If a “word” is any arrangement of 3 different letters, how many 3-letter “words” can be formed from the letters B, O, N, and K, where each letter is to be used once?

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Explanation:

We have 3 slots, which I'll call slot 1, slot 2, slot 3.

Once all the slots are accounted for, we multiply the values mentioned: 4*3*2 = 12*2 = 24.

There are 24 different three-letter "words" that can be formed where any letter selected cannot be reused.

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A slightly different approach:

Order matters because a "word" like BON is different from a "word" like BNO.

Since order matters, we'll use a permutation

We have n = 4 letters to pick from and r = 3 slots to fill.

Apply those values into the nPr permutation formula

We end up with the same result as before.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have