Answer:
Probability that next week's show will have between 30 and 37 million viewers is 0.2248.
Step-by-step explanation:
We are given that the distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26 million with a standard deviation of 8 million.
<em>Let X = number of viewers for the American Idol television show</em>
So, X ~ N(
)
Now, the z score probability distribution is given by;
Z =
~ N(0,1)
where,
= population mean = 26 million
= standard deviation = 8 million
So, probability that next week's show will have between 30 and 37 million viewers is given by = P(30 < X < 37) = P(X < 37) - P(X
30)
P(X < 37) = P(
<
) = P(Z < 1.38) = 0.91621
P(X
30) = P(
) = P(Z
0.50) = 0.69146
<em>Therefore, P(30 < X < 37) = 0.91621 - 0.69146 = 0.2248</em>
Hence, probability that next week's show will have between 30 and 37 million viewers is 0.2248.
Answer:
The 135 external angle means its corresponding internal angle is (180–135) 45 degrees. The other internal angle of 65 plus the 45 is 110 degrees. Since the sum of degrees in the angles in a triangle is 180, the other interior angle is (180–110), or 70 degrees.
Step-by-step explanation:
<h3>
Answer: Choice B</h3>
Explanation:
Cosine is positive in quadrants I and IV, but quadrant IV isn't shaded in so we can rule out choice A.
Sine is positive in quadrants I and II. So far it looks like choice B could work. In fact, it's the answer because sin(pi/6) = 1/2 and sin(5pi/6) = 1/2. So if 0 ≤ sin(x) < 1/2, then we'd shade the region between theta = 0 and theta = pi/6; as well as the region from theta = 5pi/6 to theta = pi.
Choice C is ruled out because tangent is positive in quadrants I and III, but quadrant III isn't shaded.
Choice D is ruled out for similar reasoning as choice A. Recall that ![\sec(x) = \frac{1}{\cos(x)}](https://tex.z-dn.net/?f=%5Csec%28x%29%20%3D%20%5Cfrac%7B1%7D%7B%5Ccos%28x%29%7D)
A.) is the correct answer.
5 liter bucket with the 3 liter bucket twice, and then use the 3 liter bucket and the 4 liter bucket twice.