-- He must have at least one of each color in the case, so the first 3 of the 5 marbles in the case are blue-green-black.
Now the rest of the collection consists of
4 blue
4 green
2 black
and there's space for 2 more marbles in the case.
So the question really asks: "In how many ways can 2 marbles
be selected from 4 blue ones, 4 green ones, and 2 black ones ?"
-- Well, there are 10 marbles all together.
So the first one chosen can be any one of the 10,
and for each of those,
the second one can be any one of the remaining 9 .
Total number of ways to pick 2 out of the 10 = (10 x 9) = 90 ways.
-- BUT ... there are not nearly that many different combinations
to wind up with in the case.
The first of the two picks can be any one of the 3 colors,
and for each of those,
the second pick can also be any one of the 3 colors.
So there are actually only 9 distinguishable ways (ways that
you can tell apart) to pick the last two marbles.
Answer: 49 students
Step-by-step explanation:
2 /7 of students in a school wore shorts today. The number of students to be selected in order to get 14 students who will wear shorts to school will be:
Let the number of students that will be sampled be y. This will be:
2/7 of y = 14
2/7 × y = 14
2y/7 = 14
Cross Multiply
2y = 7 × 14
2y = 98
y = 98/2
y = 49
49 students will be selected randomly.
These two angles are congruent so
12x + 3 = 11x + 9
X = 6
Plug in 6 so 12(6)+3=75
Both angles measure 75 degrees
In order to determine the answer to this item, we just have to substitute x² + 2 to all x's of the first function. That is,
f(x) = 4x + 10
will become,
f(x²+2) = 4(x²+2) + 10
Simplifying will give us an answer of,
f(x²+2) = 4x²+18
Answer:
INCORRECT
Step-by-step explanation:
Given a rectangular prism,
Total Surface Area = 2(LW+LH+WH)
If Length = 12, Width =20, and; Height = 16.
Total Surface Area = 2(12*20+12*16+20*16)
=2(240+192+320)
=2(752)
=1504
The Surface Area is 1504 Square Units, therefore if someone says the surface Area is 3,840, they are incorrect!
