The radius of a quarter circle is 2 yards. What is the quarter circle's perimeter?

The differential equation of y'' + 3y' + 2y = 1/4+ex is

               [tex]y=c_{1} e^-^2^x+c_{3} e^-^x+4e^-^2^xln(4+e^x)+e^xln(4+e^x)[/tex]

The given differential equation is y'' + 3y' + 2y = 1/4+ex

As we are considering the LHS part looks like a Quadratic equation.

y''+3y'+2y=m²+3m+2

m²+3m+2=0 ---(1)

finding the roots for eq(1)

m²+2m+m+2=0

m(m+2)+1(m+2)

(m+2) (m+1)=0

m=-2,m=-1

Yc=C₁e⁻²ˣ+C₂eˣ   ----(2)

equation (2) is called a complementary function.

A complementary function is only one part of the solution to a linear, and autonomous differential equation.

An ordinary differential equation (ODE) defines the sum of a function and its derivatives. When the explicit functions y = f(x) + cg(x) form the solution, g is called the complementary function; f is the particular integral.

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Answer: 187.567 < 187.68

Step-by-step explanation:

0.6 is larger than 0.5 so 187.68 is bigger than 187.567

Answer:

x ≥ -3 3/4

Step-by-step explanation:

-1/3x + 1/2 ≥ -3/4

1/3x ≥ -5/4

x ≥ -3 3/4

A graph of each function is shown in the image attached below.

The number of commercials (x) is equal to 7 commercials while the number of movies (y) is equal to 2 movies.

In order to graphically solve the system of equations, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:

Since Victoria would earn $40 every time one of her songs is played in a commercial and $140 every time one of her songs is played in a movie, an equation which models it is;

40x + 140y = 560

Additionally, Victoria earned a total of $560 in royalties on 9 commercials and movies;

x + y = 9

Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (7, 2) as shown in the image attached below.

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The area for the trapezoid is 35 square inches. Last option

The formula for the decomposition method of finding trapezoid is given as: ( x + y ) / h

The variables are given as

x = 3

y = 4

h = 5

we would have to fix the values into the formula in order to get the area of the trapezoid

Hence we would have

( 3 + 4) * 5

7 * 5

= 35 square units

Hence the area of the trapezoid by decomposition is given as 35 square units.

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The approximate number of packets containing blades with no defective is :  9802

We are given the probability of defect per blade = 1/500 = 0.002

The general formula for Poisson distribution is;

Pₓ (k) = (x^k)/k × e⁻ˣ

Where;

k = The number of defective blades in a packet.

For a packet of 10 blades the mean number of defect is;

x = 0.002 × 10

x = 0.02

When there is no defective in a consignment, then it means k = 0

Thus;

Pₓ(0) = (0.02⁰ / 0!) × e^(-0.02) = 0.980199

The approximate number of packets containing blades with no defective is : 10000 × 0.980199 = 9802

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On solving the provided question we can say that the Volume of the sphere with radius 11.2 in is 5885 .

A sphere is a geometrical entity that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its center.

characteristics of a sphere

The symmetry of a sphere is flawless.

A polyhedron is not a sphere.

Each point on the surface is equally spaced from the center.

There is no surface of centers on a sphere.

The mean curvature of a sphere is constant.

The breadth and circumference of a sphere are fixed.

Radius of sphere = 11.2 in

Volume = 4 pi r ^ 2 = 4 X 3.14 X 11.2 X 11.2 = 5885 .

Volume of the sphere with radius 11.2 in is 5885 .

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On solving the provided question we can say that the Volume of the sphere with radius 11.2 in is 5885 .

A sphere is a geometrical entity that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its center.

characteristics of a sphere

The symmetry of a sphere is flawless.

A polyhedron is not a sphere.

Each point on the surface is equally spaced from the center.

There is no surface of centers on a sphere.

The mean curvature of a sphere is constant.

The breadth and circumference of a sphere are fixed.

Radius of sphere = 11.2 in

Volume = 4 pi r ^ 2 = 4 X 3.14 X 11.2 X 11.2 = 5885 .

Volume of the sphere with radius 11.2 in is 5885 .

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Answer:

y = 1/3x

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (0,0) (3,1), we see the y increase by 1 and the x increase by 3, so the slope is

m = 1/3

The y-intercept is located at (0,0)

So, our equation is

y = 1/3x

Answer:

1.23 calculator on cellphone do have that apps

Answer: 1.23

Step-by-step explanation: To find this answer, we need to move the decimal place. So, the 7 will move 1 place to the right of the 7, and then the decimal place will move to the right of the 8. So, now it should look like this:

[tex]\frac{08.61}{7}[/tex]

Then, divide using long division. You should get 1.23. To check, you can multiply 1.23 by 7, to get the dividend, 0.861. I hope this helped!

Answer:

[tex]c = \sqrt{74}[/tex]

Step-by-step explanation:

To find the distance between the two, we will use the Pythagorean theorem ([tex]a^{2} + b^{2} = c^{2}[/tex]). To find a and b, we need to subtract the distances between the y coordinates and the x coordinates respectively. For the x coordinates, we have 8 - 1 = 7 units. For the y coordinates, we have 7 - 2 = 5. Plugging this into our equation gives us:

[tex]7^{2} + 5^{2} = c^{2}[/tex]

We will simplify our exponents:

[tex]49 + 25 = c^{2}[/tex]

Then adding them together gives us:

[tex]74 = c^{2}[/tex]

Then, we square root both sides giving us:

[tex]\sqrt{74} = c[/tex]

Then, we cannot simplify past this, since 74's prime factorization doesn't allow it. So, [tex]c = \sqrt{74}[/tex].

Hope this helped!

Answer:

the patient would receive 375 mL of fluid in 3 hours.

Step-by-step explanation:

To calculate the amount of fluid a patient would receive in 3 hours, we can use the formula:

Flow rate (mL/hr) = Total volume (mL) / Time (hr)

Flow rate = 1000 mL / 8 hr = 125 mL/hr

To find the amount of fluid a patient would receive in 3 hours, we can use the formula:

Volume = Flow rate x Time

Volume = 125 mL/hr x 3 hr = 375 mL

So the patient would receive 375 mL of fluid in 3 hours.

The numeric values of each function at x = 3 are given as follows:

f(3) = 50.

g(3) = 10.

The division is given as follows: f(3)/g(3) = 5.

The space of f(x)/g(x) is given as all genuine values with the exception of x = - 7, as the function g(x), which is the denominator of the division, expects a worth of 0 at x = - 7.

To track down the numeric worth of a function or of articulation, we supplant each example of the variable in the function or in the articulation with the worth at which we need to track down the numeric worth.

Subsequently, the numeric values are found to supplant the solitary example of x by 3 in each function, as follows:

f(3) = 5(3) + 35 = 15 + 35 = 50.

g(3) = 3 + 7 = 10.

Subsequently, the division is given as follows:

(f/g)(3) = f(3)/g(3) = 50/10 = 5.

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The eigenvalues of the matrix are -1,1,3 and the corresponding eigenvectors are [-1,2,2], [1,-1,-1], [1,1,1] respectively.

The matrix is given as

2 1 -1

3 2 -3

3 1 -2

To find the eigenvalues and eigenvectors of a matrix A, we need to solve the following equation:

Av = λv

where v is the eigenvector and λ is the eigenvalue.

So, we have

(2 1 -1) (x) = λ (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

We can find the eigenvalues by solving the characteristic equation which is det(A-λI) = 0.

The characteristic equation for the above matrix is

(2-λ)((-λ-2)(-λ+1) - 2) - 3(1)(-λ+1) + 3(1)(-λ-2) = 0

Solving the above equation we get λ = -1,1,3

Now we can find the eigenvectors for each eigenvalue.

For λ = -1

(2 1 -1) (x) = -1 (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

Solving the above equation we get x = -1, y = 2 and z = 2. So the eigenvector is [-1,2,2].

For λ = 1

(2 1 -1) (x) = 1 (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

Solving the above equation we get x = 1, y = -1 and z = -1. So the eigenvector is [1,-1,-1].

For λ = 3

(2 1 -1) (x) = 3 (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

Solving the above equation we get x = 1, y = 1 and z = 1. So the eigenvector is [1,1,1].

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The value of -0.6675 for the correlation coefficient of X and Y indicates that there is a negative correlation between the two variables.

The correlation coefficient, denoted as p, is a measure of the linear relationship between two random variables X and Y. It is defined as the ratio of the covariance of X and Y to the product of their standard deviations:

p = cov(X,Y) / (stdDev(X) × stdDev(Y))

To compute the correlation coefficient, we need to first calculate the covariance and the standard deviations of X and Y.

Since the marginals pdfs of X and Y are the same, we know that the expected value (mean) of X is equal to the expected value of Y, which is denoted as Mu x = Mu y = A.

The expected value of XY is given as E(XY) = 2/5.

The covariance of X and Y is defined as E((X-Mu x )(Y-Mu y )), which simplifies to E(XY) - Mu x × Mu y

Substituting the given values, we have:

cov(X,Y) = E(XY) - Mu x × Mu y = 2/5 - A²

To calculate the standard deviation of X and Y, we need to calculate the variance first. The variance of X is defined as E(X²) - (Mu x )²,

which can be easily calculated by replacing x with y in fx(x) and applying the same formula.

The standard deviation is the square root of the variance, so we have:

stdDev(X) = √(variance(X)) = √(E(X²) - (Mu x )²)

stdDev(Y) = √(variance(Y)) = √(E(Y²) - (Mu y )²) = √(E(X²) - (Mu x )²)

Now we can substitute these values into the formula for p:

p = cov(X,Y) / (stdDev(X) × stdDev(Y)) = (2/5 - A²) / (√(E(X²) - (Mu x )²) × √(E(X²) - (Mu x )²)).

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The equation of the line passing through the points (0, 3) and (-5, 0) is y = -3/5 x + 3

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.

Here,

To find the equation of the line passing through the points (0, 3) and (-5, 0), we can use the slope-intercept form and the slope formula:

m = (y2 - y1) / (x2 - x1) = (0 - 3) / (-5 - 0) = -3/5

where (x1, y1) = (0, 3) and (x2, y2) = (-5, 0) are the coordinates of the given points.

Now we can substitute the value of m and the coordinates of one of the points into the equation of the line to find the value of b:

y = mx + b

3 = (-3/5)*0 + b

b = 3

So the equation of the line passing through the points (0, 3) and (-5, 0) is:

y = -3/5 x + 3

We can also convert the equation to point-slope form as :

y - y1 = m(x - x1)

y - 3 = (-3/5)(x - 0)

y - 3 = -3/5 x

y = -3/5 x + 3

Hence, the equation of the line passing through the points (0, 3) and (-5, 0) is y = -3/5 x + 3

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Doing moves to keep an equation balanced is a powerful part of solving equations, but thinking about what the structure of an equation tells us about the solutions is just as iimportant

Sometimes it’s possible to look at the structure of an equation and tell if it has infinitely many solutions or no solutions. For example, look at

2(12x + 18) + 6 = 18x + 6(x + 7)

Using the distributive property on the left and right sides, we get

24x + 36 + 6 = 18x + 6x + 42

From here, collecting like terms gives us

24x + 42 = 24x + 42

Since the left and right sides of the equation are the same, we know that this equation is true for any value of x without doing any more moves!

Similarly, we can sometimes use structure to tell if an equation has no solutions. For example, look at

6(6x + 5) = 12(3x + 2) + 12

If we think about each move as we go, we can stop when we realize there is no solution

1/6 · 6(6x + 5) = 1/6 · (12(3x + 2) + 12) Multiply each side by 1/6

6x + 5 = 2(3x + 2) + 2 Distribute 1/6 on the right side.

6x + 5 = 6x + 4 + 2 Distribute 2 on the right side.

The last move makes it clear that the constant terms on each side, 5 and 4 + 2, are not the same. Since adding 5 to an amount is always less than adding 4 + 2 to that same amount, we know there are no solutions.

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The line parallel to Line 1 which is given by the equation: −6y + 3x = 12 and passes through (−1, − 5) is written in slope intercept form as

\y = 0.5x - 4.5

A linear function consists of functions where the variables has exponents of 1. the relationship is expressed in the slope intercept form as below.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The given equation is rewritten in slope intercept form as follows

−6y + 3x = 12

−6y = 12 - 3x

y = 1/2 x - 2

the slope is 1/2

equation of the line of slope = 1/2 passing through point (-1, -5) is calculated using the point slope formula which is

(y - y') = m(x - x')

(y + 5) = 1/2(x + 1)

y + 5 = 1/2 x + 1/2

y = 1/2 x + 1/2 - 5

y = 0.5x - 4.5

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A graph which could represent a cubic function include the following: C. Graph C.

In Mathematics, a function is a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.

In Mathematics, a cubic function is sometimes referred to as a cubic polynomial and it can be defined as a type of polynomial in which the degree of the highest term (coefficient or exponent) is equal to three (3).

In this context, we can reasonably infer and logically deduce that a graph that represents a cubic function is graph C because it models this polynomial y = x³.

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To add 2 1/2 + 4/5 using a number line, we can start by marking off the whole numbers along the number line. Then, we can divide each whole number into equal parts to represent the fractions. For example, if we divide each whole number into fifths, we can mark off 2 1/5, 2 2/5, 2 3/5, etc.

After the above, the next thing is that we can find the point on the number line that represents 2 1/2 by starting at 2 and moving 1/5 of the way to the right. Similarly, we can find the point that represents 4/5 by starting at 4 and moving 1/5 of the way to the right.

Finally, to add the two numbers, we can simply move from the point that represents 2 1/2 to the point that represents 4/5. The final point we reach will be the sum of 2 1/2 + 4/5. In this example, the final point will be 3 3/10.

Therefore, 2 1/2 + 4/5 will be 3 3/10.

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Two equivalent fractions to 2/25 are given as follows:

4/50 and 8/100.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

The terms are classified as follows:

Two fractions are called equivalent when the ratio between their numerators and denominators is the same.

The fraction in this problem is defined as follows:

2/25.

To obtain an equivalent fraction, we multiply both the numerator and denominator by the same constant, hence:

The problem asks for two equivalent fractions to 2/25.

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Under the translation (x, y) (x-2, y-3) via transformation, the translation image of (2, -6) is (0, -9)

A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations.  Each change must be carried out, and you must be able to tell which transformations have been carried out. The function translation and transformation guidelines are: F (x) + b moves the function up by b units. The function is moved downward by f (x) b. The function is moved left b units by the formula f (x + b).

given

(2 , -6 )

under this (x, y) → (x-2, y-3)

( 2 - 2, -6 , -3 )

(0 , -9)

Under the translation (x, y) (x-2, y-3) via transformation, the translation image of (2, -6) is (0, -9) .

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The fifth term of the binomial expansion is; 76545x³y⁴

We are given the algebraic expression as; (3x - 3y)⁷

To solve this problem, we will make use of Pascals triangle which is the triangular array of numbers that begins with 1 on the top and with 1's running down the two sides of a triangle. Each new number will lie between two numbers and below them, and its value is the sum of the two numbers above it. It is expressed as;

                                 1

                        1              1

                 1              2              1

            1            3             3           1

      1         4             6            4           1

   1       5         10           10          5          1

1     6        15         20          15         6        1

1   7      21        35          35         21       7        1

Using binomial expansion, we have;

(3x - 3y)⁷ = 1(3x)⁷(-3y)⁰ + 7(3x)⁶(-3y)¹ + 21(3x)⁵(-3y)² + 35(3x)⁴(-3y)³ ...... 1(3x)⁰(-3y)⁷

= 2187x⁷ - 15309x⁶y + 45927x⁵y² - 76545x⁴y³ + 76545x³y⁴ - 45927x²y⁵......

The fifth term here is; 76545x³y⁴

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The length of the midsegment of 28. is 17 units and 29. is 27 units.

A line drawn by joining the midpoints of any two of the triangle's sides is known as the midsegment. All three sides of a triangle can be divided in half, with the midpoint being the point that is equally spaced from either vertex, regardless of whether the triangle is a right triangle, isosceles triangle, or sometimes an equilateral triangle.

If the slope and sides are same then we can cut the midsegment ad paste it such that it becomes an rectangle.

28. Now the length of the rectangle = n + 12 + n + 12 = 4n + 6 + 2n - 2

⇒ 2n + 24 = 6n +4

⇒ 20 = 4n

⇒ n = 20/4

⇒ n = 5

Length of midsegment = 5 + 12

                                       =  17 units

29. Now the length of the rectangle = 2n+ 11 + 2n+ 11 = 5n - 2 + n + 8

⇒ 4n + 22 = 6n + 6

⇒ 16  = 2n

⇒ n = 16/2

⇒ n = 8

Length of midsegment = 2(8) + 11

                                       =  27 units

Thus, he length of the midsegment of 28. is 17 units and 29. is 27 units.

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Answer: 3

Step-by-step explanation: Whenever we have midsegment, the length of it is half of the base which is 30 so 5x =15.

