4. Are these two functions inverses of each other?
g(x)=1/4 x
f(x)= 4x

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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A statement that associates s with a set that contains the following elements: 23, 42, -11, 89 is s = set ( [ 23 , 42 , -11 , 89 ] )

Given :

a statement that associates s with a set that contains the following elements: 23, 42, -11, 89.

Statement :

A statement is an instruction that the Python interpreter can execute.

We have seen two kinds of statements: print and assignment.

When you type a statement on the command line, Python executes it and displays the result, if there is one. The result of a print statement is a value.

we can write :

s = set ( [ 23 , 42 , -11 , 89 ] )

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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 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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Based on the probability concept, the population is number of children in gymnastic class is 5 and the parameter is mean number of steps taken by the 5 children.

Probability:

In math probability  deals with the occurrence of a random event and the value is expressed from zero to one.

Given,

Suppose that there are 5 children in a gymnastics class.

One day, they count the number of steps each person takes while walking on their hands until they lose balance and come down.

The mean number of steps these children took while walking on their hands is 20 steps.

Here we need to find the the population and parameter.

Based on the given question,

We know that the parameters are descriptive measures of an entire population and their values are usually unknown because it is infeasible to measure an entire population.

Therefore, you can take a random sample from the population to obtain parameter estimates.

Similarly, for the population could simply be referred to as the total number or set of similar objects or subjects related to a certain study or research.

Here the given scenario described above, the area of interest is a particular gymnastic class, therefore all individuals or children belonging to this particular gymnastic class makes up the population.

And then the parameter on the other hand are statistical metrics, values or calculations derived from the population figure or information.

So, the mean value of steps obtained from the step counts of the population data is called the parameter.

And the parameter is a value that describes a characteristic of an entire population, such as the population mean.

Therefore, the population mean and standard deviation are two common parameters.

=> Population = number of children in gymnastic class = 5.

=> Parameter = mean number of steps taken by the 5 children.

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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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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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Answer: x = 3

Step-by-step explanation:

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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49 is the smallest possible value of x.

Given: x, y, and z are three perfect square numbers.

What is the least x that can be?

Currently, we have three numbers by the stipulation:

x > y > z > 0

and AP has these figures.

Let's now list every perfect square from 1 to 10 in the following order: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

As a result, we can observe that 25 is equal to the product of 1 plus 49.

The possible outcomes are 1, 25, and 49.

If x = 49 and z = 1, then

x + z / 2 = y

49 + 1 / 2 = y

y = 50 / 2

y = 25

Y is therefore 25 and X is 49.

As a result, 49 is the lowest value of x that can exist.

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Answer: it should be C.

Step-by-step explanation: because its ascking to describe the formation.

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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The area of cheese is 38 square centimeters.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given that the height of the cheese is 2.5 inches and the base is 4.75 inches.

The value of 1 inch is 2.54 centimeters.

Now convert 2.5 inches and 4.75 inches into centimeter:

2.5 inches = (2.5 × 2.54) centimeters = 6.35 centimeters

4.75 inches = (4.75 × 2.54) centimeters = 12.065 centimeters

The area of triangle is (1/2) × base × height

The area of the cheese is [(1/2) × 6.35 × 12.065] square centimeter

=38.31 square centimeter

= 38 square centimeters (nearest square centimeter)

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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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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 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 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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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 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:

y=1/3x+2

Step-by-step explanation:

................

Answer:

y=1/3x+2

Step-by-step explanation:

slope intercept form: y=xm+b

6y=2x+12

/6       /6

y=2/6x+2

y=1/3x+2

have a great day!

According to the given area of rectangle, the length and width of the rectangle is 7 and 21 respectively.

Area of rectangle

The standard form of calculating the area of the rectangle is written as,

A = l x w

where l refers the length and w refers the width of the rectangle.

Given,

Here we have given that the area of a rectangle is 147 square feet. And we need to determine the length and width if the length is three times the width.

Let us consider length of rectangle is n,

Then the width of rectangle is 3n.

Here we have to remember that the area of a rectangle is

=> A = n x 3n = 3n²

Here we are told that the area,

=> 3n²=147

Then the value of n² = 49

Therefore, the length is 7 and the width is 21.

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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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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 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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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.

It is false that if the rank of the augmented matrix of a system of n linear equations in n unknowns is greater than the rank of the matrix of coefficients, then the matrix of coefficients is nonsingular

The augmented matrix is an extension of a matrix in which we add a column ( non homogeneous part of the system)

Say , Ax = b

Here , b is column part

So , Augmented matrix will be [ A : b ]

The Rank of augmented matrix can be found by performing elementary row operations on a augmented matrix and counting the number of the rows without zero comparing the rank of an augmented matrix

The rank of coefficient matrix can determined if there is a  solution to the system of solution

In the question this statement,

If the rank of the augmented matrix of a system of n linear equations in n unknowns is greater than the rank of the matrix of coefficients, then the matrix of coefficients is nonsingular is false

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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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Answer:

yeah im sorry i have no idea

Step-by-step explanation:

bro im soooooooo sorry

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:

A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.