Answer:
theoretical probability
Step-by-step explanation:
This is theoretical probability. The 7 pieces of paper each bear one number from {1, 2, ... , 6, 7}. There is only one piece of paper marked 7. So the probability of drawing a 2 is 1/7.
Answer:
- 3x² is a term in the numerator
- x + 1 is a common factor
- The denominator has 3 terms
Step-by-step explanation:
You can identify terms and count them before you start factoring. Doing so will identify 3x² as a term in the numerator, and will show you there are 3 terms in the denominator.
When you factor the expression, you get ...
This reveals a common factor of x+1.
So, the above three observations are true of this rational expression.
Now subtract, then add.
4 - 2 = 2 then add 12.
2 + 12 = 14.
Answer is 14.
We can create two equations here:
(1) Volume = area of square * height of box
85.75 = s^2 h
(2) Cost = 3 * area of square + 1.5 * area of side box
C = 3 s^2 + 1.5 s h
From (1), we get:
h = 85.75 / s^2
Combining this with (2):
C = 3 s^2 + 1.5 s (85.75 / s^2)
C = 3 s^2 + 128.625 s-
Taking the 1st derivative and equating dC/ds =
0:
dC/ds = 6s – 128.625 / s^2 = 0
Multiply all by s^2:
6s^3 – 128.625 = 0
6s^3 = 128.625
s = 2.78 cm
So h is:
h = 85.75 / s^2 = 85.75 / (2.78)^2
h = 11.10 cm
So the dimensions are 2.78 cm x 2.78 cm x 11.10 cm
The total cost now is:
C = 3 (2.78)^2 + 1.5 (2.78) (11.10)
C = $69.47
Answer:
The rigid transformation, which does not change the shape or size of the preimage. The non-rigid transformation, which will change the size but not the shape of the preimage.
Step-by-step explanation:
