a signal is monitored every second start at t= 0 when its value is recorde as an integer an example signal might look like 10 3 25 4 30 2 17

Answer:

D. (3.5, 2.25)

Step-by-step explanation:

A solution to the system is where the two equations intersect.

looking at the graph, we see that the intersection point is between x= 3 and 4, and Y = 2 and 3.

Answer:

(3.5, 2.25)

Step-by-step explanation:

To find the coordinate of the solution to the system of linear equations −3x + 2y = −6 and y = -1/2x + 4, we need to solve the system. One method to do this is substitution. We can solve one of the equations for y, then substitute the expression for y into the other equation. This will give us an equation in terms of x, which we can then solve for x. Then, we can substitute the value of x back into one of the equations to find the corresponding value of y.

Using substitution, we can solve the system as follows:

y = -1/2x + 4

-3x + 2y = -6

Substitute y = -1/2x + 4 into -3x + 2y = -6:

-3x + 2(-1/2x + 4) = -6

-3x + (-x + 8) = -6

-4x + 8 = -6

-4x = -14

x = 3.5

Substitute x = 3.5 into y = -1/2x + 4:

y = -1/2(3.5) + 4

y = 2.25

Therefore, the solution to the system is approximately (3.5, 2.25).

F(4) < F(5) means that the temperature at 7 A.M. is less than the temperature at 8 A.M.

An inequality is used to compare two or more expressions.

For example -

ax + b > c

ax + b < c

Given is that F(t) is the outside temperature (*F)t hours after 3 A.M.

It is given that -

F(4) < F(5)

This means that the temperature at 7 A.M. is less than the temperature at 8 A.M.

Therefore, F(4) < F(5) means that the temperature at 7 A.M. is less than the temperature at 8 A.M.

To solve more questions on inequations, visit the link below-

brainly.com/question/1041084

#SPJ1

x = 217.9927  = amount of mL of the 62% acid solution

y = 116.7873 = amount in mL of the 19% acid solution

This can be solved using a system of two equations and two variables.  

Let x = amount of mL of the 62% acid solution

Let y = amount in mL of the 19% acid solution

We know the total mL of the mixture of the two solutions is 600 mL,

so x + y = 334.78    ..... eq(1)

62% of solution x is acid which can be written as 0.62x and similarly acid from the second solution can be written as 0.19y. We know that 47% of the 334.78 mL solution will be acid or 0.47(334.78).

The acid in the mixture solution comes from the acid in solution x and solution y. So 0.62 x + 0.19 y = 0.47 (334.78)      ... eq(2)

from equation (1)

x = 334.78-y

So, x = 217.9927

  y = 116.7873.

learn more about solution,

https://brainly.com/question/7932885

#SPJ4

The mean of the sampling distribution is 80 and the standard deviation is 0.52.

A normal distribution in statistics is defined as the type of continuous probability distribution where the data are arranged in a symmetrical bell shaped graph.

Given that,

Population mean, μ = 80

Population standard deviation, σ = 5.2

Mean of a sampling distribution in a normally distributed sample is same as the population mean and the standard deviation of the sampling distribution = σ / √n, where n is the sample size.

Sample size, n = 100

Mean of the sampling distribution = 80

Standard deviation of the sampling distribution = 5.2 / √100 = 5.2/10 = 0.52.

Hence mean and the standard deviation of the sampling distribution is 80 and 0.52 respectively.

Learn more about Normal Distribution here :

https://brainly.com/question/29509087

#SPJ1

Answer:

Step-by-step explanation:

2/13=6 reminder 1

2/6= 3 reminder 0

2/3= 1 reminder 1

2/1= 0 reminder 1

13 becomes 1101 base two/ binary form

The conversion of number from decimal to binary:

[tex](13)_{10}=(1101)_{2}[/tex]

[tex](121)_{10}=(1111001)_{2}[/tex]

[tex](252)_{10}=(11111100)_{2}[/tex]

[tex](1023)_{10}=(1111111111)_{2}[/tex]

[tex](2049)_{10}=(100000000001)_{2}[/tex]

Recursively multiplying the given decimal number by two is one way to convert a decimal number to a binary number. The remainders are then recorded until we arrive at 0 as the final quotient. The remainders are then entered in reverse order to obtain the binary equivalent of the provided decimal number.

The number is 13.

13 ÷ 2 = 6, Remainder = 1

6 ÷ 2 = 3, Remainder = 0

3 ÷ 2 = 1, Remainder = 1

1 ÷ 2 = 0, Remainder = 1

So, [tex](13)_{10}=(1101)_{2}[/tex]

The number is 121.

121 ÷ 2 = 60, Remainder = 1

60 ÷ 2 = 30, Remainder = 0

30 ÷ 2 = 15, Remainder = 0

15 ÷ 2 = 7, Remainder = 1

7 ÷ 2 = 3, Remainder = 1

3 ÷ 2 = 1, Remainder = 1

1 ÷ 2 = 0, Remainder = 1

So, [tex](121)_{10}=(1111001)_{2}[/tex]

The number is 252.

252 ÷ 2 = 126, Remainder = 0

126 ÷ 2 = 63, Remainder = 0

63 ÷ 2 = 31, Remainder = 1

31 ÷ 2 = 15, Remainder = 1

15 ÷ 2 = 7, Remainder = 1

7 ÷ 2 = 3, Remainder = 1

3 ÷ 2 = 1, Remainder = 1

1 ÷ 2 = 0, Remainder = 1

So, [tex](252)_{10}=(11111100)_{2}[/tex]

The number is 1023.

1023 ÷ 2 = 511, Remainder = 1

511 ÷ 2 = 255, Remainder = 1

255 ÷ 2 = 127, Remainder = 1

127 ÷ 2 = 63, Remainder = 1

63 ÷ 2 = 31, Remainder = 1

31 ÷ 2 = 15, Remainder = 1

15 ÷ 2 = 7, Remainder = 1

7 ÷ 2 = 3, Remainder = 1

3 ÷ 2 = 1, Remainder = 1

1 ÷ 2 = 0, Remainder = 1

So, [tex](1023)_{10}=(1111111111)_{2}[/tex]

The number is 2049.

2049 ÷ 2 = 1024, Remainder = 1

1024 ÷ 2 = 512, Remainder = 0

512 ÷ 2 = 256, Remainder = 0

256 ÷ 2 = 128, Remainder = 0

128 ÷ 2 = 64, Remainder = 0

64 ÷ 2 = 32, Remainder = 0

32 ÷ 2 = 16, Remainder = 0

16 ÷ 2 = 8, Remainder = 0

8 ÷ 2 = 4, Remainder = 0

4 ÷ 2 = 2, Remainder = 0

2 ÷ 2 = 1, Remainder = 0

1 ÷ 2 = 0, Remainder = 1

So, [tex](2049)_{10}=(100000000001)_{2}[/tex]

To learn more about decimal to binary link is here

brainly.com/question/19802955

#SPJ4

In the exponential function y = 3 × q⁵ the starting value is 3.

What is an exponential function?

The formula for an exponential function is f(x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The given exponential function is -

y = 3 × q⁵

The exponential function is written in the form abˣ.

Here, a is considered to be the initial value, b is considered to be the base and x represents the growth factor.

So, the initial or starting value in function y = 3 × q⁵ is -

a = 3

Therefore, the starting value is 3.

To learn more about exponential function from the given link

brainly.com/question/12626186

#SPJ1

Homogeneous systems of linear equations can have either a unique solution or infinitely many solutions, depending on the rank of the matrix representing the system.

A homogeneous set of equations is a set of linear equations that has a trivial solution (that is, a solution consisting of only the zero vector). In other words, if the coefficients of the variables in a set of linear equations are all equal to zero, the set of equations is considered homogeneous.

The trivial solution, that is, the solution in which all variables are equal to zero, will always be a solution to a homogeneous set of equations. This is because, if all coefficients are equal to zero, then each equation in the set will reduce to 0 = 0, which is always true. Thus, the trivial solution is always a solution to a homogeneous set of equations.

In addition to the trivial solution, a homogeneous set of equations may also have non-trivial solutions, which are solutions that are not equal to only the zero vector. To find these non-trivial solutions, we typically use techniques such as Gaussian elimination, row reduction, or the use of matrices and determinants.

It is important to note that homogeneous systems of linear equations can have either a unique solution or infinitely many solutions, depending on the rank of the matrix representing the system.

Therefore, homogeneous systems of linear equations can have either a unique solution or infinitely many solutions, depending on the rank of the matrix representing the system.

To learn more about linear equations,

Visit; brainly.com/question/11897796

#SPJ4

Answer:

20 pounds

Step-by-step explanation:

250% = 2.5

8 times 2.5 = 20 pounds

So, a one-year-old baby weighs 20 pounds.

On solving the provided question, we can say thatarea of the figure = area of triangle + area of semi-circle = 12 + 14.13 = 26.13 yd sq.

The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.

area of semi-circle = 1/2 * [tex]\pi *r^2[/tex] = 0.5*3.14*3*3 = 14.13yd sq.

area of triangle = 1/2*b*h = 0.5*6*4 = 12sq. yd

area of the figure = area of triangle + area of semi-circle = 12 + 14.13 = 26.13 yd sq.

To know more about area visit:

https://brainly.com/question/13194650

#SPJ1

Answer:

because the line has a slope of 0, you know that it is horizontal

therefore, the equation is y=-8

Step-by-step explanation:

Answer:5  pounds, and x+y pounds.

Step-by-step explanation:

3 pounds + 2 pounds would equal 5 pounds ,and x pounds plus y pounds are veriables, and we do not have information on how to solve for them, so the answer would just be x pounds plus y pounds.

Step-by-step explanation:

1. If Jaxson buys 2 pounds of kiwi and 3 pounds of raspberries, he buys a total of 2 + 3 = 5 pounds of fruit.

2.If he buys a pounds of kiwi and 7 pounds of raspberries, he buys a total of a + 7 = a + 7 pounds of fruit.

The line that connects the coordinates (7,5) and (9,5) has the equation y = 5.

Due to the fact that the slope of the line across the two points (x1, y1) and (x2, y2) [tex]$\mathrm{m}=\frac{\mathrm{y}_2-\mathrm{y}_1}{\mathrm{x}_2-\mathrm{x}_1}$[/tex] Now, as shown below, we can determine the slope of the line through points (7,5) and (-9,5):

[tex]$\mathrm{m}=\frac{5-5}{-9-7}=\frac{0}{-16}=0[/tex]

As a result, the line's slope is o.

Find the y-intercept now by using the slope and one of the two points.

y = mx + b

5 = (0)(7) + b

b = 5

Equation in slope intercept form is written as follows:

y = mx + b

y = (0)x + 5

y = 5

Consequently, y = 5 is the line's equation.

The complete question is:

Find the equation of the line that passes through the points (7,5) and (−9,5)

To learn more about coordinate, refer to:

https://brainly.com/question/20935031

#SPJ1

The slope of the line given by the coordinates of two points (x1, y1) = (-7, 5) and (x2, y2) = (-7, 9) is undefined. The slope of the line for coordinates (2, 3) and (2, -3) is undefined.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Given that,

The coordinates of two points are:

(x1, y1) = (-7, 5) and

(x2, y2) = (-7, 9).

The slope of the line is given by the following equation:

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

Substituting the value of the given coordinates we have:

m = (9 - 5) / (-7 - (-7))

m = (4)/ -7 + 7 = undefined

The slope of the line given by the coordinates of two points (x1, y1) = (-7, 5) and (x2, y2) = (-7, 9) is undefined.

Similarly, for the coordinates (2, 3) and (2, -3):

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

m = (-3 -3) / (2 - 2)

m = undefined.

Hence, the slope of the line for coordinates (2, 3) and (2, -3) is undefined.

Learn more about slope here:

https://brainly.com/question/11559942

#SPJ1

The given equation e(x)=f(x)f(-x) is an even function since e(x)=e(-x) and f(x)^2=f(-x)^2.

let f(x) be a function with domain double-struck r. (a) show that e(x) = f(x) f(−x) is an even function. (simplify your answers completely.) e(x) = f(x) f(−x) = f(x) f(x) = f(x)^2 e(x) = f(x)^2

e(x) = e(-x) Therefore, e(x) is an even function.

(-x) is an even function, we need to show that e(x)=e(-x).

We start by replacing -x with x in the equation:

e(x)=f(x)f(-x)

e(x)=f(x)f(x)

e(x)=f(x)^2

Now, we replace x with -x in the equation:

e(-x)=f(-x)f(-x)

e(-x)=f(-x)^2

Since the left-hand side of both equations are the same (e(x)=e(-x)), and the right-hand sides of both equations are the same (f(x)^2=f(-x)^2), we can conclude that e(x) is an even function.

The given equation e(x)=f(x)f(-x) is an even function since e(x)=e(-x) and f(x)^2=f(-x)^2.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The volume of the solid generated is [tex]\pi (2/3) (44)^{3/2}.[/tex]

We have,

To find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of y = √(44 - x²) and the x- and y-axes about the y-axis, we can use the method of cylindrical shells.

The volume can be calculated using the following integral:

V = ∫[a,b] 2πx f(x) dx

where [a, b] is the interval of x-values that defines the region in the first quadrant.

In this case, the curve y = √(44 - x²) intersects the x-axis when y = 0, which gives us:

0 = √(44 - x²)

Squaring both sides and solving for x, we get:

x² = 44

x = ±√44

Since we're considering the region in the first quadrant, we take the positive square root:

x = √44 = 2√11

Now we can set up the integral:

V = ∫[0, 2√11] 2πx (√(44 - x²)) dx

Simplifying the integrand:

V = 2π ∫[0, 2√11] x (√(44 - x²)) dx

To evaluate this integral, we can make the substitution u = 44 - x²,

du = -2x dx:

V = 2π ∫[0, 44] (√u) (-du/2)

V = -π ∫[0, 44] (√u) du

Integrating:

V = -π [2/3 u^(3/2)] [0, 44]

V = -π [2/3 (44)^(3/2) - 0^(3/2)]

V = -π (2/3) (44)^(3/2)

Finally, taking the absolute value and simplifying:

V = π (2/3) (44)^(3/2)

So, the volume of the solid generated is π (2/3) (44)^(3/2).

Thus,

The volume of the solid generated is [tex]\pi (2/3) (44)^{3/2}.[/tex]

Learn more about the volume of solids here:

https://brainly.com/question/23705404

#SPJ6

Answer:

n=32 That's all and the stepss

Explanation: Fractions must have a common denominator to add or subtract because if you think of pieces of a pizza, if you split one pizza into quarters and one into fifths, then each piece won't be the same size, so 1/5 isn't equivalent to 1/4. Therefore, if you subtract or add fractions you need to find a common denominator. One easy way to find a common denominator is list out the multiples of the two (or more) denominators and find the LCM (Least common multiple). Then find the quotient of the LCM divided by the denominator, and multiply that number by the numerator, and you have successfully changed your fraction to an equivalent fraction with a different denominator. Hope this helped. Please vote me brainliest.

Answer: -35/18

Step-by-step explanation: Hello!

The main thing that you need to know when dividing fractions is what the reciprocal is. Here is an example of finding the reciprocal:

1/2 divided by 2/3 = 1/2 x 3/2.

Basically, you flip the second fraction upside down (Put the number under the fraction line over the fraction line and put the number above the fraction line under the fraction line).  Then, you multiply the two fractions.  Then, you will find the answer.  Here is how to do that with the problem you have:

5/3 divided by (-6/7) = ?

After finding the reciprocal, you would get:

5/3 x (-7/6)

To find the answer, multiply the numerators together (5 and -7) and the denominators (3 and 6) together.

For the new numerator, you get -35.  For the new denominator, you get 18.  Put the new numerator above the fraction line and the new denominator below the fraction line.

The answer is:

-35/18

Adding and subtracting mixed numbers with unlike denominators requires converting them into equivalent fractions with a common denominator. for example 3 3/5 + 2 1/7 = 5 8/35.

3 3/5 + 2 1/7 = 5 8/35, 5 1/5 - 3 2/3 = 1 7/15, 4 1/4 + 2 2/7 = 6 11/28, 6 3/4 - 3 5/6 = 2 13/24, 1 1/2 + 3 4/7 = 4 11/14, 2 5/6 - 1 1/4 = 1 7/12, 5 1/2 + 3 3/4 = 9 1/4, 3 1/5 - 2 3/7 = 0 16/35, 4 2/3 + 2 4/5 = 6 17/15 , 2 3/4 - 1 5/6 = 1 1/12

To add or subtract mixed numbers with different denominators, you must convert them into identical parts with common factors. Similarities can be found by looking at the most unusual differences between the two denominators. Mixed numbers are converted to bad parts, added or subtracted, and returned to perfect mixed numbers. How to find the common factor, that is,

Switch completely to unwise parts, extend or subtract, then switch completely to mixed numbers. Consider exact calculations of mixed numbers with different denominators.

To learn more about mixed numbers, refer:

https://brainly.com/question/7986705

#SPJ4

The slope of the line containing the points ( 3, 4 ) and ( 3, - 6 ) is -8.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

Given;

The two points ( 3, 4 ) and ( 3, - 6 ).

Now, to find the slope

m=-6-4/4-3

m=-8/1

m=-8

Therefore, the slope will be -8.

Learn more about slope here:

https://brainly.com/question/2503591

#SPJ1

Answer:27

Step-by-step explanation:

Answer:

The store would need to sell 40 bikes to break even.

Step-by-step explanation:

In order to break even the store needs to make $4000 a month. They spend $50 per bike and sell them for $150, an easy equation to get their profit per bike is to subtract how .uch they pay for a bike from how much they make per bike which is $150-50=$100. So now we just need to divide $4000 by $100 to find out how many bikes they need to sell. $4000÷$100=40.

Answer:

point-slope form: y - 3 = 2(x+8)

slope-int form: y = 2x + 19

Step-by-step explanation:

For slope-int form, find the slope of the line.  

7-3 / -6-(-8) = 4/2 = 2

This becomes y = 2x + b

To find b: plug in a y-coordinate for the y in the equation and plug in an x-coordinate for the x

7 = 2(-6) + b

7 = -24/2 + b

7 = -12 + b

7 + 12 = -12 + 12 +b

19 = b

The final equation is: y = 2x + 19

The total force acting on the system ABC. The total force is equal to the sum of the force of gravity, normal force, friction force, tension force and applied force (Ftotal = Fg + FN + Ff + T + Fapp).

The force of gravity (Fg) acts on the system in the downward direction. This force is equal to the mass of the body multiplied by the acceleration due to gravity (Fg = mg).

The normal force (FN) is the force that acts perpendicular to the surface on which the body is resting. This force is equal to the weight of the body multiplied by the coefficient of friction between the body and the surface (FN = m * g * μ).

The force of friction (Ff) is the force that acts in the opposite direction of the motion of the body. This force is equal to the coefficient of friction multiplied by the normal force (Ff = μ * FN).

The tension force (T) is the force exerted by a string or a cable on the body. This force is equal to the mass of the body multiplied by the acceleration due to the applied force (T = m * a).

The applied force (Fapp) is the force that is applied to the body by an external force. This force is equal to the mass of the body multiplied by the acceleration due to the applied force (Fapp = m * a).

By combining all of these forces, we can determine the total force acting on the system ABC. The total force is equal to the sum of the force of gravity, normal force, friction force, tension force and applied force (Ftotal = Fg + FN + Ff + T + Fapp).

Learn more about sum of the force here:

https://brainly.com/question/25521104

#SPJ4

Complete question:

What is the free-body diagram of the system ABC?

Answer: 90%

Step-by-step explanation: To find the probability of not choosing a red marble, we need to calculate the total number of marbles in the bag and subtract the number of red marbles. The total number of marbles is 3 red + 3 green + 15 yellow + 9 purple = 30. So, the probability of not choosing a red marble is P(not red) = (30 - 3) / 30 = 27 / 30 = 9 / 10=90/100=90%

The distance is 5.5 meters from the sensor.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

Let us assume that d means distance and t means time.

