A store salesperson is paid 3% of his sales as a commission. He made sales of $2500. How much was his commission?​

Answer:

.101265823

Step-by-step explanation:

2 x + 4 y = 1 has the simultaneous equation \(x=\frac{1-4 y}{2}\) .Eliminate a variable by using the elimination procedure.

for x, solve, \(2 x+4 y=1 \quad: \quad x=\frac{1-4 y}{2}\)

2 x + 4 y=1

4 y in the correct direction

2 x = 1 - 4 y

multiply both sides by two.

\(\frac{2 x}{2}=\frac{1}{2}-\frac{4 y}{2}\)

Simplify

\(x=\frac{1-4 y}{2}\)

You can find answers to both unknowns in two separate equations that have the same two unknowns in each. The three most popular approaches to solving are addition/subtraction, substitution, and graphing. simultaneous problems Equations: Elimination, Substitution, Graphical, and Matrix Methods | Vivax Solutions.

Steps for Solving Multiple Equations at Once Using the Elimination Method. Selecting a variable to remove is step one. Find the LCM of the variable's coefficients in step two. Step 3: Multiply the equations' two sides to create the coefficient of the variable you want to remove from the LCM.

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Answer:2730

Step-by-step explanation:

The number of ways we can choose three different numbers in order for a unique code for this case is 2730

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of \(^mC_k = \dfrac{m!}{k! \times (m-k)!}\) ways.

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

\(^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}\)

This is called permutation of k items chosen out of m items (all distinct).

Given that:

In a lock, the order of the way numbers are arranged matters.

Because of no repetition allowed, we can simulate this situation as:

The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.

And we have:

The number of ways we can choose 3 numbers out of 15 numbers with order = \(^{15}P_3 = \dfrac{15!}{(15-3)!} = \dfrac{15 \times 14 \times 13 \times 12!}{12!} = 2730\)

Thus, the number of ways we can choose three different numbers in order for a unique code for this case is 2730

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Answer:

2x3 - x2 - 50x + 25

Step-by-step explanation:

So the first thing you would do is multiply (x - 5)(x + 5)

x2 + 5x - 5x - 25

then you would simplify

x2 - 25

then you would multiply it by 2x - 1

(x2 - 25)(2x - 1)

2x3 - x2 - 50x + 25

so your answer is  

2x3 - x2 - 50x + 25

The projected revenue for the year ended December 31, Year 2 is $3,673.4 million.

How to find Revenue?

The amount of gross income generated by sales of goods or services is referred to as revenue (or sales revenue) in various contexts. Revenue can be calculated simply by multiplying the quantity of sales by the average service price or sales price:

Revenue = Sales x Average Price of Service or Sales Price

To find the projected revenue for the year ended December 31, Year 2, we can use the following formula:

Projected revenue = Current revenue * (1 + Expected revenue growth)

In this case, the current revenue is equal to the NOA, which is $3,532.1 million. The expected revenue growth is 5%, so the projected revenue is:

$3,532.1 million * (1 + 0.05) = $3,673.4 million

Therefore, The projected revenue for the year ended December 31, Year 2 is $3,673.4 million.

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a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

See attached

Step-by-step explanation:

\(M(t)= 0.5t^4 + 3.45t^3 -96.65t^2 +347.7t\)

for t = 0, 1, 2, 3, 4, 5 and 6

\(M(0)= 0.5(0^4) + 3.45(0^3) -96.65(0^2) +347.7(0) = 0\\\\M(1)= 0.5(1^4) + 3.45(1^3) -96.65(1^2) +347.7(1) =255\\\\M(2) = 0.5(2^4) + 3.45(2^3) -96.65(2^2) +347.7(2)=344.4\\\\M(3)= 0.5(3^4) + 3.45(3^3) -96.65(3^2) +347.7(3) =306.9\\\\M(4)= 0.5(4^4) + 3.45(4^3) -96.65(4^2) +347.7(4)=193.2\\\\M(5)= 0.5(5^4) + 3.45(5^3) -96.65(5^2) +347.7(5)=66\\\\M(6)= 0.5(6^4) + 3.45(6^3) -96.65(6^2) +347.7(6)=0\\\)

Plotting M(t) against t we will get the graph

Answer:

\(\begin{array}{c|c}t&M(t)\\\cline{1-2} 0&0\\1&255\\2&344.4\\3&306.9\\4&193.2\\5&66\\6&0\end{array}\)

See attached for the graph of the function.

Step-by-step explanation:

Given polynomial function:

\(M(t)= 0.5t^4 + 3.45t^3 -96.65t^2 +347.7t\)

The given polynomial function can be used to estimate the number of milligrams of the pain relief medication ibuprofen in the bloodstream t hours after 400 mg of the medication has been taken.

To find the number of milligrams of ibuprofen in the bloodstream at different time points, substitute the given values of t into the given function M(t).

\(\begin{aligned}t=0 \implies M(0)&= 0.5(0)^4 + 3.45(0)^3 -96.65(0)^2 +347.7(0)\\&=0+0+0+0\\&=0\; \sf mg\end{aligned}\)

\(\begin{aligned}t=1 \implies M(1)&= 0.5(1)^4 + 3.45(1)^3 -96.65(1)^2 +347.7(1)\\&=0.5(1)+ 3.45(1) -96.65(1) +347.7(1)\\&=0.5 + 3.45 -96.65 +347.7\\&=255\; \sf mg\end{aligned}\)

\(\begin{aligned}t=2 \implies M(2)&= 0.5(2)^4 + 3.45(2)^3 -96.65(2)^2 +347.7(2)\\&= 0.5(16) + 3.45(8) -96.65(4) +347.7(2)\\&=8+27.6-386.6+695.4\\&=344.4\; \sf mg\end{aligned}\)

\(\begin{aligned}t=3 \implies M(3)&= 0.5(3)^4 + 3.45(3)^3 -96.65(3)^2 +347.7(3)\\&= 0.5(81) + 3.45(27) -96.65(9) +347.7(3)\\&=40.5+93.15-869.85+1043.1\\&=306.9 \; \sf mg\end{aligned}\)

\(\begin{aligned}t=4 \implies M(4)&= 0.5(4)^4 + 3.45(4)^3 -96.65(4)^2 +347.7(4)\\&= 0.5(256) + 3.45(64) -96.65(16) +347.7(4)\\&=128+220.8-1546.4+1390.8\\&=193.2\; \sf mg\end{aligned}\)

\(\begin{aligned}t=5 \implies M(5)&= 0.5(5)^4 + 3.45(5)^3 -96.65(5)^2 +347.7(5)\\&= 0.5(625) + 3.45(125) -96.65(25) +347.7(5)\\&=312.5+431.25-2416.25+1738.5\\&=66\; \sf mg\end{aligned}\)

\(\begin{aligned}t=6 \implies M(6)&= 0.5(6)^4 + 3.45(6)^3 -96.65(6)^2 +347.7(6)\\&= 0.5(1296) + 3.45(216) -96.65(36) +347.7(6)\\&=648+745.2-3479.4+2086.2\\&=0\; \sf mg\end{aligned}\)

To sketch a graph of the function, plot these values on a graph with time on the x-axis and ibuprofen concentration on the y-axis, and draw a smooth curve through the plotted points. An appropriate scale to use is x-axis : y-axis = 1 : 50.

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Hello!

The distance, d, is less than 200 miles.

B. d > 200

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

The cylinder has a volume of 150.796 in³. The cylinder has a surface area of 175.929 in².

The quantity of three-dimensional space that an object or closed surface occupies is referred to as volume in mathematics. The cubic units of volume are m³, cm³, in³, and so on.

The sum of all of an object's faces is its surface area in three dimensions. Wrapping, painting, and finally building things to achieve the best possible design are examples of real-world applications of the concept of surface areas.

Given that a volume of cylinder = h × r² × π

                         h = 12 in

                          r = 2 in

                       volume = ?

Volume of cylinder = h × r² ×π

                                 = =12 × 3.14×(2)²

                                       =37.68 × 4

                                       =150.796 in³

B). Surface area of cylinder= 2πr² + 2πrh

                                         =2× 3.14 × (2)²+2× 3.14× 2×12

                                          =175.929in²

The formula V=r²(h) can be used to determine a cylinder's volume. Simply multiplying the area of the circular base shape by the height is all that is required to determine a cylinder's volume.

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Answer:

A is correct.

0 < x < 75 represents the correct domain.

The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).

The statement that applies to the sample math is:

B. the work shown to remove all fractions is not correct

The given steps are:

y = ¹/₄x + 2

- I first isolate the constant.

- After doing so, I get the equation: -¹/₄x + y = 2

- To remove the fraction, I multiply by –4, giving the equation x - 4y=2, which is the final answer.

The correct steps are as follows:

y = ¹/₄x + 2

First isolate the constant to get: y - ¹/₄x = 2

To remove the fraction, Multiply the obtained equation by –4

So, Equation : x - 4y = -8

On comparing both the work we can see that in the given work the removal of fraction is done incorrectly

They didn't multiply -4 on the right hand side .

Thus, option B applies.

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Answer:

x = 90

y = 44

is the answer for the question

A rhombus is a quadrilateral whose 4 sides are equal, it means all have the same length

Once given the length of one of the sides, all sides have the same length. As we also know one of the angles of this rhombus, we are limited to construct one unique rhombus.

The answer is that only one rhombus can be constructed using this information.

