CPhill

Order the data from low to high

(25   35    45   50)   60    (80   90   95   100)

The median  is 60

The median of the data grouping in the parentheses to the right  of this  gives us the third quartile value

Do you know how to get the median of this grouping, NSS ???

OK, NSS...to find the mean......add the calories  and divide by  4

If you want to post your answer...I'll double-check it...

Edit to correct an earlier mistake...

Order the data from  lowest to highest

(1  3    4   5    6)  ( 7   8   8   8   10 )

The median  is  [ 6 + 7] / 2 =  13/2  = 6.5

The median of the data group in the left set of parentheses is   4  = 1st quartile

The median of the data group in the second set of parentheses is 8  = 3rd  quartile

The interquartile range is    8 - 4  = 4

h(t)    =-3t^2  + 12t + 60

Let h(t)  = y

We want the form

y  = a (x - h)^2  + k      where k  will give us the max  height

Factor out the  -3

y  = -3 (t^2 - 4t - 20)          take 1/2 of 4  = 2...square it = 4 ...  add and subtract this within the parentheses

y = -3 ( t^2  - 4t + 4  - 20  - 4)  simplify within the parenthese

y = -3 (t^2 - 4t + 4   - 24)      factor the first three terms

y = -3 [ (t - 2)^2  - 24 ]     distribute the "-3"  across the terms in the bracket

y = -3 (t - 2)^2  + 72

k = 72  =  max ht  (in feet)

First....find the mean  =   [ 4 + 16 + 21 + 32 + 11 + 12 ] / 6   = 16

Calculate the sum of the squared differences between the mean and each data point

(4 - 16) ^2   = (-12)^2  = 144

(16 - 16)^2  = 0^2  = 0

(21 - 16)^2  = 5^2  = 25

(32 - 16)^2  = 16^2  = 256

(11 - 16)^2  = (-5)^2  = 25

(12 - 16)^2  = (-4)^2  = 16

Add these  =  144 + 0 + 25 + 256 + 25 + 16  = 466    

The variance  =  √ [ 466  /  nuumber  of data points ]   =  √ [466/6 ]  ≈  8.81

Answered here  :   https://web2.0calc.com/questions/math-help_148

We can solve the first with the mid-point formula

The x coordinate of the other unknown point can be found as

(2 + x) / 2  =  -1   multiply both sides by 2

2 + x  =  -2    subtract 2 from both sides

x  = -4

Since only one answer has -4 as the x coordinate, the answer must be  (-4, -2)  ⇒ "H"

For the second  x^3 - 64  factors as a difference of cubes  =

(x - 4) (x^2 + 4x  + 16)

So  (x - 4)  is a factor and  "A"  must be correct

The mistake is that she forgot to take both square roots  of   9   =   3  or  -3

Look at the diagram ;

A) ΔPXQ≅ΔRXS  is true

and

C) ΔSPQ≅ΔQRS   is true

The standard deviation is the square root of the variance  = 3.46 ⇒  B