Here are the first four terms of a sequence
4 , 11 , 22 , 37
find an expression, in terms of n, for the nth term of this sequence

Answers

Answer 1

Answer:

Step-by-step explanation:

Determine an algebraic expression for the nth term of the following sequence.

A set of 3 figures are connected squares. Figure 1 is a column of 5 squares next to a column of 3 shaded squares. Figure 2 is figure 1 with an additional column of 3 shaded squares to the right. Figure 3 is figure 2 with an addition column of 3 shaded squares to the right to make 9 shaded squares.


Related Questions

a rectangular field will be bounded by a wall on one side and by fencing on the other three sides. what is the largest area you can enclose with 120 feet of fencing?

Answers

The largest area you can enclose with 120 feet of fencing is 900 square feet.

To find the maximum area you can enclose with 120 feet of fencing, you can use the formula for the area of a rectangle, which is A = lw, where A is the area, l is the length, and w is the width. Since the length of the rectangle is bounded by a wall and cannot be changed, the width will be the variable we seek to maximize.

Since the perimeter of the rectangle is fixed at 120 feet, we can set up the following equation:

2l + 2w = 120

This equation represents the total length of the fence needed to enclose the rectangular field. We can solve for w in terms of l by rearranging the equation as follows:

2w = 120 - 2l

w = (120 - 2l)/2

To maximize the area of the rectangle, we want to maximize the value of w. We can do this by making l as small as possible, since this will make w as large as possible. Therefore, we can set l equal to the minimum possible value, which is the length of the wall.

Let's say the length of the wall is x feet. Then, we can substitute x for l in the equation for w to find the maximum possible width:

w = (120 - 2x)/2

To find the maximum area, we can then substitute this value for w back into the formula for the area of a rectangle:

A = lw

= x((120 - 2x)/2)

= (120x - 2x^2)/2

This is a quadratic function, and we can use the techniques for maximizing quadratic functions to find the maximum value of A. To do this, we take the derivative of the function and set it equal to zero:

A' = (120 - 4x)/2 = 0

120 - 4x = 0

x = 30

Substituting this value back into the equation for A, we find that the maximum possible area is:

A = (120 * 30 - 2 * 30^2)/2

= (3600 - 1800)/2

= 1800/2

= 900 square feet

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Characterize observational study with respect to nature of the sample and treatment.

Answers

An observational study is used to answer a research question based purely on what the researcher observes.

What Is an Observational Study?

An observational study is a statistical study that does not have any treatment or intervention done by the researchers.

Observational research allows the researcher to see what their subjects really do when confronted with various choices or situations. The term refers to the study of non-experimental situations in which behaviour is observed and recorded.

Statistics is the process of collecting data about a group of objects to draw conclusions about populations of those objects. For example, a statistician may take a sample group of workers from company XYZ and have them rate their job satisfaction with the company. Based on the results of that sample, the statistician can make educated assumptions about all the employees of company XYZ and their job satisfaction.

However, observational studies can only establish that significant associations exist between predictor and outcome variables. Observational studies cannot establish that the associations identified represent cause-and-effect relationships.

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How do you identify the type of similarity that two triangles might be?

Answers

To easily recognize comparable triangles, you can apply three theorems that are peculiar to triangles.

Two triangles can be compared using one of three theorems: Angle-Angle (AA), Side-Angle-Side (SAS), and Angle-Angle-Side (SS-AS) (SSS).

The symbol representing two triangles with the same angles on all three sides is SSS, which stands for "side, side, side." If two triangles' third sides match those of another triangle, the two triangles are said to be congruent.

The SAS regulation states as much. If the two sides and included angle of one triangle match the two sides and included angle of another triangle, the triangles are congruent. Any angle formed by two specified sides is considered to be an included angle.

A triangle is comparable to another if its two matching angles are congruent, according to the AA postulate of Euclidean geometry. The AA postulate is derived from the observation that the total internal angle of a triangle is always equal to 180°.