According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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Answer:

-42/7

Step-by-step explanation:

The only matrix that is certainly symmetric is a)\((a^2 - b^2).\)

We know that a matrix A is symmetric if it is equal to its transpose, that is \(A = A^T.\)

a) \((a^2 - b^2)\)

We can write the transpose of this matrix as

\((a^2 - b^2)^T = (a^2)^T - (b^2)^T = a^2 - b^2\), which is equal to the original matrix. Therefore, this matrix is symmetric.

b) (A+B)(A-B)

Expanding this expression, we get \((A+B)(A-B) = A^2 - AB + BA - B^2.\)

Taking the transpose of this, we get \((A^2)^T - (AB)^T + (BA)^T - (B^2)^T = A^2 - BA + AB - B^2.\)

Since AB and BA may not be equal, we cannot say for certain that this matrix is symmetric.

c) ABA

Taking the transpose of this matrix, we get\((ABA)^T = A^T B^T A^T\). Since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

d) ABAB

Taking the transpose of this matrix, we get \((ABAB)^T = B^T A^T B^T A^T\). Again, since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

Therefore, the only matrix that is certainly symmetric is a) \((a^2 - b^2).\)

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Answer: It is one-half the area of a rectangle with sides 2 units × 3 units.

It is twice the area of a square of side length 3 units.

It is one-half the area of a square of side length 3 units.

Step-by-step explanation:

Answer:

It is one-half the area of a rectangle with sides 2 units × 3 units.

Step-by-step explanation:

because the base of the triangle is connected in the "quadrilateral way" the base is one-half the rectangle and the units are 2x3 so therefore that answer is the correct one.

Answer:

1.09 is the answer for the question

Answer:

1.09

Step-by-step explanation:

25/23 to the nearest hundred is mean to round up the decimal points.

25/23= 1.08695652174.

1.08695652174 to the nearest hundred would be 1.09.

Please give the brainliest! :D

Answer:

Step-by-step explanation:

sin(A)=2/5

\(cos^2(A) +sin^2(A)=1\\cos^2(A)+[\frac{2}{5}]^2=1\\cos^2(A)+\frac{4}{25}=1\\ cos^2(A)=1-\frac{4}{25}\\ cos^2(A)=\frac{21}{25}\\ cosA=\frac{\sqrt{21} }{5}\)

Answer: The radius of the circle is 5 3/8 inches.

Step-by-step explanation:

The radius of the circle is half of the diameter. We can start by converting the mixed number diameter to an improper fraction:

10 3/4 = (10 × 4 + 3)/4 = 43/4

So, the diameter of the circle is 43/4 inches. The radius is half of this, which we can find by dividing by 2:

r = (43/4) ÷ 2 = 43/8

To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 1:

r = 43/8 = 5 3/8

Therefore, the radius of the circle is 5 3/8 inches.

Answer:5 3/4

Step-by-step explanation:

10 3/4 * 1/2

1/2 * 43/4 = 43/8

8/43=5 3/4

Hello!

3x + 4 = 1

3x + 4 - 4 = 1 - 4

3x = -3

3x/3 = -3/3

x = -1

The solution of the equation 3x + 4 = 1 is -1.

The answer is:

C) x = -1

Work/explanation:

To solve this equation, I subtract 4 from each side:

\(\sf{3x+4=1}\)

Subtract :

\(\sf{3x=-3}\)

Divide each side by 3:

\(\sf{x=-1}\)

Hence, C is correct.

Using the Empirical Rule, it is found that 99.7% of the weights are between 180 g and 480 g.

It states that, for a normally distributed random variable:

Hence, the bounds of the interval containing 99.7% of the weights is given by:

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Answer:

y= 0.5x + 8.2

$13.6 per hour

Step-by-step explanation:

(Is it weird that I had the same exact question? Maybe not. But I also found another person with the same question as me. It was a different question though. This is probably too late. But I'm just gonna try to answer it for anyone who needs it.

"Linear regression" is just a fancy word for scatter plots. Scatter plots take place in graphs. The dots or plots are scattered and the way they are scattered means something. If it's going down, it's negative, up it's positive, and if it's scattered, it has no corrolation.

Also, you should have learned this in 9th grade. So, check your notes.

If you don't have it, WRITE IT!!!

To find it in your calculator:

1. Go to "Lists and Spreadsheets"

2. Rename the first column "x" and the second on "y"

3. Write all of your numbers in the right column

1, 5, 3, 7 under the "x"

8.67, 10.50, 9.58, 11.41 under the "y"

4. Move your cursor to an empty cell

4. Click: "MENU" #4 #1 #3

5. Rename the correct rows "x" and "y" and press enter

6. Now you can find "m" and "b"

7. Then move your cursor to an empty cell and click "doc" "insert" #7

8. Find the x-axis and find "x"

9. Find the y-axis and find "y"

10. Now press "MENU" #4 #6 #1

And you found your y=mx+b: y=0.5x+8.2

Now, how much money per hour.

So you've found your m and b but now you have to:

1. Replace y with 15 and solve it

15=0.5x+8.2

-8.2       -8.2

6.8=0.5x

Divide 0.5 on both sides

6.8/0.5=13.6

13.6=x

$13.6 per hour