Answer: 12
Step-by-step explanation:
Answer:
Both A and B are possible.
Step-by-step explanation:
It's both!
This is a might tricky. First you have to find the altitude. You have to determine if this is a real triangle.
Sin(22) = opposite / hypotenuse. The hypotenuse = 111. The angle is 22
opposite = hypotenuse * sin(22)
opposite = 111 * sin(22)
opposite = 41.58 and this is the altitude.
What have you learned?
Since 42 is larger than 41.58 you have 2 solutions to the triangle. One of the angles is acute, and the other one is obtuse. They are supplementary angles.
Sin(C) / c = Sin(A) / a
Sin(C) = c * Sin(22) / 42
Sin(C) = 111*sin(22)/ 42
Sin(C) = .99003
Sin(C) = 81.9
So that's your first answer. The second answer comes from Finding the supplement to this angle
supplement + 81.9 = 180
supplement = 180 - 81.9
supplement = 98.1
Answer:
Option c:
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of 
.
For this problem, we have that:
You have access to first year enrolment records and you decide to randomly sample 119 of those records. You find that 89 of those sampled went on to complete their degree. This means that 
.
90% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
Sample of 90 people with a sample proportion of 0.25
This means that 
.
Confidence interval:
Which is option c.
Answer:
The curvature of the plan curve at t=2 is 0.
Step-by-step explanation:
First, we find take a derivative of r(t) = ti + t^2j
r'(t) = i + 2tj
we can also write it like r'(t) = < 1, 2t>
Now, we take a magnitude of it
|r'(t)| = √(1)^2 + (2t)^2
|r'(t)| = √17
Now, we assume a variable T(t)
T(t) = r'(t)/|r'(t)|
T(t) = (i + 2tj) / √17
T(t) = 1/√17 (< 1, 2t>)
Take derivative of T(t)
T'(t) = 1/√17 (< 0, 2>)
|T'(t)| = √(1/√17)^2 + (0)^2 + (2)^2
|T'(t)| = √69/17
Therefore,
Curvature = |T'(t)| / |r'(t)|
Curvature = (√69/17) / √17
Curvature = √69 .
Answer:
-9
Step-by-step explanation:
7+2n=-11
subtract 7 from 7 and -11
2n=-18
then divide 2 to both sides
and you get -9
