Answer:
(b) I, III
Step-by-step explanation:
The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).
<h3>General shape</h3>
The leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.
If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.
<h3>Specific shape</h3>
The answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).
f(2) = 2² -7·2 +10 = 4 -14 +10 = 0
f(5) = 5² -7·5 +10 = 25 -35 +10 = 0
This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.
Answer:
hope this helps you out good luck
Answer: 0.4402
Step-by-step explanation:
Given : The proportion of the registered voters in a country are Republican = P=0.50
Sample space = 36
The test statistic for proportion :-
![z=\dfrac{p-P}{\sqrt{\dfrac{P(1-P)}{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bp-P%7D%7B%5Csqrt%7B%5Cdfrac%7BP%281-P%29%7D%7Bn%7D%7D%7D)
For p= 0.477
![z=\dfrac{0.477-0.50}{\sqrt{\dfrac{0.50(1-0.50)}{36}}}\approx-0.276](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.477-0.50%7D%7B%5Csqrt%7B%5Cdfrac%7B0.50%281-0.50%29%7D%7B36%7D%7D%7D%5Capprox-0.276)
For p= 0.58
![z=\dfrac{0.58-0.50}{\sqrt{\dfrac{0.50(1-0.50)}{36}}}\approx0.96](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.58-0.50%7D%7B%5Csqrt%7B%5Cdfrac%7B0.50%281-0.50%29%7D%7B36%7D%7D%7D%5Capprox0.96)
Now, the probability that the proportion of freshmen in the sample is between 0.477 and 0.58 (by using the standard normal distribution table):-
![P(0.477](https://tex.z-dn.net/?f=P%280.477%3Cx%3C0.58%29%3DP%28-0.276%3Cz%3C0.96%29%5C%5C%5C%5C%3DP%28z%3C0.96%29-P%28z%3C-0.276%29%5C%5C%5C%5C%3D0.8314724-%200.391274%3D0.4401984%5Capprox0.4402)
Hence, the probability that the proportion of freshmen in the sample is between 0.477 and 0.580 = 0.4402
Hi there!
The included angle of sides JG and GH is angle G (JGH). This is because that is the angle the two line segments create.
Angle H is the opposite angle to side JG. If you draw a line from the angle straight down and extended the base, you'd see that the line intersected that side and that side only.
The side opposite to angle J is side GH. As I explained above, drawing a line would show you the intersection.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Answer:
.5
Step-by-step explanation:
Sin(x)cos(y) + cos(x)sin(y) = sin(x+y)
sin(17+13) = 1/2