The answer is D
Hope that was fast enough
Answer:
3003
Step-by-step explanation:
The number of differents menus containing 10 main courses that the restaurant can make if it has 15 main courses from which to chose is calculated through the combination: 15C10. The formula of the combination is: nCr = n! / ((r!) x(n - r)!)
Where r=10 and n=15
Substituting the values to the equation: 15C10 = 15! / (10!)x(10 - 5)! = 3003
Then there are 3003 different menus that a restaurant can makeif it has 15 main courses from which to choose.
For the answer to the question above,
1. If we let x as the side of the square cut-out, the formula for the capacity (volume) of the food dish is:
V = (12 - 2x)(8 - 2x)(x)
V = 96x - 40x^2 + 4x^3
To find the zeros, we equate the equation to 0, so, the values of x that would result to zero would be:
x = 0, 6, 4
2. To get the value of x to obtain the maximum capacity, we differentiate the equation, equate it to zero, and solve for x.
dV/dx = 96 - 80x + 12x^2 = 0
x = 5.10, 1.57
The value of x that would give the maximum capacity is x = 1.57
3. If the volume of the box is 12, then the value of x can be solved using:
12 = 96x - 40x^2 + 4x^3
x = 0.13, 6.22, 3.65
The permissible value of x is 0.13 and 3.65
4. Increasing the cutout of the box increases the volume until its dimension reaches 1.57. After that, the value of the volume decreases it reaches 4.
5. V = (q -2x) (p - 2x) (x)
Answer:
3y / (y+3)
Step-by-step explanation:
3y^2 - 6y / y^2 + y - 6
= 3y(y-2) / (y+3)(y-2)
=3y / (y+3)
Reflect over the Y axis, then translate (x+[-2], y+[-3])
