Hello can you please help me posted picture of question

Mathematics

1 answer:

Liono4ka [1.6K]4 years ago

3 0

Since the order of selection does not matter we will use combinations to solve this problem.

Total number of students = 20
Number of students to be selected = 4

We are to find the combinations of 20 objects taken 4 at a time. This can be expressed as 20C4

20C4 = 4845

Thus, there are 4845 ways to select the 4 students.

So, the correct option is D

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A trapezoid has an area of 20 cm2 and a height z cm. The lengths of the parallel sides are (2z + 3) cm and (6z – 1) cm. Find the

andriy [413]

Check the picture below.

$\bf A=\cfrac{h(a+b)}{2}\quad 
\begin{cases}
A=20\\
a=6z-1\\
b=2z+3\\
h=z
\end{cases}\implies 20=\cfrac{z[(6z-1)~+~(2z+3)]}{2}
\\\\\\
20=\cfrac{z(8z+2)}{2}\implies 20=\cfrac{2z(4z+1)}{2}\implies 20=z(4z+1)
\\\\\\
20=4z^2+z\implies 0=4z^2+z-20$

$\bf \qquad \qquad \textit{quadratic formula}\\\\
\begin{array}{llccll}
0=&{{ 4}}z^2&{{ +1}}x&{{ -20}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
z= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}
\\\\\\
z=\cfrac{-1\pm\sqrt{1+320}}{8}\implies z=\cfrac{-1\pm\sqrt{321}}{8}\implies z\approx 
\begin{cases}
\boxed{2.1146}\\
-2.3646
\end{cases}$

since the height is just a length unit, it can't be -2.3646.