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astraxan [27]
3 years ago
10

Tom has 4 navy socks and 6 black socks in a drawer. One dark morning he randomly pulls if 2 socks. What is the probability that

he will selects a pair of navy socks ?
Mathematics
1 answer:
miv72 [106K]3 years ago
8 0

Answer:

2/3 of a probability. 33%

Step-by-step explanation:

You might be interested in
Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.
frutty [35]
<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

2^n\leq 2^{n+1}-2^{n-1}-1

where n is a positive integer.

  • Let us take n=1

then we have:

2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2

Hence, the result is true for n=1.

  • Let us assume that the result is true for n=k

i.e.

2^k\leq 2^{k+1}-2^{k-1}-1

  • Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u>  2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Let us take n=k+1

Hence, we have:

2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)

( Since, the result was true for n=k )

Hence, we have:

2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2

Also, we know that:

-2

(

Since, for n=k+1 being a positive integer we have:

2^{(k+1)+1}-2^{(k+1)-1}>0  )

Hence, we have finally,

2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

2^n\leq 2^{n+1}-2^{n-1}-1  where n is a positive integer.

6 0
3 years ago
The one selected is wrong please help meee!
GREYUIT [131]

Answer:

  (a)  ΔARS ≅ ΔAQT

Step-by-step explanation:

The theorem being used to show congruence is ASA. In one of the triangles, the angles are 1 and R, and the side between them is AR. The triangle containing those angles and that side is ΔARS.

In the other triangle, the angles are 3 and Q, and the side between them is AQ. The triangles containing those angles and that side is ΔAQT.

The desired congruence statement in Step 3 is ...

  ΔARS ≅ ΔAQT

5 0
2 years ago
Wassily Leontief (1906-1999) was a Russian-born, American economist who, aside from developing highly sophisticated economic the
yKpoI14uk [10]

Answer:

The reason for the columns adding up to 1 is that each individual consumes a proportion or a fraction of the total quantity produced under each product category and every product is consumed.  There is no leftover.

When the proportions of all the individuals are added up, the sum is always 1 under each product category because each individual can only consume a part of the whole.

Step-by-step explanation:

a) Data and Calculations:

                        Food   Clothes  Housing  Energy  High Quality 100

                                                                                Proof  Moonshine

Farmer             0.25      0.15       0.25        0.18            0.20                    

Tailor                0.15      0.28       0.18         0.17            0.05

Carpenter        0.22      0.19       0.22        0.22           0.10

Coal Miner       0.20      0.15       0.20        0.28           0.15

Slacker Bob     0.18      0.23        0.15        0.15            0.50

Total                 1.00      1.00        1.00         1.00            1.00

6 0
3 years ago
Can someone help me with this answer I’m on a test and it’s almost due
Brrunno [24]

16.5 / p = 11 / 18

p = 16.5 × 18 / 11

p = ( 16.5 / 11 ) × 18

p = 1.5 × 18

p = 27

6 0
3 years ago
Simplify (use only positive exponents) : (3y^10)(2y^2)/8y^5
nadezda [96]
When multiplying variables with exponents, all you have to do is to add the exponents and that’s the ‘product.’

So;

(3y^10)(2y^2) is equal to (3)(2)(y^10+2).

6y^12/8y^5


When dividing exponents, you do the opposite and subtract the exponents. And you divide the whole number by half.


6y^12/8y^5 = 3y^7/4

5 0
3 years ago
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