Alawyer owns 4 pairs of pants, 5 dress shirts and 6 ties. how many days can the lawyer go without wearing the same combination of three items?

4 × 5 × 6 = 120

Explanation:

1) This is a direct use of the counting principle, which states that the number of different ways a combination of independent events can happen is equal to the product of the number of different outcomes for each event.

That is, if event A can have m different outcomes, event B can have n different outcomes, and event C can have p different outcomes, the total number of different combinations is m × n × p.

2) In this case, the lawyer can use 4 different pais of pants, 5 different shirts, and 6 different ties, so the number of different combinations of the three items is: 4 × 5 × 6 = 120.

3) You can see that if you make a diagram (may be a tree diagram).

With that you can see that each pair of pants, can go with 5 shirts, which make 4 × 5 different couples of pants - shirts. After that, each different couple of pants - shirts can go with 6 different ties, so you have 4 × 5 × 6 three-piece combinations.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: