Answer:
A
Step-by-step explanation:
The volume of a rectangular prism is:
Since the prism has a square base, each side length being 2, this means that both the length and width of our prism is 2. Therefore:
So, we can write:
The height h increases at a rate of about 8 inches or 8/12 = 2/3 feet per minute.
So, after t minutes, the height will be 2/3(t) feet. Thus, we can substitute:
We want to find after how long it will be until the volume is 64 cubic feet. So, V = 64:
Solve for t:
The correct answer is A.
Answer:
E.
Step-by-step explanation:
Let's look at the sequence:
The sequence has a common difference. We say it has a common difference because 8-3 has the same value as 13-8.
The common difference is what these differences are equal which is 5.
The sequence is therefore linear or arithmetic (same thing).
So it has form 
where the slope/common difference is 5.
We need to find the 
intercept 
.
The list of points is related to the above sequence:
I only need one of these points to find .
Let's use the first one since it has smallest numbers and I don't wish to use the calculator unless I really have to.
with 
:
Subtract 5 on both sides:
So the equation for the set of points is:
Now they are using 
instead of x[/tex]:
Since all summations begin at 
, then the choices are done to either choice C and choice E.
I need to find how many terms are in the given series. The last number is 33. So what term number is associated with the value 33.
Add 2 on both sides:
Divide both sides by 5:
So there are 7 terms and the 7th term is 33.
So the answer is choice E.
Answer:
J = -2
Step-by-step explanation:
You must isolate the variable by dividing each side by factors that dont contain the variable.
So J would equal -2
Answer:
17
Step-by-step explanation:
This flight makes a right triangle
The sides are 8 and 15. The hypotenuse isnt know and that is the answer.
8^2 + 15^2 = c^2
c^2 = 289
c = 17
The purpose of the grid is to help you record possible and impossible combinations. The repeat of the headings 1st, 2nd, 3rd, 4th helps you compare to both shirt color and name.
Each given statement has certain implications. You are expected to be able to determine as many of those as you can, and mark the grid accordingly.
The first statement says two girls slide down before two other girls. This means the first two girls listed cannot be 3rd or 4th in line, and the last two girls listed cannot be 1st or 2nd in line. It also means that none of the named girls is wearing the blue shirt (so Madeline must be wearing it). These implications are marked in the attachment with X and a circled 1, to indicate to you that the first statement was where we got the X. The X is used to signify an impossible combination.
The second statement tells you the purple shirt will not be 3rd or 4th in line, since at least two girls are after it. It tells you that Alexis is not wearing purple or yellow (so must be wearing white), and it tells you that Alexis and the yellow shirt are not first in line. (We alread knew that about Alexis.)
The third statement lets you finish the problem. We just found that Alexis is wearing the white shirt, so it tells you Madeline is 2nd in line and Alexis is 3rd. (Alexis is 3rd or 4th, but so is Lauren. The only way Madeline can be next to Alexis is for Madeline to be 2nd and Alexis 3rd.) The check marks labeled with a circled 3 are the conclusions we drew from statement 3.
Since the yellow shirt is not first, Lauren must be wearing it 4th in line.
The final conclusion is ...
- Hanna, purple
- Madeline, blue
- Alexis, white
- Lauren, yellow
Once you have identified a combination, it can help to mark off the others in that row and column (of the group of 4 rows and columns) as being impossible. This can narrow the choices for the others. I didn't do that here because it makes the diagram busier and the sequence of marks less clear.
_____
It is a good idea to check your final answer with the original problem statements to make sure the answer is consistent with them.
