Carlos is almost old enough to go to school! Based on where he lives, there are 666 elementary schools, 333 middle schools, and 222 high schools that he has the option of attending.

There are 36 education paths available to Carlos based on the schools around where he lives.

Step-by-step explanation:

Complete Question

Carlos is almost old enough to go to school. Based on where he lives, there are 6 elementary schools, 3 middle schools, and 2 high schools that he has the option of attending. How many different education paths are available to Carlos? Assume he will attend only one of each type of school.

Solution

We can use mathematics or manually writing out the possible combinations of elementary, middle and high school that Carlos can attend.

Using Mathematics

There are 6 elementary schools, meaning Carlos can make his choice in 6 ways.

There are 3 middle schools, meaning Carlos can make his choice in 3 ways.

Together with the elementary school choice, Carlos can make these two choices in 6 × 3 ways.

There are 2 high schools, Carlos can make his choice in 2 ways.

Combined with the elementary and middle school choices, Carlos can make his choices in 6×3×2 ways = 36 ways.

Manually

If we name the 6 elementary schools letters A, B, C, D, E and F.

Name the 3 middle schools letters a, b and c.

Name the 2 high schools numbers 1 and 2.

The different combinations of the 3 choices include

Aa1, Aa2, Ab1, Ab2, Ac1, Ac2

Ba1, Ba2, Bb1, Bb2, Bc1, Bc2

Ca1, Ca2, Cb1, Cb2, Cc1, Cc2

Da1, Da2, Db1, Db2, Dc1, Dc2

Ea1, Ea2, Eb1, Eb2, Ec1, Ec2

Fa1, Fa2, Fb1, Fb2, Fc1, Fc2

Evident now that there are 36 ways in which the 3 stages of schools can be combined. There are 36 education paths available to Carlos based on the schools around where he lives assuming that he will attend only one of each type of school.

Hope this Helps!!!

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

answer is c

step-by-step explanation: