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3 years ago

How many integers between 100 and 999 have all distinct digits (i.e., no two digits the same)?

1 answer:

4 0

Answer: 648

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Explanation:

We have this set of digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
From that set, we can only pick three items. We cannot select the same digit twice.

Consider a blank three digit number such that it is composed of slot A, slot B, slot C.

Since the number must be larger than 100, this means that we cannot select 0 as the first digit. We go from a pool of 10 digits to 10-1 = 9 digits for our first selection.
In other words, we have this subset to select from
{1, 2, 3, 4, 5, 6, 7, 8, 9}
So we have 9 choices for slot A.

For slot B, we also have 9 choices since 0 is now included. For instance, if we selected the digit '4' then we have this subset of choices left over: {0, 1, 2, 3, 5, 6, 7, 8, 9} which is exactly 9 items.

For slot C, we have 9-1 = 8 items left to choose from. For example: If we choose '4' for slot A, and '2' for slot B, then we have this subset to choose from: {0, 1, 3, 5, 6, 7, 8, 9} exactly 8 items

In summary so far, we have...
9 choices for slot A
9 choices for slot B
8 choices for slot C

Giving a total of 9*9*8=81*8=648 different three digit numbers. You'll notice that I'm using the counting principle which allows for the multiplication to happen. Think of a probability tree.

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How do you write 5,392,029,004 in expanded form

Neko [114]

5,000,000,000 + 300,000,000 + 90,000,000 + 2,000,000 + 20,000 + 9,000 + 4

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4 years ago

The base of an isosceles triangle is one and a half times the length of the other two sides.A smaller triangle has a perimeter t

Anna11 [10]

Answer:

Perimeter of the smaller triangle = 1.75x

Step-by-step explanation:

Let the two equal sides of an isosceles triangle = x

Therefore, length of the base = $(1\frac{1}{2})x$

Perimeter of this isosceles triangle = x + x + $(1\frac{1}{2})x$

= 2x + $(1+\frac{1}{2})x$

= 2x + x + $\frac{x}{2}$

= $\frac{5x}{2}$

Since, smaller triangle has a perimeter that is half the perimeter of the larger triangle,

Length of each corresponding side of smaller triangle will be half of the larger triangle.

Length of sides of the smaller triangle = $\frac{x}{2},\frac{x}{2},(1\frac{1}{2})\frac{x}{2}$

Perimeter of the smaller triangle = $\frac{x}{2}+\frac{x}{2}+(1\frac{1}{2})\frac{x}{2}$

= x + $\frac{x}{2}+\frac{x}{4}$

= $\frac{3}{2}x+\frac{x}{4}$

= $\frac{6}{4}x+\frac{x}{4}$

= $\frac{7}{4}x$

= 1.75x

Therefore, expression that represents the perimeter of the smaller triangle is (1.75x)

4 0

3 years ago

How can an expression written in either radical form or rational exponent form be rewritten to fit the other form?

adell [148]

When dealing with radicals and exponents, one must realize that fractional exponents deals directly with radicals. In that sense, sqrt(x) = x^1/2
Now, how to go about doing this:

In a fractional exponent, the numerator represents the actual exponent of the number. So, for x^2/3, the x is being squared.

For the denominator, that deals with the radical. The index, to be exact. The index describes what KIND of radical (or root) is being taken: square, cube, fourth, fifth, and so on. So, for our example x^2/3, x is squared, and that quantity is under a cube root (or a radical with a 3). Here are some more examples to help you understand a bit more:
x^6/5 = Fifth root of x^6
x^3/1 = x^3
^^^Exponential fractions still follow the same rules of simplifying, so...
x^2/4 = x^1/2 = sqrt(x)

Hope this helps!

8 0

3 years ago

Given that <br> x<br> = 7.3 m and <br> θ<br> = 52°, work out AB rounded to 3 SF.

trapecia [35]

Answer:

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3 years ago

What is the percent of decrease from 200 to 110? A. 45% B. 55% C. 82% D. 90%

strojnjashka [21]

A) 45%, (100-200)/200=0.45 which also equals 45% :)

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3 years ago