There are four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag. Which expression represents the probability of randomly selecting a blue marble, replacing it, and then randomly selecting a red marble? StartFraction 4 over 10 EndFraction (StartFraction r over 10 EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction 4 over 10 r EndFraction) StartFraction 4 over 10 + r EndFraction (StartFraction r over 10 + r EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction r over 10 r EndFraction)

4/ (10+r) * r/ (10+r)

Step-by-step explanation:

four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag = 4+r+6 = 10+r marbles

P( blue) = blue marbles / total marbles

             = 4/ (10+r)

Then replace

P( r) = red marbles / total marbles

             = r/ (10+r)

P( blue replace ,red) =P ( blue ) * P(red)

                                    =  4/ (10+r) * r/ (10+r)

                                    = 4r / ( 10+r) ^2

ans789

step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;