For p = (3, 5), the value of - 3p is (- 9, - 15).

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The values are,

⇒ p= (3, 5) and q = (-2, 10)

Now, We can find the value of - 3p as;

⇒ - 3 p

Substitute p = (3, 5) we get;

⇒ - 3 × (3, 5)

⇒ (3×- 3, - 3×5)

⇒ (- 9, - 15)

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Answer: i) dy/dx of x = 1

ii) dy/dx of xy = y

iii) dy/dx of y = 2y

iv) dy/dx of xy = 2xy

Step-by-step explanation:

The equation that represents the line that has a slope of 1/3 and an x-intercept of 5 is y - 0 = 1/3(x - 5). The correct option is b. y - 0 = 1/3(x - 5)

From the question, we ae to write the equation of a line that has the given slope and x-intercept.

From the equation for the point-slope form of a line,

y - y₁ = m(x - x₁)

Where m is the slope

and (x₁, y₁) is a point on the line

From the given information,

m = 1/3

and

The x-intercept is 5, that is, (5, 0)

Thus,

The equation of the line is

y - 0 = 1/3(x - 5)

Hence, the equation is y - 0 = 1/3(x - 5)

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a)The probability Space, S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6), (2, 1) (2, 2) (2,3) (2,5) (2,4),(2,6), (3,1) (3,2) ,(3,3), (3,4) (3,5)(3,6), (4,1) (4,2) (4,3) (4,4) (4,5) (4,6), (5,1) (5,2) (5,3) (5,4) (5,5) (5,6),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5),(6,6)}

b) i) Probability that the sum of the rolls is even, P(A) = 0.5

ii)Probability that first roll is equal to the second, P(B) 0.166

iii) Probability that the first roll is larger than the second, P(C) = 0.4166.

We have a pair of dice are rolled, then the Sample space is same as probability space.

a) The probability space , S is a non-empty set contains all possible outcomes. The probability space is written as

S = {(1,1) (1,2) (1,3) (1,4) (1,5) (1,6), (2, 1) (2, 2) (2,3) (2,5) (2,4),(2,6), (3,1) (3,2) ,(3,3), (3,4) (3,5)(3,6), (4,1) (4,2) (4,3) (4,4) (4,5) (4,6), (5,1) (5,2) (5,3) (5,4) (5,5) (5,6),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5),(6,6)}

b) Total possible outcomes from rolling = 36

Let us consider the events,

A : sum of the rolls is even

B : first roll is equal to the second

C : first roll is larger than the second.

Now, favourable outcomes for event A = 18

i) Probability (Sum is even), P( A) = 18/36

= 0.5

Favourable outcomes for event B = 6 = { (1,1),(2,2),(3,3),(4,4), (4,1) (4,2) (4,3), (5,5),(6,6)}

ii) So, Probability that first roll is equal to the second, P(B) = 6/36 = 0.166

Favourable outcomes for event C = 15 = { (2,1),(3,2),(3,1),(4,1),(5,1) (5,2) (5,3) (5,4),(6,1) (6,2) (6,3) (6,4) (6,5) (6,4), (6,5)}

iii) So, probability that the first roll is larger than the second, P(C) = 15/36

= 0.4166.

Hence, we get all required probabilities.

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The probability of P(Sum is even)=0.5, P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex], P(the first roll is larger than the second)=0.4167.

A pair of dice are rolled

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur.

a) Sample space,

[tex]$$\begin{aligned}S= & \left\{\begin{array}{l}(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\end{array}\right. \\& (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\& (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\& (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\& (6,1)(6,2)(6,3)(6,4)(6,5)(6,2)\}\end{aligned}$$[/tex]

(b).

(i).The probability of each of the following events

Probability of event to happen

⇒P(Sum is even)=[tex]\frac{18}{36} =\frac{1}{2}[/tex]=0.5

⇒P(Sum is even)=0.5

(ii). P(the first roll is equal to the second)=[tex]\frac{6}{36} =\frac{1}{6}[/tex]

⇒P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex]

(iii). P(the first roll is larger than the second)=[tex]\frac{15}{36}=0.4167[/tex]

⇒P(the first roll is larger than the second)=0.4167

Therefore, the P(Sum is even)=0.5, P(the first roll is equal to the second)=[tex]\frac{1}{6}[/tex], P(the first roll is larger than the second)=0.4167.

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Answer:

Step-by-step explanation:

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