Answer:
a) 1470 ways
b) 2835 ways
Step-by-step explanation:
the question is not correct, in the correct question The number of independents should be 3 not 2
there are 7 republicans, 10 democrats and 3 independents.
C(n,r) is the number of different combinations of n distinct objects taken r at a time.
C(n,r) = 
a) it will consist of 1 Republican and 4 Democrats
The number of ways this can be chosen is = C(7,1) × C(10,4) = 
= 7 × 210 = 1470 ways
(b) it will consist of 2 Republicans, 2 Democrats, and 2 Independents (consist of 2 independents not 3)
The number of ways this can be chosen is = C(7,2) × C(10,2) × C(2,2)
=
= 21 × 45 × 3 = 2835 ways
Answer:
Step-by-step explanation:
This is modeled after an exponential function which, at its simplest, is
where, for us and in this particular situation, y is the final height, a is the initial height, b is the rate of growth or decline, and x is the number of bounces. We know the initial height is 20, but we need to find the rate of decline. Rewriting the formula to model a rate of decay or decline is
, or more closely related to our circumstances:
and simplifying that a bit:
, choice D.
(2/3)x = 10
(3/2)(2/3)x = 10(3/2)
x = 30/2 = 15
Answer:
The function has been flipped due to the negative in front.
The function has been shifted 17 units to the left.
The function has been shifted 4.3 units down.
Step-by-step explanation:
When functions are transformed there are a few simple rules:
- Adding/subtracting inside the parenthesis to the input shifts the function left(+) and right(-).
- Adding/subtracting outside the parenthesis to the output shifts the function up(+) and down(-).
- Multiplying the function by a number less than 1 compresses it towards the x-axis.
- Multiplying the function by a number greater than 1 stretches it away from the x-axis.
- Multiplying by a negative flips the graph.
The graph of 
compares to 
in the following ways:
The function has been flipped due to the negative in front.
The function has been shifted 17 units to the left.
The function has been shifted 4.3 units down.
5.5 quarts equals 22 cups. (There are 4cups in a quart, so 4 * 5.5 = 22)
22-4= 18 cups
