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Wow...that's pretty  amazing  !!!!

7 remaining

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floor x  = 15

Solutions for  x

15  ≤  x   <  16

So

15 - 2  ≤  x - 2  <   16 - 2

13  ≤   x - 2 <   14

1/a  +  1/b  =  1/6

a, b  must  be >  6

So.....let    z = 6         a =  z + m        b = z +  n

So   we  have

1/ ( z + m)  +    1/ ( z + n)   =     1  / z         simplify

z [ 2z + m + n)  =    (z + m) (z + n)

2z^2  + zm + zn   =   z^2  + zm + zn  +  mn

z^2  =  mn

6^2  = mn

36  =  mn

m      n           a  = z + m          b   =  z +  n

1      36                  7                         42

2      18                  8                         24

3      12                  9                         18                   

4       9                 10                         15

6      6                  12                         12   (reject this)

So...we  can wirite  1/6    as the  sum of four  different  pairs of unit fractions

(0,3)  and  (1,5)    are on the  graph

Slope =  (5 -3) / ( 1 - 0)  =   2 / 1  = 2

Using  (0,3).....the  equation of the line  is

y =  2x   +  3        re-write  as

2x - y  =  -  3

See my  answers  under  your earlier post, Luckystar

a)   (55-60 ) / 3.4   =   - 1.47    =  .0708

      (106  - 110 /6.8 =    -.588  ≈ .2810

He did better on the aptitude trst

b)  ( 67 - 60) / 3.4   = 2.65  =  .996

     (119  - 110) / 6.8  = .132  = .5517

She did better  on  the knowledge  test

c )  -.43   =  .3336

He did better on  the  logic test  than on the  other two tests

          1    2    3   4    5   6    7

        _____________________

1              2    3   4    5   6    7    

2                         2         3

3                                    2

4

5

6

7

We  have   C(7,2)  =  21  possibiities

Only  9    meet  the  criteria

So

9  / 21  =     3 /  7

(a,b) = (22,12)

The probability is pi/8.

(  x -  23)

_______  =      1.25

   3.8

x -  23  =  1.25 (3.8)

x - 23  = 4.75

x =  4.75 + 23   =    27.75   =  Allan's BMI 

By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4).  Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i.  Then the other roots work out as

4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,

4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and

4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.

3. Last year, the numbers of skateboards produced per day at a certain factory were normally distributed with a mean of 20,300 skateboards and a standard deviation of 52 skateboards.

(a) On what percent of the days last year did the factory produce 20,404 skateboards or fewer?

Calculate  the  z score  =   ( 20404 - 20300) /   52    =   2 

The  z score  translates to    .9772 =   about  97.7  % 

(b) On what percent of the days last year did the factory produce 20,248 skateboards or more?

Calculate  the z score   =    [ 20248  - 20300 ] /  52   =  -1

The  z score translates  to  =  .1587

So....the  %  days  that  they produced  20,248  skateboards or more =  1 - .1587  = .8413  = about  84.13%

(c) On what percent of the days last year did the factory produce 20,196 skateboards or fewer?

z  =  [ 20196  -20300  ] / 52     = -2

The   z score translates to   . 0228  = 2.28% 

The answer is 13/25.

The smallest possible value of a is 10.

The answer is 15.

Add the  equations and we  get  that

2x  =  10y

x = (10/2) y  = 5y

Sub  this into the  first equation for  x

5y  +  (5y)y  =  250 y

5y  =  250y - 5y

5y^2 - 245y  =  0

5y ( y  -  49)  =  0

5y  =  0                    y  -  49  =  0

x = 5(0)  = 0             y =  49

                                x = 5(49)  = 245

x  =  0,  245

Ok yep it was 960

No prob.....

I answered  a simialr  question  here  :  https://web2.0calc.com/questions/help_55674

Only  the  numbers  are different, but the solution method should  be exactly  the  same.....

Thank you👍

june=6 months, 6*8.75=52.5

250-52.5 = $197.5?

Determine what special type of quadrilateral HIJK is without graphing.

4. H(0, 0), I(5, 0), J(7, 9), K(1, 9)

This  is  a trapezoid

Reasons  :   

HI  is  parallel to  JK

HK  and IJ  are not parallel

5. H(0, 1), I(2, -3), J(-2, -1), K(-4, 3)

Slope of  HI   =  -2

HI  =  sqrt (20)

Slope of  JK =  -2

JK   = sqrt (20)

Parallelogram....opposite sidex are  equal and parallel

106 because you need to find smallest 3 digit multiple of 7, then add 1