Question

1. four identical glasses are shown below. one glass is empty, and the other 3 glasses are $\frac{1}{4}$ full, $\frac{1}{2}$ full, and $\frac{4}{5}$ full of water, respectively. if the water were redistributed equally among the 4 glasses, what fractional part of each glass would be filled?

f. $\frac{2}{11}$
g. $\frac{8}{11}$
h. $\frac{3}{22}$
j. $\frac{31}{60}$
k. $\frac{31}{80}$

1. aurelio is purchasing carpet tiles to cover an area of his living - room floor that is $8\frac{1}{3}$ feet wide by 10 feet long. each carpet tile is a square 20 inches wide by 20 inches long. what is the minimum number of carpet tiles that aurelio must purchase to cover this area of his living - room floor?

a. 5
b. 11
c. 21
d. 30
e. 84

1. in the standard $(x,y)$ coordinate plane, a circle with its center at $(8,5)$ and a radius of 9 coordinate units has which of the following equations?

f. $(x - 8)^2+(y - 5)^2 = 81$
g. $(x - 8)^2+(y - 5)^2 = 9$
h. $(x + 8)^2+(y + 5)^2 = 81$
j. $(x + 8)^2+(y + 5)^2 = 9$
k. $(x + 5)^2+(y + 8)^2 = 81$
use the following information to answer questions 35 - 38.
many humans carry the gene yq77. the yq test determines, with 100% accuracy, whether a human carries yq77. if a yq test result is positive, the human carries the yq77 gene. if a yq test result is negative, the human does not carry yq77. sam designed a less expensive test for yq77 called the sam77 test. it produces some incorrect results. to determine the accuracy of the sam77 test, both tests were administered to 1,000 volunteers. the results from this administration are summarized in the table below.

positive yq test	negative yq test
negative sam77 test	25	375

1. it cost $2,500 to administer each yq test and $50 to administer each sam77 test. what was the total cost to administer both tests to all the volunteers?

a. $1,537,500
b. $1,556,750
c. $1,568,250
d. $2,500,000
e. $2,550,000

1. what percent of the volunteers actually carry yq77?

f. 57.5%
g. 60.0%
h. 60.5%
j. 61.5%
k. 62.5%

1. for how many volunteers did the sam77 test give an incorrect result?

a. 10
b. 25
c. 35
d. 385
e. 400

1. one of the volunteers whose sam77 test result was positive will be chosen at random. to the nearest 0.001, what is the probability the chosen volunteer does not possess yq77?

f. 0.017
g. 0.026
h. 0.035
j. 0.041
k. 0.063

Explanation:

Step1: Find the total amount of water

The amounts of water in the three non - empty glasses are $\frac{1}{4}$, $\frac{1}{2}$, and $\frac{4}{5}$. First, find a common denominator, which is 20. Then $\frac{1}{4}=\frac{1\times5}{4\times5}=\frac{5}{20}$, $\frac{1}{2}=\frac{1\times10}{2\times10}=\frac{10}{20}$, and $\frac{4}{5}=\frac{4\times4}{5\times4}=\frac{16}{20}$. The sum of the water is $\frac{5 + 10+16}{20}=\frac{31}{20}$.

Step2: Divide the total water by 4

To distribute the water equally among 4 glasses, divide $\frac{31}{20}$ by 4. $\frac{31}{20}\div4=\frac{31}{20}\times\frac{1}{4}=\frac{31}{80}$.

Answer:

K. $\frac{31}{80}$