100(whole class is 100%) / 6060(number of students total) = any random student chance
0.0165
A) for democrats multiply chance of any random student with number of democrats
0.0165×4040=66.66666...
B) for business majors, multiply that chance with number of business majors
0.0165×1010=16.66666...
C) for both business major and democrat multiply chance with numbers of students who are both
0.0165×33=0.544...
ANSWER
EXPLANATION
If the graph of y=cosx is transformed to y=a cos (x−c)+d by a vertical compression by a factor of 1/3 and a translation 2 units down,
then
a=1/3
and d=-2.
The 'c' is a phase shift since it is not given, it means it is zero.
Therefore the new equation is:
y=1/3cos(x-0)−2
This simplifies to:
y=1/3cosx−2
The correct option is C.
Step-by-step explanation:
look at the picture !
she has to paint actually 6 rectangles :
the 3 tops of the 3 stairs.
and the 3 vertical front boards (the front of each step of the stairs).
what is the area of these rectangles ? summing up all 6 - that is the surface area to be painted.
each top rectangle is clearly
82×19 (19 cm deep) = 1558 cm²
each front board is
82×12 (12 cm high) = 984 cm²
so, in total we have
3×1558 + 3×984 = 4674 + 2952 = 7626 cm²
as surface area to be painted.
Answer:
x = -14
Step-by-step explanation:
Simplifying
7x + 156 = 9x + 184
Reorder the terms:
156 + 7x = 9x + 184
Reorder the terms:
156 + 7x = 184 + 9x
Solving
156 + 7x = 184 + 9x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9x' to each side of the equation.
156 + 7x + -9x = 184 + 9x + -9x
Combine like terms: 7x + -9x = -2x
156 + -2x = 184 + 9x + -9x
Combine like terms: 9x + -9x = 0
156 + -2x = 184 + 0
156 + -2x = 184
Add '-156' to each side of the equation.
156 + -156 + -2x = 184 + -156
Combine like terms: 156 + -156 = 0
0 + -2x = 184 + -156
-2x = 184 + -156
Combine like terms: 184 + -156 = 28
-2x = 28
Divide each side by '-2'.
x = -14
Simplifying
x = -14
