Answer:
Step-by-step explanation:
1.

2. q-p = 3p +5
q = 4p+5
4p = q-5
p = (q-5)/4
3. y = 2a -b

The probability is 1/1024.
Each tetrahedron has a 1/4 chance of landing on 3, since there are 4 sides and only one of them is marked 3.
Each tetrahedron roll is independent, since no roll is affected by another.
This means we multiply the probabilities:
1/4(1/4)(1/4)(1/4)(1/4) = 1/1024
Average speed of cyclist = x
average speed of car = 3x
x = 225/5
x = 45km/h
3x = 3(45)
3x = 135km/h
average speed of cyclist = 45km/h
average speed of car = 135km/h
Answer:
B
Step-by-step explanation:
Answer:
Either
(approximately
) or
(approximately
.)
Step-by-step explanation:
Let
denote the first term of this geometric series, and let
denote the common ratio of this geometric series.
The first five terms of this series would be:
First equation:
.
Second equation:
.
Rewrite and simplify the first equation.
.
Therefore, the first equation becomes:
..
Similarly, rewrite and simplify the second equation:
.
Therefore, the second equation becomes:
.
Take the quotient between these two equations:
.
Simplify and solve for
:
.
.
Either
or
.
Assume that
. Substitute back to either of the two original equations to show that
.
Calculate the sum of the first five terms:
.
Similarly, assume that
. Substitute back to either of the two original equations to show that
.
Calculate the sum of the first five terms:
.