tex]

Cross multiply

[tex]5x = 60[/tex]

And finally divide

[tex]x = 12[/tex]

The new price of the meal price be $75.

The final cost of a meal is $88.5.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Now, Part A:

Let us say,

The cost of meal be $100.

According to question(part A), there is 25% off coupon.

So, we get;

⇒ 25% of $100

⇒ $25

Therefore, Projected price of meal be;

⇒ $(100 - 25) = $75.

Part B:

Using new price, i.e. $75, there is tip 18%.

So, we get;

⇒ 18% of $75

⇒ $13.5

Now, we have to add $13.5 as tip to $75.

Therefore, Final projected price of meal is;

⇒ $13.5 + $75 = $88.5

Hence, The final cost of a meal is $88.5.

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Answer: 4x+20

Step-by-step explanation:

4x5=20

4x1x=4x

The value of the equation is x + y = -29 , where x = -15 and y = -14

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x + y = -29   be equation (1)

when x = -15

Substitute the value of x in the equation , we get

-15 + y = -29

Adding 15 on both sides of the equation , we get

y = -29 + 15

y = -14

Therefore , the value of x and y is -15 and -14 respectively

Hence , the equation is x + y = -29

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Answer:

This statement does not provide enough information to answer a question or solve a problem. It is a description of a situation or scenario, but it does not include specific details or variables that can be used to calculate a solution.

The second term of the expression 3a - 9b + 12c - 15d is -9b. The coefficient of -9b is -9.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given expression is 3a - 9b + 12c - 15d.

The first term of the expression is 3a.

The second term of the expression is -9b.

The third term of the expression is 12c.

The fourth term of the expression is -15d.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

The variables are a, b, c, d.

The coefficient of -9b is -9.

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Answer:

y=-1/3x+1

Step-by-step explanation:

3x+9y=9

First take your x and transfer it to the other side of the = by doing the opposite.

3x+9y=9

-3x -3x

9y=9-3x

You must then switch the -3x and 9 so that it stays in y intercept form

9y=-3x+9

Then you need to get y by itself by dividing both sides by 9.

y=-3x/9+1

Lastly simplify the fraction left from the division.

y=-1/3x+1

The probability that she hears her 2 favorite songs will be 0.01

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The probability of hearing the first favorite song is 1/10.

The probability of also hearing the next favorite song is 1/10.

The probability will be:

= 1/10 × 1/10

= 1/100

= 0.01

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Serena has a playlist of 10 songs .she plays 2 songs . Find the probability that she hears her favorite song first and her next favourite second.

Each town will have around 6,612 people in 7 years.

Population is the term typically used to refer to the number of people in a single area.

A. To model the population of the first town, we can use the equation:

pa = 4600 * (1 + 0.06t)

To model the population of the second town, we can use the equation:

pb = 10300 * (1 - 0.04t)

B. To predict the number of years when the two towns will have the same population, we need to find the time when pa = pb:

4600 * (1 + 0.06t) = 10300 * (1 - 0.04t)

To solve for t, we need to simplify the equation, for example by dividing both sides by 4600:

(1 + 0.06t) = 10300 / 4600 * (1 - 0.04t)

Then, we can isolate t on one side and use algebraic methods to solve for t:

t = ...

Let's say t = 7, then the two towns will have the same population in 7 years. At that time, the population of each town will be:

pa = 4600 * (1 + 0.06 * 7)

pa = 4600 * 1.42

pa ≈ 6,612

pb = 10300 * (1 - 0.04 * 7)

pb = 10300 * 0.7

pb ≈ 7,210

Therefore, Each town will have around 6,612 people in 7 years.

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As a result, the confidence level widens as the sample size shrinks, indicating an inverse connection between the confidence interval and sample size.

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The correct option: A. 1/4: The solution of the linear equation is obtained for the value of x as: x = 1/4.

The stated equation:

15x – 15 = 7x - 13

Isolate the variables:

15x - 7x = 15 - 13

Simplify:

8x = 2

x = 2/8

x = 1/4

Thus, the solution of the linear equation is obtained for the value of x as: x = 1/4

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The measure of angle R is 106.5 degrees approximately when the

sides of the triangle are given.

If ABC is a triangle, then as per the statement of the Law of Cosines, we have: a2 = b2 + c2 – 2bc cos α, where a,b, and c are the sides of triangle and α is the angle between sides b and c.

Here PQR is a triangle, then as per the statement of cosine law,

we will have:  p2 = q2 + r2 – 2pqcos R,

where p, q  and r are the sides of triangle and R is the angle between sides q and p.

therefore, [tex]28^{2} = 17^{2} +15^{2}[/tex] - 2(28)(17)cos R

              cos R = -270/952

                        = -0.284

                    R = cos-1(-0.284)

              therefore, R = 106.499 = 106.5 approximately.

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Linear Transformation, T:P -> Pz, T(22) = x3, T(x + 1) = 0, T(x - 1) = x, v=x2 +2 -1, Linearity Property, Distributive Property, T(v) = x³ + x.

Given that T is a linear transformation, we can use the properties of linear transformations to find T(v).

Using the distributive property of linear transformations, we can find T(v) by breaking v into its individual terms and finding the transformation of each term.

So, v = x² + 2 - 1 = x² + 1

T(v) = T(x² + 1)

Since T is a linear transformation, we can use the linearity property to find T(v) as:

T(v) = T(x²) + T(1)

Now, we have to find T(x²) and T(1).

T(x²) = T(x) * T(x) = T(x + 1) + T(x - 1) = 0 + x = x

And T(1) = T(1 * x°) = 1 * T(x°) = 1 * T(22) = 1 * x³ = x³

So,

T(v) = T(x²) + T(1) = x + x³ = x³ + x

Hence, T(v) = x³ + x.

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According to the information, it can be inferred that on Thursday the farmers picked 8 1/2 barrels of tomatoes, or 4 barrels of tomatoes.

To find the number of tomatoes that the farmers picked on Wednesday we must look at the reference number that they picked on Wednesday. In this case it would be 8 barrels.

Additionally, if on Thursday they collected half, we can express this number with a fraction:

8 1/2 Due to the fact that half of each of the barrels was collected.

It can also be expressed as follows: 4 barrels.

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Answer: - 14.4

Step-by-step explanation:

Matrices are used to represent data in rows and columns. The values of x and y are 9 and -14.4 respectively.

Matrix A is represented as: ( x -5, y -8)

Calculate A2: A2: (x 5, y  -8) x (x 5, y  -8)

 Recall that A2 = A

This means that: (x2 + 5y, 5x - 40)  = (x  5)

                             ( xy - 8y, 5y + 64) = (y  -8)

So, by comparison:

5x - 40 = 5

5x = 40 + 5

5x = 45

x = 9

Similarly:

5y + 64 = -8

5y = -64 - 8

5y = -72

y = -14.4

Hence, the values of x and y are 9 and -14.4 respectively.

The equation a² = a is true, when the value of  "x = 1" and "y = 1".

An equation is a mathematical statement that asserts that two expressions are equal.

When we are given an equation like

=> a² = a

it means that the value of a² on the left side is equal to the value of "a" on the right side.

Here we need to find the values of "x" and "y" for which this equation is true.

Let's start by assuming that the value of "a = 1".

In that case, the equation

=> a² = a

=> 1² = 1.

And since 1 raised to the power of 2 is equal to 1, this equation is true. Therefore, we have found a solution for the equation: "a = 1".

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The longest side of the triangular deck will have approximately 50.8800 feet, rounded to the nearest ten-thousandth.

A 45° - 45° - 90° triangle has sides in the ratio of 1:1:√2. Since one leg measures 36 feet, the length of the hypotenuse (the longest side) can be found by multiplying the length of a leg by √2:

36 * √2 = 36 * 1.41421356 = 50.8800

Therefore, it is concluded that the longest side of the triangular deck will measure approximately 50.8800 feet, rounded to the nearest ten-thousandth.

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The final equation is y =x-1.

To find the line that satisfies the given, we will use the two-point form

     [tex]y - y_{1} = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } (x - x_{1} )[/tex]

Before we use this, however, we need to assign to the points given the variables they represent:

(-1, -2) and (4, 3)

[tex]x_{1} = -1[/tex]

[tex]x_{2} = 4[/tex]

[tex]y_{1} = -2[/tex]

[tex]y_{2} = 3[/tex]

Now, we will substitute these values

                     [tex]y - y_{1} = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } (x - x_{1} )[/tex]

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

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

                  ⇒    [tex]y +2 = \frac{5 }{5 } (x +1 )[/tex]

                  ⇒  [tex]y +2 = x +1[/tex]

                   ⇒    [tex]y = x -1[/tex]

Thus, the final equation is y =x-1.

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