Answer:
The correct answer is
(0.0128, 0.0532)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence interval
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
Z is the zscore that has a pvalue of ![1 - \frac{\alpha}{2}](https://tex.z-dn.net/?f=1%20-%20%5Cfrac%7B%5Calpha%7D%7B2%7D)
For this problem, we have that:
In a random sample of 300 circuits, 10 are defective. This means that
and ![\pi = \frac{10}{300} = 0.033](https://tex.z-dn.net/?f=%5Cpi%20%3D%20%5Cfrac%7B10%7D%7B300%7D%20%3D%200.033)
Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool.
So
= 0.05, z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 - 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0128](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7B300%7D%7D%20%3D%200.033%20-%201.96%5Csqrt%7B%5Cfrac%7B0.033%2A0.967%7D%7B300%7D%7D%20%3D%200.0128)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 + 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0532](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7B300%7D%7D%20%3D%200.033%20%2B%201.96%5Csqrt%7B%5Cfrac%7B0.033%2A0.967%7D%7B300%7D%7D%20%3D%200.0532)
The correct answer is
(0.0128, 0.0532)
Sinθ=opposite side/hypotenuse
cosθ=adjacent side/hypotenuse
where both the sides are relative to theta.
in this case, 22 is your hypotenuse. theta (θ) is the angle you are examining. i've included a diagram for reference because the equations may format differently depending on which angle you choose as theta.
using my diagram:
sinθ = o/h
sin 15 = o/22
sin 15(22) = o
o=5.69m/s
therefore the vertical component is about 5.69m/s.
cosθ=a/h
cos15 = a/22
cos15(22) = a
a = 21.25m/s
therefore, your horizontal component is about 21.25m/s.
Step 1
Multiply the denominator by the whole number
8 × 1 = 8
Step 2
Add the answer from Step 1 to the numerator
8 + 1 = 9
Step 3
Write answer from Step 2 over the denominator
9/8
Answer:
A
Step-by-step explanation:
Remarks
- The given angle is an exterior angle.
- It's value is 46 degrees.
- An exterior angle is the sum of the two remote angles. (A remote angle is one that is not supplementary to the given exterior angle.
Solution
- 46 = <u + <t
- <t = 29
- 46 = <u + 29 Subtract 29 from both sides.
- 46 - 29 = <u
- <u = 17 degrees
Answer:
y=3x−4
Step-by-step explanation:
find the tangent line to f(x)=x2−3x+5 at x=3
First, find the value of the function at the given point: y0=f(3)=5
Second, find the slope of the tangent line, which is the derivative of the function, evaluated at the point: m=f′(3)
Find the derivative: f′(x)=2x−3
Next, we evaluate the derivative at the given point to find the slope.
m=f′(3)=3
Finally, the equation of the tangent line is y−y0=m(x−x0)
Plug the values that we found, we get that y−(5)=3(x−(3))
So basically: y=3x−4