Paul is going to have the exterior of his home painted. Painting USA charges $75.00 to come out and evaluate the house plus $25.00 per hour of labor. Upscale Home Painting does not charge to evaluate the house. However, they charge $40.00 per hour. If it takes 25 hours to paint Paul’s house, the most cost effective company will be?


The cost of painting the house will be the same for both companies if the number of hours required to paint Paul’s house is?

Answers

Answer 1
Answer: The most cost effective company will be:

$75.00
25 hours

Painting USA: Fixed Cost: $75; Variable Cost: $25x
Total Cost = 75 + 25(25) = 75 + 625 = 700

Upscale Home Painting: Fixed Cost: $0; Variable Cost: $40x
Total Cost = 40(25) = 1,000

The most cost effective company will be Painting USA whose charges will amount to $700


The cost of painting the house will be the same for both companies if the number of hours required to paint Paul's house is:

Painting USA:
Total Cost: 75 + 25(25) = 75 + 625 = 700

Upscale Home Painting
Total Cost: 40(16.5) = 40 + 660 = 700

The cost of painting the house will be the same for both companies if the number of hours required to paint Paul's house is approximately between 16.5 and 25 hours.








Answer 2
Answer:

The most cost effective company will be:

$75.00
25 hours

Painting USA: Fixed Cost: $75; Variable Cost: $25x
Total Cost = 75 + 25(25) = 75 + 625 = 700

Upscale Home Painting: Fixed Cost: $0; Variable Cost: $40x
Total Cost = 40(25) = 1,000

The most cost effective company will be Painting USA whose charges will amount to $700


The cost of painting the house will be the same for both companies if the number of hours required to paint Paul's house is:

Painting USA:
Total Cost: 75 + 25(25) = 75 + 625 = 700

Upscale Home Painting
Total Cost: 40(16.5) = 40 + 660 = 700

The cost of painting the house will be the same for both companies if the number of hours required to paint Paul's house is approximately between 16.5 and 25 hours.

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Express 0.001 in words.
14a + 13a + 8 = 22

What is the 2x2 identity matrix?

Answers

Answer:

a matrix with 1's in the main diagonal and zeros everywhere. The identity matrix of order 2×2 is: [1 0 0 1].

Final answer:

The 2x2 identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere. It serves as the multiplicative identity in matrix multiplication, leaving the original matrix unchanged when multiplied.

Explanation:

In mathematics, the 2x2 identity matrix, denoted by the symbol I or Id, is a square matrix containing elements that make it act as the multiplicative identity in matrix multiplication. Specifically, a 2x2 identity matrix is written as:

I = [1, 0; 0, 1]

Here, the numbers 1 are positioned on the main diagonal from the top-left to bottom-right (also termed as principal diagonal). The other elements, outside the main diagonal, are 0. This particular configuration results in special properties such as, when any matrix is multiplied by the identity matrix, the original matrix is unchanged. So, if we have a 2x2 matrix A, then multiplying by the identity gives AI = IA = A.

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What is the inverse function of d(x)= 2x-4

Answers

Formula for inverse function:
d^(-1)(y)=?\ny=2x-4\n2x=y+4\nx= (y+4)/(2)\n d^(-1)(y)= (y+4)/(2)
y=2x-4 \n Replace \ x \ by \ y:\n x=2y-4\n Isolate \ y:\n 2y=x+4\n y=(x+4)/(2)\n \n \boxed{d^(-1)(x)=(x+4)/(2)}

On a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?

Answers

Answer:

89.84375

Step-by-step explanation:

Given that on a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93.

To find weighted mean.

Here weights can be considered as number of majors in each subject

Marks x     90        85       93\nWeights     15          7         10\nProduct     1350    595     930\n

Weighted total = 1350+595+930 = 2875

Weighted mean = weighted total/total students

=(2875)/(32) =89.84375

An object launched vertically from a point that is 37.5 feet above ground level with an initial velocity of 48.6 feet per second can be represented by the equation h=−16t^2+48.6t+37.5, where h is the height of the object and t is the time after the object is launched. How long does it take the object to hit the ground?

Answers

Answer: 3.675 seconds

Step-by-step explanation:

Hi, when the object hits the ground, h=0:

h=−16t^2+48.6t+37.5

0=−16t^2+48.6t+37.5

We have to apply the quadratic formula:  

For: ax2+ bx + c  

x =[ -b ± √b²-4ac] /2a  

Replacing with the values given:  

a=-16 ; b=48.6; c=37.5

x =[ -(48.6) ± √(-48.6)²-4(-16)37.5] /2(-16)  

x = [ -48.6 ± √ 4,761.96] /-32

x = [ -48.6 ± 69] /-32

Positive:  

x = [ -48.6 + 69] /-32 = -0.6375

Negative:  

x = [ -48.6 - 69] /-32 = 3.675 seconds (seconds can't be negative)

Feel free to ask for more if needed or if you did not understand something.  

The object to hit the ground takes 3.675 seconds.

An initial velocity of 48.6 feet per second

When the object hits the ground, h=0:

h=−16t²+48.6t+37.5

0=−16t²+48.6t+37.5

We have to apply the quadratic formula:  

For: ax²+ bx + c  

x =[ -b ± √b²-4ac] /2a  

Substituting with the values given:  

a=-16 ; b=48.6; c=37.5

x =[ -(48.6) ± √(-48.6)²-4(-16)37.5] /2(-16)  

x = [ -48.6 ± √ 4,761.96] /-32

x = [ -48.6 ± 69] /-32

Positive:  

x = [ -48.6 + 69] /-32 = -0.6375

Negative:  

x = [ -48.6 - 69] /-32 = 3.675 seconds (seconds can't be negative)

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Please help!!Solve the equation and express each solution in a+bi form.
x^4-7x^2-8=0
a. x = -1, 1, 2 sqrt 2, or -2 sqrt 2
b. x = -i, i, 2 sqrt 2, or -2 sqrt 2
c. x = -1, 1, 2 sqrt 2i, or -2 sqrt 2i
d. x = -i, i, 2 sqrt 2i, or -2 sqrt 2i

Answers

Because this is a fourth degree that will be tricky to factor as it is, we will do a u substitution. Let x^2=u. We can now rewrite that polynomial in terms of u: u^2-7u-8=0. Filling into the quadratic formula we have u=(7+/-√(49-4(1)(-8)))/(2). Simplifying down u=(7+/-√(81))/(2) and u=(7+9)/(2) or u=(7-9)/(2). That means that u = 8 or u = -1. But don't forget that we let u=x^2, so we have to put x-squared back in for u. That gives us x^2=8 which simplifies down to +/-2√(2). That also gives us x^2=-1. When we take the square root of -1, we have to use the fact that -1 = i^2, so we sub that in to get x=+/-i. All in all, your solutions are as follows: 2√(2),-2√(2),i,-i which is choice b.

If m = 2 and n = 3, then m 2 + n 2 is equal to _____.

25
625
10
13

Answers

The value of m² + n² will be 13 ( option D)

What is algebraic expression?

An algebraic expression is a mathematical phrase that combines numbers, variables, and operations like addition, subtraction, multiplication, and division.

It represents a value that can vary depending on the values assigned to the variables. For example, "3x + 5" is an algebraic expression where 'x' is a variable.

The algebraic expression is m² + n² and the value of m and n are given as

m = 2 and n = 3

2² + 3²

= 4 + 9

= 13

Therefore, m² + n² will be 13

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Final answer:

When m = 2 and n = 3, m2 + n2 equals 13.

Explanation:

To find the value of m2 + n2 when m = 2 and n = 3, we substitute the values of m and n into the expression.

So, m2 + n2 = 22 + 32 = 4 + 9 = 13.

Therefore, when m = 2 and n = 3, m2 + n2 equals 13.

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