Answer: the function g(x) has the smallest minimum y-value.
Explanation:
1) The function f(x) = 3x² + 12x + 16 is a parabola.
The vertex of the parabola is the minimum or maximum on the parabola.
If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.
The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.
When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).
Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.
Then, finding the minimum value of the function is done by finding the vertex.
I will change the form of the function to the vertex form by completing squares:
Given: 3x² + 12x + 16
Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4
That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).
Then the minimum value is 4 (when x = - 2).
2) The othe function is <span>g(x)= 2 *sin(x-pi)
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The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.
When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2
Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.
<u>Testing the hypothesis</u>, it is found that since the <u>p-value of the test is 0.0042 < 0.01</u>, it can be concluded that the proportion of subjects who respond in favor is different of 0.5.
At the null hypothesis, it is tested if the <u>proportion is of 0.5</u>, that is:
At the alternative hypothesis, it is tested if the <u>proportion is different of 0.5</u>, that is:
The test statistic is given by:
In which:
is the sample proportion.- p is the value tested at the null hypothesis.
- n is the sample size.
In this problem, the parameters are given by:
The value of the test statistic is:
Since we have a <u>two-tailed test</u>(test if the proportion is different of a value), the p-value of the test is P(|z| > 2.86), which is 2 multiplied by the p-value of z = -2.86.
Looking at the z-table, z = -2.86 has a p-value of 0.0021.
2(0.0021) = 0.0042
Since the <u>p-value of the test is 0.0042 < 0.01</u>, it can be concluded that the proportion of subjects who respond in favor is different of 0.5.
A similar problem is given at brainly.com/question/24330815
19-14? I think first you need to find sea level.
<span>C.
glacial melting<<<<<<<<<<<<<<<</span>
