One sample has a mean of M=7.2 and a second sample has a mean of M=12.8. The two sample are combined into a single set of scores. a. What is the mean for the combined set if both the samples have n=5? b. What is the mean for the combined set if the first sample has n=5 and the second sample had n=35?

a. M = 50

b. M = 242

Step-by-step explanation:

mean =  

⇒ sum of scores = mean x number of samples

Let the mean be represented by M, and the number of samples be represented by n,

sum of scores = M x n

a. When n = 5 for both samples,

The first sample's sum of scores = M x n

                                     = 7.2 x 5

                                     = 36

The second sample's sum of scores = M x n

                                     = 12.8 x 5

                                     = 64

The mean for the sum of scores of the combined set =

                                     = 50

When both samples have n = 5, the mean of the combined set is 50.

b. When the first sample has n = 5, the sum of scores = 36.

If n = 35 for the second sample, the sum of scores = M x n

                                                          = 12.8 x 35

                                                          = 448

The mean for the sum of scores of the combined set =

                                                    = 242

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752