The dot plots below show the scores for a group of students who took two rounds of a quiz:
which of the following inferences can be made using the dot plot?
a. there is no overlap between the data.
b. round 1 scores were lower than round 2 scores.
c. round 2 scores were higher than round 1 scores.
d. the range of round 1 is greater than the round 2 range.

Option: D is the correct answer.

        D. The range of round 1 is greater than the round 2 range.

Step-by-step explanation:

Round-1

       Score                Frequency          Total

         5                           1                       5×1=5

         6                           4                       6×4=24

         7                            2                      7×2=14

         8                            2                      8×2=16

         9                            1                       9×1=9

                                              Total--      68

Hence, total score obtained in Round 1 are: 68

Round-2

       Score                Frequency          Total

         5                           3                      5×3=15

         6                           1                       6×1=6

         7                            6                      7×6=42

                                              Total--      63

Hence, total score obtained in Round 1 are: 63

Hence, Round-1 scores were higher than Round-2 scores,=.

Hence, option: B and C are discarded.

Also, there is a overlap in the data ( since there are some scores which are obtained in both the rounds)

Hence, option: A is discarded.

Now,

Range of round-1 score is:

Maximum score-Minimum score

=9-5

=4

Hence, Range of Round-1 is: 4

Similarly Range of Round-2 is: 2

( Since, Maximum score in round-2 is: 7

and Minimum score is: 2

Hence, Range=7-5=2  )

                Hence, the correct answer is:

       D. The range of round 1 is greater than the round 2 range.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.