Question

1. lyai needs to complete this table for his consumer - science class. he knows the 1 tablespoon contains 3 teaspoons and that 1 cup contains 16 tablespoons.

number of teaspoons	number of tablespoons	number of cups
12
36	48	3

a. complete the missing values in the table.
b. write an equation that represents the number of teaspoons, t, contained in a number of tablespoons, b.

1. the volume of dry goods, like apples or peaches, can be measured using bushels, pecks and quarts. a bushel contains 4 pecks, and a peck contains 8 quarts.

what is the relationship between number of bushels, b, and the number of quarts, q? if you get stuck, try creating a table.

1. from unit 1, lesson 10

the data show the number of free - throws attempted by a team in its first ten games: 2 11 11 11 12 12 13 14 14 15
the median is 12 attempts and the mean is 11.5 attempts. after reviewing the data, it is determined that 2 should not be included, since that was an exhibition game rather than a regular game during the season.
a. what happens to the median if the “2” is removed from the data set?
b. what happens to the mean if the “2” is removed from the data set?

Explanation:

3.

a.

We know that 1 tablespoon contains 3 teaspoons and 1 cup contains 16 tablespoons.

Step1: Find number of teaspoons in 2 cups

Since 1 cup has 16 tablespoons and 1 tablespoon has 3 teaspoons, then 1 cup has $16\times3 = 48$ teaspoons. So 2 cups have $2\times48=96$ teaspoons.
Since 1 cup has 16 tablespoons, for 12 tablespoons, the number of cups is $\frac{12}{16}=\frac{3}{4}$ cup.

Step2: Find number of tablespoons in 3 cups

Since 1 cup has 16 tablespoons, 3 cups have $3\times16 = 48$ tablespoons. And the number of teaspoons in 3 cups is $3\times16\times3=144$ teaspoons.
The completed table:

number of teaspoons	number of tablespoons	number of cups
12	4	$\frac{3}{4}$
144	48	3

b.

Let $t$ be the number of teaspoons, $b$ be the number of tablespoons and $c$ be the number of cups.
We know that $b = \frac{t}{3}$ (because 1 tablespoon = 3 teaspoons) and $c=\frac{b}{16}$ (because 1 cup = 16 tablespoons). Substituting $b=\frac{t}{3}$ into $c=\frac{b}{16}$, we get $c=\frac{t}{3\times16}=\frac{t}{48}$, or $t = 48c$.

4.

Since 1 bushel contains 4 pecks and 1 peck contains 8 quarts, then 1 bushel contains $4\times8=32$ quarts.
The relationship between the number of bushels $b$ and the number of quarts $q$ is $q = 32b$.

5.

a.

The original data set is 2, 11, 11, 11, 12, 12, 13, 14, 14, 15. There are $n = 10$ data - points. The median of a set with $n = 10$ (an even - numbered set) is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. The $\frac{10}{2}=5$th and $(\frac{10}{2}+1)=6$th ordered data - points are 12 and 12, so the median is $\frac{12 + 12}{2}=12$.
If we remove 2 from the data set, the new data set is 11, 11, 11, 12, 12, 13, 14, 14, 15. There are $n=9$ data - points. The median of a set with $n = 9$ (an odd - numbered set) is the $(\frac{n + 1}{2})$th ordered data - point. $\frac{9+1}{2}=5$th ordered data - point, which is 12. So the median remains the same.

b.

The original mean $\bar{x}=\frac{2+11 + 11+11+12+12+13+14+14+15}{10}=\frac{115}{10}=11.5$.
The sum of the original data set is $S=2 + 11+11+11+12+12+13+14+14+15 = 115$.
After removing 2, the new sum is $S'=115 - 2=113$.
The new number of data - points is $n'=9$.
The new mean is $\bar{x}'=\frac{113}{9}\approx12.56$. The mean increases.

Answer:

3a. See completed table above.
3b. $t = 48c$

1. $q = 32b$

5a. The median remains the same.
5b. The mean increases.