For binomials of the form (x - y)^n, explain how to determine the sign of a term without writing out the entire expansion.

Answer with explanation:

We know that the (p+1)th term of a binomial is given by :-

Similarly we can write pth term (where ) of by the above rule as :-

We can see that if p is a odd number then the term is negative and if p is a even number then the term is positive.

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b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: