Answer:
14,146 years
Step-by-step explanation:
The annual multiplier is (1 -0.0049%) = 0.999951. We want to find the number of times this needs to be multiplied to make the product 1/2.
0.5 = 0.999951^t
log(0.5) = t·log(0.999951)
log(0.5)/log(0.999951) = t ≈ 14,145.514
The half-life is about 14,146 years.
Answer:
The probability is 
≅ 
Step-by-step explanation:
Let's analyze the question.
There are 15 students in the 8th grade.
The students are randomly placed into three different algebra classes of 5 students each.
We are looking for the probability that Trevor, Terry and Evan will be in the same algebra class.
One possible way to solve this question is to think about the product probability rule.
We can use it because we are in an equiprobable space. (And also the events are independent).
Let's set for example a class for Evan.
The probability that Evan will be in a class is 
Then for Terry there are 
places out of 
that puts Terry in the Evan's class.
We write 
Finally for Trevor there are 
places out of the remaining 
that puts Trevor in the same class with Evan and Terry.
Using the product rule we write :
The probability of the event is ≅
Hey there!
The perimeter of the floor plan is 30 inches.
Perimeter is length + length + width + width, so we can do 9 + 9 + 6 + 6 = 30
The area of the floor plan is 54 inches²
Area is length x width, so we can do 9 x 6 = 54
The perimeter of the actual size is 105 feet
First, we can solve the dimensions for the actual size. We know that 2 inches = 7 feet, so we can do 7/2 and get 3.5. This means that for every 1 inch, it's 3.5 feet. Then, we multiply the dimensions by 3.5:
9 x 3.5 = 31.5 feet
6 x 3.5 = 21 feet
Then we solve for perimeter. Perimeter is length + length + width + width, so we can do 31.5 + 31.5 + 21 + 21 = 105
The area of the actual size is 661.5 inches²
Area is length x width, so we can do 31.5 x 21 = 661.5
Hope this helps! Tell me if you need more help.
Answer:
One number, let's call it x, is 6 more than twice the other number, let's say this number is y.
x= 2y+6
x+y=21
We're left with a system of equations.
If we substitute the first equation in the second we find the value of y.
(2y+6)+y=21
3y+6=21
3y=15
<u><em>y=5</em></u>
Now that we have found the value of y, we can take that value and substitute it in the second equation (since it's easier) to find the value of x.
x+ (5)=21
<u><em>x=16</em></u>
<u><em>Now to check if our answers are correct, we plug in both values into any equation and see if they equate.</em></u>
x+y=21
(16)+(5)=21
21=21
Our solution is correct!
