21.6 units
Calculate the length of the 2 inclined sides using the distance formula
d = √(x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (3, 4 )
d = √(3 + 3 )² + (4 - 3)² = √(36 + 1 ) = √37
repeat for (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (3, - 3 )
d = √(3 + 3 )² + (- 3 - 3 )² = √(36 + 36 ) = √72
the vertical side has a length of 7 units
perimeter = √37 + √72 + 7 = 21.6 ( nearest tenth of a unit )
Answer:
a. 24
b. 2
c. 0.0833 = 8.33%
Step-by-step explanation:
a.
The first "slot" of person to arrive has 4 possibilities, then the second "slot" will have 3 possibilities, as one has already arrived, then the third "slot" has 2 possibilities, and the fourth "slot" has just 1 possibility.
So, multiplying all these combinations, we have 4*3*2*1 = 24 possible ways they can arrive
b.
If the first and the last person are already "locked", we just have possibilities for the second and third person. The second will have 2 possibilities (Sergio or Tyrone), and the third will have only 1 (the person that wasn't the second between Sergio and Tyrone). So, the number of possibilities is 2*1 = 2
c.
If we have 2 cases where Dawn is first and Jim is last, from a total of 24 possible cases, the probability is 2/24 = 1/12 = 0.0833 = 8.33%
Answer:
does not exist
Step-by-step explanation:
According to the divergence test, for an infinite series ∑ aₙ, the series diverges if lim(n→∞) aₙ ≠ 0.
Applying the divergence test here:
lim(n→∞) (3n⁵ / (4n⁵ + 1)) = 3/4
This is not 0, so the series does not converge, meaning the sum does not exist.
Answer:
91 short stories
Step-by-step explanation:
You just add 1 + 2 + 3 + 4 + 5 + 6... all the way to 13, and then at the end of 16 months, Troy still only wrote 91 stories since he only wrote them up until 13 months, and then stopped afterwards.
Get y by itself so subtract 2x from both sides. So next it would be -4y=-2x+2. To get y by itself divide both sides by -4. So then it would be y= -2/-4x +2/-4. They both reduce down to y=1/2x-1/2. So the slope is 1/2 because the formula y=mx+b
m=slope. Hope this helps! :)
