stirling's approximation is an incredibly accurate approximation of factorials using a continuous and differentiable function.

The answer choice which corrects justifies the step as described is; Choice B; addition property of equality.

It follows from the task content that the answer choice which corrects justifies the step as given is to be determined.

Since the starting step is;

2x + 3 = -5x - 1

By adding 5x to both sides of the equation;

2x + 5x + 3 = -5x - 1 + 5x

7x + 3 = -1

Recall that; the addition property of equality postulates that;

if x = y;

Then, x + a = y + a.

On this note, the property which justifies the step is; Choice B; Addition property of equality.

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The statement that correctly compares -9 and 2 is A. -9 < 2 because 9 is to the left of 2 on a number line.

In arithmetic, a number line is a depiction of a graduated straight line which functions as a graphic representation of real numbers. It is presumed that every number line point and every real number correspond to one another.

Horizontal straight lines termed number lines have integers along them spaced equally apart. All of the numbers in a series can be shown on a number line. This line extends indefinitely at both ends.

In this case, -9 is on the left of a number line since it's negative. In conclusion, the correct option is A

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Answer:

A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.

Answer: -26/27

Step-by-step explanation:

If n is a multiple of 8, then n is even, according to commutativity. However, n is not an even number. As a result, n is not a multiple of 8.

Commutativity is a mathematical term that explains sums that can be shifted about and still produce the same solution.

'Commutative' is derived from the term 'commute,' which means to move and go around; thus, commutative equations feature integers that can be moved within the equation.

In mathematics, commutative law is one of two laws relating to number operations of addition and multiplication that are symbolically written as

a + b = b + a and ab = ba.

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As the cube size increases, the surface -area - to - volume ratio decreases .

Given :

as the cubes increased in size, describe what happened to the surface area to volume ratio, mathematically why this happened in terms of the formula for each.

Volume :

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Volume of cube = a^3

Surface area :

Surface area is the amount of space covering the outside of a three - dimensional shape.

Surface area of cube = 6a^2

suppose side length = 1

1^3 : 6 * 1^2

= 6 * 1 : 1

= 6 : 1

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The material that she has left after the cut of 1/2 yard of the material is 2/5 yards left

While I show you how to solve this problem, I would like to highlight some of the words and how they convert into a mathematical equation.

"She cut 1/3 yard off the material."

 This means you multiply whatever you are starting with by 1/3.

 So in this case Mineko begins with 3/5 yards.

 So,

3/5 • 1/3 = 1/5

She used 1/5 yard to make the pillow.

This will translate to Mineko having left

Therefore 3/5-1/5

She has 2/5 yards left.

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The given expression can be simplified to obtain the quotient and remainder as 3x + 4 and -4 respectively.

The polynomial p(x) divided by the other polynomial g(x) gives remainder r(x) and quotient as q(x) such that degree of r(x) is not greater than g(x).

The given expression is (3x²+ 22x + 27)/(x+6).

The division can be done as follows,

First take the quotient as 3x so that that the remainder is,

3x²+ 22x - 3x(x + 6)

= 4x

Now, the new dividend is 4x + 6.

Take the quotient as 4 to get the remainder as,

4x + 6 - 4(x + 6)

= -18

It cannot be further divided because the degree of -18 is less than x + 6.

Which implies that the quotient is 3x + 4 and the remainder is -18.

Hence, the quotient and remainder for the given division of polynomials is 3x + 4 and -4 respectively.

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The subtended arc is 2.14 times as long as the circle's radius.

What is radius of circle?

A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of those line segments. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."

Given:

A circle with a radius 7 cm long is centered at an angle's vertex, and the angle's rays subtend an arc length of 15 cm along the circle.  

The radius of the circle is 7 and length of the subtend are is 15 cm. The required value is given by:

Subtended arc / Radius = 15 / 7 = 2.14

Therefore, option (e) is the correct answer.

Hence, the subtended arc is 2.14 times as long as the circle's radius.

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The two consecutive positive integers as detailed in the question are;

15 and 16

Let the two consecutive integers be;

x and (x + 1).

We are told that the product of two consecutive positive integers is greater than their sum by 209.

Thus, the expression for this is;

x(x + 1) - 209 = x + x + 1

x² - x - 210 = 0

Using quadratic equation formula, we get;

x = -(-1) ± √((-1)² - 4(1 * -210))]/2(1)

x = (3 ± √(9 + 840)]/2

x = 15

Thus, the second number is; x + 1 = 15 + 1 = 16

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The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number be represented as A

Now , the value of A is calculated as

Five subtracted from the product of 6 and a number is at most -25

So , the inequality equation will be

And , substituting the values in the equation , we get

6A - 5 ≤ -25   be equation (1)

Now , adding 5 on both sides of the equation , we get

6A ≤ -25 + 5

6A ≤ -20

Divide by 6 on both sides of the equation , we get

A ≤ -3.33

Therefore , the value of A is -3.33

Hence ,

The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33

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The value of the expression; 6 × 10 + 4³ as given in the task content is; 124.

