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harina [27]
3 years ago
13

you randomly pick two numbers from 1 to 9. If you could pick the same number twice and the first of the two numbers are in less

than five in the probability that the sum of the two numbers is less than five is
Mathematics
1 answer:
Ivenika [448]3 years ago
5 0
Alright, so the number is less than 5, we pick it twice, and the sum (2*number) is less than 5, we have 2 options - 2 or 1. 3 or more doesn't work because 3*2=6. The probability of choosing 2 is 1/9, and choosing 2 again is 1/9. Since they don't have anything to do with each other, we multiply 1/9 by 1/9 to get 1/81 as the chance of choosing 2 twice. Since we can have 1 twice too, we add 1/81 to 1/81 to get 2/81
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How do you simplify <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%20%2B%5Csqrt%7B6%7D%20%7D%7B%5Csqrt%7B8%7D%20%2B%
blondinia [14]

The trick is to exploit the difference of squares formula,

a^2-b^2=(a-b)(a+b)

Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:

(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2

Whatever you do to the denominator, you have to do to the numerator too. So

\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2

Expand the numerator:

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}

So we have

\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2

But √12 = √(3•4) = 2√3, so

\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}

7 0
3 years ago
Joel earns $5.50 an hour and time-and-a-half for overtime. how much does he earn for a 44.5-hour week?
vova2212 [387]
The expression which can be used to solve this problem is 5.50h + 1.5h. 

Since the given data is 44.5 hour week, all we need to do is substitute the given data to the expression. Since it takes 56 hours a week for a complete office/working hour without overtime, Joel's 44.5 hour week means he did not have overtime hours. Therefore the solution is,

5.50(44.5) = 244.75 Dollars.
3 0
4 years ago
Rewrite 50 - 15 using the distributive property and a common factor
Vesna [10]
It is not too difficult. Just do this
50-15
5(10-3)
The answer is 5(10-3)
4 0
4 years ago
Read 2 more answers
How do I square numbers
jonny [76]
Hellooo, it's me, you square numbers by
6 0
3 years ago
Read 2 more answers
32 is 56% of what? Mathematics
adell [148]

Answer:

i dont know if this is what youre looking for but here  again sorry if this is wrong

We have, 56% × x = 32

or,  

56

100

× x = 32

Multiplying both sides by 100 and dividing both sides by 56,

we have x = 32 ×  

100

56

x = 57.14

If you are using a calculator, simply enter 32×100÷56, which will give you the answer.

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
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