In this item, we are given with a system of linear equation as written below.
y = 0.5x + 3.5
y = -2x/3 + 1/3
To determine the values of x and y, we use the substitution method. We substitute the expression for y from the first equation to that of the second equation so that the equation becomes.
0.5x + 3.5 = -2x/3 + 1/3
Multiply the equation by 6.
3x + 21 = -4x + 2
Transpose all the terms with variables to one side and the constants to the other.
(3x + 4x) = 2 - 21
7x = -19
Divide the equation by 7,
x = -19/7
The value of y,
y = (0.5)(-19/7) + 3.5 = 15/7
<em>ANSWER:</em>
<em> x = -19/7</em>
<em> y = 15/7</em>
For a standard normally distributed random variable <em>Z</em> (with mean 0 and standard deviation 1), we get a probability of 0.0625 for a <em>z</em>-score of <em>Z</em> ≈ 1.53, since
P(<em>Z</em> ≥ 1.53) ≈ 0.9375
You can transform any normally distributed variable <em>Y</em> to <em>Z</em> using the relation
<em>Z</em> = (<em>Y</em> - <em>µ</em>) / <em>σ</em>
where <em>µ</em> and <em>σ</em> are the mean and standard deviation of <em>Y</em>, respectively.
So if <em>s</em> is the standard deviation of <em>X</em>, then
(250 - 234) / <em>s</em> ≈ 1.53
Solve for <em>s</em> :
16/<em>s</em> ≈ 1.53
<em>s</em> ≈ 10.43
Ok.
Convert 3/4 to 6/8.
There is your answer. 3/8.
The Gestalt principle of proximity states that objects and shapes form groups if they are close to one another. The shapes, sizes, and objects do not matter in this case even when there are visible differences. The law shows that smaller elements come together in a composition.