It follows from the task content that the value of the expression given in the task content; 6 × 10 + 4³ is to be determined.

Hence, the value of the expression can be evaluated using PEMDAS guidelines as follows;

Since the given expression is;

6 × 10 + 4³

Since the exponent, so that we have;

6 × 10 + 64

Next, solve the multiplication, so that we have;

60 + 64

= 124.

On this note, the value of the expression is; 124.

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Answer:

yeah im sorry i have no idea

Step-by-step explanation:

bro im soooooooo sorry

Centroid and Incentre always lie inside the triangle.

The centroid is the center point of the object. The point in whereby the three medians of the triangle intersect is called the centroid of a triangle. It is also described as the point of intersection of all the three medians. The median is a line which joins the midpoint of a side and the opposite vertex of the triangle.

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be described as the point in which the internal angle bisectors of the triangle cross.

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The mean of x is 1.8 and standard deviation of X is 0.98 using calculations for mean and standard deviation by given values or data.

What is mean and standard deviation?

The standard deviation is a summary measure of the differences of each  observation from the mean.

In the given que:

X         1     2     3     4

P(X)     .5   .3     .1      .1

For mean :

Mean = 1(.5) + 2(.3) + 3(.1) + 4(.1)

          = 1.8

For standard deviation :

Standard deviation = √.5(1-1.8)² + .3(2-1.8)² + .1(3-1.8)² + .1(4-1.8)²

                                = .98

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As a result, the second table agrees with the formula y= 3x -3.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

-3x - 3 = -6

y= 3x -3

Therefore, the second table matches the equation y= 3x -3.

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Answer: x = 3

Step-by-step explanation:

The age of the bones from the skeleton of s fish is 2000 years.

The formula to be used for calculation of age is-

ln (N/No) = - kt, where N/No represents remaining time, k represents constant of proportionality and t refers to the age or time period.

The remaining time = 100 - 22

Remaining time = 78% or 0.78

Keep the values in mentioned formula to find the time.

ln 0.78 = - 0.000124t

Keeping the value of ln 0.78 on Left Hand Side of the equation

- 0.248 = - 0.000124t

Negative sign will be cancelled as it is present on both sides of the equation

t = 0.248/0.000124

Performing division on Right Hand Side of the equation

t = 2000

Hence, the age is around 2000 years.

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Answer: 6,845.9, or to whole number 6,846

Step-by-step explanation:

The Future value of an annuity due of $200 each quarter for 2 1 2 years at 13%, compounded quarterly is $10263.734 ..

The future value of an annuity is the value of a group of regular payments at some point in the future. It assumes a particular rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value.

P = PMT× ((1+r)ⁿ −1)/r

where:

P---> Future value of an annuity stream

PMT---->Dollar amount of each annuity payment

r -->Interest rate (also known as discount rate)

n--->Number of periods in which payments will be

We have given that

Present value for an Annuity = $200

compounded rate , r = 13%

but compounded quarterly, then, r = 13%/4

= 0.13/4 = 0.325

Number of years , n = 2 + 1/2 = 5/2

then change into quarterly, n = 5/2 × 4 = 10

Future value formula ,

F.V = PMT ( (1+i)ⁿ - 1)/r

=> Future value = 200((1+0.325)^10/0.325)

=> F.V = 10263.734

Hence, the future value of an annuity is $10263.734..

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Answer:

35:1 because that is the most likely answer

Correct option is C

The plot of normal distributions A and B

A has the larger standard deviation

Standard Deviation

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The name standard deviation for SD came from Karl Pearson. I would guess no more than that he wanted to recommend it as a standard measure. If anything, I guess that references to standardization either are independent or themselves allude to SD.

Mean

In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set. The mean, median and mode are the three commonly used measures of central tendency.

Normal Distribution

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the normal distribution appears as a bell curve.

The plot of normal distributions A and B

A has the larger standard deviation

Correct option is C

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The equality property that is used to prove the statement is the addition property of the equality.

Let's start with the general equation

A = B

That we assume is a true equation.

There is a property called the addition property of the equality, it says that we can add the same number in both sides of the equation.

Then if we add a number C in both sides, we will get:

A + C= B + C

And that equation is still true.

Ok, let's go to our equation:

x - 2 = 9

We can add the same number in both sides which is 2, then we get:

x - 2 + 2 = 9 + 2

x = 11

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Answer:

-20

Step-by-step explanation:

We see the number line is counting by 5's so let's count down by 5's until we get to the blue dot!

5

0

-5

-10

-15

-20!

We moved down 3 points from -5 on the number line!

Answer:-20

Step-by-step explanation:

The base case in a recursive solution to the problem of finding the factorial of a number is n = 0 .

Given :

the base case in a recursive solution to the problem of finding the factorial of a number. recall that the factorial of a non-negative whole number is defined as n! .

Base case :

The base case is the condition to stop the recursion. The recursive case is the part where the function calls on itself .

we know that ,

def func ( n ) :

     if   n == 0 :

return 1

Here the base case is clearly n = 0

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The number of toy cars that can be kept in: 9 boxes and 8 boxes is 153 and 136 respectively .

Given :

288 toy cars can be kept in either 16 boxes or 18 boxes .

if 288 toy cars kept in 16 boxes .

number of toy cars in one box = 288 / 16

= 18 toy cars

if 288 toy cars kept in 18 boxes

number of toy cars in one box = 288 / 18

= 16 toys cars

Average = 18 + 16 / 2 = 34/2 = 17 toy cars .

Number if toy cars in 9 boxes = 9 * 17

= 153 toy cars

Number of toy cars in 8 boxes = 8 * 17

= 136 toy cars

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If the bucket is allowed to fall, then its linear acceleration is 8.687 m/s^2.

From the given question,

We have to solve, if the bucket is allowed to fall, then its linear acceleration

Mass of Pulley(M)= 0.692 kg

Radius of pulley(r)= 0.131 m

Mass of bucket(m)= 2.70 kg

Net torque on pulley,

[tex]\Sigma[/tex] r = rT = Iα

T = Iα/r

T= tension on string(connecting pulley and bucket)

I= moment of inertia of pulley

α= angular acceleration of pulley

linear acceleration of bucket(a),

a = rα

α = a/r

Pulley is disc shaped so

I = 1/2 Mr^2

Now, T= Iα/r = (1/2 Mr^2) (a/r)/r

T = 1/2 Ma

Now considering the motion of bucket

ma = mg-T

ma = mg-1/2 Ma

ma+1/2 Ma = mg

a = m/(m+1/2 M) g

Now putting the value

a = (2.70)×9.8/ (2.70+1/2 (0.692))

After solving

a = 8.687 m/s^2

If the bucket is allowed to fall, then its linear acceleration is 8.687 m/s^2.

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The right question is;

A 2.70 kg bucket is attached to a disk-shaped pulley of radius 0.131 mm and mass 0.692 kg . If the bucket is allowed to fall, What is its linear acceleration.

If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

Given that,

The combined length and girth of a priority mail package cannot exceed 171 inches, according to postal standards.

We have to find calculate the size of the largest volume, cylindrical container that can be sent via priority mail.

We know that,

Let

Length= Breadth =x

Height=y

Volume can be written as

V=x²y

Now,

Combined length and girth is

7x+y=171

y=171-7x

V(x)=x²(171-7x)

V(x)=171x²-7x³

Differentiating with respect to x.

V'(x)=343x-21x²

The maximum value

V'(x)=0

343x-21x²=0

7x(49-3x)=0

x=0

and

49-3x=0

3x=49

x=49/3

Once again differentiating with respect to x.

V''(x)=343-42x

V''(x)=343-42(0)=343>0(min)

V''(x)=343-42(49/3)=-343<0(max)

The maximum volume is

Vmax=V(49/3)=(49/3)(171-7(49/3))

Vmax=925

Therefore, If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

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Answer:

Step-by-step explanation:To calculate the total cost of the cement manufacturing company, you need to consider the unit variable cost, the commission, and the fixed costs.

First, calculate the total variable cost per day by multiplying the unit variable cost by the number of tons of cement produced per day: $80/ton * 5000 tons/day = $400,000/day

Then, calculate the total commission cost by multiplying the total variable cost by the commission rate: $400,000/day * 5% = $20,000/day

Next, calculate the total fixed cost per day by dividing the monthly fixed cost by the number of days in a month: $12,000/month / 30 days/month = $400/day

Finally, add the total variable cost, the total commission cost, and the total fixed cost to calculate the total cost per day: $400,000/day + $20,000/day + $400/day = $420,400/day

To calculate the break-even revenue, divide the total cost by the difference between the sales price and the unit variable cost, then multiply by the number of tons of cement sold per day: ($420,400/day) / ($150/ton - $80/ton) * 5000 tons/day = $600,000/day

This means that the cement manufacturing company needs to generate at least $600,000 in revenue per day in order to break even.

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Answer:

[tex]\begin{aligned}\textsf{1.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{2.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{3.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

Step-by-step explanation:

Root Multiplicity

Odd multiplicity → the graph will cross the x-axis at the root.

Even multiplicity → the graph will touch the x-axis at the root (but will not cross the x-axis).

Given function:

[tex]p(x)= \dfrac{2}{3}(3x - 6)(x + 2)(x - 3)^2[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The x-intercepts of a function are when f(x)=0.  

Therefore, the x-intercepts are:

Therefore, the graph of the given function has 3 turning points.

Given function:

[tex]p(x)=(x - 3)^2 (x + 2) (2x + 7)^2[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The x-intercepts of a function are when f(x)=0.  Therefore, the x-intercepts are:

Therefore, the graph of the given function has 4 turning points.

Given function:

[tex]p(x)=(x - 5)(x + 2)(x - 1)-30[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The graph has 2 turning points.