A rectangular floor 8 feet long and 6 feet wide is to be completely covered with tiles. Each tile is a square with a perimeter of 2 feet. What is the least number of such tiles necessary to cover the floor?

A)7
b)12
c)24
d)48
e)192
^I got C

A culture of bacteria initially contained p cells, where p is greater than 100. After one hour, this population decreased by 1/3. In the second and third hours, however, the population increased by 40% and 50%, respectively. At the end of those first three hours, what was the population of the culture?
A)1.3p
B)1.4p
C)1.5p
D)1.6p
^I do not know

A jar contains only red, white, and blue marbles. It contains twice as many red marbles as white marbles and three times as many white marbles as blue marbles. If a marble is chosen at random, what is the probability that is NOT red?
A)1/5
B)2/5
C)3/5
D)4/5

1.

8 feet = 96 inches
6 feet = 72 inches

A = LW
A = 96 * 72
A = 6912 square inches

6912 / 36 = ______ tiles

1) (B)

Area of the floor = 6*8 = 48 square units
Area of each tile = 2*2 = 4 square units
Tiles needed = 48/4 = 12

The answer is 12

2) (B)

Let's take the initial number of cells as p.

After one hour -> Decrease of 1/3 -> (2/3)p remains

After another hour -> Increase of 40% -> New amount is 140/100 times the old amount -> New amount is (2/3)p * (140/100) = (14/15)p

After another hour -> Increase of 50% -> New amount is 150/100 times the old amount -> New amount is (14/15)p*(150/100) = (7/5)p = 1.4p

The answer is 1.4p

3) (B)

Blue marbles = x
White marbles = 3x
Red marbles = 2(3x) = 6x

Total = 10x

Probability of not being red = (3x + x)/10x
= 4x/10x
4/10 = 2/5

2) After the first hour, p decreased by 1/3 of p, so it became p-p/3=2p/3.

Then, when it increased by 40% it became 2p/3*1.4
2p/3*14/10
2p/3*7/5
14p/15
Finally, it increased by 50%
14p/15*1.5
(14p*1.5)/15
21p/15
7p/5
in decimal form this is 1.4p, which is B

3) let us call the number of blue marbles "b". then the number of white marbles is thrice as much, or 3b. The number of red marbles is twice the number of white marbles, or 2*3b=6b
Blue: b
White: 3b
Red: 6b
The total amount is 10b
the amount that is not red is b+3b=4b
4b/10b=2/5, choice B

a square tile with a 2 ft perimeter is 1/2 ft on each side

you can fit 16 tiles on the 8 ft dimension, and 12 on the 6 ft dimension
16 * 12 = ?

2/3 * 1.4 * 1.5 = ?

w = 3 b
r = 2 w = 6b
b + 3b + 6b = 10b
fraction r = 6b / 10b = 6/10 = 3/5
so, not r is ... 1 - 3/5

1 out of 3 for jerkthug

To find the least number of tiles necessary to cover the floor, we need to calculate the total number of tiles required by dividing the area of the floor by the area of each tile.

The area of the floor is given by length times width, so the area is 8 feet * 6 feet = 48 square feet.

The area of each tile is side length times side length, and since the perimeter of each tile is 2 feet, the sides of the tile are 2 feet / 4 = 0.5 feet. Therefore, the area of each tile is 0.5 feet * 0.5 feet = 0.25 square feet.

To find the least number of tiles necessary to cover the floor, we divide the area of the floor by the area of each tile: 48 square feet / 0.25 square feet = 192 tiles.

Therefore, the least number of tiles necessary to cover the floor is 192.

For the second question about the population of bacteria, let's break it down step by step:

According to the problem, initially, the population of bacteria is p.

After the first hour, the population decreased by 1/3, which means it became (1 - 1/3) * p = 2/3 * p.

In the second hour, the population increased by 40%, or 0.4. So the new population after the second hour is (1 + 0.4) * (2/3 * p) = 1.4 * (2/3 * p).

In the third hour, the population increased by 50%, or 0.50, from the population after the second hour. So the new population after the third hour is (1 + 0.50) * (1.4 * (2/3 * p)) = 1.5 * (1.4 * (2/3 * p)).

Simplifying this expression gives us 1.5 * 1.4 * 2/3 *p = 2.1 * 2/3 * p = 4.2/3 * p = 1.4 * p.

Therefore, the population of the culture at the end of three hours is 1.4p.

For the third question about the probability of choosing a non-red marble from the jar, let's find the total number of marbles first:

Let's assume the number of blue marbles is x.

The number of white marbles is three times the number of blue marbles, so it is 3x.

The number of red marbles is twice the number of white marbles, so it is 2 * 3x = 6x.

The total number of marbles in the jar is x + 3x + 6x = 10x.

The probability of choosing a non-red marble is the probability of choosing either a blue or a white marble.

The probability of choosing a blue marble is x / (x + 3x + 6x) = x / 10x = 1/10.

The probability of choosing a white marble is 3x / (x + 3x + 6x) = 3x / 10x = 3/10.

So, the probability of choosing a non-red marble is (1/10 + 3/10) = 4/10 = 2/5.

Therefore, the probability that the marble chosen is not red is 2/5.