Answer:
78 ounces of dough
52 ounces of sauce
12 guests are coming (not including you)
Step-by-step explanation:
13x6=78
13x4=52
78+52=130 ounces
We assume all employees are either full-time or part-time.
36 = 24 + 12
If the number of full-time employees is 24 or less, the number of part-time employees must be 12 or more. (Thinking, based on knowledge of sums.)
_____
You can write the inequality in two stages.
- First, write and solve an equation for the number of full-time employees in terms of the number of part-time employees.
- Then apply the given constraint on full-time employees. This gives an inequality you can solve for the number of part-time employees.
Let f and p represent the numbers of full-time and part-time employees, respectively.
... f + p = 36 . . . . . . given
... f = 36 - p . . . . . . . subtract p. This is our expression for f in terms of p.
... f ≤ 24 . . . . . . . . . given
... (36 -p) ≤ 24 . . . . substitute for f. Here's your inequality in p.
... 36 - 24 ≤ p . . . . add p-24
... p ≥ 12 . . . . . . . . the solution to the inequality
Answer: 60%
Step-by-step explanation: 24/40 = .6 x 100 = 60
So it starts with 12 in the bacterial population. After 1 hour, 6 are added. After another hour passed, 9 are added. 12/1, 18/6, 27/9.
Answer: The field F has a continuous partial derivative on R.
Step-by-step explanation:
For the field F has a continuous partial derivative on R, fxy must be equal to fyx and since our field F is ∇f,
∇f = fxi + fyj + fzk.
Comparing the field F to ∇f since they at equal, P = fx, Q = fy and R = fz
Since P is fx therefore;
∂P ∂y = ∂ ∂y( ∂f ∂x) = ∂2f ∂y∂x
Similarly,
Since Q is fy therefore;
∂Q ∂x = ∂ ∂x( ∂f ∂y) = ∂2f ∂x∂y
Which shows that ∂P ∂y = ∂Q ∂x
The same is also true for the remaining conditions given
