PLEASE HELP!! Identify the minium value of the function
1 answer:
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.
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Answer:
We conclude that the mean IQ of her students is different from the national average.
Step-by-step explanation:
We are given that the national mean (μ) IQ score from an IQ test is 100 with a standard deviation (s) of 15.
The dean of a college want to test whether the mean IQ of her students is different from the national average. For this, she administers IQ tests to her 144 students and calculates a mean score of 113
Let, Null Hypothesis, :
= 100 {means that the mean IQ of her students is same as of national average}
Alternate Hypothesis, :
100 {means that the mean IQ of her students is different from the national average}
(a) The test statistics that will be used here is One sample z-test statistics;
T.S. = ~ N(0,1)
where, Xbar = sample mean score = 113
s = population standard deviation = 15
n = sample of students = 144
So, test statistics =
= 10.4
Now, at 0.05 significance level, the z table gives critical value of 1.96. Since our test statistics is more than the critical value of z which means our test statistics will fall in the rejection region and we have sufficient evidence to reject our null hypothesis.
Therefore, we conclude that the mean IQ of her students is different from the national average.
Answer:
The equation is a function, for each value of x, corresponds a y-value. The domain and the range is for all the real numbers.
Step-by-step explanation:
To sketch the graph you need to make a table, propose different values of x, including negative and positives. You can see that for any value of x, you will have any value of y.
For example:
x y
-20 -59
-15 -44
-10 -29
-5 -14
0 1
5 16
10 31
15 46
20 61
Remember the following concepts:
The domain of a function f (x) is the set of all the values for which the function is defined. In other words is the collection of all possible inputs that can be plugged into a function to produce a y-value. To find the domain depends of the function type. For example a polynomial function without radicals or variables in the denominator will have all the real numbers in its domain. Usually we have to avoid 0 on the bottom of a fraction, or negative values under the square root sign.
The range of the function is the set of all the values that y takes, it is the collection of all possible outputs, depending of the function can have a minimum y-value or a maximum y-value.
We can see that the function y = 3x +1, or f(x) = 3x +1, has no restrictions, therefore the domain is all real numbers. From the graph we can see easily that y can be positive or negative. So the domain and the range can be expressed as (-∞, ∞) .
You can see the graph in the attached file.