The dot plot below shows the amount of time two random groups of students took to solve a puzzle: a dot plot shows puzzle solving time in seconds on the horizontal axis. for group a, there is 1 dot on 65, 1 dot on 67, 1 dot on 77, 1 dot on 79, 1 dot on 88, 1 dot on 90, 2 dots on 92, 1 dot on 100, 2 dots on 102, 1 dot on 109, 1 dot on 110, 2 dots on 112, 1 dot on 122, 1 dot on 136, and 1 dot on 139. for group b, there are 2 dots on 50, 1 dot on 55, 1 dot on 61, 2 dots on 70, 2 dots on 80, 2 dots on 89, 1 dot on 95, 3 dots on 100, 1 dot on 110, and 1 dot on 114. based on visual inspection of the dot plots, which of the following groups, if any, shows a greater average time required to solve the puzzle? group a group b both groups show about the same average time. no conclusion about average time can be made from the data.

It's hard to visually inspect a description of the plot. Let's calculate.

A = ( 1(65) + 1(67) + 1(77) + 1(79) + 1(88) + 1(90) + 2(92)+1(100)+2(102)+1(109)+1(110)+2(112)+1(122)+1(136)+1(139)) / 18 = 99.7

B = ( 2(50)+1(55)+1(61)+2(70)+2(80)+2(89)+1(95)+3(100)+1(110)+1(114))/ 16=82.1

Group A averaged around 17 or 18 seconds longer.

Group A

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

x

step-by-step explanation: