Can tar and QRS be proven congruent by SAS?

Answers

Answer 1

Yes,△TSR is Congruent to △QRS ( i.e,△QRS ≅ △TRS) by SAS , because there is all enough information to prove that the triangles are congruent by SAS rule.

What is SAS Congruence rule?

The word "congruent" for figures means the same thing in all respects, mainly shape and size. The relationship between two congruent entities is described by congruence. SAS congruence is a term also known as side angle side congruence. According to this rule, two triangles are congruent if two sides of a triangle are equal to two sides of another triangle and the angles formed by those sides of the two triangles are equal. We have two triangles, TSR and △QRS as we can see in above figure and we get ,

RS = RS ( common side)∠RST = ∠RSQ = 90° SQ = ST ( similar as provide )

Thus, two sides and one angle of triangle is similar to corresponding sides and angle of other triangle, so SAS Congruence criteria is applicable here. Therefore, △QRS ≅ △TRS by the SAS Congruence Postulate.

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Complete question :

Can TSR and QRS be proven congruent by SAS ? and the triangles are shown above figre.

Can Tar And QRS Be Proven Congruent By SAS?

Related Questions

please help me with this question
step by step please

Answers

Answer:

[tex]36.77150[/tex], or 37 (rounded)

Step-by-step explanation:

1. [tex]\sqrt{97} = 9.84885[/tex]

2. [tex]9.84885[/tex] + [tex]8.169178744[/tex] = [tex]18.01803[/tex]

3. [tex]\frac{18.01803}{0.49}[/tex]

4. = [tex]36.77150[/tex]

You can simplify 36.77150 to 37

... Hope this helped! Have a wonderful New Year!

The value of the equation is A = 36.77

What is an Equation?

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

A = ( √97 + 2.014³ ) / 0.49   be equation (1)

On simplifying the equation , we get

√97 = 9.8488578

2.014³ = 8.169178744

Substituting the values in the equation , we get

A = ( 9.8488578 + 8.169178744 ) / 0.49

A = 18.018036544 / 0.49

A = 36.77150

Therefore , the value of A is 36.77

Hence , the equation is A = 36.77

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What is the range of Y 3x 1?

Answers

{y | y ∈ ℝ} or (-∞, ∞) is the range of y = 3x + 1

What is range?

To determine the range of a group of observations, firstly arrange them in ascending order. The range may then be determined by comparing the difference between the highest and least numbers.

A function's range includes all conceivable values for y.  y = f(x) is the formula to determine a function's range (x). It is only a function in a relationship if each x value has exactly one y value.

Think about the function y = f(x). The function's range is defined as the range of all y values, from least to maximum. Substitute all possible values of x into the provided expression of y to see if it is positive, negative, or equal to other values.

For, y = 3x + 1

domain is all real numbers

so, {x | x ∈ ℝ} or (-∞, ∞)

range:

y = 3x + 1

or, -3x = -y + 1

or, 3x = y - 1

or, x = (y - 1)/3

so, {y | y ∈ ℝ} or (-∞, ∞)

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The complete question is as follows:

What is the range of y = 3x + 1

Is equidistant the same as parallel?

Answers

In Euclidean geometry, parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.

A point is said to be equally far from a group of objects if there is an equal distance between it and each member of the group. 

The perpendicular bisector of two specified (different) points is their location in two-dimensional Euclidean geometry. The locus of points equidistant from two provided points in three dimensions is a plane, and generalizing further, the locus of points equidistant from two given locations in n-dimensional space is a (n1)-space.

The circumcenter of a triangle is a location that is equally spaced from each of the three vertices.

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What stays the same when you perform a rigid motion transformation?

Answers

When a point or object is moved but its size and shape don't change, it is said to have undergone rigid motion, sometimes referred to as a rigid transformation.

What is rigid motion transformations?

The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape. The form remains the same after being pushed left and right, rotated, and flipped.

When the mold was created using putty, the opposite was true. The thing can then be twisted and stretched. These conversions, nevertheless, are not exact. Stretching a form alters the distances between each pair of its points.

