Answer:
3(8) + 3d
24+3d
Step-by-step explanation:
I am not sure which two answer choices you have provided for you but these two expressions work for this problem
You know the following information:
1. The amount of money (in dollars) earned last year was:
2. The amount of money (in dollars) earned this year, is:
Then, to estimate the sum (the total amount of money the Software Company earned in those two years, you can round the numbers to the nearest billion.
Having:
You need to look at the digit located in the Hundred millions place. Notice that this is:
Then, since:
You need can't round up. Then:
Now, having:
You can identify that the digit in the Hundred millions place is
Therefore:
Now you can add the numbers rounded:
Hence, the answer is: Option B.
This is a geometric sequence with first term 1 and common ratio -1/2. r=-1/2.
a(n) = a(1)*(r)^(n-1).
Check: If n=2 our formula must return -1/2. Does it?
a(2) = 1(-1/2)^(2-1) = (-1/2)^1 = - 1/2. Yes.
a(3) should be 1/4. Is it? a(3) = (-1/2)^(3-1) = 1/4 Yes.
Then a(8) = (-1/2)^(8-1) = (-1/2)^7 = -1 / 2^7 = -1/128 (answer)
This is rationalising the denominator of an imaginary fraction. We want to remove all i's from the denominator.
To do this, we multiply the fraction by 1. However 1 can be expressed in an infinite number of ways. For example, 1 = 2/2 = 3/3 = 4n^2 / 4n^2 (assuming n is not zero!). Let's express 1 as the complex conjugate of the denominator, divided by the complex conjugate of the denominator.
The complex conjugate of (3 - 2i) is (3 + 2i). Then do what I just said:
4/(3-2i) * (3+2i)/(3+2i) = 4(3+2i)/(3-2i)(3+2i) = (12+8i)/(9-4i^2) = (12+8i)/(9+4) = (12+8i)/13
This is the answer you are looking for. I hope this helps :)
Answer:
Smallest rate for the train is 50 mph and largest is 60 mph.
For the bus it is 25 and 30 mph.
Step-by-step explanation:
If the speed of the train is 2x then speed of the bus is x mph, and the train travels twice as far as the bus in a given time.
Distance = speed * time
For the largest rate:
d = 2x * 0.5 for the train
x = d
0.5d = x for the bus
d - 0.5d = 15
0.5d = 15
d = 30
So the rate for the train = 30 / 0.5 = 60 mph.
In a similar fashion we can show that the smallest rate for the train is
25/ 0.5 = 50 mph.
