Because this is a positive parabola, it opens upwards, like a cup, and the vertex dictates what the minimum value of the function is. In order to determine the vertex, I recommend completing the square. Do that by first setting the function equal to 0 and then moving the 9 to the other side by subtraction. So far: 
. Now, to complete the square, take half the linear term, square it, and add that number to both sides. Our linear term is 6. Half of 6 is 3 and 3 squared is 9. So add 9 to both sides. 
. The right side reduces to 0, and the left side simplifies to the perfect square binomial we created while completing this process. 
. Move the 0 back over and the vertex is clear now. It is (-3, 0). Therefore, 0 is the minimum point on your graph. The first choice above is the one you want.
Which point is on the circle centered at the origin with a radius of 5 units?
1 answer:
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Answer:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0):
Alternative hypothesis (H1):
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no
Step-by-step explanation:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0):
Alternative hypothesis (H1):
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no
