By what number would you multiply -3/8 (fraction) to get a product of 1?

The perimeter of a rectangular swimming pool is 446 centimeters. The width of the pool is 7 centimeters less than the length of

Akimi4 [234]

Answer:

length = 115 cm

width = 108 cm

Step-by-step explanation:

The perimeter of a rectangular swimming pool is 446 centimeters

LEt L be the length of the pool

The width of the pool is 7 centimeters less than the length of the pool.

width = length - 7

W= L-7

Given perimeter = 446

Perimeter of rectangle = 2(length)+2(width)

446 = 2(L) + 2(W) we know W = L-7

446 = 2(L) + 2(L-7)

446 = 2L + 2L - 14

Add 14 on both sides

460 = 4L

divide by 4 on both sides

L= 115

Length L= 115

Width W = L - 7 = 115 - 7= 108

5 0

3 years ago

If you roll two six-faced dice together, you will get 36 possible outcomes. 4 pts 1. List all possible outcomes of the experimen

bezimeni [28]

Given:

Two dice are rolled together.

Total number of possible outcomes.

To find:

The list of total possible outcomes.

The probability of getting a sum of 11 in these outcomes.

The probability of getting a sum less than or equal to 4.

The probability of getting a sum of 13 or more.

Solution:

If two dice are rolled together, then the total number of possible outcomes is 36 and list of total possible outcomes is

S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Sum of 11 in these outcomes = {(5,6),(6,5),(6,6)} = 3

The probability of getting a sum of 11 in these outcomes is

$P(\text{sum=11})=\dfrac{3}{36}$

$P(\text{sum=11})=\dfrac{1}{12}$

Therefore, the probability of getting a sum of 11 in these outcomes is $\dfrac{1}{12}$ .

Sum less than or equal to 4 = {(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)} = 6

The probability of getting a sum less than or equal to 4 is

$P({sum\leq 4})=\dfrac{6}{36}$

$P({sum\leq 4})=\dfrac{1}{6}$

Therefore, the probability of getting a sum less than or equal to 4 is $\dfrac{1}{6}$ .

Sum of 13 or more = empty set because maximum sum is 12.

The probability of getting a sum of 13 or more is

$P(sum\geq 13)=\dfrac{0}{36}$

$P({sum\geq 13})=0$

Therefore, the probability of getting a sum of 13 or more is 0.

8 0

2 years ago

A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the rati

AnnyKZ [126]

Answer:

3:7

Step-by-step explanation:

So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or <em>20%</em> is alcohol. So let's just say that x=alcohol and y=water, this means that: $x+y=c$ where c is the total amount in the glass. This means that: $x=0.20c$

Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: $j+k=c$ and that: $j=0.40c$ .

So if we're going to add the two glasses, we simply add the two sides, and get: $j+x+k+y=2c$ . Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: $(0.4c+0.2c)+x+k=2c$ Now we can add like terms to get the equation: $0.6c+y+k=2c$ . We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.