Answer:
Option B. 5P5 × 20P15
Step-by-step explanation:
It is very important to remember that the second grade students are sitting in the front row, therefore, it is only necessary to organize 15 first grade students in 20 seats.
Permutations allow you to calculate the number of ways in which m objects can be arranged in n positions.
The permutation of m in n is written as:
nPm
Where n is the number of elements and m are chosen.
The way in which the 5 second grade students can be organized in the 5 seats is from the first row is:
5P5
Then, the number of ways in which 15 first-year students can be organized into 20 seats is:
20P15
Then, the number of ways to organize all students on the bus is the product of both permutations
5P5 * 20P15
(2x+3y)⁴
1) let 2x = a and 3y = b
(a+b)⁴ = a⁴ + a³b + a²b² + ab³ + b⁴
Now let's find the coefficient of each factor using Pascal Triangle
0 | 1
1 | 1 1
2 | 1 2 1
3 | 1 3 3 1
4 | 1 4 6 4 1
0,1,2,3,4,.. represent the exponents of binomials
Since our binomial has a 4th exponents, the coefficients are respectively:
(1)a⁴ + (4)a³b + (6)a²b² + (4)ab³ + (1)b⁴
Now replace a and b by their real values in (1):
2⁴x⁴ +(4)8x³(3y) + (6)(2²x²)(3²y²) + (4)(2x)(3³y³) + (1)(3⁴)(y⁴)
16x⁴ + 96x³y + 216x²y² + 216xy³ + 81y⁴
<span>On an indifference curve, all bundles give the same amount of utility. (32,8) gives a utility of
U(32,8)=32x8=256
If (4,y) is on the same indifference curve, then it must give the same utility. Hence,
256 = 4y
y=64
64 bananas</span>
The total revenue that is gained from the sales of the cakes is determined by multiplying the number of cakes by the price. If we let x be the number of $1 that should be deducted from the price and y be the total revenue,
y = (25 - x)(100 + 5x)
Simplifying,
y = 2500 + 25x - 5x²
We get the value of x that will give us the maximum revenue by differentiating the equation and equating the differential to zero.
dy/dx = 0 = 25 - 10x
The value of x is 2.5.
The price of the cake should be 25 - 2.5 = 22.5.
Thus, the price of the cake that will give the maximum potential revenue is $22.5.
Then make up a word problem that you can use decimals in.