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7. Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a
flight had 52 passengers who paid $1360, how many first class and tourist class passengers were
there?

Answers

Answer:

12 first class and 40 tourist

Step-by-step explanation:

Answer:

40 tourist class passengers, and 12 first class passengers.

Step-by-step explanation:

Here's my explanation:

We let X be the number of passengers booking for the tourist class.

If there were 52 passengers who paid 1360, then to find the number of passengers who booked first class, we write:

52-x

And if the airline fares are 30 per first class and 25 dollars for tourist class, you would say 30.00(first class)+25.00(tourist class)=1360

Using substitution, plug-in 52-x for the first class:

30(x)+25(52-x)=1360

30x+1560-25x=1360

1360-1560 =25x-30x

-200=-5x

x=40

Plug in 40 for x,

52-40=12

So, 40 tourist class passengers, and 12 first class passengers.

How do you find 3 missing angles?

Answers

An angle is a figure found by two rays with the same initial point. In geometry, various names are given to different angles and their combinations depending upon the type of angles they make.

various geometrical shapes such as a triangle or a quadrilateral contain a set of angles that are governed by a set of rules.

For example, there are three interior angles in a triangle, the sum of which is always equal to 180 degrees. This means that if we are cultured of two of the angles in a triangle, we can find the third.

alike using different rules and the available information we can find the missing angle in a geometrical figure.

But, before understanding different state where we can find the missing angles, we should first recall some of the properties of different geometric shapes that will be useful in finding missing angles.

1. The sum of the measure of the three interior angles of a triangle is always 180 degrees.

2. If one of the angles of a triangle is 90 degrees, the sides that make the right angle is called the base and the perpendicular while the third side is called the hypotenuse.

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Use the method of completing the square to transform the equation 3x^2−12x+8=0. Which equation shows the transformed equation?
Is my answer correct?

Answers

By completing squares, we can rewrite the quadratic equation as:

3*(x - 2)^2 = 4

How to complete squares?

Here we have the quadratic equation:

3x^2 - 12x + 8 = 0

If we take "3" as a common factor for the first two terms:

3*(x^2 - 4x) + 8 = 0

Now we can add and subtract 12, then we will get:

3*(x^2 - 4x) + 8 = 0

3*(x^2 - 4x) + 8  +12 - 12 = 0

We can put the positive one inside the parenthesis:

3*(x^2 - 4x + 4) + 8 - 12 = 0

3*(x - 2)^2 - 4= 0

3*(x - 2)^2 = 4

That is our quadratic equation, the correct option is the third one.

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Raíz cuadrada de 64 la necesito para hoy, por favor

Answers

In fact, if we knew that 64 = 8 sqrt 64 = pm 8 64 = 8, then x would no longer be a function and would instead be a relationship, causing the graph to be repeated twice with the value 64. (en 8 y -8).

What is the 64-bit binary radix?

For instance, the 64-bit number, which is written as 4, is 4, since 64. Additionally, it is the length of a 64-volume cube's arista.

Who is the sixth of 64?

What our community finds fascinating. La raiz sexta es 2 because cuando dividimos 64/2 obtenemos un resultado especfico and cuando multiplicamos seis veces dos obtenemos 64.

conversation of 64 into binary

Binary value for 64 is 1000000. In a binary number system, we only utilize the digits 0 and 1, as opposed to the decimal number system, which uses the numbers 0 to 9 to express a number (bits).

= [tex]64_{10}[/tex] = [tex]1000000_{2}[/tex]

here, the binary of [tex]64_{2} = 1000000_{2}[/tex]

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Which is an expression for the derivative of P(x)=f(x)/1-f(x)?

Answers

Here the correct expression for the derivative of P(x) is: option B

What is mean by derivative?

The fact that the initial function f implies a second, distinct function f′(x) gives origin to the name "derivative" (x). As a result, we have deduced one from another. When we deduce one from the other, the terms differential, etc. pertain more to the real mathematics that is taking place.

The definition of a derivative in mathematics is a technique for displaying the simultaneous rate of change. The amount by which the provided function is changing at a certain instant is thus represented by it.

