There are 16 possible hands.
Choosing 3 aces from 4 possible is expressed by:
Choosing 1 queen from 4 possible is expressed by:
This gives us 4*4 = 16 possible hands.
If the markers are 4.5 inches away on the map, and 2.5 inches represents 10 miles, then we need to make ratios we can work with.
Inches / Miles:
4.5 / x
2.5 / 10
Now, we can cross multiply to end up with:
2.5 * x = 4.5 * 10
Simplify:
2.5x = 45
Divide 2.5 on each side:
2.5x / 2.5 = 45 / 2.5
Simplify:
x = 45 / 2.5
x = 18
Awesome! Now we have a real ratio on the real distance of the markers.
<span>2.5 : 10 & 4.5 : </span><span>18.
</span>
18 miles is the actual distance between the two markers.
Hope I could help! If my math is wrong, or it isn't the answer you are looking for, please let me know!
<span>Have a good one!</span>
<span>12.3
Volume function: v(x) = ((18-x)(x-1)^2)/(4pi)
Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x.
The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is
v(x) = (18-x)pi((x-1)/(2pi))^2
v(x) = (18-x)pi((x-1)^2/(4pi^2))
v(x) = ((18-x)(x-1)^2)/(4pi)
The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative:
v'(x) = (x-1)(3x - 37) / (4pi)
Convert to quadratic equation.
(3x^2 - 40x + 37)/(4pi) = 0
3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0
Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi)
The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3</span>
C is the answer for this question (2/10)
The answer is A.All real numbers except -2.
