if two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}? hint [see example 2.]

Answer:

Perpendicular

Step-by-step explanation:

We can change the number of shapes on it by putting one rectangle to the right and put two triangles to the left.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Let's say the circle is A, Triangle is B, and Rectangle is C.

2A + 4C = 2A + 4B + 2C

So, C = 2B    ( 4C = 4B + 2C, 2C = 4B, C = 2B)

That one rectangle and two triangles are equally weighed. So, put one rectangle to the right and put two triangles to the left. The hanger is still in the balance.

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The possible probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice is 0.2.

Probability is a branch of math that studies the chance or likelihood of an event occurring.
A biased dice was rolled and the probability distribution of the outcomes are as follows then the outcomes are [tex] 1, 2, 3, 4, 5, 6[/tex]

Probability: [tex]0.2, 0.1, 0.3, 0.1, 0.2, 0.1[/tex]

To find the probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice.

Probability of getting [tex]3[/tex]:

Outcome = [tex]3[/tex]

Probability of getting = [tex]^3P(3) = 0.3[/tex]

So, the possible probability of getting [tex]3[/tex] is [tex]0.3[/tex].

Probability of getting [tex]5[/tex]

So, the outcome of [tex]5[/tex]

Probability of getting [tex]^5P(5) = 0.2[/tex]

So, the possible probability of getting 5 is 0.2.

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Each pair of numbers (m, h) which meet the inequality is the answer to the inequality. m < h plus 2.

A factor pair is a collection of two factors that, when multiplied together, produce a certain result in mathematics. In those other words, it's a pair of integers that we multiply to produce a result. For instance, the factor pair that yields the result in the multiplication formula 6 7 = 42 is composed of the numbers 6 and 7. 42

By adding 14 to both sides, starting with -14 + 7m 7h, we may simplify the left side:

-14 + 7m plus 14 < 7h plus 14

Even more condensed, we get at:

7m < 7h plus 14

The inequality can then be divided by 7 on both sides: m h + 2.

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Answer:

Step-by-step explanation:

We can set up a proportion to solve this problem:

(height of boy) / (length of boy's shadow) = (height of man) / (length of man's shadow)

We are given that the boy is 3 feet tall and his shadow is 7 feet long. Let's use "h" to represent the height of the man. We are also given that the man's shadow is 14 feet long. Substituting these values into the proportion, we get:

3/7 = h/14

To solve for h, we can cross-multiply and simplify:

3 × 14 = 7h

42 = 7h

h = 42/7

h = 6

Therefore, the man is 6 feet tall.

The required probability is obtained as:

(a) P(X^2 < 1) = 0.8413.

(b) P(X^2 + Y^2 < 1) = 0.7854.

(a) We know that X^2 follows a chi-squared distribution with 1 degree of freedom, which can be written as X^2 ~ chi-squared(1). Therefore, we can find P(X^2 < 1) as:

P(X^2 < 1) = P(Z < √1) (where Z ~ chi-squared(1))

Since the square of a standard normal distribution is a chi-squared distribution with 1 degree of freedom, we can rewrite the above equation as:

P(X^2 < 1) = P(Z < 1) (where Z ~ N(0,1))

Using a standard normal distribution table or calculator, we can find that P(Z < 1) = 0.8413. Therefore, P(X^2 < 1) = 0.8413.

(b) We can rewrite X^2 + Y^2 < 1 as the inequality r^2 < 1, where r is the distance from the origin to the point (X,Y) in the xy-plane. Therefore, we need to find the probability that the point (X,Y) falls within the unit circle centered at the origin.

We can use polar coordinates to express X and Y as:

X = Rcosθ

Y = Rsinθ

where R is the distance from the origin to (X,Y), and θ is the angle between the positive x-axis and the line connecting the origin and (X,Y). Since X and Y are independent N(0,1) random variables, R^2 = X^2 + Y^2 follows a chi-squared distribution with 2 degrees of freedom, which can be written as R^2 ~ chi-squared(2).

Therefore, we can find P(X^2 + Y^2 < 1) as:

P(X^2 + Y^2 < 1) = P(R^2 < 1) (where R^2 ~ chi-squared(2))

Using the cumulative distribution function (CDF) of the chi-squared distribution with 2 degrees of freedom, we can find that:

P(R^2 < 1) = 0.7854

Therefore, P(X^2 + Y^2 < 1) = 0.7854.

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Answer: Let's start by using algebra to represent the given information.

If we let "a" be Anita's current age, then we know that Sarun's current age is 3a (since he is thrice as old as Anita).

According to the problem, if we subtract 5 years from Anita's age and add 7 years to Sarun's age, then Sarun will be 5 times Anita's age. In other words, we have the equation:

3a + 7 = 5(a - 5)

Simplifying and solving for a, we get:

3a + 7 = 5a - 25

32 = 2a

a = 16

So Anita is currently 16 years old, and Sarun is 3 times as old, or 48 years old.

To find out how old they were three years ago, we simply subtract 3 from their current ages:

Anita was 13 years old three years ago (16 - 3), and Sarun was 45 years old (48 - 3).

Step-by-step explanation:

The domain of discourse of the propositional function P(x) is {1,2,3,4}, by using negation, disjunction, and conjunction are:

a)  "there does not exist an x in the domain for which P(x) is false."

b) "there exists an x in the domain for which P(x) is false."

c)  "there exist exactly three x's in the domain for which P(x) is true."

d) -(E. P(x)) can be rewritten as “Every x is not P(x)”

We are given that the domain of discourse of the propositional function P(x) is {1, 2, 3, 4}. We need to rewrite each propositional function below using only negation, disjunction, and conjunction.

a) The propositional function "Vx P(x)" means "for all x in the domain, P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:

-(Ex -P(x)), which means "there does not exist an x in the domain for which P(x) is false."

b) The negation of "Vx P(x)" is "there exists an x in the domain for which P(x) is false." Using De Morgan's law again, we can rewrite this as:

Ex -P(x).

c) The propositional function "3x P(x)" means "there exist exactly three x's in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can break it down into two statements:

Using the symbols for negation, disjunction, and conjunction, we can write this as:

(Ex_1 P(x_1) ∧ Ex_2 P(x_2) ∧ Ex_3 P(x_3)) ∧ -(Ex P(x)).

d) The propositional function "-(E. P(x))" means "it is not true that there exists an x in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:

Ax -P(x),

which means "for all x in the domain, P(x) is false."

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The value of (37)-2 is 1/1369, in its simplest form as an improper fraction.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In other words, it is a fraction that is larger than a whole number.

When an expression is written in the form of [tex]x^{(-n)[/tex], it means the reciprocal of [tex]x^n.[/tex] In this case, we have the expression[tex](37)^{(-2)[/tex] which means the reciprocal of 37².

The expression (37)-2 means 37 raised to the power of -2, or 1/(37²). To simplify this fraction, we can multiply the numerator and denominator by 1,296 (37²):

1/(37²) = 1 * 1 / (37 * 37)

= 1/1369

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Answer:<x=105

Step-by-step explanation:

180-75=105

The graph of the function f(x) = x - 2 is a straight line that passes through the origin and has a slope of 1.

Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.

This means that for every unit increase in x, the value of f(x) increases by 1 unit. Therefore, when x is equal to 0, the value of f(x) is equal to -2. When x is equal to 1, the value of f(x) is equal to -1. When x is equal to 2, the value of f(x) is equal to 0. When x is equal to 16, the value of f(x) is equal to 14. As you can see, for every increase in x, the value of f(x) increases by 2 units.  This is the reason why the line drawn from the value of x to the corresponding value of f(x) increases by 2 units when x is increased by 1 unit.

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In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).

Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.
In this example, the function f(x) = x-2 is being represented by a line that connects each value of x to the corresponding value of f(x).

When x = 4,

then f(x) = 4-2

f(x) = 2,

so the line extends from (4, 2) to the origin (0, 0).

Similarly, when x = 0,

then f(x) = 0-2

f(x) = -2,

so the line extends from (0, -2) to (4, 2).

When x = 1,

then f(x) = 1-2

f(x) = -1,

so the line extends from (1, -1) to (4, 2).

Finally,

when x = 2,

then f(x) is undefined.

In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).

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The series of transformations consists of a translation down two units and a reflection across the y-axis. Thus, option C is correct.

The points A and C will be replaced with D and F, respectively, by a reflection across the y-axis, leaving B in the same location. As a result, the image of AABC is given, A'D'BCF.

The final image, denoted by the letters ADEF, is produced by translating all the points of the image A'D'BCF' down by two units.

ADEF and AABC are not in the same location, even if they are the same height and shape.

The first thing we notice is that ADEF and AABC are oriented the same way, so we don't need to rotate them. Instead, by utilising a reflection over the y-axis, we may swap out the places where A and B were for D and E, respectively.

A'B'C' is still not in the appropriate place even though it is 2 units to the left of ADEF. Hence, we must translate 2 units down in order to position A'B'C' where ADEF is.

Therefore, A reflection across the y-axis and a translation 2 units down.

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Answer:

The answer to your problem is, -3000

Step-by-step explanation:

:Write down the points through which the line passes through

:The line is passing through a point at (0, 80000) and (10, 50000)

Next, ( important )

Find the slope of the line

Since the line is passing through the point (0, 80000) and (10, 50000)

So the slope of the line:

= m

[tex]\frac{80,000 - 50,000}{0 - 10}[/tex]

= [tex]\frac{30,000 }{-10}[/tex]

= -3,000

Techniquelly the answer is, 30,000 but for more explanation here it is :)

Find the number that will complete the point-slope equation that models this scenario

The required point-slope equation that models this scenario is

[tex]y - y_{1} - m( x - x_{1} )[/tex]

y - 50,000 = -30,000 ( x - 10 )

Thus the answer to your problem is, - 3,000

Any questions? Write them down below \/

Answer:

We need to prove that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.

Let's consider an isosceles triangle ABC where AB = AC. We draw the altitude from A to BC and call the point where it intersects BC as D.

Now, we need to prove that AD is the angle bisector, median, and altitude to the base BC.

To prove AD is the angle bisector:

We need to prove that the angle ADB and ADC are equal. We know that angle ABD and angle ACD are right angles because BD and CD are altitudes. We also know that AB = AC because the triangle is isosceles. Therefore, the triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion.

Thus, angle ADB = angle ADC, which means that AD is the angle bisector of angle BAC.

To prove AD is the median:

We need to prove that BD = CD. Since AB = AC and AD is perpendicular to BC, triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion. Therefore, BD = CD, which means that AD is also the median to the base.

To prove AD is the altitude:

We need to prove that angle BAD and angle CAD are right angles. This is true because AD is perpendicular to BC, and BD and CD are also perpendicular to BC. Therefore, AD is also the altitude to the base BC.

Hence, we have proved that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.

Check the picture below.

Answer:

x=-3

Step-by-step explanation:

The number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.

The population of Drosophila has 1000 individuals, 360 of which display the recessive phenotype. Homozygous dominant and heterozygous for this trait in Drosophila would be expected to be found in how many individuals?

In Drosophila, the dominant allele for normal-length wings is denoted as 'V' and the recessive allele for vestigial wings is denoted as 'v.'To determine the number of individuals who are homozygous dominant or heterozygous for this trait, we'll first determine the number of individuals who are homozygous recessive:

Homozygous recessive individuals in the population = number of individuals displaying the recessive phenotype = 360

This indicate that there are 360 individuals with the genotype vv (homozygous recessive), which will be used to determine the remaining genotypes via the Punnett square. To get the number of individuals who are heterozygous (Vv), we first need to identify the number of individuals with the dominant V allele (VV and Vv). The sum of these two genotypes equals the total number of individuals minus the homozygous recessive individuals, as follows:

Total number of individuals - homozygous recessive individuals = (VV + Vv) individuals+ (vv) individuals = 1000 individuals

Hence, VV + Vv = 1000 - 360 = 640 individuals.Now that we know VV + Vv = 640, we can use the expected genotypic ratio of 1:2:1 to calculate the number of homozygous dominant (VV) and heterozygous (Vv) individuals.1:2:1 represents the expected genotypic ratio in the progeny derived from a cross involving two heterozygotes of the same gene. The first "1" represents the proportion of dominant homozygotes, the second class, or class "2", the heterozygotes, and the second "1" the recessive homozygotes.

Therefore, homozygous dominant (VV) and heterozygous (Vv) individuals in the population would be expected in the following ratio:VV:Vv:vv = 1:2:1. Therefore, the number of individuals who are homozygous dominant (VV) is 1/4 of the total individuals (VV + Vv + vv):

Number of individuals who are homozygous dominant (VV) = 1/4 (VV + Vv + vv)= 1/4 (640) = 160 individuals

And the number of individuals who are heterozygous (Vv) is 2/4 of the total individuals (VV + Vv + vv):

Number of individuals who are heterozygous (Vv) = 2/4 (VV + Vv + vv)= 2/4 (640) = 320 individuals

Therefore, the number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.

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Answer:

-15

Step-by-step explanation:

4.1.60 - (15) + (-13) = 32

4.2. -2(3) + 27 ÷ (-3) = -2(3) - 9 = -15

In the equation A’ = 364V relating the surface area A and the volume V of a spherical balloon. We are also given that the volume is increasing at a rate of 18 cubic inches per second.so the rate at which the surface area of the balloon is increasing is 6552 square inches per second

We want to find the rate at which the surface area is increasing when A = 153.24 square inches and V = 178.37 cubic inches.

To find the rate of change of A with respect to time, we can use the chain rule of differentiation:

dA/dt = dA/dV × dV/dt

We know that dV/dt = 18 cubic inches per second, so we just need to find dA/dV and then we can find dA/dt.

To find dA/dV, we differentiate the equation A’ = 364V with respect to volume V:

dA/dV = 364

Now we can find dA/dt:

dA/dt = dA/dV × dV/dt ⇒ 364 × 18 ⇒ 6552 square inches per second

So the rate at which the surface area of the balloon is increasing is 6552 square inches per second when A = 153.24 square inches and V = 178.37 cubic inches.

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Answer:

36 × 10^6 m²

Step-by-step explanation:

Given the side length of a square = 6 × 10³m,

To solve for the area of a square, use the following formula:

A = S² where:

S = side of the square

Substitute the given value for the side into the formula:

A = S²

A = (6 × 10³)²

A = 36000000 or 36 × 10^6 m²

NOTE:

6 × 10³ is also the same as 6 × 1000 = 6000,

(6 × 10³)² is essentially 6,000² = 36,000,000

Therefore, its area in square meters is 36 × 10^6

To form a parallelogram, the opposite sides of the quadrilateral should be parallel. Let's find the coordinates of point D such that AB is parallel to DC.

The slope of line AB = (yB - yA) / (xB - xA) = (6 - 1) / (-2 - 3) = -1

Therefore, the slope of line DC should also be -1.

Let's assume the x-coordinate of point D is xD.

The slope of line CD = (yD - yC) / (xD - xC)

Since the slope of CD is -1, we can write:

(yD - yC) / (xD - xC) = -1

yD - yC = -(xD - xC)

yD = -(xD - xC) + yC

Substituting the coordinates of points C and A, we get:

yD = -(xD - 6) + 4

yD = -xD + 10

Therefore, the coordinates of point D are (xD, -xD + 10).

To find the x-coordinate of point D, we can use the fact that BC is parallel to AD.

The slope of line BC = (yC - yB) / (xC - xB) = (4 - 6) / (6 + 2) = -1/4

Therefore, the slope of line AD should also be -1/4.

The slope of line AD = (yD - yA) / (xD - xA)

Substituting the coordinates of points A and D, we get:

(yD - 1) / (xD - 3) = -1/4

yD - 1 = -(xD - 3) / 4

yD = -(xD - 3) / 4 + 1

yD = -xD/4 + 5/4

Substituting the equation we found for yD in terms of xD, we get:

-xD/4 + 5/4 = -xD + 10

3/4 xD = 35/4

xD = 35/3

Therefore, the coordinates of point D are (35/3, -35/3 + 10) = (35/3, 5/3).

We can now plot the points A, B, C, and D on the coordinate axes, and verify that they form a parallelogram.

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The value οf sin F is 5/6.

