What is the Value of 1/4 + 1 1/8
Expressed as a fraction in simplest form.

Answer:

3.2÷0.32×(0.73+0.27)^2= 10

there were 28,800 handshakes that occurred at the meeting.

How to solve the question?

In order to calculate the number of handshakes that occurred, we can use the formula for the sum of the first n-1 positive integers. The reason we use n-1 is because each person shakes hands with n-1 other people (themselves excluded).

The formula is:

(n-1) + (n-2) + (n-3) + ... + 1

where n is the number of people in the group.

In this case, n = 240, so we plug in:

(240-1) + (240-2) + (240-3) + ... + 1

Simplifying:

239 + 238 + 237 + ... + 1

We can see that this is an arithmetic series with a common difference of -1 and a first term of 239. Using the formula for the sum of an arithmetic series, we get:

S = n/2 * (first term + last term)

S = 240/2 * (239 + 1)

S = 240/2 * 240

S = 28,800

Therefore, there were 28,800 handshakes that occurred at the meeting.

It's worth noting that this calculation assumes that each handshake is counted twice (once for each person involved). If we only counted each handshake once, then we would need to divide our final answer by 2, giving us 14,400 handshakes.

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Answer:

23=45

Step-by-step explanation:

4 + 4 = 5 1

Answer:

(a^2+2)(a+2)

Step-by-step explanation:

Factor a^3+2a+2a^2+4.

Using Factoring by grouping

a^3+2a   +    2a^2+4

Factor out a from the first two terms and 2 from the last two terms.

a( a^2 +2) + 2 ( a^2+2)

Factoring out a^2+2.

(a^2+2)(a+2)

The given function is solved using the power rule. The nth derivative of the given function f(x)=xⁿ is  \(f^{(n)}(x) = n!x^{n-n }= n!\).

The power rule instructs how to differentiate xⁿ. It is used to determine the slope of polynomial functions as well as any other function with a real number exponent.

The given function is considered a power function. This is because the x is raised to the power (n). This n is considered a real number. So the derivative of this function is derived using the power rule.

First, differentiating the given function as follows,

\(\begin{aligned}f'(x)&=nx^{n-1}\\f''(x)&=n(n-1)x^{n-2}\\f'''(x)&=n(n-1)(n-2)x^{n-3}\end{aligned}\)

So observing the pattern, the nth derivative is found as follows, \(f^{(n)}(x) = n!x^{n-n }= n!\)

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The complete question is -

Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.

f(x)=xⁿ

Answer:

B /second bubble -3 1/3 is 10/3 and 4/9 is a reciprocal 9/4

The solution of the given IE by Adomian Decomposition method is, \(\[u(x)=x+\frac{1}{3} x^{3}+\frac{2}{15} x^{5}+\frac{17}{315} x^{7}+\cdots\].\)

Adomian Decomposition is a powerful numerical method for solving differential equations. It is an iterative procedure for solving nonlinear differential equations in an easy and efficient way.

The Adomian Decomposition Method involves the iterative decomposition of nonlinear differential equations into a series of linear differential equations.

The Adomian Decomposition method is used to solve the given integral equation as follows:

The equation is,

\(\[ u(x)=\int_{0}^{x}\left(x+u^{2}\right) d x \].\)

We start by assuming the solution of the given integral equation in the following form:

\(\[ u(x)=\sum_{n=0}^{\infty} A_{n} x^{n} \]\)

We find the Adomian polynomials of the given integral equation. The Adomian polynomials of the given integral equation are as follows:

\(\[ A(x)=x+\sum_{n=2}^{\infty} A_{n} x^{n} \]\)

We use the Adomian polynomials to calculate the Adomian decomposition of the given integral equation. The Adomian decomposition of the given integral equation is as follows:

\(\[ u(x)=A(x)+\sum_{n=1}^{\infty} u_{n}(x) \]\)

Where,

\(\[u_{n}(x)=\frac{\left(-1\right)^{n}}{n !} \int_{0}^{x} A^{n}(s) u^{n+1}(s) d s\]\)

We find the approximate solution of the given integral equation by using the Adomian decomposition of the given integral equation. The approximate solution of the given integral equation is as follows:

\(\[u(x)=x+\frac{1}{3} x^{3}+\frac{2}{15} x^{5}+\frac{17}{315} x^{7}+\cdots\]\)

Therefore, the solution of the given IE

\(\[ u(x)=\int_{0}^{x}\left(x+u^{2}\right) d x \]\)

by Adomian Decomposition method is

\(\[u(x)=x+\frac{1}{3} x^{3}+\frac{2}{15} x^{5}+\frac{17}{315} x^{7}+\cdots\].\)

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Answer:

1/4

Step-by-step explanation:

To find the PDF of Z=X+Y, we can use the convolution of probability density functions. Let fX(x) and fY(y) be the PDFs of X and Y, respectively. Then, the PDF of Z is:

fZ(z) = ∫fX(x)fY(z−x)dx

Since X and Y are exponentially distributed, we have:

fX(x) = λe^−λx for x > 0

fY(y) = μe^−μy for y > 0

Substituting these expressions into the convolution formula, we obtain:

fZ(z) = ∫λe^−λx μe^−μ(z−x) dx

= λμe^−μz ∫e^−(λ−μ)x dx

= λμe^−μz / (λ−μ) [1−e^(−(λ−μ)z)]

Thus, the PDF of Z is:

fZ(z) = { λμe^−μz / (λ−μ) [1−e^(−(λ−μ)z)] } for z > 0

To find the PDF of U=X−Y, we can use the change of variables technique. Let g(u,v) be the joint PDF of U and V=X. Then, we have:

g(u,v) = fX(v)fY(v−u)

Substituting the expressions for fX and fY, we get:

g(u,v) = λμe^−λve^−μ(v−u) for u < v

The PDF of U is obtained by integrating out V:

fU(u) = ∫g(u,v)dv

= ∫_u^∞ λμe^−λve^−μ(v−u) dv

= λμe^−μu ∫_0^∞ e^−(λ+μ)v dv

= λμe^−μu / (λ+μ) for all u

Therefore, the PDF of U is:

fU(u) = { λμe^−μu / (λ+μ) } for all u

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The percentage of the corals at the dive site that Sarah observes died more than 12 months ago is 21%.

A percentage is a specification of the quantity of an item in a collection per 100 of all items in the  collection.

The observations of the corals are;

The percentage of the corals that are healthy = 30%

Percentage of the corals that are unhealthy = 40%

Percentage of the corals that are dead = 30%

Percentage of the dead corals that died in the past 12 months = 30%

The percentage of corals Sarah observed died more than 12 months ago; required.

The 30% of the dead corals that died in the last 12 months, indicatesa that the percentage of the dead corals that died more than 12 months ago = 100% - 30% = 70%

The percentage of the dead corals that died more than 12 months ago = 70%

Therefore, the percentage of the population of corals at the dive site that died more than 12 months ago = 70% × 30% = 21%

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The explicit formula for the sequence is \(a_n = 125 \times (\frac{1}{5})^{n-1}\).

A geometric sequence is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed constant. This fixed constant is called the common ratio and is denoted by the letter r.

\(\mathrm{ \large{a_n }= a_1 \times r^{n-1} }\)

where aₙ is the nth term of the sequence, a₁ is the first term of the sequence, r is the common ratio, and n is the position of the term in the sequence.

The common ratio of a geometric sequence determines how quickly the terms increase or decrease. If the common ratio is greater than 1, the terms will increase exponentially. If the common ratio is between 0 and 1, the terms will decrease exponentially. If the common ratio is negative, the terms will alternate between positive and negative values.

The sum of a finite geometric sequence can be calculated using the formula:

\($\mathrm{S_n = a_1 \times \frac{1-r^n}{1-r}}\)

Geometric sequences have applications in many areas of mathematics and science, including finance, physics, and computer science. They are used to model exponential growth and decay, as well as to analyze patterns in data and algorithms.

The given sequence is a geometric sequence with a common ratio of 1/5. The first term is 125.

The explicit formula for a geometric sequence is given by:

\(\mathrm{ \large{a_n }= a_1 \times r^{n-1} }\)

where a₁ is the first term and r is the common ratio.

Substituting the given values, we get:

\(a_n = 125 \times (\frac{1}{5})^{n-1}\)

Hence, the explicit formula for the sequence is  \(a_n = 125 \times (\frac{1}{5})^{n-1}\).

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Answer:

D

Step-by-step explanation:

Answer:

700607

Step-by-step explanation:

Answer:

x^4y^2

Step-by-step explanation:

x^5 * y^6 / x * y^4

= x^5 * x^(-1) * y^6 * y^(-4)

= x^(5-1) * y^(6-4)

= x^4 * y^2

point K and J grew up together there like brothers , so I would say they would be the closer duo. Your welcome;)

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer:

Step-by-step explanation:

1) Understand the formula for volume

The formula to find volume is: area of cross section x height

In this case the cross section is the area of the triangular side and the height is 2 inches

2) Work out the volume

Area of cross section: \(\frac{8x4}{2}\) = 16

16 x 2 = 32 inches

This means our answer is 32 inches³

Hope this helps, have a lovely day! :)

The real variables among the given options are: Bushels of Wheat and Numbers of bees per hectare used to pollinate farm crops. The nominal values are: Price of a pen and Price of a computer.

Real variables are measurable quantities that can take on any value within a given range. In this case, "Bushels of Wheat" and "Numbers of bees per hectare used to pollinate farm crops" are real variables. These variables can be measured and expressed as continuous quantities, such as the amount of wheat harvested or the number of bees present.

On the other hand, nominal values are categories or labels that cannot be measured on a numerical scale. They represent different groups or classes. The "Price of a pen" and "Price of a computer" are nominal values as they represent different price categories or labels for pens and computers, but they do not have a numerical measurement scale associated with them.

In summary, "Bushels of Wheat" and "Numbers of bees per hectare used to pollinate farm crops" are real variables, while "Price of a pen" and "Price of a computer" are nominal values.

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Answer:

Step-by-step explanation:

250 is 125% of 200

So,

He gained 25% in profit

Based on the information given his gain as a percentage of the  cost price is 25%.

Using this formula

Cost price percentage=Selling price-Cost price/Cost price

Where:

Selling price=$250

Cost price=$200

Let plug in the formula

Cost price percentage=$250-$200/$200

Cost price percentage=$50/200

Cost price percentage=0.25×100

Cost price percentage=25%

Inconclusion his gain as a percentage of the  cost price is 25%.

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Answer:

The rate of change of the function is 9

Step-by-step explanation:

Mathematically, the rate of change of the function refers to the slope of the line that passes through the given points

Thus, we use the slope equation as follows;

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

(x1,y1) = (6,6)

(x2,y2) = (7,15)

Substituting these values, we have

m = (15-6)/(7-6) = 9/1 = 9

y^0 = 1

Thus :

y^5 ÷ 1 = y^5

Answer:

no its not correct .

hope it helps.

Answer: 37.5%

Step-by-step explanation:

Percentage = Given Quantity/Total Quantity*100

So here, it will be like: 45/120*100

                                    =0.375*100

                                    =37.5%

Answer:

9y(3y+2)

Step-by-step explanation:

Answer:

C

____________

Step-by-step explanation:

4-3

6-5

8-6

10-4

13-3

Answer:

p(-6) = -15

Step-by-step explanation:

To find p(-6), we will need to plug in -6 for n in the given function. So, we have p(-6) = 3(-6) + 3. Then, we have p(-6) = -18 +3 which is essentially just -15. The final answer is p(-6) = -15.

Answer:

Step-by-step explanation:

x²-3x+4+x=4

x²-3x+x=4-4

x²-2x=0

x²-x=0/2

x²-x=0

x=0

Answer:

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

To solve this you need the intersecting secants theorem, which states:

Apply this to the given lengths to get:

Substitute values to get equation:

Solve the quadratic equation to get roots:

The first root is the answer and the second root is not considered a solution as it is negative.

The matching choice is A.