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The equation of a parabola is y=5x^2+15x–25. Write the equation in vertex form.
Write any numbers as integers or simplified proper or improper fractions

Answers

The equation of the parabola y = 5 · x² + 15 · x - 25 in vertex form is y + 145 / 4 = 5 · (x + 3 / 2)².

How to find the vertex form of a quadratic equation

Herein we find the equation of a parabola in standard form, that is, an equation of the form:

y = a · x² + b · x + c

Where:

a, b, c - Real coefficientsx - Independent variabley - Dependent variable

From this equation we must derive the vertex form, whose definition is shown below:

y - k = C · (x - h)²

Where:

C - Vertex constant(h, k) - Coordinates of the center.

The vertex form is found by algebra properties. First, write the equation of the parabola:

y = 5 · x² + 15 · x - 25

Second, use algebra properties until the vertex form is found:

y + 25 = 5 · x² + 15 · x

y + 25 = 5 · (x² + 3 · x)

y + 25 + 45 / 4 = 5 · (x² + 3 · x + 9 / 4)

y + 145 / 4 = 5 · (x + 3 / 2)²

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i need help please. ​

Answers

Answer: ( x + 5, y + 11)

Step-by-step explanation:

Let's pick point S at ( -9, -9); it changes to point S' at (-4, 2)

We see the x increase by 5 and the y increase by 11, so the answer is

( x + 5, y + 11)

What is a linear graph formula?

Answers

y = MX + b is the required linear graph formula.

What is the linear graph formula?

Linear equations with two variables have straight-line graphs.

There are numerous ways to express linear equations: Y = mx+ b is the slope-intercept form.

The slope is m and the y-intercept is the point in an equation of the type y = MX + b, such as y = 2x 3. (0, b).

Write the equation in the form y = MX + b to determine the slope m and the y-intercept.

This will allow you to graph the equation using the slope and y-intercept (0,

b).

Plot the y-intercept next.

3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.

Therefore, y = MX + b is the required linear graph formula.

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Please help me with this question
many thanks

Answers

answer :

d÷d = 0

then 10 remain

find an equation of the tangent line to the curve at the given point. y = 8ex cos(x), (0, 8)

Answers

The equation of the line tangent  to the curve at the points , y = 8ex cos(x), (0, 8) as calculated is y' = 0.

We will differentiate y = 4ex cos(x) so as to find the required equation.

we get the differential as ,

y' = - 8eˣsin(x)

given the value of x as 0 and y as 8

y' = -8e⁰sin(0)

Now as we know that the value of sin( 0 ) is 0 , therefore the equation becomes,

y'= 0  

Differentiation is a branch of calculus which is used to calculate the rate of change in a given object in a specified time. The other  branch of calculus is integration.

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What are the 3 types of forecasting?

Answers

The three main types of forecasting are qualitative, quantitative, and time series.

What is forecasting?

Forecasting is a predictive tool used to make decisions and plan for the future. It involves analyzing past trends and data to predict future events and outcomes. Forecasting helps businesses and organizations prepare for potential market changes, plan ahead for budgeting, and make informed decisions. It is also an invaluable tool for understanding consumer behavior and market trends.
Qualitative forecasting is a subjective approach that relies on expert opinion, intuition, and past experiences. Quantitative forecasting is a more structured approach that uses statistical techniques and data-driven models to make predictions. Time series forecasting is a form of quantitative forecasting that uses historical data to predict future values. It is especially useful for predicting cyclical trends and seasonal variations. All three approaches can be used together to create a comprehensive forecasting strategy for a business.

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Which expression is equivalent to the following complex fraction (- 2 x 5 y )/( 3 y 2 x?

Answers

The expression expressed as a single fraction is -2y(yx-2)/3x(yx+5)

How to simplify the expression as a single fraction?

