Which inequality is true?

Mathematics

1 answer:

DENIUS [597]1 year ago

5 0

Answer:

A. 7pi>21

Step-by-step explanation:

7*pi=21.99

21.99>21

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A recent survey of 50 executives who were laid off during a recent recession revealed it took a mean of 26 weeks for them to fin

g100num [7]

Answer: $(24.28,\ 27.72)$

Step-by-step explanation:

Given : Sample size : $n=50$

Sample mean : $\overline{x}=26$

Standard deviation : $\sigma =6.2$

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

Formula to find the confidence interval for population mean :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=26\pm(1.96)\dfrac{6.2}{\sqrt{50}}\\\\\approx26\pm1.72\\\\=(26-1.72,\ 26+1.72)\\\\=(24.28,\ 27.72)$

Hence, a 95% confidence interval for the population mean = $(24.28,\ 27.72)$

6 0

2 years ago

I’m not sure how to write this equation. Please check the picture to see the graph for yourself! Help will be much appreciated!

Makovka662 [10]

let's notice something, the parabola is a vertical one, so the squared variable is the x, and is opening downwards, meaning the x² will have a negative coefficient.

the distance from the vertex to the directrix/focus is the amount of "p" units, let's see in the graph, the distance from the vertex to the directrix is 2, and since the parabola is opening downwards, "p" is a negative 2, p = -2. The vertex is of course at (0, 2).

$\bf \textit{parabola vertex form with focus point distance}
\\\\
4p(y- k)=(x- h)^2
\qquad
\begin{array}{llll}
vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\begin{cases}
h=0\\
k=2\\
p=-2
\end{cases}\implies 4(-2)(y-2)=(x-0)^2\implies -8(y-2)=x^2
\\\\\\
y-2=\cfrac{x^2}{-8}\implies \blacktriangleright y=-\cfrac{1}{8}x^2+2 \blacktriangleleft$