<span>P(black socks): 24/42 or 12/21
P(black socks without replacement): 23/41. Consequently, the chance of randomly selecting 2 black socks, without replacement, from the basket is 12/21×23/41=276/861, equivalent to 32%. Hope this helps!</span>
The complete question reads:
Peter created two rays, AC and AP, sharing a common vertex at point A. Which of the following statements
might accurately describe Peter's drawing?
I. AC and AP are parallel.
II. PAC represents an angle.
III. AC and AP are at right angles.
A. I and II
B. II and III
C. I and III
D. I, II, and III
Answer:
Option B: II & III
Step-by-step explanation:
We know Peter has drawn rays AC and AP.
Since the point A is shared as the endpoint, it indicates an angular relationship at this common point.
This angle could potentially be 90°, suggesting that rays AC and AP may be perpendicular.
Thus, the valid statements that characterize his drawing are: II & III.
Answer:
- 8
Step-by-step explanation:
Given the expression
(3x² - 5)(4 + 4x²)
Each term from the second factor is multiplied by every term in the first factor, meaning
3x²(4 + 4x²) - 5(4 + 4x²) ← distribute both parentheses
= 12x² + 12
- 20 - 20x² ← combine like terms
= 12 - 8x² - 20
The coefficient for the x² term is - 8
1,680 grams
To determine this, we can set up a proportion as follows:
grams/people=grams/people
The recipe requires 480 grams for 4 individuals and we need to find how many grams (x) are necessary for 14 individuals.
480 grams/4 people=x grams/14
480/4=x/14
Now, let's isolate x, the grams necessary for 14 people. Currently, x is divided by 14, so we will multiply both sides by 14 as multiplication is the inverse of division.
14(480/4)=(x/14)14
14(480/4)=x
14*120=x
1680=x
Thus, she requires 1,680 grams of couscous to serve 14 individuals.
