Pl question: the line plot represents the number of quiz questions each of 12 students answered during a class period. after 5 more students participated, the mode increases and the median decreases. which could be the new graph?

Line plot represented by 3rd option is the correct choice.

Step-by-step explanation:

Please find the attachment

We have been given a line plot that represents the number of quiz questions each of 12 students answered during a class period. After 5 more students participated, the mode increases and the median decreases.

Upon looking at our given line plot we can see that there are scores of 12 students and median will be average of 6th and 7th term, that is 30.

Since mode is the number that appears most often in a data set. We can see that mode for given data set is 25 as there are 3 students with 25 answered questions.  

Now look at our given options, in which mode is greater than 25 and median is less than 30.  

1. Upon looking at 1st option we can see that mode is 55 that is greater than 25. The median is 50, which is also greater than 30, therefore, 1st option is not a correct choice.    

2. Upon looking at line plot represented by 2nd option we can see that mode is 10 as there are 4 students with 10 questions. Hence 10 is less than 25, therefore, 2nd option is not a correct choice.    

3. Upon looking at line plot represented by 3rd option we can see that mode is 55 as there are 4 students with 55 answered questions. The median is 25, which is less than 30, therefore, 3rd option is the correct choice.

4. Upon looking at line plot represented by 3rd option we can see that mode is 25, which is same as our given line plot. The median is 35, which is greater than 30, therefore, 4th option is not a correct choice as well.  

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

p(x)= 8 x³ - 36 x² + 54 x - 27

q(x) = 2 x -3

you can check your mistake and then you can choose the correct option.

dividend =   8 x³ - 36 x² + 54 x - 27

divisor = 2 x -3

if you want to find quotient, proceed as follows

q(x)= 0

2 x - 3=0

x =

now , i have used division method , to find quotient and remainder