How many different committees can be formed from 12 teachers and 43 students if the committee consists of 3 teachers and 4 ​students? The committee of 7 members can be selected in BLANK
different ways.​

Step-by-step explanation:

we are two conditions

In choosing a committee, order doesn't matter; in case of teachers we need the number of combinations of 3 people chosen from 12

remember that,

with the condition we obtain that,

therefore substitute:

simplify Parentheses:

rewrite:

reduce fraction:

rewrite 12 and 10:

reduce fraction:

simplify multiplication:

In case of students we need the number of combinations of 4 students choosen from 43 therefore,

simplify which yields:

hence,

The committee of 7 members can be selected in BLANK different ways is

and we're done!

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

the 4th choice is the correct one

step-by-step explanation: