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Mathematics

1 answer:

andriy [413]2 years ago

8 0

Answer:

14/27 feet

Step-by-step explanation:

2 1/3 feet : 4 1/2 feet

= 7/3 : 9/2

= 7/3 ÷ 9/2

= 7/3 × 2/9

= (7*2)/(3*9)

= 14/27 feet

2 1/3 feet : 4 1/2 feet = 14/27 feet

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A survey found that women's heights are normally distributed with mean 63.2 in. and standard deviation 2.4 in. The survey also

Effectus [21]

Answer: 99.51%

Step-by-step explanation:

Given : A survey found that women's heights are normally distributed.

Population mean : $\mu =63.2 \text{ inches}$

Standard deviation: $\sigma= 2.4\text{ inches}$

Minimum height = 4ft. 9 in.= $4\times12+9\text{ in.}=57\text{ in.}$

Maximum height = 6ft. 2 in.= $6\times12+2\text{ in.}=74\text{ in.}$

Let x be the random variable that represent the women's height.

z-score : $z=\dfrac{x-\mu}{\sigma}$

For x=57, we have

$z=\dfrac{57-63.2}{2.4}\approx-2.58$

For x=74, we have

$z=\dfrac{74-63.2}{2.4}\approx4.5$

Now, by using the standard normal distribution table, we have

The probability of women meeting the height requirement :-

$P(-2.58$

Hence, the percentage of women meeting the height requirement = 99.51%

8 0

3 years ago

Given the quadratic function : f(x)=x^24x-12<br> Find the vertex.<br> Can you show the steps?!?

vlada-n [284]

$\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
\begin{array}{llcccl}
\stackrel{f(x)}{y} = & 1x^2& +4x& -12\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad 
\left(-\cfrac{ b}{2 a}\quad ,\quad c-\cfrac{ b^2}{4 a}\right)
\\\\\\
\left(-\cfrac{4}{2(1)}~~,~~-12-\cfrac{4^2}{4(1)} \right)\implies (-2~~,~~-12-4)\implies (-2~~,~~-16)$