The first question's answer is:
0<-100x^2+350x-150
The second question "Look at the factorization shown below.
0 < –100x2 + 350x – 150
0 < –50(2x2 – 7x + 3)
0 < –50(2x – 1)(x – 3)
Select the range that Mario can choose from to price his muffins and make a positive profit.
The answer is:
$0.50 < x < $3.00
the inequality that shows the business will make a positive profit is
[tex]\:\frac{1}{2}<x<3[/tex]
Given :
Profit P for Mario’s business is given by [tex]p(x)=-100x^2+350x-150[/tex]
When profit is positive then P(x)>0
[tex]-100x^2+350x-150>0[/tex]
now we solve for x
Divide whole equation by 50
[tex]-2x^2+7x-3>0\\-\left(2x-1\right)\left(x-3\right)>0\\\left(2x-1\right)\left(x-3\right)<0\\[/tex]
Now we check the intervals that makes the inequality true
[tex]2x-1=0,x=\frac{1}{2}[/tex]
[tex]x=-3=0, x=3[/tex]
so we make three intervals (-∞ ,1/2) (1/2,3) and (3,∞)
Pick a number from each interval and check
[tex]x=0\\-2x^2+7x-3>0\\-2(0)^2+7(0)-3>0, false\\\\x=1\\-2(1)^2+7(1)+-3>0, true\\\\x=4\\-2(4)^2+7(4)+-3>0, false\\\\[/tex]
the inequality that shows the business will make a positive profit is
[tex]\:\frac{1}{2}<x<3[/tex]
Learn more : brainly.com/question/17810527
