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gtnhenbr [62]
3 years ago
12

From a phone survey, a researcher determined that the true estimate for the proportion of voters who will reelect the mayor is l

ikely to be in the interval (0.39, 0.47) .
What is the survey’s margin of error?

Enter your answer in the box.
Mathematics
1 answer:
eduard3 years ago
6 0
Here, p^ = (0.39 + 0.47)/2 = 0.43

The given interval is (0.43 - 0.04, 0.43 + 0.04).

Therefore, the margin of error is 0.04.
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2 years ago
What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)
lutik1710 [3]

so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).

\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}

so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?

\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill

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3 years ago
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