The general formula of a pyramid with any base is 1/3 bh where b is the area of the base and h is the height. In this case, the height of the pyramid is said to be twice the height of the prism, h. Hence the area becomes 1/3 b*2h or equal to option A. 2/3
Answer:
Approximately
(
.) (Assume that the choices of the
passengers are independent. Also assume that the probability that a passenger chooses a particular floor is the same for all
floors.)
Step-by-step explanation:
If there is no requirement that no two passengers exit at the same floor, each of these
passenger could choose from any one of the
floors. There would be a total of
unique ways for these
passengers to exit the elevator.
Assume that no two passengers are allowed to exit at the same floor.
The first passenger could choose from any of the
floors.
However, the second passenger would not be able to choose the same floor as the first passenger. Thus, the second passenger would have to choose from only
floors.
Likewise, the third passenger would have to choose from only
floors.
Thus, under the requirement that no two passenger could exit at the same floor, there would be only
unique ways for these two passengers to exit the elevator.
By the assumption that the choices of the passengers are independent and uniform across the
floors. Each of these
combinations would be equally likely.
Thus, the probability that the chosen combination satisfies the requirements (no two passengers exit at the same floor) would be:
.
Answer:
The height of the pole is 105ft,
Step-by-step explanation:
Let us call
the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is
.
The wire length
is 14 ft longer than height
, hence
.
Thus we get a right triangle with hypotenuse
, perpendicular
, and base
; therefore, the Pythagorean theorem gives

which upon expanding we get:

further simplification gives
,
which is a quadratic equation with solutions

Since the first solution
will give the triangle base length of
which is negative; therefore, we disregard it and pick the solution
.
Hence, the height of the pole is 105ft.
Hi there!
When we have an equation standard form...

...the formula of the discriminant is
D = b^2 - 4ac
When
D > 0 we have two real solutions
D = 0 we have one real solutions
D < 0 we don't have real solutions
1.) Find the value of the discriminant and the the number of real solutions of
x^2-8x+7=0
Plug in the values from the equation into the formula of the discriminant

D > 0 and therefore we have two real solutions.
2.) Find the value of the discriminant and the number of real solutions of
2x^2+4x+2=0
Again, plug in the values from the equation into the formula of the discriminant.

D = 0 and therefore we have one real solution.
~ Hope this helps you.
Answer:
y= 8th grade class,
y + 24 =160
subtract 24 from both sides
y=136
there are 136 students in the eight grade class
Step-by-step explanation: