CPhill

We can solve this proportion

4x / x = 48 / (x + 2)     simplify

4  = 48 / (x + 2)     multiply both sides by  (x + 2)

4(x + 2)  = 48

4x + 8 = 48     subtract 8 from both sides

4x  = 40    divide both sides by 4

x  =10

Width of the badge  = 4x  =  4 (10)   = 40 cm

Order the data from low to high

(30, 32, 33, 36)   ( 37, 40, 40, 46)

The 3rd quartile  = median of second data grouping  =  40      (1)

The 1st quartile  = median of first data grouping = [32 + 33] / 2 = 65/ 2  =  32.5     (2)

The interquartile range  =  (1) - (2) =  40 - 32.5   =   7.5  ⇒  "B"

A is incorrect...animated movies last 75 minutes...comedies, 90  minutes

B is incorrect....we only know how long each type of movie is...we don't know how many are in each category

C is incorrect....a movie  could last  4 hours!!!

D is correct.....romance movies are typically longer than comedies

We can look at it this way, NSS

The total number of points he needs to average an "80"   =  5 tests * 80 average  = 400

So far....he has this many points ⇒   4 tests  *  78 average  = 312

So...he needs to make  [400 - 312] =  88  on the last test to get an average of  "80"

Mean  = [ 10 + 19 + 21 + 28 + 12 +  20 + 16 ] / 7  = 18

Squared  differences  from  mean

(10 - 18)^2  = (-8)^2  = 64

(19 - 18)^2  = 1^2  = 1

(21 - 18)^2  =  3^2  = 9

(28 -- 18)^2  = 10^2  = 100

(12 - 18)^2  = (-6)^2  = 36

(20 - 18)^2 = 2^2  = 4

(16 -  18) ^2  =  (--2)^2  = 4

Variance  = sum of  squared differences / number of values = [ 64 + 1 + 9 + 100 + 36 + 4 + 4 ] / 7  = 31.14

The range of the data set in the box and whisker plot  is  [highest value - lowest value ]  = [10 - 4  ] = 6

Arranging "A" from low to high we have  14, 20, 26, 32  ...range  = 32 - 14  = 18   

Arranging "B" from low to high we have  60, 62, 63, 63, 64 , 65  ....range  = 65 - 60  = 5

Arranging "C" from low to high  we have  16, 18, 19, 23, 26.....range = 26 - 16  = 10

Arranging "D" from low to high we have   9, 9, 11, 12, 14, 15.....range  = 15 - 9  = 6

Let x be the  missing value we need

Average (mean)  = [ sum of the values ] / [ number of values          ....so we have....

80  =  [ 71 + 91 + 82 + 90 + 88 + 61 + 70 + x ]  / 8

80  = [553  + x ]  / 8     multiply both sides by 8

640  = 553 + x        subtract 553 from both sides

87  = x  = the missing value

We need to be careful about lining up the decimals

118,000. 00

+  3,491. 04

_________

121,491.04   

Add 118,000.00 and 3491.04.....what do you get  ???

Correct  !!!