The number of dairy cows in a farm can vary from month to month. The amount of milk produced each month depends on the number of dairy cows on the farm. If g is the number of gallons of milk produced and n is the number of dairy cows on the farm, which of the following statement or statements are true about the variables? Select two answers.
A.
g is the independent variable
B.
g is the dependent variable
C.
n is the independent variable
D.
n is the dependent variable
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Marco is putting some sweaters into storage for the winter he has 10 sweaters and he can fit 6 sweaters into a box how many different groups of 6 sweaters can marco pack into a box
Marco can pack $\boxed{252}$ different groups of 6 sweaters into a box.
We can use combinations to solve this problem. The number of ways to choose 6 sweaters out of 10 is $\binom{10}{6}=\frac{10!}{6!4!} = 210$, which represents the number of different unordered groups of 6 sweaters that Marco can select. However, the order in which the sweaters are selected does not matter for packing purposes. Therefore, the number of different groups of 6 sweaters Marco can pack into a box is the same as the number of different combinations of 6 sweaters, which is also $\binom{10}{6}=252$.
Marco is putting some sweaters into storage for the winter he has 10 sweaters and he can fit 6 sweaters into a box how many different groups of 6 sweaters can marco pack into a box
A. 210
B. 5,040
C. 7,560
D. 151,200
The correct answer is A. 210.
To find out how many different groups of 6 sweaters Marco can pack into a box, we need to use combinations. The formula for combinations is $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ where $n$ is the total number of items and $k$ is the number of items being chosen.
In this case, $n = 10$ (the total number of sweaters) and $k = 6$ (the number of sweaters that can be packed into a box).
So, the number of different groups of 6 sweaters that Marco can pack into a box is:
$\binom{10}{6} = \frac{10!}{6!4!} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 210$
Therefore, the answer is A. 210.