well, let's notice something, a cube, all equal sides, has a side of 6, thus its volume is simply 6*6*6 = 216 cm³.
now, a rectangular prism, is a cuboid as well, but with varying dimensions.
let's notice something 6*6*6 is simply a multiplication of 3 numbers, let's then do a quick <u>prime factoring</u> of those numbers, well, 6 factors only into 2 and 3, so then the product of 6*6*6 can really be rewritten as (2*3)(2*3)(2*3).
well, regardless on how we rearrange the factors, the product will be the same, commutative property, so the rectangular prism will more or less have the same product and thus just about the same prime factors.
so let's rearrange on say hmmm height = 3 cm, length = 3*3 cm and width = 2*2*2 cm, notice, is still the same prime factors, 3*9*8 = 216 cm³.
Check the picture below.
Answer:
B.
Step-by-step explanation:
Because of isosceles triangle, AB = CB.
Because of the median, AD = CD.
Because of congruence of segments being reflexive, BD = BD.
By SSS, the triangles BAD and BCD are congruent.
Answer: B.
Answer:
part 1) 0.78 seconds
part 2) 1.74 seconds
Step-by-step explanation:
step 1
At about what time did the ball reach the maximum?
Let
h ----> the height of a ball in feet
t ---> the time in seconds
we have

This is a vertical parabola open downward (the leading coefficient is negative)
The vertex represent a maximum
so
The x-coordinate of the vertex represent the time when the ball reach the maximum
Find the vertex
Convert the equation in vertex form
Factor -16

Complete the square


Rewrite as perfect squares

The vertex is the point 
therefore
The time when the ball reach the maximum is 25/32 sec or 0.78 sec
step 2
At about what time did the ball reach the minimum?
we know that
The ball reach the minimum when the the ball reach the ground (h=0)
For h=0



square root both sides


the positive value is

Answer:
$3,000
Step-by-step explanation:
There two possible outcomes:
There is a 3/4 chance that the bid is rejected for a value of -$1,400
There is a 1/4 chance that the bid is accepted for a value of $17,600 - $1,400.
The expected value of the situation is:

The expected value is $3,000.