Multiple 3/8 by the whole part and the fractional part

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

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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.

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Answer: the answer is -193

Answer:

To find the account balance after 17 years, we need to first calculate the annual interest rate. Since the interest is compounded 4 times per year, the effective annual interest rate is equal to (1 + 0.04/4)^4 - 1, which is about 4.169%.

To find the account balance after 17 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. Plugging in the values we know, we get:

A = 5360(1 + 0.04169/4)^(4*17)

A = $9,907.35

So the account balance after 17 years will be about $9,907.35.

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.

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Answer:

Formula 1 Racing

Step-by-step explanation:

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:

128,340 words

Step-by-step explanation:

Answer:

[tex]\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}[/tex]

[tex]\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]

[tex]\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]

[tex]\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=2x-1[/tex]

where:

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

f(1) means the value of the function when x = 1.  

Therefore, substitute x = 1 into the given function to find f(1):

[tex]\begin{aligned}x=1 \implies f(1)&=2(1)-1\\&=2-1\\&=1\end{aligned}[/tex]

[tex]\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}[/tex]

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

f(4.5) means the value of the function when x = 4.5.

Therefore, substitute x = 4.5 into the given function to find f(4.5):

[tex]\begin{aligned}x=4.5 \implies f(4.5)&=2(4.5)-1\\&=9-1\\&=8\end{aligned}[/tex]

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6.  Therefore, rolling a "4.5" does not make sense.

[tex]\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]

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

f(10) means the value of the function when x = 10.

Therefore, substitute x = 10 into the given function to find f(10):

[tex]\begin{aligned}x=10 \implies f(1)&=2(10)-1\\&=20-1\\&=19\end{aligned}[/tex]

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6.  Therefore, rolling a "10" does not make sense.

[tex]\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]

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

The domain of a function is the set of all possible x-values.

As the faces of the six-sided die are labelled 1 to 6, the only possible values of x are 1, 2, 3, 4, 5 and 6.  

[tex]\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}[/tex]

The domain can also be written as:

[tex]\{x \in \mathbb{N} \; | \; 1 \leq x \leq 6 \}[/tex]  

or [tex]\{x \in \mathbb{Z} \; | \; 1 \leq x \leq 6 \}[/tex]

Answer:

3x + 4y = 16

Step-by-step explanation:

3x + 4y = 12

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

Answer: 3x + 4y = 16

Answer:

0

Step-by-step explanation:

The [tex]y[/tex] coordinates are the same, meaning the line is horizontal. Thus, the slope is 0.

A table of values is a collection of ordered pairs that is often produced by replacing numbers in an equation (relation).

Given,

Table of value;

When numbers are substituted into an equation, they typically produce a set of ordered pairs called a table of values (relation). Each ordered pair of numbers in the values table's table of values is related to one another according to the equation.

The relationship between the various data points is displayed using tables of values. In scientific lesson, a table of values could be used. Tables of values are used by scientists and researchers to record their data, which is subsequently examined for patterns. Then, they can utilize this pattern to forecast outcomes.

Therefore,

The process of substituting numbers in an equation results in the creation of a table of values, which is a collection of ordered pairs (relation).

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Answer:

x=12degrees

Step-by-step explanation:

1st Angle=23degrees

2nd Angle=(4x+19)

3rd Angle=(In order to find this angle we need to take this angle as angle3)

angle3+90=180

angle3=180-90

angle3=90degrees

Now lets start with the sum

Sum of angles of a triangle=180degrees

23+(4x+19)+90=180

113+(4x+19)=180

(4x+19)=180-113

(4x+19)=67

4x=67-19

4x=48

x=48/4

x=12degrees

Hope this helps you

Kinetic Energy is referred to as "energy possessed by an object as a result of its MOTION".

What is Kinetic Energy?

The energy that an item or particle has as a result of its motion is known as kinetic energy. An object accelerates and gains kinetic energy when work—the transfer of energy—is done on it by exerting a net force.

An object in motion always has a velocity, or "v," at any given moment. This energy is referred to as "kinetic energy," and it comes from:

Kinetic Energy = 12×m×v2

Here, m = Mass of the object in motion

Kinetic energy is a type of power that a moving object or particle possesses. An item accumulates kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force. A moving object or particle has kinetic energy, which depends on both its mass and its rate of motion. The type of motion can be vibration, rotation on an axis, translation (or travel along a path from one place to another), or any combination of these.

A body's translational kinetic energy is equal to 1/2mv2, which is the product of its mass, m, and square of its velocity, v.

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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.

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Answer:

6.23yx-8y

Step-by-step explanation:

simplified answer!

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%

The probability that all four will be heads or all four will be tails is 1/8.

What is probability?

Total number of outcomes = 2⁴

Probability of all four will be tails:

P(TTTT) = 1/2⁴

Probability of all four will be heads:

P(HHHH) = 1/2⁴

P(TTTT or HHHH)

= P(TTTT) + P(HHHH)

=  1/2⁴ +  1/2⁴

= 1/16 + 1/16

= 2/16

P(TTTT or HHHH) = 1/8

Hence, the probability that all four will be heads or all four will be tails is 1/8.

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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.

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The combination selecting five players from a 10-member tennis team to make a trip to a match at another school = 252

What do you mean by permutations and combinations?

A permutation is an act of arranging objects or numbers in order.

Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

given that

selecting five players from a 10-member tennis team to make a trip to a match at another school

we solve this by using combinations

=10[tex]C_{5}[/tex]

= [tex]\frac{10!}{5!(10-5)!}[/tex]

=[tex]\frac{3628800}{120*5!}[/tex]

=252

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Answer:

19,200

Step-by-step explanation:

multiply them all together

The value of sin(e) in the given right angle triangle DEF is 3/5

Given the Right angle DEF,

It is not specified whether angle D= angle F =90°.

Based on the alternatives presented, either base and altitude =3 or 4 and

5 is the hypotenuse.

Case 1. When ∠D=90° In Δ E D F

Sin (E) =altitude/hypotenuse

= 3/5  OR 4/5 [ if base=3, then altitude =4 and if Base =4, Altitude=3]

Case 2. When ∠F=90°, In ΔEFD

Sin (E) =altitude/hypotenuse

= 3/5 or 4/5 [Depending on whether Base =3 then altitude  =4, OR Altitude =3 , then Base =4]

Looking at all of the possibilities, 3/5 and 4/5 are accurate.

However, the solution is 3/5, so whether you pick angle D or angle F as 90°, take Altitude=3, Hypotenuse =5, and Base=4.

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Answer:

A. 3/5

Step-by-step explanation:

For right triangle, c^2 = a^2 + b^2

given c = EF = 10, a = DE = 8, b = DF

10^2 = 8^2 + DF^2

DF^2 = 100 - 64 = 36

DF = 6

sin(E) = opposite/hypotenuse = 6/10 = 3/5

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)

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.

Answer:

It sounds like the store is offering a sale on televisions where you can get a 30% discount on the original price of the television, as well as an additional $100 off with a coupon. This means that you can use both the discount and the coupon to save money on your purchase of a television. If you have a coupon for $100 off, you can use it to save an additional $100 on top of the discount you receive from the sale. This can help you save even more money on your purchase. It's always a good idea to check for sales and coupons when shopping for big-ticket items like TVs, as it can help you save a significant amount of money.

Answer:

Jamie swims 1/2 the length of the swimming pool every 1/4 of a minute. This means that Jamie swims 1/8 of the length of the pool in one second. If the pool is 25 meters long, it would take Jamie 200 seconds, or about 3 minutes and 20 seconds, to swim the length of the pool. This is just an estimation, as the actual time it would take Jamie to swim the length of the pool would depend on factors such as Jamie's swimming ability and the speed at which they swim.

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 ?

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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.

The cos(m) In the right triangle lmn is  19/20.

Complementary angles are formed when the total of two angles equals 90 degrees. 30 degrees and 60 degrees, for example, are complementary angles.

We have L + M = 90 because the angles L and M are complimentary.

Assuming that,

sin L = sin (90 - L) = sin M

sin (L) = 19/20.

As we know from our rule, the sine of angle L is equal to the cosine of L's complement, which is M.

This implies that the cosine of M is 19/20.

As a result, cos(M) equals 19/20.

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