The branch οf Mathematics which helps in dealing with measure οf three sides οf a right-angled triangle is called Trigοnοmetry.

sin θ  = Perpendicular/Hypοtenuse

cοs θ = Base/Hypοtenuse

tan θ = Perpendicular/Base

cοsec θ = Hypοtenuse/Perpendicular

sec θ = Hypοtenuse/Base

cοt θ = Base/Perpendicular

Cοs D = 5/6 (given)

We knοw, cοs θ =Base / Hypοtenuse

Thus, base = 5  and hypοtenuse = 6

Therefοre, DE = 5 and DF = 6

Sin  θ = Perpendicular / Hypοtenuse

Sin F = DE / DF

Sin F = 5/6

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Answer:

Choice 2
∠1 and ∠7, ∠2 and ∠8

Step-by-step explanation:

This is a good example of a problem that can be solved by POE(process of elimination)

First choice: ∠2 and ∠3 are on the same straight line so they cannot be congruent. They are supplementary in that they add up to 180°

The same applies for ∠3 and ∠4 (third choice)

The same applies for ∠1 and ∠4 (fourth choice)

That leaves choice 2

We can prove ∠1 ≅ ∠7 as follows:

∠1 ≅ ∠3 since they are vertically opposite angles

∠3 ≅ ∠7 since they are exterior angles

So ∠1 ≅ ∠7

By similar reasoning,
∠2 ≅ ∠8

So correct choice is Choice 2

The probability that a randomly selected student likes coconut is 0.6.

Step-by-step explanation:

Given that,

Now we have to find the probability that a randomly selected student likes coconut.

P (student likes coconut) = the number of students who liked coconut / total number of students

= 60/100

= 0.6

Therefore, the probability that a randomly selected student likes coconut is 0.6.

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It would take the three of them about 6 hours to paint the four rooms.

Let t represent the time that it would take all three of them to paint one room.

It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room.

Therefore:

(1/6 + 1/4 + 1/8)t = 1

(2/3)t = 1

t = 1.5 hours

It would take all of them 1.5 hours each to paint one room.

For 4 rooms:

Total time = 1.5 hours * 4 = 6 hours

It would take the three of them about 6 hours to paint the four rooms.

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Answer:

A: -3/2

Step-by-step explanation:

-4x²-12x-9=0 First split the b value so that it equals a×c, or -4×-9

-4x²-6x-6x-9=0 Factor by grouping

(-2x-3)(2x+3)=0 Solve for x

x= -3/2

Answer:

Step-by-step explanation:

is 8,15,24

The probability of a printer failure given hardware problems is 0.9, given software problems are 0.2, and given any other type of problem is 0.5. The customer should diagnose the printer failure by looking for a hardware issue.

The probability of printer failure is dependent on three problem types, hardware, software, and others (like connectors). The respective probabilities are 0.1_, 0.6, and 0.3_.

We have hardware problems, the probability of printer failure is 0.9, given software problems the probability is 0.2, and given any other problem type the probability is 0.5. By using Bayes' theorem, the most probable cause of the failure can be determined.

Let A represent the cause of the problem, and B is the evidence that the customer sees. Let's calculate the probability that A = hardware given B, which is P(A|B) = P(B|A)*P(A)/P(B).

Here, P(A) is the prior probability of the cause being hardware,

P(B|A) is the likelihood of observing the evidence given the cause being hardware, and P(B) is the probability of observing the evidence.

Given hardware problems, the probability of printer failure is 0.9, while the probability of observing this evidence given hardware problems is 0.9. Since there are three problem types, each of them having a prior probability of 1/3, we get P(A) = 1/3.

The probabilities of observing the evidence in the case of other types of problems and software problems are 0.5 and 0.2, respectively. Therefore, the most likely cause of printer failure is hardware problems.

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In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers.

The probability of guessing on an exam can be calculated by using the formula:n(C)/(n(T))where n(C) is the number of favorable events and n(T) is the total number of events. Let's solve the given problem:

Probability of getting the first question correct: P (1st) = 1/4 Probability of getting the second question correct: P (2nd) = 1/4Probability of getting the third question correct: P (3rd) = 1/4 Probability of getting the fourth question correct: P (4th) = 1/4Probability of getting the fifth question correct: P (5th) = 1/4 The probability of guessing all questions correctly can be calculated by multiplying the probability of each question together. P (all) = P (1st) * P (2nd) * P (3rd) * P (4th) * P (5th)= 1/4 * 1/4 * 1/4 * 1/4 * 1/4= 1/1024Therefore, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977. (rounded to four decimal places)Answer: 0.000977

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Answer:

1

----

20

Step-by-step explanation: Total there are 20 Combinations as 5*4 = 20 ab>0 when b