You should know that simplification involves making an expression look more simpler than it was

The given expression is  2/(x+5/y)÷3/(y-2/x)

First of all let us express the denominator as a single fraction

x+5/y

⇒(yx +5)/y

In the same way express the expression y-2/x = (yx-2)÷x

By substitution we have

(-2)/yx+5)/(y/3)÷(yx-2/x)

⇒(-2y)/(yx+5) ÷ (3x/ (yx -2)

Simplifying this further to get

(-2y)/(yx +5) * (yx -2)/(3x)

⇒-2y(yx-2)/3x(yx +5)

In conclusion, the expression expressed as a single fraction is -2y(yx-2)/3x(yx+5)

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Correct question:

Which expression is equivalent to the following complex fraction? -2/x+5/y/3/y-2/x

Answer:the answer is

Step-by-step explanation:

just did the test

The graph represents a quadratic function. Write an equation of the function in standard form.

Answers

The equation for the quadratic function in standard form is f(x) = x² - 11x + 24

Writing Quadratic equation

From the question, we are to write an equation for the quadratic function in standard form.

From the given quadratic graph,

The roots of the function are 3 and 8.

That is,

x = 3 and x = 8

Then,

The factors of the quadratic function are (x -3) and (x - 8)

Thus,

We can write that

(x - 3)(x - 8) = 0

x² - 8x - 3x + 24 = 0

Simplify

x² - 11x + 24 = 0

Hence, the equation is f(x) = x² - 11x + 24

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Answers

When plug in the numbers

√900/16

7.5 seconds before it hits the ground

Brainly pls

What are the 3 different options for horizontal asymptotes?

Answers

The 3 different options for horizontal asymptotes are:

If the degree of the numerator < the degree of the denominator.If the degree of the numerator = degree of the denominator. If the degree of the numerator > the degree of the denominator.What are horizontal asymptotes?

This refers to a horizontal line y = b where the graph approaches the line as the inputs approach infinity (∞) or negative infinity (–∞).

The 3 different options for horizontal asymptotes

If the degree of the numerator < the degree of the denominator, y = 0 (x-axis), and If n<m, the x-axis, y=0 is the horizontal asymptote.If the degree of the numerator = degree of the denominator. If n=m, then y=an / bm . That is, the ratio of the leading coefficients.It is the horizontal asymptote. If the degree of the numerator > the degree of the denominator. If n>m, there is no horizontal asymptote.

Note: If n=m+1, there is an oblique or slant asymptote.

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Your friend hides a dollar bill under one of three plastic cups. Under the other
two cups is a paper clip. You get to keep whatever is under the cup you
choose, but you don't know which contains the dollar bill. After you choose,
your friend lifts one of the other cups to reveal a paper clip and then gives you
the option of changing your choice.
Should you switch to the other cup?

Answers

Answer:

Yes, you should

Step-by-step explanation:

Because the probability of winning the dollar increases from \frac{1}{3} 3 1​ to \frac{2}{3} 3 2​ by switching.

What is the discriminant and nature of roots of 2x² 3x 5 0?

Answers

The discriminant of the quadratic equation 2x² + 3x - 5 = 0 is 49 and the nature of the roots are -3/4 + 7/4 and -3/4 - 7/4.

The discriminant of the quadratic equation 2x² + 3x - 5 = 0 is b² - 4ac = 9 - 4(2)(-5) = 49.

The nature of the roots of the equation can be determined by the discriminant. If the discriminant is positive, then the roots are real and distinct; if it is zero, then the roots are real and equal; and if it is negative, then the roots are complex and conjugate. In this case, the discriminant is positive, so the roots are real and distinct.

To calculate the roots, we use the quadratic formula:

x = [-b ± √b² - 4ac]/2a.

For this equation, a = 2, b = 3, and c = -5,

so x = [-3 ± √49]/2(2) = [-3 ± 7]/4 = -3/4 ± 7/4.

This means the two roots of the equation are -3/4 + 7/4 and -3/4 - 7/4.

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What is the process of forecasting future expenses and savings called?

Answers

The process of forecasting future expenses and savings is called financial planning.

What is forecasting?

Forecasting is the process of predicting future events or outcomes based on past data, trends, and other information. It is an important tool for businesses, allowing them to plan ahead and make informed decisions. Forecasting can help organizations anticipate changes in the market, anticipate customer demand, plan investments, and more. If done properly, it can help organizations achieve their goals and maximize profits.

Financial planning is the process of creating a budget, setting goals, and developing strategies to help manage money and reach financial goals. It includes estimating future income and expenses, assessing current financial resources, and creating a plan for spending, saving, and investing. Financial planning can help you to stay on track towards meeting your financial goals and create a secure financial future.

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Can in text citations be shortened?

Answers

Harvard in-text citations allow for the inclusion of up to three authors. When there are four or more authors, et al. is used to shorten the citation.

What are text citations?

In-text citations in APA style are used to quickly describe the sources of your information within the text of your research report.

The reader is directed to more detailed information in the Reference list by succinct in-text citations.

The author's last name and the year of publication are used in APA in-text citations,: (Field, 2005). Include the page number when using direct quotations, as in the following example: (Field, 2005, p. 14).

Reduce the source title or organization name, excluding any articles, to the first word or phrase in the in-text citation if it is longer than four words (a, an, and the).

The alphabetized word for the source in the Works Cited should be the first word in the abbreviated title or organization name.

Therefore, Harvard in-text citations allow for the inclusion of up to three authors. When there are four or more authors, et al. is used to shorten the citation.

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How do you add rational expressions examples?

Answers

The Example of addition of Rational Expressions is "Add 2/3 and 6/7" .

The Rational Expression is defined as the expression , that is represented in the form of p/q , where q ≠ 0 .

Example of Addition of Rational Expression is

Add 2/3 + 6/7 .

In order to add the above two rational expression , we first make the denominator of both the terms same by taking LCM ,

the LCM of denominators 3 and 7 is 21 .

So , the expression becomes  ⇒ 14/21 + 18/21 .

⇒ (14 + 18)/21

Simplifying further ,

we get ;

⇒ 32/21

Therefore , the example of addition of rational expressions is explained above .

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Solve the equation:5(3+6a)=-15+6(5+5a)

Answers

Answer:

0.5

Step-by-step explanation:

To solve the equation 5(3+6a) = -15+6(5+5a), we need to use the rules of algebra to isolate the variable "a" on one side of the equation and simplify the other side.

First, we can distribute the 5 on the left side of the equation to obtain 53 + 56a = -15+6(5+5a). This gives us 15 + 30a = -15+6(5+5a).

Next, we can distribute the 6 on the right side of the equation to obtain 15 + 30a = -15+65 + 65a. This gives us 15 + 30a = -15+30 + 30a.

Now we can combine like terms on both sides of the equation to obtain 30a = -15 + 30, which simplifies to 30a = 15. Finally, we can divide both sides of the equation by 30 to obtain a = 0.5.

Therefore, the solution to the equation 5(3+6a) = -15+6(5+5a) is a = 0.5

E-loan, an online lending service, recently offered 36-month auto loans at 6% compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of $539, how much can you borrow from E-loan? What is the total interest you will pay for this loan?

Answers

I can borrow $17717.48from E-Loan.

The interest I will pay for the loan is $1,686.52

Now, According to the question:

We know,

The formula of present value is

PV = PMT [tex](\frac{ 1-(1+i)^-^n}{i} )[/tex]

PMT = The monthly payment = $539

i= Rate of interest per period  = 6%/12 = 0.005

n = The number of month = 36 months

Therefore,

PV = 539[tex](\frac{ 1-(1+0.005)^-^3^6}{0.005} )[/tex]

    ≈$17717.48

Therefore I can borrow $17717.48 from E-Loan.

The interest = Paid amount - Loan amount

                      =$[(539×36)-17717.48]

                      = $1,686.52

The interest I will pay for the loan is $1,686.52

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What is a parallel class 6?

Answers

In geometry, parallel lines are the lines which maintain the same distance apart from each other and never intersect at any point.

What is parallel class 6?

In geometry, parallel lines are the lines which maintain the same distance apart from each other and never intersect at any point.

All rungs are perpendicular to the left post is a line perpendicular to one of a set of parallel lines, it is perpendicular to all parallel lines.

The rungs are parallel

lines that are perpendicular to the same line are parallel.

The rungs are perpendicular to both posts and the posts are parallel  to each other.

if a line is perpendicular to one of a set of parallel lines, it is perpendicular to all the parallel lines.

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Why is the power of 2 called square?

Answers

The power of 2 is called a square due to the definition of the area of a square.

What are a square and Power?

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.

The base number is the factor that is multiplied by itself, and the exponent is the number of times the same base number has been multiplied. Power is defined as a base number raised to the exponent.

The power of two is called a square.

The square function's name derives from the fact that a square with sides of length [tex]l[/tex] equals [tex]l^2[/tex] has a significant role to play in the definition of area.

The area is inversely proportional to size: the area of a form that is [tex]n[/tex] times larger is [tex]n^2[/tex] times larger.

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How to find all pairs in array of integers whose sum is equal to given number?

Answers

To find all pairs in an array of integers whose sum is equal to a given number, iterate through the array and for each element, check if there is another element in the array that, when added to the current element, is equal to the given number, and if such an element is found, add the pair (current element, other element) to a list of pairs; repeat this process until all elements in the array have been checked.

What is an array?

A group of objects, pictures, or numbers organized in rows and columns is known as an array. Arrays provide as concrete examples of multiplication concepts.

Why do we need arrays?

Arrays are needed in cases where you need  to store and manipulate large amounts of data efficiently.

Some of the benefits of using arrays include:

Arrays allow you to store a large number of items in a single data structure, which makes it easier to work with large datasets. Arrays allow you to access and modify the items in the array quickly, using the index of the item.

There are numerous techniques for locating all pairs in an integer array whose total is equal to a specific value. Here is one strategy you may employ:

In order to store the pairs you find, create a blank list.Check if there are any other elements in the array that, when combined with the current element, equal the specified number as you iterate over the array.Add the pair (current element, other element) to the list of pairs if you come across such an element.Once you have tested each entry in the array, repeat this step.

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which of the following sets of transformations could be used to prove that the line segments are congruent?

Answers

A transition of AB6 units to the right followed by a transition 6 unit down this transformations could be used to prove that the line segments are congruent.

How do you know if a line segment is congruent?Line segments of the same length are known as congruent segments. Congruent refers to equality. The standard method for identifying congruent line segments is to draw the same number of tiny, perpendicular tic lines in the middle of each section. By placing a line over the two endpoints of a line segment, we can identify it.A line segment is a section of a straight line that is enclosed by two clearly defined end points and contains every point on the line located within. The Euclidean distance between two ends of a line segment determines its length.Half-open line segments contain exactly one of the endpoints, while closed line segments have both of the endpoints. Open line segments do not contain either of the endpoints.

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How do you solve 7 step equations?

Answers

To solve a 7 step equation, identify the equation, isolate the variable to one side of the equation, simplify the equation if necessary, divide both sides of the equation by the coefficient of the variable.

1. Identify the equation.

2. Limit the variable to only one side of the problem.

3. Simplify the equation, if necessary.

4. Divide both sides of the equation by the coefficient of the variable, if necessary.

5. Continue carrying out steps 2-4 until the equation is resolved.

6. Check your solution by substituting the solution back into the equation.

7. Write the solution in the form of an equation.

To solve a 7 step equation, identify the equation, isolate the variable to one side of the equation, simplify the equation if necessary, divide both sides of the equation by the coefficient of the variable, repeat steps 2-4 until the equation is solved, check your solution by substituting it back into the equation, and then write the solution in the form of an equation.

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What is the value of |a-b|+|b-a| if a=b-1/2

Answers

The value of the absolute expression |a - b| + |b - a| will be 1.

What is the value of the expression?

