Using the Fundamental Counting Theorem, it is found that there are 10 positive three-digit integers have the hundreds digit equal to 7 and the units (ones) digit equal to 1.
<h3>What is the Fundamental Counting Theorem?</h3>
It is a theorem that states that if there are n things, each with
ways to be done, each thing independent of the other, the number of ways they can be done is:
![N = n_1 \times n_2 \times \cdots \times n_n](https://tex.z-dn.net/?f=N%20%3D%20n_1%20%5Ctimes%20n_2%20%5Ctimes%20%5Ccdots%20%5Ctimes%20n_n)
The number of options for each selection are given as follows, considering there are 10 possible digits, and that the last two are fixed at 7 and 1, respectively:
![n_1 = 10, n_2 = n_3 = 1](https://tex.z-dn.net/?f=n_1%20%3D%2010%2C%20n_2%20%3D%20n_3%20%3D%201)
Hence, the number of integers is given by:
N = 10 x 1 x 1 = 10.
More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866
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Use the FOLD method<span>
(a+b)(c+d)=ac+ad+bc+bd
</span><span>−12<span>s<span><span>^2 </span><span></span></span></span>+ 3st + 8ts − 2<span>t<span><span>^2</span><span>
</span></span></span></span>Collect like terms
-12{s}^{2}+(3st+8st)-2{t}^{2}
Simplify
<span>-12{s}^{2}+11st-2{t}^{2}<span>−12<span>s<span><span>2</span><span></span></span></span>+11st−2<span>t<span><span>2
The answer is = -12s^2 + 11st - 2t^2</span></span></span></span></span>
Answer:
Step-by-step explanation:
By definition, a rational number is a precise number: or in other terms, we know its exact value. Irrational numbers are number that has endless digits on the right of the decimal points: in other terms, we can't know its exact value.
First question:
√2.5 = 1.58113.... It's endless, so irrational.
-√64 = -8 it's a whole number, so rational.
4√5 = 8.94427.... Endless, so irrational.
√14.4 = 3.7947... Endless so irrational.
So -√64 is the rational number.
Second:
7.885 is rational because has a defined number of digits after the decimal points.
π² = 9.8696.... Endless, so irrational.
√0.144 = 0.3794.... Endless, so irrational
√91 = 9.5393.... Endless, so irrational
So 7.885 is the rational number.
Third:
-7.8 bar: You can notice the line over the 8, this means that there's an infinite number of 8 after the decimal points. So it's 7.88888888888.... Endless, so irrational.
√25 = 5, whole number so rational
25.8125 Has a definite number of digits after the decimal point, so is rational.
√0.025 = 0.1581... Endless, so irrational.
So -7.8 bar and √0.025 are irrational.
Fourth:
π= 3.1415... Endless, so irrational.
1.425 has a definite number of digits after the decimal point, so rational.
√50 = 7.0710.... Endless, so irrational
√-4 Doesn't exist. Finding the square root of a negative number is mathematically impossible.
So 1.425 is the rational number.
Fifth:
√10 = 3.1622..... Endless, so irrational.
√100 = 10, a whole number so rational.
√1000 = 31.6227..... Endless, so irrational
√100000 = 316.2277...... Endless, so irrational.
√100 is the rational number.
Hope this helps!! :D And I hope you understood the lesson a bit more xD
It is called codomininance or incomplete dominance