Tutor profile: Maryann T.

Evaluate 3x^{2}+7xy+4y^{3}, when: 1. x = 4 and y= 5 2. x = -1 and y=2

Evaluating algebraic expressions simply means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the equation with the given value, then use the order of operations to simplify the resulting expression. 1. x = 4 and y = 5 a. Substitute the value of x and y = 3(4^{2})+7(4)(5)+4(5^{3}) b. Simplify. =3(16)+7(20)+4(125) c. Combine the numbers by applying the rules in adding integers. = 48+140+500 Answer: 688 2. x = -1 and y=2 a. Substitute the value of x and y = 3(-1)^{2}+7(-1)(2)+4(2^{3}) b. Simplify. =3(1)+7(-2)+4(8) c. Combine similar terms by applying the rules in adding/subtracting integers = 3-14+28 = 31-14 Answer: 17

Are the zeros in the number 4.280094 significant? If so, how many significant figures does it have?

According to the rules of significant numbers, all the zeroes between any two non-zero digits are significant. This condition is satisfied by the 0 between 8 and 9. Also, in a number with a decimal point, all the terminal zeroes are significant. As a result, both zeros in the provided number are significant.

A group of students will conduct a poll to find out what residents of a specific town think about the price spike on basic goods during the pandemic. What should the sample size be if the community has 10,000 residents and the students aim to use a sample with a 10% margin of error?

Here the population size (N) is 10000 and the margin of error (e) is 10% or 0.10. Substituting the given values in the formula n=\frac{N}{1+Ne^{2}}, we have n=\frac{N}{1+Ne^{2}} n=\frac{10000}{1+(10000)(0.10)^{2}} n=\frac{10000}{1+(10000)(0.01)} n=\frac{10000}{1+100} n=\frac{10000}{101} n= 99.01 or 99 As a result, the students' group will only perform the poll with 99 residents. A margin of error of 10% indicates that the student is 90% confident that the result obtained using the sample will closely approach the result obtained using the population.