The following are some uses for derivatives: to ascertain the pace at which one item is changing in relation to another. The saddle points of a function are used to calculate maximum and minimum. to establish a function's concavity and convexity.

P(x) = [tex]\frac{f(x)}{1-f(x)}[/tex]

or, [tex]\frac{d}{dx} P(x) =[/tex] [tex]\frac{d}{dx} \frac{f(x)}{1-f(x)}[/tex]

or, [tex]\frac{d}{dx} P(x) =[/tex] [tex]\frac{f'(x)}{1-f(x)}[/tex]

Correct option: B

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What is the standard deviation of 1 2 3 4 5?

Answers

The standard deviation of

{1,2,3,4,5}=[52−112]12

=√2

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists.

The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Like the variance, if the data points are close to the mean, there is a small variation whereas the data points are highly spread out from the mean, then it has a high variance.

Standard deviation calculates the extent to which the values differ from the average. Standard Deviation, the most widely used measure of dispersion, is based on all values.

Therefore a change in even one value affects the value of standard deviation. It is independent of origin but not of scale.

It is also useful in certain advanced statistical problems.

Let's develop a general formula then as a particular you get standard deviation of

1,2,3,4 and 5

If we have

{1,2,3,....,n}

and we need to find the standard deviation of this numbers.

Note that

Var(X)=1nn∑i=1 x2i−(1nn∑i=1xi)2

⇒Var(X)=1nn∑i=1i2−(1nn∑i=1 i)2

⇒Var(X)=1n⋅n(n+1)(2n+1)6−(1n⋅n(n+1)2)2

⇒Var(X)=(n+1)(2+1)6−(n+12)2

⇒Var(X)=n+12[2n+13−n+12]

⇒Var(X)=n+12⋅n−16

⇒Var(X)=n2−112

So, Standard deviation of

{1,2,3,....,n}

is

[Var(X)]12=[n2−112]12

In particular, your case the standard deviation of

{1,2,3,4,5}

=[52−112]12=√2.

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PLEASE HELP ASAP

At a local high school, the student population is growing at 12% a year. If the original population was 242 students, how long will it take the population to reach 300 students? Round to the nearest tenth of a year.

A. 0.7 Years
B. 3.2 Years
C. 1.9 Years

Answers

It will take 2 year the population to reach 300 students.

What is rounding to the nearest tenth?

Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5. To the nearest tenth, 4.6, for instance, is 4.624.

Given that, the initial number of students is 242.

The student population is growing at 12% a year.

The number of students that increases is 300 - 242 = 58.

Applying formula

I = PRT

I = The number of students that increased = 58

P = initial number of students = 242

T = Time

R = rate of increasing =12% = 0.12

Therefore,

58 = 242 × T × 0.12

T = 58/(242 × 0.12)

T = 1.997

T = 2.0 years

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How do you find a unique value?

Answers

Utilize Excel's Advanced Filter to locate singular values. You have the option of extracting unique values or filtering for them. Use the magical UNIQUE function if you have Excel 365 or Excel 2021.

How can I develop a distinctive value proposition?

To develop a distinctive value proposition that complements a company's objectives and core principles, think about doing the following seven steps: 1. Examine the offerings of the business. When developing a distinctive value proposition, a company's products or services might serve as a source of inspiration. These services demonstrate the value the business provides to its clients.

How can I acquire an Excel list of unique values?

Select a data set cell by clicking it.

Then, choose Advanced from the Sort&Filter group by clicking the Data tab.

Select "Copy to Another Location" from the menu.

Excel will show the List Range as the cell reference for the whole data set or Table object.

If there is a criteria range, remove it.

You should always provide a text label at the top of each data column when using Excel's Advanced Filter.

1. Select a list range cell by clicking it.

2. Click Advanced under the Sort & Filter category on the Data tab.

The dialog box for the Advanced Filter opens.

3. Click the Copy button (see image below).

4. Select cell C1 by clicking in the Copy to box.

5. Verify only unique records.

6. Press OK.

Lion in cell A7 and Elephant in cell A9 are two examples of duplicate values that Excel eliminates before sending

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Clinical trials enroll individual subjects and enable randomization of subjects to receive or not receive the intervention. True or False

Answers

The given statement w.r.t clinical trials is true.

What are clinical trials?

Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments and known interventions that warrant further study and comparison.

Given is a statement about the clinical trials.

The given statement that Clinical trials enroll individual subjects and enable randomization of subjects to receive or not receive the intervention is true.

Therefore, the given statement w.r.t clinical trials is true.

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What kind of roots does 3x² 2x 1 0?

Answers

The nature of the roots of the given equation is real, distinct and rational.

What is the discriminant of a quadratic equation?

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

Given that a quadratic equation, 3x²+2x-1 = 0,

To find the nature of the roots, we will find the discriminant, of the equation,

We know that,

1) A positive discriminant indicates that the quadratic has two distinct real number solutions.

2) A discriminant of zero indicates that the quadratic has a repeated real number solution.

3) A negative discriminant indicates that neither of the solutions are real numbers.

D = √b²-4ac

b = 2, a = 3 and c = -1

D = √(2)²-4 × (-1) × (3)

D = √16

D = 4

Since, D > 0

Hence, the nature of the roots of the given equation is real, distinct and rational.

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What is the slope of the line that passes through the points (2,−3) and(1,−2)? Write your answer in simplest form.

Answers

Answer: -1

Step-by-step explanation:

slope form is [tex]m = \frac{y^{2} - y^{1} }{x^{2} - x^{1} }.[/tex] M is the slope. x1 and y1 are coordinates of a point along the line. x2 and y2 are the coordinates of another point along the line.

So we need to substitute in the points you have. let's put in (1, -2) for x1 and y1, and (2, -3) in x2 and y2. it makes [tex]m = \frac{-3-(-2)}{2-1}[/tex]

Now all you have to do is solve the equation.

[tex]m = \frac{-3-(-2)}{2-1}[/tex]

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

m = -1

(btw the line's equation would be y = -x - 1)

Answer:

-1

Step-by-step explanation:

To find the slope between two points we can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -2 - -3)/(1 -2)

   = ( -2 +3)/( 1-2)

  = 1/-1

  = -1

How many rows and columns are there in Excel 2007?

Answers

A maximum of 1,048,576 rows are allowed in Microsoft Excel 2007. 15,384 columns. Columns and rows make up an Excel spreadsheet.

what are columns and rows ?

The arrangement of items next to or horizontally across one another is referred to as a row. As a vertical grouping of items according to category, a column can be said to exist. Left to right is the direction of arranging. From top to bottom, the set up is made. At far right is where the total is displayed.

here

Numbers 1, 2, 3, and 4 are used to designate the rows, which are horizontally oriented.

A, B, C, D, etc., are used to denote the letters that run horizontally along the columns.

Cells are what happen when a column and row intersect.

A maximum of 1,048,576 rows are allowed in Microsoft Excel 2007. 15,384 columns.

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HELP PLSSS I NEED TO SHOW WORK ALSO … The band has at most $3000 for its annual trip to Six Flags. The budget consisted of $1000 for travel cost, and $25 for each student's expenses. Write an inequality that represents the maximum number of sudents, x, that would be able to attend the trip. ( i’ll give you 50 points)

Answers

Answer: The maximum students that would be able to attend the trip is 40 students. Because 25 multiplied by 40 is = 1,000 and the budget is only 3,000 the answer is 40 students

Step-by-step explanation: Hope this helps =)

What is the slope of the line represented by the equation y 4 5x 3?

Answers

The line has a 4/5 slope. The solution is 4/5 if the line's equation is y = 4x/5 - 3.

The ratio in which y increases as x increases is known as a line's slope. The slope of a line not only shows how steep it is but also how much y increases as x increases. Along the entire line, there is a constant slope (the same).

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We have a line equation.

y = (4/5)x - 3

or

y = 4x/5 - 3

A straight line, as we all know, is made up of countless points that are connected on both sides of the point.

The straight line's typical form is as follows:

y = mx + c

The slope of the line is m.

