The table of values below represents a linear function and shows Marco’s progress as he is pumping gas into his car. What is the output for the initial value?

Gas in Marco’s Car
Seconds Spent Pumping Gas
0
12
24
36
48
Gallons of Gas in Car
3
5
7
9
11

If Martina has already spent $22 and will spend more than $36 in total, then we can set up an inequality to represent the possible additional amounts she will spend:

$22 + c > $36

To solve for c, we can isolate it on one side of the inequality by subtracting $22 from both sides:

c > $36 - $22

c > $14

Therefore, the possible additional amounts Martina will spend (represented by c) must be greater than $14. The inequality solved for c is c > $14.

The the exact measurement of the height of the student is 6.279m.

A number can be expressed as a fraction of 100 using a percentage. It is frequently used, particularly in financial and statistical contexts, to depict ratios and proportions in a more practical and intelligible way. For instance, 50% denotes 50 out of 100, or half of a specified amount. It is represented by the letter "%".

Let's start by calculating the absolute error made in the measurement of the height of the pole:

Absolute error = 5% of 5.98m = 0.05 x 5.98m = 0.299m

If the actual height is 0.299m more than the measured value, then the actual height would be:

Actual height = 5.98m + 0.299m

                      = 6.279m

Therefore, the exact height is 6.279m.

To know more about Percentage check:

https://brainly.com/question/29306119

#SPJ9

Where is your question so we may help

Answer:

Step-by-step explanation:

mark me brainliest so i can solve

The down payment is $450.

The total dollar amount of the monthly installment payments is $4,860.

The Loan amount Jeanie contracted was $4,050.

The total interest Jeanie paid was $810.

The down payment is the cash payment made upfront when an asset is bought on credit.

The down payment represents a percent of the total price, indicating the buyer's willingness and capacity to enter the contract.

The price of the snowmobile = $4,500

Down payment = 10% = $450 ($4,500 x 10%)

Loan amount = $4,050 ($4,500 - $450)

Installment periods = 18 months

Monthly payments = $270 ($4,050/18)

Total installment payments = $4,860 ($270 x 18)

The total interest = $810 ($4,860 - $4,050)

Learn more about the down payment at https://brainly.com/question/15623552.

#SPJ1

The solution 143 milliters of HCl.

To answer this question, we need to calculate the ratio of HCl to water in the first solution, then apply that ratio to the second solution.

In the first solution, there are 66 milliliters of HCl and 90 milliliters of water, so the ratio of HCl to water is 66/90 = 0.733.

To make the second solution with the same concentration of HCl, it must have the same ratio of HCl to water. This means that for the second solution, 0.733 of the 195 milliliters of water must be HCl.

To calculate the amount of HCl in the second solution, we multiply 0.733 and 195: 0.733 * 195 = 143.985 milliliters of HCl. Since we cannot have part of a milliliter, the answer is 143 milliliters of HCl.

To know more about concentration of HCl click on below link:

https://brainly.com/question/29721078#

#SPJ11

Answer: 8 * 8 = (distance between PQ and RS) * 8

distance between PQ and RS = 8" PQRS in units: 16 because 8 (PQ) + 8 (RS)=16, measurement type is units so 16 units

Step-by-step explanation:

*I used A.I to help explain this better.* It should make sense, just read/scan through it, as it explains the question very throughly.

"First, let's find the length of the sides of the rectangle. Since P and Q have the same x-coordinate, we know that PQ is a vertical line segment with length 8 units (since the y-coordinates of P and Q differ by 8). Similarly, since P and Q have the same y-coordinate, we know that RS is a horizontal line segment with length 8 units. Therefore, the length and width of the rectangle are both 8 units.

To find the coordinates of points R and S, we need to consider two cases:

a) Points R and S are to the left of points P and Q.

In this case, we can imagine that the rectangle is reflected across the y-axis, so that points P and Q become points P'(-1, -4) and Q'(-1, 4), respectively. Then, points R and S must lie on the line x=-2 (to the left of point P'), and the distance between them must be 8 units.

Since the area of the rectangle is 64 square centimeters, the length of RS is 8 units, and the length of PQ is 8 units, we know that the distance between PQ and RS (i.e., the height of the rectangle) is also 8 units. This means that the y-coordinates of R and S must differ by 8 units.

Let's choose a y-coordinate for point R. Since R is to the left of P', its x-coordinate is -2, and its y-coordinate must be between -4 and 4 (since the y-coordinates of P' and Q' are -4 and 4, respectively). Let's say that the y-coordinate of R is yR. Then, the y-coordinate of S must be yR + 8.

The area of the rectangle is (length)(width) = (8)(8) = 64 square centimeters. Since PQ is a vertical line segment, its length is the difference between the y-coordinates of P and Q, which is 8 units. Therefore, the length of RS is also 8 units. The distance between PQ and RS (i.e., the height of the rectangle) is also 8 units. Therefore, we can write:

8 * 8 = (distance between PQ and RS) * 8

distance between PQ and RS = 8

So, the y-coordinates of R and S differ by 8 units. Therefore, we can write:

yR + 8 - yR = 8

yR = 0

Therefore, the coordinates of R are (-2, 0), and the coordinates of S are (-2, 8).

b) Points R and S are to the right of points P and Q.

In this case, we can imagine that the rectangle is reflected across the x-axis, so that points P and Q become points P''(1, 4) and Q''(-1, 4), respectively. Then, points R and S must lie on the line y=-6 (to the right of point P''), and the distance between them must be 8 units.

Again, the area of the rectangle is (length)(width) = (8)(8) = 64 square centimeters. Since RS is a horizontal line segment, its length is the difference between the x-coordinates of R and S, which is 8 units. Therefore, the length of PQ is also 8 units. The distance between PQ and RS (i.e., the height of the rectangle) is also 8 units. Therefore, we can write:

8 * 8 = (distance between PQ and RS) * 8

distance between PQ and RS = 8"

Answer:7.9

Step-by-step explanation:

square root of 63 is 7.9

Answer:

Step-by-step explanation:

[tex]\sqrt{63} =[/tex] [tex]\sqrt{7}[/tex]×[tex]\sqrt{9}[/tex]

     = [tex]\sqrt{7}[/tex] × 3

    = 3[tex]\sqrt{7}[/tex]

The answer of the given question based on the  image of the given rotation of the preimage is given below,

Rotation is a transformation in which an object or figure is turned around a fixed point or center by a certain angle or degree. The fixed point is known as the center of rotation, and the angle of rotation is measured in degrees or radians.

Based on the given rotation specification, "r(270,0)(x,y)", the preimage should be rotated 270 degrees counterclockwise around the origin.

To draw the image of the rotated preimage, you can use the following steps:

Plot the coordinates of the preimage points on a coordinate plane.

Draw  line from of each point to origin.

Measure an angle of 270 degrees counterclockwise from each line, using a protractor or angle tool.

Draw a new line from each point to the endpoint of the measured angle. These lines represent the rotated points.

Label the new coordinates of the rotated points.

To know more about Angle visit:

https://brainly.com/question/15277238

#SPJ1

Answer:

Yes

Step-by-step explanation:

They both are added by 4

Therefore, ∑F(i) = F(n+2) - 1 is true for the disk transportation problem.

The disk transportation problem described in the question is a classic example of the Tower of Hanoi puzzle. The goal of the puzzle is to move all the disks from peg A to peg C while following the rules mentioned in the question. The recurrence relation for computing the total number of moves required to transfer the n disks from peg A to peg C can be written as follows:

F(n) = 2F(n-1) + 1

This recurrence relation can be derived by considering the fact that to move n disks from peg A to peg C, we first need to move the top n-1 disks from peg A to peg B using peg C as an intermediate peg. This requires F(n-1) moves. Next, we need to move the largest disk from peg A to peg C, which requires 1 move. Finally, we need to move the n-1 disks from peg B to peg C using peg A as an intermediate peg, which again requires F(n-1) moves. Therefore, the total number of moves required to transfer the n disks from peg A to peg C is F(n) = 2F(n-1) + 1.

Now, to show that ∑F(i) = F(n+2) - 1, we can use the recurrence relation F(n) = 2F(n-1) + 1 and the fact that F(1) = 1. By substituting n = 1, 2, 3, ..., n-1, n in the recurrence relation and adding all the equations, we get:

∑F(i) = 2∑F(i-1) + n

Using the fact that F(1) = 1 and rearranging the terms, we get:

∑F(i) = F(n+1) - 1

Therefore, ∑F(i) = F(n+2) - 1 is true for the disk transportation problem.

Learn more about disk transportation

brainly.com/question/13627620

#SPJ11

Evaluating the function for the given values we have:

A function is a relation between two sets, called domain and range, that assigns to each element of the domain exactly one element of the range.

To evaluate the function (f(x) = 6x-2) for the given values, we simply need to plug in the values for x and then simplify.

f(1) = 6(1) - 2 = 6 - 2 = 4

f(-1) = 6(-1) - 2 = -6 - 2 = -8

f(12.6) = 6(12.6) - 2 = 75.6 - 2 = 73.6

f(23) = 6(23) - 2 = 138 - 2 = 136

So the function values are 4, -8, 73.6, and 136 for the given values of x.

See more about function at https://brainly.com/question/2284360.

#SPJ11

The function f(x)=6x−2 evaluated as follows:

a. f(1) = 4

b. f(-1) = -8

c. f(12.6) = 74.6

d. f(23) = 136

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Evaluating the function f(x) = 6x - 2 for the given values:

a. f(1) = 6(1) - 2 = 4

b. f(-1) = 6(-1) - 2 = -8

c. f(12.6) = 6(12.6) - 2 = 74.6

d. f(23) = 6(23) - 2 = 136

Therefore, the function evaluated at the given values is f(1)=4, f(-1)=-8, f(12.6)=73.6, and f(23)=136.

Learn more about the function here:

brainly.com/question/12431044

#SPJ11

The following operations with functions:

1. (g-f)(1) = 7

2. (h-g)(t) = -1

3. (g -f(a) = -38 - a

4. g(3) - h(3) = -16

5. (h+g)(10) = -6

6. (f-g)(4) = 1

Complete each operation with functions.
1. (g-f)(1) = g(1) - f(1) = (2-1) - (-2-4) = 1 + 6 = 7
2. (h-g)(t) = h(t) - g(t) = (2t+1) - (2t+2) = -1
3. (g-f)(a) = g(a) - f(a) = (-30-3) - (a+5) = -33 - a - 5 = -38 - a
4. g(3) - h(3) = (2(3)-5) - (4(3)+5) = (6-5) - (12+5) = 1 - 17 = -16

5. (h+g)(10) = h(10) + g(10) = (3(10)+3) + (-4(10)+1) = (30+3) + (-40+1) = 33 - 39 = -6
6. (f-g)(4) = f(4) - g(4) = (4(4)-3) - (4+2(4)) = (16-3) - (4+8) = 13 - 12 = 1

For more such questions on Operation of functions.

https://brainly.com/question/30190962#

#SPJ11

Answer: In the given square-based pyramid: The edge length of the square base (a)=10 m ( a ) = 10 m . The slant length of the pyramid (l)=12 m

Step-by-step explanation:

Answer:

I found this i hope it is correct

Step-by-step explanation:

The volume of a square-based pyramid is given by the formula:

V = (1/3) * base area * height

The base area of the pyramid is the area of a square with side length 10 cm:

base area = 10 cm * 10 cm = 100 cm^2

Substituting the given values into the formula:

V = (1/3) * 100 cm^2 * 12 cm

V = 400 cm^3

Therefore, the volume of the pyramid is 400 cubic centimeters.

Given -The area of the square is 36 sq.cm

To find - the perimeter of the square

Explanation- we know that the formula for area is

[tex]a^2=36[/tex]

we get side as

[tex]a=\sqrt{36} \\a=6[/tex]

The perimeter is given as

[tex]a4=4(6)=24[/tex]

Hence the perimeter is 24 sq.cm

Final answer- the perimeter is 24 sq.cm

Answer: 19

Step-by-step explanation: The formula for the area of a quadrilateral is length x width.

Here, we have the width missing. So our equation would be,

12x=228.

dividing both sides by 12 gives us x=228/12.

solving this, we get x=19.

So, your answer will be 19.

Answer:

The width of the rectangle is 19 feet

Step-by-step explanation:

The formula for the area of a rectangle is length times width which can be expressed as

[tex]A=lw[/tex]

We can rearrange the equation and solve for the width.

Divide both sides of the equation by [tex]l[/tex].

[tex]\frac{A}{l}=w[/tex]

Now we have an equation to evaluate the width.

Numerical Evaluation

Substituting our values into the equation yields

[tex]\frac{228}{12}=w[/tex]

[tex]w=19[/tex]

The simplified expression is u^(3) - v^(3).

To perform the indicated operation on the algebraic expressions, we need to multiply each term in the first expression by each term in the second expression and then simplify the resulting expression.

Step 1: Multiply each term in the first expression by each term in the second expression:

(u)(u^(2)) + (u)(uv) + (u)(v^(2)) - (v)(u^(2)) - (v)(uv) - (v)(v^(2))

Step 2: Simplify the resulting expression by combining like terms:

u^(3) + u^(2)v + uv^(2) - u^(2)v - uv^(2) - v^(3)

Step 3: Simplify further by canceling out terms that are equal but opposite in sign:

u^(3) - v^(3)

Therefore, the simplified expression is u^(3) - v^(3).

Learn more about simplified expressions here:

brainly.com/question/403971#

#SPJ11

The value of function  f[g(10)] = 198.

Given value of functions f(x) and g(x)

F(x) = 10x + 8

g(x) = x+9

To find f[g(10)], we need to first evaluate g(10), which means plugging in x=10 into the expression for g(x):

g(10) = 10 + 9 = 19

Now we can use this result to evaluate f[g(10)], which means plugging in x=19 into the expression for f(x):

Put the value of x=19  in F(x)

f[g(10)] = f(19) = 10(19) + 8 = 190 + 8 = 198.

Therefore, the function f[g(10)]  value is = 198.

To learn more about  expression

https://brainly.com/question/29296925

#SPJ4

The number of each type of coin they have is 42 quarters and 12 nickels.

To find out how many of each type of coin Kevin and Randy Muise have, we can use a system of equations. Let's call the number of quarters "q" and the number of nickels "n". We can create two equations based on the information given:

q + n = 54 (the total number of coins)

0.25q + 0.05n = 11.10 (the total value of the coins)

Now we can use the substitution method to solve for one of the variables. Let's solve for "n" in the first equation:

n = 54 - q

Now we can substitute this value of "n" into the second equation:

0.25q + 0.05(54 - q) = 11.10

Simplifying and solving for "q":

0.25q + 2.7 - 0.05q = 11.10

0.20q = 8.40

q = 42

Now we can plug this value of "q" back into the first equation to find "n":

n = 54 - 42

n = 12

So Kevin and Randy Muise have 42 quarters and 12 nickels in their jar.

Learn more about system of equations here: https://brainly.com/question/25976025.

#SPJ11

Answer: 3rd one

Step-by-step explanation:

formula : 2πrh+2πr^2

Answer:

Your typing speed is 82.8 WPM.

Step-by-step explanation:

Lets list was we know:

x = age in years

y = typing speed

We know the equation [tex]y=-1.4x+117.8[/tex] will produce the result for y, the typing speed. If x is the age in years, and you are 25 years old, then all you have to do is substitute 25 into the equation.

[tex]y=-1.4(25)+117.8[/tex]

Evaluate

[tex]y=-35+117.8[/tex]

[tex]y=82.8[/tex]

Your typing speed is 82.8 WPM.

The tallest tree that can be supported with the wire is 20 feet .

The tallest tree that can be supported with a 25 foot wire staked 15 feet away from the tree can be calculated as follows:

Therefore, the tallest tree can be found using Pythagoras's theorem,

Hence,

c² = a² + b²

where

25² - 15²  = b²

b² = 625 - 225

b = √400

b = 20 feet

Therefore, the tallest tree is 20 feet.

From the diagram, the tallest tree that can be supported by a 25 feet wire is 20 feet. we had to use Pythagoras's theorem to find the tallest tree that 25 feet wire can hold.  

learn more on right triangle here: https://brainly.com/question/6322314

#SPJ1

Answer:

Mate the answer is c.

The division is one of the four basic arithmetic operations in mathematics, along with addition, subtraction, and multiplication. It involves breaking a number or quantity into equal parts, or groups, and determining how many groups or how many items are in each group.

In mathematics, a division sentence is a statement that represents the operation of division. It is typically written in the form of a fraction or using the division symbol, with a dividend (the number being divided) on top and a divisor (the number by which the dividend is being divided) on the bottom. For example, the division sentence 8 ÷ 2 = 4 can also be written as the fraction 8/2 = 4/1.

The result of a division operation is called the quotient.

Division is a fundamental concept in mathematics and is used in many areas of study, including algebra, geometry, and statistics. It is also an important tool in everyday life, such as in calculating the cost per unit of a product or dividing a recipe to adjust the serving size.

Without a specific drawing to refer to, it's difficult to provide a specific explanation of how Adrian used it to solve a division sentence. However, I can provide a general explanation of how a drawing might be used to illustrate or solve a division problem.

One common way to use a drawing to solve a division problem is through the use of equal groups. For example, consider the division problem 12 ÷ 3. To solve this problem, we can draw 12 circles and group them into equal groups of 3. We would then count the number of groups to determine the quotient, which is the answer to the division problem.

Another way to use a drawing to solve a division problem is through the use of a number line. For example, consider the division problem 15 ÷ 5. We can draw a number line and mark the starting point at 0, the ending point at 15, and the intervals at 5. We would then count the number of intervals to determine the quotient, which is the answer to the division problem.

Regardless of the specific method used, a drawing can help to illustrate the concept of division and make it more concrete and visual. It can also be a useful tool for students who are just learning about division or who struggle with more abstract or symbolic representations of mathematical concepts.

To know more about divisions visit:

brainly.com/question/927962

#SPJ1

Answer:

1

Step-by-step explanation:

2 power 3 in numerator mean it is 8.

Divide th 2 power 3 in denominator it means 8.

Now upo dividing 8 and 8 it gives 1.

Same it can be understood by any number with exponent 0 is equal to 1.

The inventory turnover is 5 days and the number of days sales is  73 days if we assume 365 days a year.

The given data is as follows;

Cost of goods sold = $259,150

Average inventory = 51,830

a. Inventory turnover

Inventory turnover is calculated by dividing the cost of goods sold by the average inventory of the report.

Inventory turnover = (Cost of goods sold) / (Average inventory )

Inventory turnover = $259,150 / $51,830

Inventory turnover = 4.99 = 5

b. Number of days' sales in inventory

Assuming that 365 days in a year.

The number of days' sales in inventory is calculated by dividing the number of days in a year by the Inventory turnover

Number of days' sales = 365 days / (Inventory turnover)

Number of days' sales = 365 days / 4.999 = 73.015

Therefore we can conclude that the Inventory turnover is 5 and the Number of days' sales is 73 days.

