7/1 in simplest form​

There are 26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰ exponential generating Function to make an arrangement  of Pennies, nickels, dimes and quarters with at least one penny and an odd number of quarters.

Exponential generating Function:

An exponential generator provides a way to encode a sequence as the coefficients of a power series. This encoding helps in many ways.

Therefore, According to the Question:

The exponential generating function is,

G(x) = (x¹/1! + x²/2! + ...)(x¹/1! + x³/3! + x⁵/5! +...)(x°/0! + x¹/1! + x²/2! + ...)²

where the first factor describes the pennies, the second describes the quarters, and the last describes nickels and dimes.

We want the coefficient of  Xˣ /r!.

Using exponential identities we get,

G(x) = [tex]e^{x} - 1 (\frac{e^{x} - e^{-x} }{2} ) (e^{x} )^2[/tex]

      = [tex]\frac{1}{2} (e^{4x} -e^{2x} -e^{3x} + e^{x}[/tex]

and the coefficient is

[tex]\frac{1}{2} (4^r -2^r -3^r +1)[/tex]

The generating function is

G(x) = (x¹/1! + x²/2! + ...)⁴(x°/0! + x¹/1! + x²/2!+...)²² = ()⁴,

and we again want the coefficient of  X¹⁰/10!.

Multiplying we get,

G(x) = [tex](e^{4x} - 4e^{3x} + 2e^{2x} + 1)e^{22x}[/tex]

       = [tex]e^{26x} - 4e^{25x} + 2e^{24x} +e^{22x}[/tex]

so the coefficient of  X¹⁰/10! is

26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰

Learn more about Exponential function:

https://brainly.com/question/14355665

#SPJ4

16250 many different three-letter words—including nonsense words—have different letters in the next position.

Given that,

We have to find how many different three-letter words—including nonsense words—have different letters in the next position.

We know that,

The number of alphabets are 26

First letter has 26 choices.

Second letter can not be same has first letter so 25 choices.

Third letter can not be same has second letter so 25 choices.

So,

Total words = 26×25×25=16250

Therefore, 16250 many different three-letter words—including nonsense words—have different letters in the next position.

To learn more about letters visit: https://brainly.com/question/27833473

#SPJ4

The length of the radius of a circle with the equation x² + y² = 8 is 2√2 units  .

In the question ,

it is given that ,

the equation of the circle is ⇒ x² + y² = 8 ,

we know that the general equation of the circle is given as x² + y² = b² ;

and "b" is the radius of circle ,

On comparing both the equations ,

we get ,

b² = 8

Simplifying the above equation further ,

we get ,

b = √8 = √2 × 2 × 2

the radius "b" is

b = 2√2 units .

Therefore , the length of the radius of the circle is 2√2 units .

The given question is incomplete , the complete question is

What is the length of the radius of a circle given the equation x² + y² = 8 ?

Learn more about Radius Of Circle here

https://brainly.com/question/29618706

#SPJ4

Answer:

Formula 1 Racing

Step-by-step explanation:

The vertex of the equation is (3, -290). Then the solutions of the equation will be 99.67 and -93.67.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = 3x² - 18x - 263

Convert the equation into vertex form, then we have

y = 3x² - 18x - 263

y = (√3x)² - 2 · √3x · 3√3 + 27 - 27 - 263

y = 3(x - 3)² - 290

Then the solution of the equation will be given as,

3(x - 3)² - 290 = 0

3(x - 3)² = 290

x - 3 = ± 96.67

x = 3 ± 96.67

x = 3 + 96.67, 3 - 96.67

x = 99.67, -93.67

The vertex of the equation is (3, -290). Then the solutions of the equation will be 99.67 and -93.67.

More about the equation of the parabola link is given below.

https://brainly.com/question/20333425

#SPJ1

The supplied statement states that there are 20 large snacks and 40 little snacks.

When two separate answers to a problem are combined, a new, complete solution is produced. Setting up a table will facilitate resolving these issues.

Alignment allows us to determine the ratio in which the ingredients/items have been combined and at what price they are offered to generate profit or face loss. A mixture, as the name implies, is combining two or more things together.

Briefing:

Total number of snacks = 60

Total earnings = $220

If only tiny snacks are sold, the total cost would be $180 (60 x 3).

Earnings difference = 220 - 180 = $40

$5 - $3 = $2 is the difference in the cost of the snack.

Number of Large snacks = $40 ÷ 2 = 20

Small snack count is 60 - 20 = 40.

To know more about mixtures visit:

https://brainly.com/question/18297875

#SPJ4

Answer:

1

Step-by-step explanation:

there's no common factor between them

The relationship between the variable is the direction, strength, and linearity .

Scatterplots can be used when one continuous variable is under the control of the experimenter and the other is dependent on it, or when both continuous variables are independent. When one parameter is systematically increased and/or decreased by the other, it is called the control parameter or independent variable and is usually plotted along the horizontal axis. Measured or dependent variables are usually plotted along the vertical axis. In the absence of a dependent variable, any type of variable can be plotted on any axis and the scatter plot he only shows the degree of correlation (not causality) between the two variables.

Scatterplots can suggest different types of correlations between variables with specific confidence intervals. If the dot pattern slopes downwards from the lower left to the upper right, this indicates a positive correlation between the investigated variables. If the dot pattern slopes from top left to bottom right, it indicates a negative correlation. You can draw a line of best fit (also called a "trend line") to explore the relationship between variables. The formula for correlation between variables can be determined by established best-fit methods. For linear correlation, the optimal procedure is called linear regression, which guarantees a correct solution in finite time. There is no one-size-fits-all procedure that guarantees the correct resolution in any relationship. Scatterplots are also very useful for seeing how two comparable data sets match up to show non-linear relationships between variables.

Desired Weight:

A standardized table of desirable (or ideal) weight for adult height is based on life expectancy. Both malnutrition and obesity are associated with an increased risk of early death. A desirable weight corresponds to a body mass index (ratio of weight in kg/height in m2) between 20 and 25. Ideal weight charts based on actuarial data were first published in 1942 by the Metropolitan Life Assurance Company of New York and were replaced in 1959 by charts of average and desirable weights.

Learn more about variable:

https://brainly.com/question/787279

#SPJ4

Raw score can be computed by using arithmetical operations such as addition, subtraction, multiplication, and division.

This can be done by hand or by using a calculator or a computer program. Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to compute raw data. Raw data can also be influenced in many ways.

For example, data can be organized, filtered, and sorted into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends feasible to understand. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.

Learn more about raw scores here

brainly.com/question/29022735

#SPJ4

The value of b is 3.

The value of c is 1/8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 5 = 9 is an equation.

We have,

Two equations given are:

b = 24c ____(1)

(1/4)b + 4c = 5/4 _____(2)

Putting (1) in (2) we get,

(1/4)24c + 4c = 5/4

6c + 4c = 5/4

10c = 5/4

c = 5/40

c = 1/8

Putting c = 1/8 in (1) we get,

b = 24/8

b = 3

Thus,

b = 3.

c = 1/8.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The strategy to catch the spider is elaborated out here.

The best strategy for catching the spider after infinitely many steps is to start at one point in the grid and then move in a clockwise spiral, expanding your search area every time you move. As you move, you can use a combination of visual and physical cues, such as vibrations and sound, to detect the spider's presence. This method will ensure that the spider will eventually be caught in a finite amount of time. Additionally, if the spider changes directions, your search will be able to adjust to that change, as you will be able to detect it in the spiral pattern.

To know more about strategy refer to the link  brainly.com/question/14554110

#SPJ4

Answer:

Step-by-step explanation:

o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...

Answer:

6.48%

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

The problem is basically saying:

12 is what percent of 20, which we can make this into a solvable equation:

12   is    what percent     of    20

12   =          ?%             x      20

Now to solve by dividing 12 by 20

12/20 = 0.6

Multiply 0.6 by 100 to get 60%

Answer:

Don't overthink it.

[tex]V=\frac{1}{3} Ah[/tex] is the same as [tex]V=\frac{Ah}{3}[/tex]

Multiply both sides by 3

3V = A * h

Then get A by itself by dividing both sides by h.

[tex]A = \frac{3V}{h}[/tex]

Answer:

I think it's A= lw

Step-by-step explanation:

The question says to rearrange the formula to highlight the base area, and the formula to finding the base area of a pyramid is A = l w (length multiplied by width)

In order to calculate the slope ratio of a ramp, divide the difference between the elevations of two points by the distance between them, then multiply the quotient by 100, the resultant figure is the slope ratio.

What is the slope of a line?

The slope or gradient of a line in mathematics is a number that defines both the direction and the steepness of the line. The tangent relation or the height-to-distance ratio helps to determine the slope of the line.

The difference between the elevations is also called as the rise. And the distance between the points is known as the run.

Thus, we can also say that,

Slope ratio= rise / run x 100.

To know more about slope of a line:

https://brainly.com/question/28855452

#SPJ4

Answer:

Hope this helps you!

Step-by-step explanation:

The age of this fossil can be calculated using the following formula:

Age = (5715 years) * ln(1/0.15) / ln(2)

Age = 81,922 years

Answer:

Step-by-step explanation:

To find value of X ,first solve LHS

37*2x-37*14 =74x-518 +x

=75x-518

Now solve RHS

135x+75

Now equate LHS=RHS

75x-518=135x+75

75x-135x=75+518

-60x=593

x= -593/60

=-9.88

Answer:

v < 2.2

Step-by-step explanation:

0.5v < 1.14 – 0.04

0.5v < 1.1

v < 1.1/0.5

v < 2.2

pls mark as brainliest

Answer:

2 cups

Step-by-step explanation:

there should be two cups of milk in it. If I’m not correct I will redo this.

Answer: the answer is -193

When a six-sided die and an eight-sided are rolled then the probability that exactly one 6 is rolled is 1/4.

Given, a six-sided die (with numbers 1 through 6) and an eight-sided die (with numbers 1 through 8) are rolled.

we have to find the probability that exactly one 6 is rolled.

First we have to check the total number of outcomes on rolling both the dices.

Now, the total number of outcomes be, 48

As, we the favorable outcomes be, the outcome with exactly one 6 on the dices.

Favorable Outcomes = { (1,6) , (2,6) , (3,6) , (4,6) , (5,6) , (6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,7) , (6,8)}

The total number of favorable outcomes be, 12

So, the probability that exactly one 6 is rolled is

P(E) = Number of favorable outcomes / Total number of outcomes

P(E) = 12/48

P(E) = 1/4

Hence, the probability that exactly one 6 is rolled is 1/4.

Learn more about Probability here https://brainly.com/question/27745646

#SPJ4

Answer:

3x + 4y = 16

Step-by-step explanation:

3x + 4y = 12

3(-4) + 4(7) = -12 + 28 = 16

Answer: 3x + 4y = 16

Answer:

The expression √x+5+√1-x is defined for all values of x such that the value under the square root sign is non-negative. We can find the values of x that satisfy this condition by considering each of the square roots separately.

For the first square root, the value under the square root must be non-negative, so we have the following inequality:

x + 5 ≥ 0

x ≥ -5

For the second square root, the value under the square root must be non-negative, so we have the following inequality:

1 - x ≥ 0

x ≤ 1

Therefore, the expression is defined for all values of x that satisfy both of these inequalities. This means that the expression is defined for values of x in the range -5 ≤ x ≤ 1. The correct answer is therefore option D.

Equations −2x+5y=−2 and 4x−10y=4 have no solution.

An inconsistent system is a set of equations that cannot be solved. Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). The solution set refers to all possible answers to an equation or inequality. The no solution symbol,, is used to indicate that there is no solution to an equation or inequality. None Found: There are no solutions when the lines that make up a system are parallel because the two lines have no points in common.

Given,

Equations,

−2x+5y=−2 .. Equation 1

4x−10y=4 .. Equation 2

Multiplying equation 1 by 2

-4x + 10y = -4

4x - 10 y = 4

-----------------

0

Equations −2x+5y=−2 and 4x−10y=4 have no solution.

To learn more about no solution, visit:

https://brainly.com/question/7932885

#SPJ1

Answer:

128,340 words

Step-by-step explanation:

There are six types of possible quadrilaterals namely trapezium, parallelogram, rectangle, rhombus, square, and kite.

Explanation:

Different types of possible quadrilateral :

Therefore, there are six types of possible quadrilateral : trapezium, parallelogram, rectangle, rhombus, square, and kite.

Learn more about quadrilateral here

brainly.com/question/13805601

#SPJ4

6 socks must be removed from the drawer to guarantee that at least two socks of same color have been removed.

Given,

It makes no difference how many socks there are; what matters is how many different colours of socks there are, as there are five different colours.

So, if 6 socks are taken from the drawer, it is almost certain that at least two of them will be the same colour.

Because, after taking 5 socks, you will either have a match or a difference. To ensure a matching pair, add one more sock.

You have a pair if the first five are the same colour. If none of the first five socks match, the sixth sock will match one of the first five.

So with 6 socks, you are guaranteed that at least 2 of them will be the same color.

To learn more about logic puzzle refer here

https://brainly.com/question/126858

#SPJ4

-15/2+√31.(3/2)i is the width of the garden.

The area of Rectangle is length times of width.

Given,

As an architect, your job is to fulfill the requirements of the client.

You are demanded by your client to have a plan or sketch in planting a garden and surrounding it with decorative stones.

Let width be x

The desired length of the lot is 15 meters longer than its width.

Length =x+15

The area of the rectangular plot should not be more than 126 m²

Area=Length×width

126=x(x+15)

126=x²+15x

x²+15x-126=0

Apply it in Quadratic formula.

x=-b±√b²-4ac/2a

a=1, b=15 and c=-126.

x=-15±√15²-4(1)(-126)/2(1)

x=-15/2+√31.(3/2)i.

Hence, the width of the garden is -15/2+√31.(3/2)i.

To learn more on Area of rectangle click:

https://brainly.com/question/20693059

#SPJ1

Answer:

No, it's doesn't mean you are not smart. Just maybe you need to focus on learning most of the things to solve in math, you need to start with what is given to you.

Here given to you that every scale of 2 in = 8ft in actual truck.

So in order to know what 6in equals. Break down 6 into something you can use which is 2in = 8ft

6 = 2 + 2 + 2

So 6in = 8ft + 8ft + 8ft

Which can be simplified to 6ft = 24 ft.

Answer:

24

Step-by-step explanation:

8 divided by 2 is 4 and 4 times 6 equals 24. Or you could do 6 divided by 2 equals 3 and 8 times 3 equals 24.