Answer:
a. is True.
Step-by-step explanation:
Collinear points are on the same line.
The converse is:
If the points are on the same line the the points are collinear. This is True.
Answer:
<u>The number of pens = 120 and the number of pencils = 200</u>
Step-by-step explanation:
Let the number of pens x, and the number of pencils is y
the cost of one pen $1, and the cost of one pencil $0.5
The cost of the whole purchase was $220
1 * x + 0.5 * y = 220
x + 0.5 y = 220 ⇒ eq.(1)
there were 80 more pencils than pens
y - x = 80 ⇒ eq.(2)
from eq.(2) x = y - 80
By substitution with x from the last equation at eq.(1)
∴ (y - 80) + 0.5 y = 220
1.5y = 220 + 80 = 300
y = 300/1.5 = 200
x = y - 80 = 200 - 80 = 120
<u>So, the number of pens = 120 and the number of pencils = 200</u>
Solve for x over the real numbers:
-x^2 - 12 = -87
Add 12 to both sides:
-x^2 = -75
Multiply both sides by -1:
x^2 = 75
Take the square root of both sides:
Answer: x = 5 sqrt(3) or x = -5 sqrt(3) both Answers are correct
Answer:
126
Step-by-step explanation:
There are 9 city council members.
We have to choose 4 of them.
We have to use the combination as :
where, 9 is the population size
4 is the sample size.
Therefore, the total number of possible samples without replacement is given as :
= 126
