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artcher [175]
2 years ago
13

A business has $25,000 to spend on training sessions for its employees. It wants 45 of its employees to attend. The business wan

ts to send as many employees as it can to a technology training. The technology training costs $1,000 per person. The customer service training costs $500 per person. Create a system of equations that models how many of each type of training the business should purchase. 1,000x + 500y = 45 x + y = 25,000 1,000x + 500y = 25,000 x + y = 45 1,000x + y = 45 x + 500y = 25,000 x + 500y = 45 1,000x + y = 25,000
Mathematics
1 answer:
lilavasa [31]2 years ago
5 0

Answer: x+y=45\\\\1000 x + 500y = $2500

Step-by-step explanation:

Let x =  Number of employees taking technology training

y= Number of employees taking customer service training

Given, The technology training costs $1,000 per person. The customer service training costs $500 per person.

Total cost = 1000 x + 500y

Since, Total cost = $25,000 and total employee to attend training= 45 .

That means , the required equations are:

x+y=45\\\\1000 x + 500y = $2500

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Answer:

Inherently asymmetrical casual relationship.

Step-by-step explanation:

The dog owners are given free dog food samples which contain new vegetables. These samples are given to them by organizing booths at the dog events. The reaction of the dog owners is observed towards this new dog food. This an example of inherently asymmetrical relationship.

6 0
2 years ago
Shawna has $750 in the bank.she deposits $37.50 each week.Ruben has $850 in the bank.He deposits his paycheck of $102.75 every M
erastova [34]

Answer:

Step-by-step explanation:

Answer: it would take 20 weeks before the amount in both accounts would be the same.

Step-by-step explanation:

Let x represent the number of weeks that it will take either Ruben and Shawna to have the same amount of money in their account.

Let y represent the total amount that would be in Shawna's account after x weeks

Let z represent the total amount that would be in Ruben's account after x weeks

Shawna has $750 in the bank. She deposits $37.50 each week. This means that the total amount after x weeks would be

y = 37.5x + 750

Ruben has $850 in the bank. He deposits his paycheck of $102.75 every Monday,and he spends about $70.25 each week.. This means that the total amount after x weeks would be

z = 850 + 102.75x - 70.25x

z = 850 + 32.5x

To determine the number of weeks before the amount in both accounts will becomes the same, we would equate y to z. It becomes

37.5x + 750= 850 + 32.5x

37.5x - 32.5x = 850 - 750

5x = 100

x = 100/5 = 20

8 0
2 years ago
what is the answer to this A cylinder has a base diameter of 8ft and a height of 17ft. What is its volume in cubic ft, to the ne
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Answer:

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Step-by-step explanation:

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5 0
1 year ago
You could win a giant jar of jelly beans if only you could guess how many are in the jar. You find a smaller jar such that the g
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The giant jar of jelly beans is 5 times the size of the smaller jar. If there are 83 jelly beans in the smaller jar, the giant jar can be represented as 5(83).

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2 years ago
Read 2 more answers
The graphs of the quadratic functions f(x) = 6 – 10x2 and g(x) = 8 – (x – 2)2 are provided below. Observe there are TWO lines si
natta225 [31]

Answer:

a) y = 7.74*x + 7.5

b)  y = 1.148*x + 6.036

Step-by-step explanation:

Given:

                                  f(x) = 6 - 10*x^2

                                  g(x) = 8 - (x-2)^2

Find:

(a) The line simultaneously tangent to both graphs having the LARGEST slope has equation

(b) The other line simultaneously tangent to both graphs has equation,

Solution:

- Find the derivatives of the two functions given:

                                f'(x) = -20*x

                                g'(x) = -2*(x-2)

- Since, the derivative of both function depends on the x coordinate. We will choose a point x_o which is common for both the functions f(x) and g(x). Point: ( x_o , g(x_o)) Hence,

                                g'(x_o) = -2*(x_o -2)

- Now compute the gradient of a line tangent to both graphs at point (x_o , g(x_o) ) on g(x) graph and point ( x , f(x) ) on function f(x):

                                m = (g(x_o) - f(x)) / (x_o - x)

                                m = (8 - (x_o-2)^2 - 6 + 10*x^2) / (x_o - x)

                                m = (8 - (x_o^2 - 4*x_o + 4) - 6 + 10*x^2)/(x_o - x)

                                m = ( 8 - x_o^2 + 4*x_o -4 -6 +10*x^2) /(x_o - x)

                                m = ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x)

- Now the gradient of the line computed from a point on each graph m must be equal to the derivatives computed earlier for each function:

                                m = f'(x) = g'(x_o)

- We will develop the first expression:

                                m = f'(x)

                                ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

Eq 1.                          (-2 - x_o^2 + 4*x_o + 10*x^2) = -20*x*x_o + 20*x^2

And,

                              m = g'(x_o)

                              ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

                              -2 - x_o^2 + 4*x_o + 10*x^2 = -2(x_o - 2)(x_o - x)

Eq 2                       -2 - x_o^2 + 4*x_o+ 10*x^2 = -2(x_o^2 - x_o*(x + 2) + 2*x)

- Now subtract the two equations (Eq 1 - Eq 2):

                              -20*x*x_o + 20*x^2 + 2*x_o^2 - 2*x_o*(x + 2) + 4*x = 0

                              -22*x*x_o + 20*x^2 + 2*x_o^2 - 4*x_o + 4*x = 0

- Form factors:       20*x^2 - 20*x*x_o - 2*x*x_o + 2*x_o^2 - 4*x_o + 4*x = 0

                              20*x*(x - x_o) - 2*x_o*(x - x_o) + 4*(x - x_o) = 0

                               (x - x_o)(20*x - 2*x_o + 4) = 0  

                               x = x_o   ,     x_o = 10x + 2    

- For x_o = 10x + 2  ,

                               (g(10*x + 2) - f(x))/(10*x + 2 - x) = -20*x

                                (8 - 100*x^2 - 6 + 10*x^2)/(9*x + 2) = -20*x

                                (-90*x^2 + 2) = -180*x^2 - 40*x

                                90*x^2 + 40*x + 2 = 0  

- Solve the quadratic equation above:

                                 x = -0.0574, -0.387      

- Largest slope is at x = -0.387 where equation of line is:

                                  y - 4.502 = -20*(-0.387)*(x + 0.387)

                                  y = 7.74*x + 7.5          

- Other tangent line:

                                  y - 5.97 = 1.148*(x + 0.0574)

                                  y = 1.148*x + 6.036

6 0
1 year ago
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