Which is the absolute value function corresponding to the graph with these characteristics?
2 answers:
The parent function for an absolute value function is:
If a is positive, the graph will open upward, and if a is negative, it will open downward. Given that the graph opens downward, we know a must be negative.
Next, h represents the horizontal shift of the graph. Given that the vertex is at (-2,k), we know that h = 2.
The k value does not matter because in the given characteristics we are given a general k value that will work with any graph.
Finally, we need to find which graph passes through (-3, -1). To meet the requirements discussed above, we can narrow the answer to C or D. Now just plug in -3 for x in both functions, and whichever one equals -1 at x=-3 is our answer:
C) -4|-3 + 2| + 3 = -4(1) + 3 = -1
D) -4|-3 + 2| - 3 = -4(1) - 3 = -7
The answer is C.
If a is positive, the graph will open upward, and if a is negative, it will open downward. Given that the graph opens downward, we know a must be negative.
Next, h represents the horizontal shift of the graph. Given that the vertex is at (-2,k), we know that h = 2.
The k value does not matter because in the given characteristics we are given a general k value that will work with any graph.
Finally, we need to find which graph passes through (-3, -1). To meet the requirements discussed above, we can narrow the answer to C or D. Now just plug in -3 for x in both functions, and whichever one equals -1 at x=-3 is our answer:
C) -4|-3 + 2| + 3 = -4(1) + 3 = -1
D) -4|-3 + 2| - 3 = -4(1) - 3 = -7
The answer is C.
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Answer:
The proportion of young adults (18-25 years of age) in a certain city in the U.S. are not different from the proportion of the general population of young adults in the U.S.
Step-by-step explanation:
The hypothesis for the test can be defined as:
<em>H</em>₀: The proportion of young adults (18-25 years of age) in a certain city in the U.S. are not different from the actual proportion, i.e. <em>P</em> = <em>p</em><em>.</em>
<em>Hₐ</em>: The proportion of young adults (18-25 years of age) in a certain city in the U.S. are different from the actual proportion, i.e. <em>P</em> ≠ <em>p</em><em>.</em>
The test statistic is defined as:
Assume that the significance level of the test is, <em>α</em> = 0.05.
The decision rule is:
If the <em>p</em>-value of the test is less than the significance level then the null hypothesis will be rejected. And vice-versa.
It is provided that the <em>p</em>-value of the test is, <em>p</em>-<em>value</em> = 0.076.
The <em>p-</em>value = 0.076 > <em>α</em> = 0.05.
Thus, the null hypothesis will not be rejected at 5% level of significance.
<u>Conclusion</u>:
The proportion of young adults (18-25 years of age) in a certain city in the U.S. are not different from the proportion of the general population of young adults in the U.S.
Answer:
see below
Step-by-step explanation:
If (x+5) is a factor of p(x), then the value x=-5 will make that factor be zero. The product p(x) of which it is a part will also be zero, so p(-5) = 0.
Since p(-5) = 0 at x=-5, there will be an x-intercept at x=-5.
Dividing something by a factor of that thing will always give a remainder of zero. So, p(x)/(x+5) has a remainder of 0.
