Answer:
x = 10.52 m
Step-by-step explanation:
Given that,
Length of a park = 90 m
Width of a park = 60 m
Area, A = 9000 m²
A uniform strip borders all four sides of the park for parking. We need to find the width of the strip. Let it is x. Now the area becomes,
(90+2x)(60+2x) = 9000

So, the width of the strip is equal to 10.52 m.
Answer:
80 machines
Step-by-step explanation:
If a machine makes 20 gadgets every fourth (1/4) of an hour, it makes 80 machines every hour (20*4).
It is hard to comprehend your question. As far as I understand:
f(x,y) = e^(-x)
Find the volume over region R = {(x,y): 0<=x<=ln(6), -6<=y <= 6}.
That is all I understood. It would be easier to understand with a picture or some kind of visual aid.
Anyways, to find the volume between the surface and your rectangular region R, we must evaluate a double integral of f on the region R.

Now evaluate,

which evaluates to, 5/6 if I did the math correct. Correct me if I am wrong.
Now integrate this w.r.t. y:

So,

Given 2.50x + 3.50y < 30.
Where x represent the number of hamburgers and y represent the number of cheeseburgers.
Now question is to find the maximum value of hamburgers Ben could have sold when he has sold 4 cheeseburgers.
So, first step is to plug in y=4 in the given inequality. So,
2.50x+3.50(4)<30
2.50x+14 <30
2.50x<30- 14 Subtracting 14 from each sides.
2.50x< 16
Dividing each sides by 2.50.
x<6.4
Now x being number of hamburgers must be an integer , so tha maximum value of x can be 6,
thus x = 6 hamburgers
So, the maximum value of hamburgers Ben could have sold is 6*2.5=$15
Hope this helps!!
60% of 20 quizzes = 60/100*20 quizzes = 12 quizzes
Amount of quizzes remaining = 50 quizzes - 20 quizzes = 30 quizzes
He passes 80% of those 30 quizzes, so
80/100 * 30 quizzes = 24 quizzes
So, he passed 12 quizzes from the initial bunch and 24 quizzes from the rest, which totals to 12 quizzes + 24 quizzes = 36 quizzes.
Then, you see that he passed 36 quizzes, out of the total 50 quizzes, so the ratio is 36 quizzes / 50 quizzes = 36/50, which when converted as a percentage is 36/50 * 100% = 72%.
Therefore, he passed 72% of the quizzes for the entire year.