If you plot the points given on a coordinate plane you see that this is a hyperbola that is is horizontal in nature, meaning it opens side to side, not up and down. We can determine the center of it by taking the point equidistant from the vertices, which is (4, 5), the h and k of our center, respectively. Also, the equation looks like this when it is horizontal:
. a is the distance between the center and the vertices, so our a = 2, and c is the distance between the center and the foci, so our c = 3. We need to find b now, using Pythagorean's theorem.
and
. Now we have everything we need to rewrite the equation:
The red arc is named "minor arc EF" or simply "arc EF". This is the shortest distance from E to F along the curve.
The measure of arc EF is 68 degrees as this is the central angle that subtends this same arc.
Sample size, n = 75
Point estimate, p = 52/75 = 0.693
Z at 99.7% confidence interval ≈ 2.96
Population mean interval = p+/- Z*Sqrt [p(1-p)/n]
Substituting;
Population mean interval = 0.693 +/- 2.96*Sqrt [0.693(1-0.693)/75] = 0.693+/-0.158 = (0.535,0.851) or (53.5%,85.1%)
Answer: The approximate percent increase is 121.42857%. This is a rounded value. To get this, first you would need to find out which increased and in what direction. Of course, the 70 turned into an 85. So you can divide 85 by 70 and receive a number. Then in whatever form you found it, decimal, fraction, or even percent straight away, ensure the value is a percentage.
70 -> 85
85/70
About 1.21 [decimal]
1.21 x 100 = 121 [add the %]
121% [rounded]
Answer:
22⁰
Step-by-step explanation:
By angle sum property :
x + 127 + 31 = 180⁰
x = 180 - 158
x = 22⁰
