Same strategy as before: transform <em>X</em> ∼ Normal(76.0, 12.5) to <em>Z</em> ∼ Normal(0, 1) via
<em>Z</em> = (<em>X</em> - <em>µ</em>) / <em>σ</em> ↔ <em>X</em> = <em>µ</em> + <em>σ</em> <em>Z</em>
where <em>µ</em> is the mean and <em>σ</em> is the standard deviation of <em>X</em>.
P(<em>X</em> < 79) = P((<em>X</em> - 76.0) / 12.5 < (79 - 76.0) / 12.5)
… = P(<em>Z</em> < 0.24)
… ≈ 0.5948
We can't eliminate as is so we have to change something up there in the equations to get either the x values the same number but opposite signs, or the y values the same number but opposite signs. I chose to change the y values to the same number but different signs. In the first equation y is -3y and in the second one, y is -8y. The LCM of both of those numbers is 24, so we will multiply the first equation by an 8 (8*3=24) and the second equation by 3 (3*8=24) but since they are both negative right now, one of those multiplications has to involve a negative because - * - = +. Set it up like this:
8(-10x - 3y = -18)
-3(-7x - 8y = 11)
Multiply both of those all the way through to get new equations:
-80x - 24y = -144
21x +24y = -33
Now the y's cancel each other out leaving only the x's:
-59x = -177 and x = 3. Now plug that 3 into either one of the original equations to find the y value. Either equation will work; you'll get the same answer using either one. Promise. -7(3) - 8y = 11 gives a y value of -4. so your solution is (3, -4) or B above.
The system of linear inequalities x + 10y ≤ 80, x ≥ 30 and y ≤ 4 is represented in a graph below
<h3>Graph of Linear Inequality</h3>
The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.
To solve this problem, we would require the use of graph which can easily be done with a graphing calculator.
x + 10y ≤ 80
x ≥ 30
y ≤ 4
The graph of the inequalities is attached below
Learn more on graph of linear inequality here;
brainly.com/question/19443475
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Answer:
x=y-48, y=x+48
Step-by-step explanation:
