To evaluate the effect of a treatment, a sample of n = 6 is obtained from a population with a mean of µ = 80, and the treatment is administered to the individuals in the sample. After the treatment, the sample mean is found to be M = 72. a. If the sample variance is s2 = 54, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05? b. If the sample variance is s2 = 150, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05?

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delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)