CPhill

(  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 

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% 

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

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.....

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

Prove that the points of ABCD below form a parallelogram by
showing that opposite sides are parallel and opposite sides are congruent.

3. A(-6, -4), B(4, 2), C(6, 8), D(-4, 2)

Slope  of  AB  =   (2 - - 4)  / (4 - - 6)  =  6 / 12  =  1/2

Slope of  CD  = ( 2 - 8)  /( -4 - 6)  =  -6 / -12  = 1/2

AB  =   sqrt   [ ( -6 - 4)^2  +  ( -4 - 2)^2  ]   =  sqrt  [ (-10)^2  +(- 6)^2 ]  = sqrt 136

CD  =sqrt  [ ( -4 - 6)^2  + ( 2 - 8)^2 ]    =sqrt [ 10^2  + (-6)^2  ] = sqrt 136

Now...using the same procedure....

Find  the slope of AD    and  BC

Then....using the distance formula   find   AD  and BC

Let me know  if  you get  stuck

1)  a) Slope  of  AB    =  (4 - 0)  / ( 4 - - 2)  =  4/ ( 4 + 2)  =  4 / 6  =  2 / 3 

     b)  Any parallel line to AB  will have  the same slope

     c)  A perpendicular line has a  negative reciprocal slope =  -3 /  2

Use slopes to show that △RST is a right triangle.

2. R(-3, -4), S(2, 2), T(14, -8)

Slope of RS  = ( 2 - - 4)  / ( 2 - - 3)  =  6 / 5

Slope of  ST    = ( -8-2) /( 14 - 2)  =  -10 / 12  =  - 5 / 6

RS  and  ST  have  negative reciprocal slopes......thus......they meet at right  angles

NP   !!!!

OK.....hope it helps some......