To learn more about Average inventory

https://brainly.com/question/15170591

#SPJ4

A single point perspective projection onto the z=0 plane from a center of projection at z=-2 are A' = (3/4, 2/4, 0) = (0.75, 0.5, 0) for point A and B' = (3/8, 2/8, 0) = (0.375, 0.25, 0) for point B. There are no vanishing points at infinity along the x, y, and z-axis for this case.

To perform a single point perspective projection onto the z=0 plane from a center of projection at z=-2, we need to use the perspective projection formula:

P' = (x/z, y/z, 0)

For point A(3, 2, 4, 1), the projected point A' will be:

A' = (3/4, 2/4, 0) = (0.75, 0.5, 0)

For point B(3, 2, 8, 1), the projected point B' will be:

B' = (3/8, 2/8, 0) = (0.375, 0.25, 0)

Now, to determine the vanishing points at infinity along the x, y, and z-axis, we need to find the points where the line segment AB intersects the planes at infinity along each axis.

For the x-axis, the plane at infinity is x=∞. Since the line segment AB is parallel to the x-axis, it will never intersect this plane, and therefore there is no vanishing point along the x-axis.

For the y-axis, the plane at infinity is y=∞. Similarly, the line segment AB is parallel to the y-axis and will never intersect this plane, so there is no vanishing point along the y-axis.

For the z-axis, the plane at infinity is z=∞. The line segment AB is not parallel to the z-axis, so it will intersect this plane at a point with coordinates (x, y, ∞). To find this point, we can use the equation of the line segment AB:

(x - 3)/(3 - 3) = (y - 2)/(2 - 2) = (z - 4)/(8 - 4)

Solving for z=∞, we get:

(x - 3)/(3 - 3) = (y - 2)/(2 - 2) = (∞ - 4)/(8 - 4) = ∞

Since the denominators are all equal to zero, this equation is undefined, and therefore there is no vanishing point along the z-axis.

In conclusion, there are no vanishing points at infinity along the x, y, and z-axis for this case.

Learn more about plane: brainly.com/question/1655368

#SPJ11

The factored expression is 11u^(2)v^(2)(u^(7)v^(6) - 2y^(6)).

Factoring out a monomial from a polynomial involves finding the greatest common factor (GCF) of the terms in the polynomial and then dividing each term by the GCF to get the remaining polynomial. In this case, the GCF of the two terms in the expression is 11u^(2)v^(2). So, we can factor out this monomial from the polynomial as follows:

11u^(9)v^(8) - 22u^(2)v^(2)y^(6) = 11u^(2)v^(2)(u^(7)v^(6) - 2y^(6))

Therefore, the factored expression is 11u^(2)v^(2)(u^(7)v^(6) - 2y^(6)).

Learn more about Factoring
brainly.com/question/14209188

#SPJ11

probability π/(1-(1-p)(1-π)).

It is given that:Let Py be a discrete distribution on {0,1,2,...} and given Y = y, the conditional distribution of X be the binomial distribution with size y and probability p. We need to show that:(i) if y has the Poisson distribution with mean θ, then the marginal distribution of X is the Poisson distribution with mean pθ;(ii) if Y + r has the negative binomial distribution with size r and probability π, then the marginal distribution of X +r is the negative binomial distribution with size r and probability π/(1 -(1-P)(1 - 7)).Solution:Let us consider each part one by one.(i) If y has the Poisson distribution with mean θ, then the marginal distribution of X is the Poisson distribution with mean pθ.We are given that Y = y, the conditional distribution of X be the binomial distribution with size y and probability p.So, P(X = x | Y = y) = yCxpy(1−p)y−x  ,  x = 0,1,2,...,y.Now, we need to find the marginal distribution of X. We have:P(X = x) = ∑y=P(Y=y)P(X=x|Y=y) = ∑y=P(Y=y)yCxpy(1−p)y−xLet us calculate the above sum using the Poisson distribution of y. For this, we have to calculate the probability P(Y=y).We are given that y has the Poisson distribution with mean θ.So, P(Y=y) = e−θθy/y!∑y=0∞P(Y=y)yCxpy(1−p)y−x=∑y=0∞e−θθy/y!yCxpy(1−p)y−x=px∑y=0∞e−θθy−x/y!(y−x)!p(y−x)(1−p)y−x=px∑k=0∞e−θθk/k!(x+k)!(1−p)k=px∑k=0∞(θ(1−p)x(1−p)k/k!(x+k)!)e−θ(1−p)(1−p)kThe above sum is the sum of terms of the form akk! where ak = (θ(1−p)x(1−p)k/k!(x+k)!). Such a sum can be expressed in the form of the Poisson distribution. Thus we get:P(X = x) = ∑y=P(Y=y)P(X=x|Y=y) = px∑k=0∞(θ(1−p)x(1−p)k/k!(x+k)!)e−θ(1−p)(1−p)k= e−pθ∑k=0∞(pθ(1−p)x(1−p)k/k!(x+k)!)e−pθ(1−p)(1−p)k= e−pθ∑k=0∞Pois(pθ)(x+k)k! (1−p)kWe recognize the above sum as the Poisson distribution with mean pθ. Thus we get:P(X = x) = e−pθ(pθ)x/x!The marginal distribution of X is the Poisson distribution with mean pθ.(ii) If Y + r has the negative binomial distribution with size r and probability π, then the marginal distribution of X +r is the negative binomial distribution with size r and probability π/(1 -(1-P)(1 - 7)).Let us first consider the conditional distribution of X given Y = y. We are given that Y + r has the negative binomial distribution with size r and probability π. This means that the sum of y + r independent and identically distributed Bernoulli random variables each with probability p has the negative binomial distribution with size r and probability π.So, P(X = x | Y = y) = (y+r)xpx(1−p)y+r−x, x = 0,1,2,...,y+r.Now, we need to find the marginal distribution of X + r. We have:P(X + r = k) = ∑y=P(Y=y)P(X+r=k|Y=y) = ∑y=P(Y=y)(y+r)kpr(1−p)y+r−kLet us simplify the above sum. For this, we have to calculate the probability P(Y = y).We are given that Y + r has the negative binomial distribution with size r and probability π.So, P(Y = y) = (y + r - 1)Cyπr(1-π)y, y = 0, 1, 2, …Now, we can express the above sum in the form of the negative binomial distribution. Thus we get:P(X + r = k) = ∑y=P(Y=y)(y+r)kpr(1−p)y+r−k= ∑y=P(Y=y)(y+r-1)Cyπr(1-π)ykpπr(1-π)k-y-r+1= NegBin(k-r+r, π/(1-(1-p)(1-π)))The marginal distribution of X + r is the negative binomial distribution with size r and probability π/(1-(1-p)(1-π)).

Learn more about marginal distribution

brainly.com/question/14310262

#SPJ11

Answer:M1=50 M2=130

Step-by-step explanation:

M2=130 because corresponding angles and M1=50 because 180-130=50

a. The width of the rectangle is 28 cm

b. The width of the rectangle is 13.8 cm

A rectangle is  with four sides in which two sides are parallel and equal.

a. The width of the rectangle

Let

since the length of the rectangle is 80 cm and the length is 4 less than triple its width, we have that its width is L = 3W - 4

Making W subject of the formula, we have that

W = (L + 4)/3

Since L = 80 cm

W = (L + 4)/3

= (80 cm + 4 cm)/3

= 84 cm/3

= 28 cm

The width is 28 cm

b. The width of the rectangle

Since the length of the rectangle is 66 cm and the length is 3 less than five times its width, we have that its width is L = 5W - 3

Making W subject of the formula, we have that

W = (L + 3)/5

Since L = 66 cm

W = (L + 3)/5

= (66 cm + 3 cm)/5

= 69 cm/5

= 13.8 cm

The width is 13.8 cm

Learn more about width of rectangle here:

https://brainly.com/question/29866091

#SPJ1