Select all the correct answers.
a supermarket is testing brands of microwave popcorn. for each brand, they recorded the percentage of corn kernels in a package that popped in the recommended cooking time. let a be the data set of percentages listed below.

a = {91, 94, 89, 93, 87, 92, 86, 87, 92, 91}

the supermarket then realized they missed a brand. when the new brand was cooked, only 74% of its kernels popped.

let b be the data set of percentages for all 11 packages, including the package where the least kernels popped.

select the statements that are true.

including the percentage for the package where the least kernels popped causes the spread of the data to decrease.
the mean of a is the same as the mean of b.
including the percentage for the package where the least kernels popped causes the center of the data to increase.
the median of a is the same as the median of b.
the standard deviation of b is greater than the standard deviation of a.
the interquartile range of a is the same as the interquartile range of b.

In the 30-60-90 triangle below side s has a length of and side r has a length

Can someone check if i did this correct. it’s number 4 if you’re wondering.

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24