C is the line's y-intercept.

m = 4/5

c=-3

Consequently, the line's slope is 4/5. The solution is 4/5 if the line's equation is y = 4x/5 - 3.

The complete question is:-

What is the slope of the line represented by the equation y=4/5x-3?

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3.6432 rounded to the nearest hundredth

Answers

Answer: 3.64

Step-by-step explanation:

3.64

What is the Nearest Hundredth?

Nearest hundredth is the second digit after the decimal point.

How to Calculate Rounding to the Nearest 100th?

If the digit after hundredth is greater than or equal to 5, add 1 to hundredth. Else remove the digit. Example

124.586

The third digit of right of decimal point is 6

The second digit after decimal point is 8 which is greater than 5

So add 1 to 8

Result = 124.59

its 3.6400 I believe since you are rounding to the nearest hundredth which would be in the 2nd place value to the right of the decimal and 32 would round down to 0.

Simplify (−8b)(−15b).
120b2
−120b2
120b
−120b

Answers

Answer:

[tex]120b^2[/tex]

Step-by-step explanation:

When multiplying two terms, multiply the coefficients and the variables.

Also, remember the rules for multiplying integers:

negative * positive = negativenegative * negative = positivepositive * positive = positive

-8 * -15 = +120

b * b = [tex]b^2[/tex]

∴(-8b)(-15b) = [tex]120b^2[/tex]

[tex](-8b)(-15b)[/tex]

[tex](-8)\times b\times(-15)\times b[/tex]

[tex]120\times b^2[/tex]

[tex]=120b^2[/tex]

[tex]\fbox{Option A}[/tex]

some students equally share 8 baskets of pears. each basket has 11 pears. Write an algebraic expression to represent this situation. Then explain how you chose which variable and operations to use.

Answers

The algebraic expression for each student is 88/x

How to determine the algebraic expression to represent this situation

From the question, we have the following parameters that can be used in our computation:

Number of baskets = 8

Pears in each basket = 11

The total number of pear is calculated as

The total number of pear = Number of baskets * Pears in each basket

Substitute the known values in the above equation, so, we have the following representation

The total number of pear = 8 * 11

Evaluate

The total number of pear = 88

Represent the students with x

So, the expression is 88/x

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Please help!! very behind! 50 PTS

PICK BETWEEN:
ASSOCIATEIVE PROPERTY OF ADDITON
ASSOCIATIVE PROPERTY OF MULTIPLATION
COMMUNITAVE PROPERTY OF ADDITION
COMMUNITIVE PROPERTY OF MULTIPLICATION
DISTRIBUTIVE PROPERTY

Answers

Answer:

Line 1 to Line 2 = Distributive property

Line 2 to Line 3 = ASSOCIATIVE PROPERTY OF MULTIPLATION

Line 3 to line 4 = COMMUNITIVE PROPERTY OF MULTIPLICATION

Pls can you give me brainliest

pls :(

in example 11.3 (p. 270), when bob jumps on the cart, what kind of collision is this?

Answers

Since Bob jumps on the cart in example 11.3 (p. 270), a kind of collision which this represents is: d) Perfectly inelastic.

What is an elastic collision?

An elastic collision can be defined as a type of collision between two objects wherein the total kinetic energy of the two objects remains the same after the collision. This ultimately implies that, there isn't a net loss of momentum and kinetic energy within the system due to the collision.

What is an inelastic collision?

An inelastic collision can be defined as a type of collision between two objects wherein the total kinetic energy of the two objects changes the same after the collision. This ultimately implies that, there is a net loss of momentum and kinetic energy within the system due to the collision.

In this context, we can reasonably infer and logically deduce that the coefficient of restitution would be equal to zero (0) when bob jumps on the cart, resulting in a perfectly inelastic inelastic collision.

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Complete Question:

In example 11.3 (p. 270), when Bob jumps on the cart, what kind of collision is this?

a) Inelastic, but not perfectly inelastic

b) Rigid

c) Elastic

d) Perfectly inelastic.

plss hellppp, I've been stuckk on this questionn

Answers

Answer:

we can conclude that there are 3 solid combined in this

a + b + c = d as the total volume

[(6)(6)(2)] + [(6)(3)2)] + [(6)(2)(2)]

= 72 + 36 + 24

= 132 ft³

Step-by-step explanation:

heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ  -{ elyna s }-

I'm giving all the points I got man, pls help me with this geometry question

Answers

Answer:

Vertex = (0,0)

Focus = (0, -1/8)

Axis of symmetry; x = 0

directrix, y = 1/8

graph: (attached picture)

Step-by-step explanation:

heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ  -{ elyna s }-

Answer:

Vertex = (0,0)

Focus = (0, -1/8)

Axis of symmetry; x = 0

directrix, y = 1/8

Step-by-step explanation:

What is ten more than twenty?

Answers

10 more than 20 will be Addition of 10 and 20 which is supposed to be 10 plus 20 = 30.

Addition is the process of combining items and counting them as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.

The SUM is the result or conclusion that results from adding two or more integers. Addends are the numbers that are added.

We simply changed "more than" to "plus" and found the answer to the straightforward math issue. It is equivalent to 10 + 20 to add 10 to 20. Therefore, the answer is 30 once more.

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What are the 3 types of real numbers?

Answers

Three types of numbers fall under the heading of "real numbers," which we will discuss in a moment. Real numbers include all types of numbers, including whole, rational, and irrational numbers.

What is Real number?

A real number is a quantity that may be represented mathematically by an endless decimal expansion. In contrast to the counting-derived natural numbers 1, 2, 3,..., real numbers are used to quantify constantly altering quantities such as size and time. Rational and irrational numbers are both included in real numbers. Real numbers include both irrational and rational numbers such as 3, 22/7, and integers such as (-2, 0, 1), fractions such as (1/2), and decimal numbers such as (1/2).

whole = 0,1,2,3,4,5,6,7,8,9...….

rational = 1,2,3,3/4,5/6,...…

irrational =  [tex]\sqrt{8}[/tex], etc

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Which is not a solution to the inequality: 3x+13= -8.
A. -8
B. -7
C. -6
D.-5

Answers

Answer:

All the options except for option B.

Answer:

A,C and D are not.

where as B is solution

Shopkeeper compares sales of laptops in July and August
In August the price has increased by 1/3
And number sold has decreased by 2/5
What fraction does the income decrease in August

Answers

Answer: i think b

Step-by-step explanation:

find the probability with which bob plays l in the mixed strategy equilibrium (round your answer to the 4th decimal).

Answers

The probability with which bob plays l in the mixed strategy equilibrium = 0.9090

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here suppose Alice plays U with probability P and D * with probability ( 2 - P)

Therefore, when Bob plays L, Bob gets payoff 8 with probability P and (2) with probability ( 2 - P). Hence

= 8 * P + 2 * ( 2 - P)

= 8P +4 - 4P

= 4 + 8P

Also, when Bob plays R, Bob gets pay off 4 with probability P and 7 probability (2-P). Hence expected payoff is

= 4*P+7(2-P)

= 4P+14-7P

=14-3P

At mixed strategy nash equilibrium the expected payoffs are equal. hence,

4 +8P = 14-3P

3P+8P = 14-4

11P = 10

P = 10/11

P = 0.9090

In the mixed strategy equilibrium, Bob's chances of playing l are equal to 0.9090.

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Here suppose Alice plays U with probability P and D * with probability ( 2 - P)

Therefore, when Bob plays L, Bob gets payoff 8 with probability P and (2) with probability ( 2 - P). Hence

= 8 * P + 2 * ( 2 - P)

= 8P +4 - 4P

= 4 + 8P

Also, when Bob plays R, Bob gets pay off 4 with probability P and 7 probability (2-P). Hence expected payoff is

= 4*P+7(2-P)

= 4P+14-7P

=14-3P

At mixed strategy nash equilibrium the expected payoffs are equal. hence,

4 +8P = 14-3P

3P+8P = 14-4

11P = 10

P = 10/11

P = 0.9090

In the mixed strategy equilibrium, Bob's chances of playing l are equal to 0.9090.

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