Answer:
9.694 years
Step-by-step explanation:
Let the investment is $P.
So, we are asked to determine the time it will grow to triple with the compound interest rate of 12%.
Let the time is y years.
So, from the formula of compound interest we can write
⇒
⇒
Now, taking log both sides we get,
y log 1.12 = log 3 {Since,
}
⇒ 0.04922y = 0.477712
⇒ y = 9.694 years (Answer)
Answer:
Part 1) 
Part 2)
a) 
b) 
c) 
Step-by-step explanation:
<u><em>The complete question in the attached figure</em></u>
Part 1) Write an expression for the perimeter of the shape
we know that
The figure is composed by a larger square, a rectangle and a smaller square
1) The area of the larger square is given

so
The length and the width of the larger square is x units
2) The area of the rectangle is given

so
The length of the rectangle is x units and the width is 1 unit
3) The length and the width of the smaller square is x units
see the attached figure N 2 to better understand the problem
Find out the perimeter
The perimeter is the sum of all the sides.
so


Part 2) Find the perimeter for each of the given values of x.
a) For x=7 units
Substitute the value of x in the expression of the perimeter

b) For x=5.5 units
Substitute the value of x in the expression of the perimeter

b) For x=7/3 units
Substitute the value of x in the expression of the perimeter

Answer:
A. Plane B because it was 9.33 miles away
B. 48 units
Step-by-step explanation:
A. Since the airplanes fly at an angle to the runway, their direction forms a triangle with the runway with their height above the ground as the opposite of the angle and their distance from the airport as the hypotenuse.
So for airplane A with 44° angle of departure,
sin44° = y/h where y = height above the ground and h = distance from airport
So h = y/sin44° = 6/sin44° = 8.64 miles
So for airplane B with 40° angle of departure,
sin40° = y/H where y = height above the ground and H = distance from airport
So H = y/sin40° = 6/sin40° = 9.33 miles
Since airplane B is at 9.33 miles away from the airport whereas airplane A is 8.64 miles from the airport, airplane B is farther away.
B. We know that scale factor = new size/original size
Our scale factor = 4 and original size = 12 units. So,
new size = scale factor original size = 4 × 12 = 48 units.
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.
Answer:
they're all rational numbers
Step-by-step explanation:
rational numbers are positive, negative, or zero integers. they can be decimals as well.
first expression = 2.449.... + 3 = 5.449 (yes, it is rational)
second expression = 8 + 0.54545454... = 8.545454... (yes, it is rational)
third expression = 6 + 4.582575... = 10.4582575... (yes, it is rational)
fourth expression = 4 + 13 = 17 (yes, it is rational)
fifth expression = 17.43... + 7 = 24.43.... (yes, it is rational)
sixth expression = 6.6332... + 5 = 11.6332 (yes, it is rational)