There are 48 available subjects. Researchers should select 4 of them for their experiment.
We should find the number of possible different random samples. The order of the selected subjects is not important. This means that we need to find how many different combinations of subjects from total 48 are possible. <span>A </span>formula<span> for the number of possible </span>combinations<span> of </span>r<span> objects from a </span>set<span> of </span>n<span> objects is: n!/r!(n-r)!. In our case n=48 and r=4:
C=48!/44!*4!=48*47*46*45*44!/44!*4!=</span><span>48*47*46*45/4*3*2*1=4669920/24=
194580.</span>
C. g=-5 is the correct answer
Answer:

Step-by-step explanation:
The equation of a quadratic function in vertex form is given by:

Where (h,k) is the vertex.
It was given in the question that the vertex of the parabola is (-1,4).
When we substitute the vertex into the formula we get:

The parabola also passes through (4,19) hence it must satisfy its equation.



We divide both sides by 25 to get:

Hence the quadratic function is:

Answer:

Step-by-step explanation:
The graph is in the image

Let
g(x)--------> the translation of the function f(x)
we know that
the rule of the translation is
units left and
units down
that means

so
In the function f(x) the point
is equal at the point
in the function g(x)
therefore
the function g(x) is equal to


<u>The answer is</u>
a) the rule of the translation is 
b) The graph in the attached figure