Are the two lines parallel, perpendicular, coinciding lines, or neither?

Mathematics

1 answer:

Elena L [17]3 years ago

6 0

Answer:

Step-by-step explanation:

crosses at a 90 degree angle

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A multiple choice test has four possible answers for each question. Let X be the number of correct responses in a test of 100 qu

dimulka [17.4K]

Answer:

a. 4.33.

Step-by-step explanation:

If there is only one correct answer out of four alternatives, the expected proportion of correct answers is p =0.25

Sample size (n) = 100 questions

The standard deviation of a proportion 'p' is given by:

$s=\sqrt{\frac{p*(1-p)}{n} }$

Applying the given data:

$s=\sqrt{\frac{0.25*(1-0.25)}{100}}\\s=0.0433$

If X is the number of correct responses in 100 guesses, the standard deviation of X is:

$\sigma = n*s=100*0.0433\\\sigma = 4.33$

The standard deviation of X is 4.33 questions.

7 0

3 years ago

The midpoint of AB is at (3,7) and A is at (0,-5). Where is B located?

olga nikolaevna [1]

$\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ \square }}\quad ,&{{ \square }})\quad 
% (c,d)
&({{ \square }}\quad ,&{{ \square }})
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)\qquad thus
\\
----------------------------\\$ $\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ 0}}\quad ,&{{ -5}})\quad 
% (c,d)
B&({{ \square }}\quad ,&{{ \square }})
\end{array}\qquad
% coordinates of midpoint 
(3,7)\impliedby midpoint\qquad thus
\\ \quad \\
\left(\cfrac{{{ x_2 }} + {{ 0}}}{2}=3\quad ,\quad \cfrac{{{ y_2 }} + {{( -5)}}}{2}=7 \right)\to 
\begin{cases}
\cfrac{{{ x_2 }} + {{ 0}}}{2}=3
\\ \quad \\
\cfrac{{{ y_2 }} + {{ -5}}}{2}=7
\end{cases}
\\ \quad \\
solve\ for\ x_2\ and\ y_2$