Write x + 2 + 3x^2 in standard form

There are 7 people in Mr. Wilson's class, as Zach is the second person and Mary is the seventh person.

To calculate the total number of people in the class, we can use the formula 2x = 7, where x is the total number of people. Solving for x, we get x = 7.

To determine the number of people in Mr. Wilson's class, we can use the formula for the number of people in a circle, which is N = 2(n-1), where n is the number of people standing opposite each other in the circle. In this case, n is 2 (Zach and Mary). Therefore, N = 2(2-1) = 2 people. However, since there are 7 people in total in the circle, we can conclude that the number of people in Mr. Wilson's class is 7. To explain further, based on the given information, we can say that Zach is the second person, which means there are 2 people before him in the circle. Therefore, there are 7 people in Mr. Wilson's class. To further explain, we can break down the equation as follows: The person opposite of Zach is the seventh person, or 7th, so we can say that 7 is equal to the number of people in the class multiplied by 2, or 2x. Then, solving for x, we get x = 7. This means that the total number of people in the class is 7.

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The probability that the greater of the two numbers obtained is 3 is A) 4/n(n - 1).

It is given that two chips are drawn at random without replacement from a bowl which contains n chips numbered 1 through n and n ≥ 3.

We are asked to find the probability that the greater of the two numbers obtained is 3.

The possible outcomes when two chips are drawn at random and the greater of the two numbers obtained is 3 = (1,3) and (2, 3)

So, there are only 2 outcomes

Total possible outcomes = ⁿC₂ = n(n - 1)/2

So, Probability = 2/(n(n - 1)/2)

                        = 4/n(n - 1)

Hence, the probability of getting 3 as the greatest of the two numbers is 4/n(n - 1)

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The value of ∫ (x + 1)/(9x² + 6x + 5) dx by partial fractions is 1/18ln(9x² + 6x + 5) + 1/9 (tan^-1 (3x+1)/2)

Given ∫ (x + 1)/(9x² + 6x + 5) dx

Discriminant of is 9x² + 6x + 5 is

                                 D = 6² - 4 x 9 x 5 = - 144 < 0

So, 9x² + 6x + 5 cannot be factorized in rational factors

Observing that differential of 9x² + 6x + 5, let us split (x + 1)/(9x² + 6x + 5) as (18x + 18)/18(9x² + 6x + 5)

or (18x + 6)/18(9x² + 6x + 5) + (12)/18(9x² + 6x + 5)

So, (x + 1)/(9x² + 6x + 5) = (18x + 6)/18(9x² + 6x + 5) + (12)/18(9x² + 6x + 5)

∫ (x + 1)/(9x² + 6x + 5) dx = ∫ (18x + 6)/18(9x² + 6x + 5) dx + ∫ (12)/18(9x² + 6x + 5) dx

= 1/18∫ (18x + 6)/(9x² + 6x + 5) dx + 2/3∫ 1/(9x² + 6x + 5) dx

Let us integrate the first part and assume u = 9x² + 6x + 5

then, du = (18x + 6) dx

So, 1/18∫ (18x + 6)/(9x² + 6x + 5) dx = 1/18∫ 1/u du

                                                         = 1/18 lnu

                                                         = 1/18ln(9x² + 6x + 5)

For second part, 2/3∫ 1/(9x² + 6x + 5) dx, we will use

                     ∫ dx/(x² + a²) = 1/a tan^-1(x/a) +c

For this converting denominator into the sum of two squares, we get

    2/3∫ 1/(9x² + 6x + 5) dx = 2/27∫ 1 / ((x + 1/3)²+(2/3)²) dx

Let us now substitute u = x + 1/3 and as du = dx

so, 2/27∫ 1 / ((u)²+(2/3)²) dx = 2/27 (3/2 tan^-1 (3u/2))

                                            = 1/9 (tan^-1 (3(x+1/3)/2))

                                            = 1/9 (tan^-1 (3x+1)/2)

Hence,∫ (x + 1)/(9x² + 6x + 5) dx = 1/18ln(9x² + 6x + 5) + 1/9 (tan^-1 (3x+1)/2)

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Answer: What is the question itself you need help with?

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

1.5/5 =30%

We can say that a's reduced row echelon form will have no zero rows.

Systems of linear equations can be solved using a type of matrix called reduced row echelon form.

If Ax = b has a unique solution for every b, then A must have full row rank, meaning that its reduced row echelon form will have no zero rows. This means that the reduced row echelon form of A will have a leading 1 in every non-zero row and will be in the form of an identity matrix. Therefore, the reduced row echelon form of A is the invertible matrix and A has a unique solution for every b.

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On solving the provided question we can say that this figure is a quadrilateral and area will be = A = 38.5199475951548 units

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

x = √(a2 + b2 - 2ab cos X) = √(3.62 + 5.12 - 2*3.6*5.1 cos 108°) = 7.09345501384537

Then, we can get the area of the second triangle either by solving for one of the angles using the cosine law and using 1/2 ab sin C or use Abel's law.

Abel's law for variety.

p=(8,5 + 10.2+ 7.09345501384537)/2

A =√((p(p-a)(p-b)p-c) = 29.7892487755653

A = 8.73069881958951 + 29.7892487755653 = 38.5199475951548

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The geometric series that has been provided is of divergence, since r>5.

The series is given as /10 + 3/2 + 15/2 + 75/2 + 325/2 +.....

The common ratio is

3/2 ÷ 3/10

= 3/2 ×10/3

= 5

Then,

15/2 ÷ 3/2

= 15/2 × 2/3

= 5

Thus, the common ratio is greater than 5. Therefore, the series is divergence.

Hence, the given geometric series is divergence, since r>5.

A series is considered to be convergent if the partial sums tend to a particular value, also known as a limit. In contrast, a divergent series is one whose partial sums do not approach a limit. Typically, the Divergent series either reach, reach, or don't reach a particular number.

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The given polynomials are discussed and grouped into each given category as given below.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

We can now look into each polynomial.

a) x³ + 125

   125 is a cube of 5 and also  x³  is the power of x.

So this is a perfect cube.

b) 8p³ - 27

    8p³ is a perfect cube of 2p and 27 is a perfect cube of 3.

So it is a perfect cube.

c) 12x³-9

    This is neither a cube nor a square.

d) a²-100

   100 is a perfect square and so is a².

So this is a difference of perfect squares.

e) 4m² + 25

4m² is a square of 2m and 25 is a square of 5.

But the operator is +

So this is neither a cube nor a difference of a perfect square.

f) 16x²-9

16x² is a square of 4x and 9 is a square of 3.

Also, the operator is -

So this is a difference of perfect squares.

Therefore the above polynomials are discussed and grouped into each given category accordingly.

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Answer:

y=-3x-6

Step-by-step explanation:

y=kx+n

k= (y2-y1)/(x2-x1)= (-3) / 1 = -3

n = -6

T(-1, -3) checks out :)

y=-3x-6

By making exponential function y=12500(1.07)^t, the value of the painting in 10 years will be $24589.

What are exponential functions?

An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Now,

Initial value=$12500

Rate = 7% increase every year

so, we can make a function for the increment in value

y=12500(1+7/100)^t   where t=time in years

y=12500*1.07^t

for t=10

y=1250081.07^10

y=$24589

Hence,

         The value of the painting in 10 years will be $24589

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The correlation between two variables is an important measure that helps us understand the relationship between them. In Scenario 3-2, if the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would not change the correlation (r) between wine consumption and heart disease death rate.

The correlation coefficient (r) measures the strength and direction of the relationship between two variables. If the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would change the units in which the death rate is expressed, but it would not change the underlying relationship between wine consumption and heart disease death rate.

In other words, regardless of the units in which the death rate is expressed, the correlation between wine consumption and heart disease death rate would remain the same. This is because the correlation measures the relationship between two variables, not the units in which they are expressed. It is important to note that expressing the death rate in different units may make it easier or more difficult to understand the relationship between two variables, but it does not change the underlying correlation.

In conclusion, the correlation (r) between wine consumption and heart disease death rate would not change if the death rate were expressed as deaths per 1,000 people instead of as deaths per 100,000 people.

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Salut/Hello!

Step-by-step explanation:
/ - fraction line
Ben's probability to pass is 0,8
to make it simpler for you to understand I'm going to use percentages.

We can transform 0,8 in a fraction so 8/10 and amplify it by 10 so 80/100
so the percentage showing that Ben will pass is 80% to find out the percentage that Ben will fail we subtract 80% from 100% which results in 20%

so the probability that Ben will fail is 0,2
and Tom's probability to fail is 0,3


To find out the answer to b) we need to understand how we calculate it.

Take as an example a dice. A dice has 6 faces and you need 1 side to get out of jail (let's say you need a 6). Your probability to get that side is 1/6

But what if you have two dice and you need both to be 6? Well in that case it'll be 1/6 x 1/6 which is 1/36

So, to find out the probability of both passing, we have to do 8/10 x 7/10 which is 56/100 and it's equal to 0,56. And you might wonder why the probability both will pass seems bigger than their probability to pass. Well 0,8 actually can mean 0,800000... and so on but it's easier to just let it as 0,8

For c) the probability that only one will pass is: 0.12

We first need to find the probability both fail
100% - 56% = 44%

and we subtract 44% from 56% which is equal to 12% or 0.12


I hope it was helpful! :]

The diameter of the aperture in a 35-mm lens set to a stop of f/2 is 17.5mm.

In this question, we are asked to determine the size of the aperture or we can say Diameter of aperture

Given the focal length of lens (f) = 35 mm

The lens is set to a stop f/2

We need to find the size of the aperture

Let d be the diameter of the aperture.

So, d = f/2   --(1)

Putting the value of f = 35 mm in equation (1). We get,

d = (35 mm)/2

d = 17.5 mm

Hence, the Size (diameter) of the aperture is 17.5 mm

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Answer:

The result of dividing the polynomial (15x +14^2 -40) / (-2x-5) is -7.5x - 7^2 + 20.

Step-by-step explanation:

Answer:

Step-by-step explanation:

an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?

The distributive property states that multiplying the total of two or more addends by a number yields the same result as multiplying each addend by the number separately and adding the results together.

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The intervals in which the function is both increasing and concave up are given as follows:

x > 0.

The function in this problem is defined as follows:

f(x) = 2x^4 + 16x³ + 36x².

The first derivative of the function is given as follows:

f'(x) = 8x³ + 48x² + 72x.

The function is increasing when the first derivative is positive, hence the interval is:

x > 0.

The second derivative of the function is given as follows:

f'(x) = 24x² + 96x + 72.

The function is concave up when the second derivative is positive, hence the interval is:

x < -3 or x > -1.

The intersection of the intervals x < -3 or x > -1 and x > 0 is:

x > 0.

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Answer: t-gx divided by Y

Step-by-step explanation:

subtract gx from both sides then divide by Y to get the H variable by itself.

According to the problem statement the actual boat is 96 inches long.

Boat in math is a geometric shape that is formed when two perpendicular lines intersect at two points, forming two pairs of equal-length sides that cross each other in the middle. It looks like the bottom of a boat with two sides meeting at the center. In mathematics, the boat shape is often used to represent an equation or a function. It is also used to illustrate the concept of a mathematical set, or group of related objects. The boat shape can also be used to graphically represent relationships between two or more variables.

The actual boat is 96 inches long. The scale factor of 24:1 means that for every 1 inch on the model, there are 24 inches on the actual boat. Therefore, for the 4 inch model boat, there are 4 × 24 = 96 inches on the actual boat.

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A two-dimensional reducing bend has a linear velocity profile at section  The flow is uniform at sections  The fluid is incompressible and the flow is steady.

As given in the  problem statement,flow is in compressible and flow is internal flow

Re=5*10^5

Using equation

V=Re/density*diameter of pipe

Maximum velocity=98.98 m/s

why are the Navier-stokes equations difficult to solve?

Being nonlinear makes the Navier-Stokes equation challenging to solve. Although it's frequently used, this word has a specific meaning in this context. A linear equation can have multiple simple solutions, all of which combined can yield a complex answer.

The Navier-Stokes equations lack an additional equation to determine the pressure levels at various locations. A partial differential equation used to model the flow of incompressible fluids is the Navier-Stokes equation in fluid mechanics.

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Answer: The 4 in front of the h.

Step-by-step explanation: A coefficient simply means the number in front of a variable. If its a plain variable like x, the coefficient is basically 1.

the answer is 6h +1x

because we add the 4h and 2 than if there is one x that means is one if there is that will be 2x

i hope that helps you

thanku

The number of students were in the class is 26

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Let's call the total number of students "n".

Then:

n - 5 students liked either blue or green or both,

12 students liked both blue and green,

17 - 12 = 5 students  liked only blue,

16 - 12 = 4 students liked only green.

So:

n - 5 = 5 + 4 + 12

n = 26

There were 26 students in the class.

Therefore, The number of students were in the class is 26

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The required change in pressure to maintain the flow rate in a pipe with a reducing diameter is ρ * v² / 16.

To maintain a constant flow rate in a pipe with changing diameter, the velocity of the fluid must remain constant. This is known as the principle of continuity, which states that the product of the velocity and the cross-sectional area of a pipe must remain constant.

Given that the diameter of the pipe is reduced from 8 inches to 4 inches, the cross-sectional area of the pipe is also reduced by a factor of 4. Hence, to maintain the same flow rate, the velocity of the fluid must increase by a factor of 4.

Since the fluid is incompressible and Newtonian, the pressure drop can be calculated using the continuity equation and motion equation (Bernoulli's equation).

ΔP = ρ * v²  / 2

where ΔP is the change in pressure, ρ is the density of the fluid, and v is the velocity of the fluid.

Plugging in the values, we get:

ΔP = ρ * (v / 4)² / 2 = ρ * v² / 16

So, the required change in pressure to maintain the flow rate in a pipe with a reducing diameter is ρ * v² / 16.

Complete Question:

'It is required to reduce a pipe diameter of 8 inches to a minimum diameter of 4 inches while maintaining a constant flow rate. Assuming the pipe is circular and the fluid is incompressible and Newtonian, what is the required change in pressure to maintain the flow rate?'

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The significance of the z-score will be 1.6226.

According to the question,

The given values are:

Mean,

μ = 2.46

Standard deviation,

σ = 0.53

GPA,

x'= 3.32

Now,

→ The z-score will be:

= (x-μ)/σ

By putting the given values, we get

= [tex]\frac{3.32 - 2.46}{0.53}[/tex]  ( by using subtraction)

= [tex]\frac{0.86}{0.53}[/tex]           (by using division)

= 1.6226

So, the z-score for a GPA of 3.32 is 1.6226.

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The compound interest is ₹46,148.68 and the total amount after 4 years and 6 months is ₹1,46,148.68.

The formula to calculate compound interest is:

A = P * (1 + r/n)^(nt)

Where:

A is the total amount after t years

P is the principal amount

r is the interest rate per annum

n is the number of times the interest is compounded per year

t is the number of years

In this case:

P = ₹1,00,000

r = 10% per annum = 0.10

n = 1 (since the interest is compounded annually)

t = 4 years and 6 months = 4.5 years

A = ₹1,00,000 * (1 + 0.10/1)^(1 * 4.5) = ₹1,00,000 * 1.461486788

A = ₹1,46,148.68

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20 miles/hours best express the speed of Joey's golf cart.

speed = time + distance

That is, speed = time + distance. To put it another way, distance divided by speed equals time.

You can figure out the third input if you know the first two.

For example, if a car drives 120 miles in two hours,

Then the speed is 120/2 = 60 miles per hour.

As per the data given,

We have,

So, the value of the speed of Joey's golf cart can be expressed as a unit rate by dividing the total distance he covers by the time it takes him to cover that distance.

So, the value of the unit rate will be

=40 miles/2 hours = 20 miles/hour.

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The discount amount is $29. The sale price of the scooter is $116.

What is the percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol "%" represents it.

Given that, the market price of a scooter is $145.

The discount on the scooter is 20%.

The discount amount is $145×20%

                                        = 145 × (20/100)

                                        = 145 × (1/5)

                                         = 29

The sale price is Marke price - discount

= $(145 - 29)

=$116

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Acute triangle is the answer

An acute triangle has three acute angles (less than 90 degrees)

An obtuse angle has one obtuse angle (greater than 90 degrees)

A right triangle would have a perfect 90 degree angle

An equiangular triangle would have all equal angles.

Hope this helps!