To solve this, take a look at the images provided and first find out the number of polygons out of the total number of cards given which would be 3 polygons out of 5 cards, which would be better represented as the fraction 3/5. Now, the question asks to find the probability of Julie picking a card that shows a polygon, and since 3 out of 5 of the cards are polygons, your answer would be 3/5.
Answer:
Side lengths = 1.68 ft and width = 3.36 ft.
Step-by-step explanation:
Let the side lengths of the window be L and the width = 2r ( r is also the radius of the semi-circle).
So we have
Perimeter = 2L + 2r + πr = 12
Area = 2rL + 0.5πr^2
From the first equation
2L = 12 - 2r - πr
Substitute for 2L in the equation for the area:
A = r(12 - 2r - πr) + 0.5πr^2
A = 12r - 2r^2 - πr^2 + 0.5πr^2
A = 12r - 2r^2 - 0.5πr^2
We need to find r for the maximum area:
Finding the derivative and equating to zero:
A' = 12 - 4r - πr = 0=
4r + πr = 12
r = 12 / ( 4 + π)
r = 1.68 ft.
So the width of the window = 2 * 1.68 = 3.36 ft.
Now 2L = 12 - 2r - πr
= 12 - 2*1.68 - 1.68π
= 3.36
L = 1.68.
Answer:
Step-by-step explanation:
Let's look at the first two, and hopefully you'll be able to figure the rest out:
1. Answer below
The problem asks us to solve for 
, so that means we need to get on one side of the equation by itself. To do so, we will need to divide both sides of the equation by 
:
2. Answer below
The problem asks us to solve for 
, so that means we need to get on one side of the equation by itself. To do so, we will need to add 
to both sides of equation:
Answer:
5
Step-by-step explanation:
The area of a rectangle is given by base x height = 1 x 5 = 5
