If a cube has a volume of 216 cubic inches, what is the length of one side?

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

Learn more about equations, by the following link

brainly.com/question/2972832

#SPJ1

1.243 is the measure of the value of x from the given expression

Rational equations are those that contain rational expressions. A rational expression is a fraction with polynomial numerator and denominator. A rational expression, in other terms, is a ratio between two polynomials.

Given the following rational equation

√11 x = √17

We need to determine the measure of the value of x.

Taking the square of both sides we will have:

(√11 x)² = (√17)²

11x² = 17

x² = 17/11

x² = 1.545

Take the square root of both sides

√x² = √1.545
x = 1.243

Hence the measure of the value of x from the given equation is 1.243.

Learn more on rational equation here: https://brainly.com/question/12223525

#SPJ1

Answer:

C. $755 i got it right

Step-by-step explanation:

If you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).

percentage, a relative value indicating hundredth parts of any quantity.

To calculate the total cost of the computer if you make only the minimum payment each month, we need to use the simple interest formula:

A = P(1 + rt)

where A is the total amount paid, P is the principal or balance, r is the annual interest rate expressed as a decimal, and t is the time in years.

P = $600

r = 12.9% or 0.129 (annual interest rate)

t = 2 years

To find the monthly interest rate, we divide the annual interest rate by 12 (the number of months in a year):

Monthly interest rate = 0.129 / 12 = 0.01075

Now, we can use this monthly interest rate to calculate the minimum monthly payment:

Minimum monthly payment = 1% x P = 0.01 x $600 = $6

Therefore, the minimum monthly payment is $6.

To find the total cost of the computer over the 2-year period, we need to calculate the total amount paid (A) by making the minimum monthly payment each month:

A = P(1 + rt)

A = $600(1 + 0.01075 x 2 x 12)

A = $600(1 + 0.258)

A = $755.00

Therefore, if you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ3

The mean monthly rainfall, Rounded to the nearest thousandth, is 2.520 inches.

To determine the mean monthly rainfall, we need to calculate the average of the rainfall values provided in the table. Here is the table:

| Month | Rainfall (in inches) |

|-------|----------------|

| January   | 2.3                

| February  | 1.7                

| March     | 3.2                

| April     | 2.9                

| May       | 2.5                

To find the mean monthly rainfall, we add up the rainfall values for each month and divide the sum by the total number of months. In this case, we have five months:

Mean Monthly Rainfall = (2.3 + 1.7 + 3.2 + 2.9 + 2.5) / 5

Calculating the sum of the rainfall values:

Mean Monthly Rainfall = 12.6 / 5

Dividing the sum by the number of months:

Mean Monthly Rainfall = 2.52

Rounded the result to the nearest thousandth, the mean monthly rainfall is approximately 2.520 inches.

Therefore, the mean monthly rainfall, rounded to the nearest thousandth, is 2.520 inches.

To know more about Rounded .

https://brainly.com/question/30545728

#SPJ8

The equations for two parallel planes such that the first plane contains l1 is Ax + By + Cz = D, and the second plane contains l2 is Ax + By + Cz = E.

The equation of a plane is a mathematical representation of the position and orientation of the plane in space.

For line l1, let's take two points on the line, P1 and P2. The direction vector of the line is given by the difference between P2 and P1.

The cross product of this vector with a vector that points in the direction perpendicular to the line and the plane will give us the normal vector of the plane.

The equation of the plane containing l1 is given by:

Ax + By + Cz = D,

where A, B, and C are the coefficients of the normal vector and D is the constant that defines the position of the plane in space.

The equation of the plane containing l2 is given by:

Ax + By + Cz = E,

where A, B, and C are the same coefficients as in the first plane equation and E is the constant that defines the position of the second plane in space.

To know more about equation here.

https://brainly.com/question/10413253

#SPJ4

The width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.

What is Area of rectangle ?
Area of rectangle can be defined as product of length and breadth.