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The equation is given below.

a = b - 1/2

The expression is given as,

⇒ |a - b| + |b - a|

The value of (a - b) is given as,

a = b - 1/2

a - b = - 1/2

And the value of (b - a) is given as,

a = b - 1/2

b - a = 1/2

Then the value of the expression is calculated as,

⇒ |a - b| + |b - a|

⇒ |-1/2| + |1/2|

⇒ 1/2 + 1/2

⇒ 1

The worth of the outright articulation |a - b| + |b - a| will be 1.

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what is the largest integer that always divides $(n 1)(n 3)(n 5)(n 7)(n 9)$ for all positive even integers $n$?

Answers

The largest integer that always divides (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n is 15.

What is positive integer?

Positive integers are numbers such as 1, 2, 3, etc. They are also called countable or natural numbers. A positive number is any number greater than zero.

Let P(n) = (n+1)(n+3)(n+5)(n+7)(n+9) be a polynomial for all positive even integers, n . We have to calculate the largest integer that always divides the P(n) .

Let "l" be the largest integer that divides P(n) for each n∈N . Then, l must divide both P(1) and P(2)

i.e, P(1) = (1+1)(1+3)(1+5)(1+7)(1+9) = 2×4×6×8×10

= 2^8×5×3

P(2) = 3×5×7×9×11 , hence , l divides 15.

Since, n + 5 ≡ (n+2) mod(3), one (and exactly one) of the numbers n+1 , n+3 , n+5 must be multiple of 3 . Thus, 3/P(n) for each n∈N.

Since, n+7 ≡ (n+2)mod(5) and n+9 ≡ (n+4)mod(5),

one (and exactly one) of the numbers n+1 , n+3 , n+5 , n+7 and n+9 , must be multiple of 5.

Thus, 5/P(n) for each n∈N.

Therefore, 15/p(n) for each n∈N , so that l = 15 .

So, required value of n is 15.

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Which of the quantities below represents a velocity?
A. 25 m/s
B. 10 km/min
C. 15 mi/h eastward
D. 3 mi/h

Answers

Step-by-step explanation:

Velocity is a measure of the rate at which an object moves through space. It is a vector quantity, meaning that it has both magnitude (size) and direction. The standard unit for velocity is meters per second (m/s).

Of the quantities listed above, the following represent velocities:

A. 25 m/s: This represents a velocity of 25 m/s, because it gives both the speed (magnitude) and direction of the object's movement.

C. 15 mi/h eastward: This represents a velocity of 15 miles per hour (mi/h) in an eastward direction, because it gives both the speed and direction of the object's movement.

D. 3 mi/h: This represents a velocity of 3 mi/h, because it gives both the speed and direction (implied to be eastward or westward) of the object's movement.

B. 10 km/min: This does not represent a velocity, because it gives the distance traveled (10 km) but not the time over which the distance was traveled. Without the time, it is not possible to determine the speed or rate of movement.

Which two functions are inverses of each other?

Answers

The two functions are inverse to each other if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Functions

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

inverse functions

the inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

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A bag contains 3 basketballs, 10 baseballs, 7 golf balls, and 5 footballs. A ball is chosen at random,not replaced, then another is chosen. Find each probability


17. P(a football, then a baseball)

18.P(two baseballs)

Answers

This is based on Conditional Probability.

P(a football, then a baseball) is 0.08333 and P(two baseballs)

is 0.15

What is Conditional Probability?

The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory.  This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible. The probability of A under the condition B is typically expressed as P(A|B) or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of probability that B crosses A:

P(A|B)=P(A∩B)/P(B)

Calculation:

1) P(a football, then a baseball)= ([tex]\frac{5}{25}[/tex])×([tex]\frac{10}{24}[/tex]) =0.08333

2) P(2 Baseballs) = ([tex]\frac{10}{25}[/tex])×([tex]\frac{9}{24}[/tex]) = 0.15

This is based on Conditional Probability.

P(a football, then a baseball) is 0.08333 and P(two baseballs)

is 0.15

To know more about Conditional probability, visit:

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