When t = 1, d = 2.5

When t = 3, d = 4

d = mt + b

2.5 = m + b [t = 1]

4.0 = 3m + b [t = 2]

1.5 = 2m [subtract]

m = .75 = slope

b = 1.75 = d-intercept

d = .75t + 1.75

d = 15/4 + 7/4 [t = 5]

d = 22/4 = 5.5 m from sensor

Thus, the distance is 5.5 meters from the sensor.

To know more about distance visit: brainly.com/question/15172156

#SPJ4

the components of A in this system will be: Ah = Axi1 + Ayj1 + Azk1, A2 = Axi2 + Ayj2 + Azk2, and A3 = Axi3 + Ayj3 + Azk3. To find the components of A in a skewed coordinate system, we first need to express the vector A in terms of the unit vectors of the system.

i = i1i2i3

j = j1j2j3

k = k1k2k3

Ah = Axi1 + Ayj1 + Azk1

A2 = Axi2 + Ayj2 + Azk2

A3 = Axi3 + Ayj3 + Azk3

To find the components of A in a skewed coordinate system, we first need to express the vector A in terms of the unit vectors of the system. The unit vectors of the skewed coordinate system are given by i = i1i2i3, j = j1j2j3, and k = k1k2k3.

Therefore, the components of A in this system will be: Ah = Axi1 + Ayj1 + Azk1, A2 = Axi2 + Ayj2 + Azk2, and A3 = Axi3 + Ayj3 + Azk3.

Learn more about vector here

https://brainly.com/question/15709504

#SPJ4

Answer: 40 pages/hour

Step-by-step explanation:

12pages / 18min  *   60min/1hr

= 40pages / 1hr

OR

12 pages / 18min    SIMPLIFY

2pages / 3 min

Multiply both by 20 to get how many pages per 60 minutes.

she has to pay $736 per month, next year in rent.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, lian currently pays 640 per month to rent her apartment she has been told by her landlord that her rent will be increasing by 15% next year.

Her rent is now = 640 per month

Since, After a year her rent will increase by 15 %

Thus,

Her rent next year per month = 640(1 + 15%)

Her rent next year per month = 640(1 + 0.15)

Her rent next year per month = 640* 1.15

Her rent next year per month = 736

Therefore, she has to pay $736 per month, next year in rent.

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ1

The triangle that will be formed using the sides 12 mm , 16 mm and 20 mm will be a right trinagle.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

The characteristics of a right-angled triangle.

Let is consider the triangle is a right triangle so the base and height will be 12 mm and 16 mm respectivly.

Now using Pythagoras Theorem :

√(height² + base²) = hypotenuse

⇒√(12²+16²) = √(144+256) = √(400) = 20 mm = hypotenuse.

The triangle that will be formed using the sides 12 mm , 16 mm and 20 mm will be a right trinagle.

To learn more about right triangle refer to :

https://brainly.com/question/27395971

#SPJ4

Step-by-step explanation:

DISCUSSION QUESTIONS (DQ's).

1. Is division always a negative in a religious faith? Why or why not?

The sum of independent negative binomial and geometric random variables does not have a closed-form distribution and must be computed numerically.

What is binomial random variable ?

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success or failure.

Let X be a negative binomial random variable with parameters r and p, and let Y be a geometric random variable with parameter q. The sum Z = X + Y is also a random variable.

The cumulative distribution function (CDF) of Z is given by:

F_Z(z) = P(Z <= z) = P(X + Y <= z) = ∑_{x=0}^{z} P(X = x) * P(Y = z - x)

This expression is a double sum and does not have a closed-form solution, but it can be computed numerically.

Alternatively, the probability mass function (PMF) of Z can be found by counting the number of ways that X and Y can take on their respective values, and summing up their joint probabilities:

f_Z(z) = P(Z = z) = ∑_{x=0}^{z} P(X = x) * P(Y = z - x)

The sum of independent negative binomial and geometric random variables does not have a closed-form distribution and must be computed numerically.

To learn more about binomial random variable visit : brainly.com/question/14282621

#SPJ4