We know that the area of the rectangle is given by the function A(x) = x² + 8x, where x is the width of the rectangle. We also know that the area of the rectangle is 33 in². So we can set up the equation:

x² + 8x = 33

To solve for x, we can rearrange the equation and set it equal to zero:

x² + 8x - 33 = 0

We can now use the quadratic formula to solve for x:

\(x = (-b\±\sqrt{(b^2 - 4ac)}) / 2a\)

where a = 1, b = 8, and c = -33. Substituting these values, we get:

\(x = (-8\±\sqrt{(8^2 - 4(1)(-33))}) / 2(1)\)

\(x = (-8\± \sqrt{(256)}) / 2\)

x = (-8 ± 16) / 2

So x = -12/2 or x = 4.

Therefore, the width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.

To  learn more about Area of rectangle from given link.

https://brainly.com/question/20693059

#SPJ1

The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

Learn more about inverse here:

https://brainly.com/question/30659571

#SPJ1

In a case whereby One number is 11 less than another ,If their sum is increased by eight, the result is 81 the numbers will be 42.

The concept that will be used here is summation. A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.

Let the first number be wriiten as = x

second number = x-11

The we can add up as :

(x + x -11 + 8) =81

2x -3 =81

2x =84

x = 42

Learn more about sum at:

https://brainly.com/question/17695139

#SPJ1

Answer:

1.

\(6units\)

2.not sure about the coordinates

\(3. \sqrt{29} \)

4.the coordinates are not complete.

Answer:

The value is   \(P(3) = \frac{1}{n}\)

Step-by-step explanation:

From the question we are told that

   The number of keys is  n

    The number of keys remaining after the first key is chosen is  n-1

    The probability that he gains entrance with the first key he selects is \(\frac{1}{n}\)

      Generally the probability that the first key does not open the door is

             \(p(F_1) = 1 - \frac{1}{n} = \frac{n-1}{n}\)

      Generally the number of keys remaining after the second key is chosen is  

         n-2

      Generally the probability that he gains entrance with the second key he selects is

        \(\frac{1}{n-1}\)

       Generally the probability that the second key does not opens the door is

        \(P(F_2) = 1- \frac{1}{n-1} = \frac{n-2}{n-1}\)

   Generally the probability that he gains entrance with the third key he selects is

         \(\frac{1}{n-2}\)

Generally the probability that the door opens with the third key

        \(P(3) = p(F_1) * P(F_2) * \frac{1}{n-2}\)

=>       \(P(3) =  \frac{n-1}{n} *   \frac{n-2}{n-1} * \frac{n-2}{n-1}\)

=>        \(P(3) =  \frac{1}{n}\)

Note :  

      All the outcome of the events are independent

Answer:

See below

Step-by-step explanation:

You will just need to use your protractor to measure the given angles..

  Here is some gross guesses  starting with top row

      45     120   100  25   90   80  135  120 °

         Ensuring that each person has an equal chance to maximize their potential is what equality is all about.

Proof: Given that A = B and B = C, we can infer that A = C according to the transitive principle. A = C and C = D are both true if we also know that C = D. We shall ultimately get at A = D after one more transitive property application.

The symmetrical attribute of equality

This fact, which states that if  

18 + 10 =28,

then

28 = 10 + 18,

Serves as an example of the equality's symmetric property. The symmetric property of equality in mathematics is actually fairly straightforward. According to this principle, if a = b, then b =a.

To Learn more About equality, Refer:

https://brainly.com/question/401435

#SPJ9

Answer:

88.7 rounded and 88.66 not rounded

As a result, the set of all [u, w] Rn Rn satisfying the previous equation is the tangent space to F at [v1, v2]  by using preimage theorem.

Let F be the Stiefel manifold of orthonormal 2-frames in Rn to apply the preimage theorem. The collection of all tangent vectors to curves passing through [v1, v2] in F is what is known as the tangent space T[F] at a location [v1, v2]. Let (t) be a straight line in F such that (v1, v2) is a smooth curve. The tangent vector to t at time t = 0 is then given by

γ′(0) = [u, w] ∈ T[F].

We must now determine the requirements that [u, w] must meet in order to be in T[F]. Assume that V is a matrix with columns named v1 and v2. If Q is an orthogonal matrix, then any orthonormal 2-frame [v1′, v2′] in Rn can be represented as VQ. The category to which [v1′, v2′] belong Q is a 2 by 2 matrix with determinant 1, and F is equivalent to Q. Given that Q(0) = I, let Q(t) be a smooth curve in SO(2). Then, there is

γ(t) = VQ(t) (t),

and

γ′(0) = VQ′(0) (0).

We have Q since Q(t) is orthogonal (t)

TQ(t) = I, indicating

Q′(0)T + Q′(0) = 0.

Let [u, w] T[F] now. Once this is the case, a smooth curve Q(t) in SO(2) exists with Q(0) = I and

[u, w] = VQ′(0) (0).

Applying the equation above, we obtain

v1uv2w plus v1wv2u equals 0.

As a result, the set of all [u, w] Rn Rn satisfying the previous equation is the tangent space to F at [v1, v2].

to know more about" theorem" at https://brainly.com/question/343682

#SPJ4

When a man selects 3 items, the probability that they're all defective will be 1/64.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

From the information, bag contains 8items of which two are deffective. The probability of a defective item is:

= 2/8

= 1/4

When a man selects 3 items, the probability that they're all defective will be:

= (1/4)³

= 1 / 64

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Complete question

A bag contains 8items of which two are deffective. A man selects 3 items, what is the probability that they're all defective?

The ratio of blue paints to yellow paint is a mixture of 2 : 3.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or

\(\dfrac{a}{b}\)

The Total cans of blue paint = 14

Total cans of yellow paint = 20

Day 1:

Yellow paint = 6 cans

Blue paint = 4 cans

The ratio of blue paints to yellow paint

= 2 : 3

Day 2:

Yellow paint = 9 cans

Blue paint = 6 cans

The ratio of blue paints to yellow paint

2 : 3

Day 3:

Cans of yellow remaining after 2 days

Yellow paint = Total cans of yellow paint - day 1 cans of yellow paint - day 2 cans of yellow paint

= 20 - 6 - 9

= 20 - 15

= 5 cans

Cans of blue remaining after 2 days

Blue paint = Total cans of blue paint - day 1 cans of blue paint - day 2 cans of blue paint

= 14 - 4 - 6

= 14 - 10

= 4 cans

Learn more about ratios here:

brainly.com/question/186659

#SPJ1

QUESTION:- SOLVE EQUATION BY FACTORISATION

EQUATION:-

\( {x}^{2} + x - 72 = 0\)

ANSWER:-

\( {x}^{2} + x - 72 = 0\\{x}^{2} + 9x - 8x - 72 = 0 \\ x(x + 9) - 8(x +9) = 0 \\ (x - 8)(x + 9) = 0 \\ \)

NOW FOR VALUE OF X ->

\(x - 8 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 9 = 0\\ x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 9\)

(5x³-7)(2x²+1)

OPTION D is the correct answer

Answer:

The expected value of lateness \(\frac{7}{20}\) hours.

Step-by-step explanation:

The probability distribution of lateness is as follows:

  Lateness             P (Lateness)

  On Time                     4/5

1 Hour Late                  1/10

2 Hours Late                1/20

3 Hours Late                1/20​

The formula of expected value of a random variable is:

\(E(X)=\sum x\cdot P(X=x)\)

Compute the expected value of lateness as follows:

\(E(X)=\sum x\cdot P(X=x)\)

         \(=(0\times \frac{4}{5})+(1\times \frac{1}{10})+(2\times \frac{1}{20})+(3\times \frac{1}{20})\\\\=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20}\\\\=\frac{2+2+3}{20}\\\\=\frac{7}{20}\)

Thus, the expected value of lateness \(\frac{7}{20}\) hours.

An expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment.

Expected value of lateness is  \(\frac{7}{20}\) hours.

Let us consider, P(x) is represent that probability of lateness and x represent number of hours late.

So, below a table is formed.

         x       0             1            2           3

      P(x)      4/5         1/10      1/20       1/20

From formula of expected value,

        E(x) = ∑ x P(x)

\(E(x)=(0*\frac{4}{5} )+(1*\frac{1}{10} )+(2*\frac{1}{20} )+(3*\frac{1}{20} )\\\\E(x)=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20} \\\\E(x)=\frac{7}{20}\)

So, expected value of lateness is 7/20 hours.

Learn more:

https://brainly.com/question/23286309

Answer:

Infinetly many (d)

Step-by-step explanation:

The graphs are the same, so they will all have the same solutions.

hope this helps!

ibrahim

Answer:

Step-by-step explanation:

4(30+5)

4(30)+4(5)

120+20

140

Step-by-step explanation:

The graphs are not give but the graph looks like the above picture.

Answer:

-14x² - x + 4

Step-by-step explanation:

(-10x² + 5x - 3) - (4x² + 6x - 7)

= (-10x² + 5x - 3) - (+4x²) - (+6x) - (-7)

= (-10x² + 5x - 3) -4x² -6x +7

= -10x²-4x² +5x-6x -3+7

= -14x²  - x + 4

9514 1404 393

Answer:

  y = x -11

Step-by-step explanation:

The table values don't have "nice" differences, so it is not easy to identify the pattern immediately. I found it worked to plot the points on a graph. This shows they are all on a line with a slope of 1. The point (0, -11) tells us that the y-intercept is -11.

A line with a slope of 1 and a y-intercept of -11 has the equation ...

  y = x - 11

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

For more such questions on height, click on:

https://brainly.com/question/28122539

#SPJ8

a) The amount of overhead cost that would have been applied to each job during May, based on the predetermined overhead rate, was as follows:

                                   Job X        Job Y        Job Z

Overhead applied   $9,000       $3,600     $5,400

b) The work-in-process inventory reported in the company's May 31 balance sheet was $10,500 for Job Z only.

c) The finished goods inventory that would be reported in the company’s May 31 balance sheet was $4,050.

d) The cost of goods sold that would be reported in the company's income statement for May was $14,500.

The predetermined overhead rate is the rate per unit at which overhead costs are applied to production units or jobs.

The predetermined overhead rate is the quotient of the total budgeted overhead cost divided by the relevant total cost driver units (e.g. direct labor hours).

Predetermined overhead rate = $45 per direct labor-hour

                                   Job X        Job Y        Job Z

Direct labor hours        200             80             120

Direct materials      $4,800       $1,800      $3,600

Direct labor               2,400         1,000         1,500

Overhead applied   9,000         3,600        5,400

                         ($45 x 200)  ($45 x 80)   ($45 x 120)

Production costs $16,200       $6,400    $10,500

Unit costs of Job X   $81 ($16,200/200)

Sold units of Job X = 150

Unsold units of Job X = 50 (200 - 150)

Work in process inventory = Job Z's total cost.

Finished Goods Inventory = $4,050 ($81 x 50)

Cost of Goods Sold = $14,500 ($6,400 + $81 x 100)

Learn more about the predetermined overhead rate at https://brainly.com/question/4337723

#SPJ1

Answer:

Step-by-step explanation:

Parallel lines have the same slope. The slope of the given line is 3. The easy way to do this, the one that uses our logical brains as opposed to our mathematical brain, tells us that since there is only one choice that has a given slope of 3, that is the one that we want. The second choice down is the only one that has a slope of 3.

Mathematically,

\(y-2=3(x-3)\) and

\(y-2=3x=9\) and

\(y=3x-9+2\) so

y = 3x - 7 (the second choice)