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Questions 5
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 #5
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total number of points  =  ( 2 * number correct ) - ( 0.5 * number incorrect )

 

a.     score   =   ( 2 * 30 ) - ( 0.5 * 5 )   =   60 - 2.5   =   57.5

 

b.     No, you must know the number correct and the number incorrect to determine the score.

 

c.     We want to set the score equal to  80  and solve for the number incorrect.

        Also...let's say  c = number correct  and  w = number incorrect

 

80  =  2c - 0.5w            We want to solve this equation for  w  .  Subtract  2c  from both sides.

-2c + 80  =  -0.5w         Multiply both sides by  -2 .

4c - 160  =  w

w  =  4c - 160

 

d.  To graph it, we can say  y = w   and  x = c  .

 

y  =  4x - 160            To find the x-intercept, plug in  0  for  y  and solve for  x .

0  =  4x - 160

40  =  x                     The x-intercept is  40 .

 

When there are  0  incorrect, there must be 40 correct to get  80  total points.

 

y  =  4x - 160            To find the y-intercept, plug in  0  for  x  and solve for  y .

y  =  4(0) - 160

y  =  -160                  The y-intercept is  -160 .

 

When there are  0  correct, there must be  -160  incorrect to get  80  total points.

Realistically...that is impossible to do!!!

 

e.     Using the points we just found:     (40, 0)  and  (0, -160)

 

slope   =   [-160 - 0] / [0 - 40]   =   160/40   =   4

For every  4  additional wrong answers, there must be  1  additional right answer.

 

f.     w  =  4c - 16                          If  c = 43 ,  then

       w   =   4(43) - 160   =   12

 

The student must answer  12  questions wrong to get  80  points on the test.

 

But  43 + 12  =  55 , and there are only  50  questions on the test.

 

The student cannot get 12 wrong and 43 correct because there aren't enough questions. It's impossible for the student to get exactly  80  points on the test if he gets  43  correct.

 

The most he can get correct is  42 , which means he must get  8  wrong....remember....this is in order to get exactly 80 points on the test...no more, no less!

hectictar Nov 16, 2017