27 david plans to cover the floor of his room with new material. the floor is an isosceles trapezoid whose…

27 david plans to cover the floor of his room with new material. the floor is an isosceles trapezoid whose bases are 16 feet and 26 feet and sides are 13 feet in length. each piece of new material has an area of 2.5 square feet. assuming the pieces of new material can be cut as needed, how many pieces does david need? a 101 b 126 c 202 d 252 28 which method is most likely to produce a random sample of 5 students from a school club? a selecting 5 club members who have brown hair b selecting the 5 club members who have raised the most funds for the club c selecting 5 club members from a hat containing the names of all members d selecting the 5 club members who arrive last to a club meeting

27 david plans to cover the floor of his room with new material. the floor is an isosceles trapezoid whose bases are 16 feet and 26 feet and sides are 13 feet in length. each piece of new material has an area of 2.5 square feet. assuming the pieces of new material can be cut as needed, how many pieces does david need? a 101 b 126 c 202 d 252 28 which method is most likely to produce a random sample of 5 students from a school club? a selecting 5 club members who have brown hair b selecting the 5 club members who have raised the most funds for the club c selecting 5 club members from a hat containing the names of all members d selecting the 5 club members who arrive last to a club meeting

Answer

27

Explanation:

Step1: Calculate area of trapezoid

The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the bases and $h$ is the height. First, find the height. Using the Pythagorean theorem in the right - triangle formed by half of the difference of the bases and the non - parallel side. The difference of the bases is $26−16 = 10$ feet, half of it is $5$ feet. The non - parallel side is $13$ feet. So, $h=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}=12$ feet. Then $A=\frac{(16 + 26)\times12}{2}=\frac{42\times12}{2}=252$ square feet.

Step2: Calculate number of pieces

Divide the area of the floor by the area of each piece. Let $n$ be the number of pieces. $n=\frac{252}{2.5}=100.8$. Since the pieces can be cut as needed, we need to round up to the next whole number, so $n = 101$.

Answer:

A. 101

28

Brief Explanations:

A random sample should give every member of the population an equal chance of being selected. Selecting from a hat containing the names of all club members (Option D) gives each member an equal probability of being chosen, which is the characteristic of a random sample. Options A, B, and C are non - random as they are based on specific non - random criteria (hair color, fundraising amount, arrival time).

Answer:

D. selecting the 5 club members from a hat containing the names of all members