Suppose s is a set of 10 integers (any integers at all). prove that there are a pair of numbers in s whose difference is a multiple of 9; i. e. prove that there exists a, b ∈ s and an integer k ∈ z such that a − b = 9k. (hint: apply the pigeonhole principle to the potential remainders of elements of s with respect to division by 9).

.19875994384

step-by-step explanation:

1699/ 8548

no he doesnt because "-16' is negatiive

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;

step-by-step explanation:

what is the figure? attach a picture.