Answer:
A person can select 3 coins from a box containing 6 different coins in 120 different ways.
Step-by-step explanation:
Total choices = n = 6
no. of selections to be made = r = 3
The order of selection of coins matter so we will use permutation here.
Using the formula of Permutation:
nPr = 
We can find all possible ways arranging 'r' number of objects from a given 'n' number of choices.
Order of coin is important means that if we select 3 coins in these two orders:
--> nickel - dime - quarter
--> dime - quarter - nickel
They will count as two different cases.
Calculating the no. of ways 3 coins can be selected from 6 coins.
nPr = = 
nPr = 120
We know that
the equation of the vertical parabola in the vertex form is
<span>y=a(x-h)²+k
</span>where
(h,k) is the vertex of the parabola
if a> 0 then
the parabola opens upwards
if a< 0
then the parabola open downwards
in this problem we have
f(x)=−5(x+7)²<span>+6
</span>a=-5
so
a< 0 -------> the parabola open downwards
the vertex is the point (-7,6) is a maximum
the answer is the option<span>
a = -5, opens down</span>
see the attached figure
Answer:
Step-by-step explanation: We have been given 4 expressions. We are asked to choose the expression that represents sum of cubes.
We know that sum of cubes is in form .
We can see that 1st and 2nd option has a negative sign. Therefore, these options cannot be sum of cubes.
Let us check 3rd and 4th options one by one.
We can rewrite our expression by writing terms as cubes:
Therefore, expression is a sum of cubes.
In 4th expression, we can see that . We cannot represent it as a cube. Similarly, we cannot represent as a cube. Therefore, 4th expression is not correct.
-10 and 2
-10 x 2 = -20
-10 + 2 = -8
