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Digiron [165]
3 years ago
6

1. (10 pts.) Suppose you have a language with only 3 letters: A, B, and C, which occur with frequencies 0.7, 0.2, and 0.1, respe

ctively. The following ciphertext was encrypted by the Vigen`ere method: BABABCBCAC. Assume that the key length is either 1, 2, or 3. Find the most likely key length and determine the most likely key using the method from class. Solution: We compare BABABCBCAC with its shifts by 1, 2, and 3, looking for overlaps. There are no overlaps for a shift of 1 or 3, but there are 6 overlaps for a shift of 2. Thus we expect the key length to be 2. Looking at every other letter, we see BBBBA and AACCC for the letters in even and odd positions, respectively. Due to the overwhelming frequency of the letter A in the language, we can reasonably assume that B decrypts to to A in the first sequence and C decrypts to A in the second. This gives us the key BC.

Mathematics
1 answer:
butalik [34]3 years ago
3 0

Answer:

The solution to this question is attached below:

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53. Which of the following diagrams show a pair of corresponding angles?
sashaice [31]

Answer:

Diagram A is correct one

3 0
2 years ago
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What are all of the real roots of the following polynomial? f(x) = x5 + 5x4 - 5x3 - 25x2 + 4x + 20
Nadusha1986 [10]
F(x)=x^5 + 5*x^4 - 5*x^3 - 25*x^2 + 4*x + 20

By examining the coefficients of the polynomial, we find that
1+5-5-25+4+20=0 => (x-1) is a factor
Now, reverse the sign of coefficients of odd powers,
-1+5+5-25-4+20=0 => (x+1) is a factor

By the rational roots theorem, we can continue to try x=2, or factor x-2=0
2^5+5(2^4)-5(2^3)-25(2^2)+4(2)+20=0
and similarly f(-2)=0
So we have found four of the 5 real roots.
The remainder can be found by synthetic division as x=-5


Answer: The real roots of the given polynomial are: {-5,-2,-1.1.2}

8 0
3 years ago
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What is the answer to x (x+8)=9​
marta [7]

Answer:

x=1 or x=−9

Step-by-step explanation:

Let's solve your equation step-by-step.

x(x+8)=9

Step 1: Simplify both sides of the equation.

x2+8x=9

Step 2: Subtract 9 from both sides.

x2+8x−9=9−9

x2+8x−9=0

Step 3: Factor left side of equation.

(x−1)(x+9)=0

Step 4: Set factors equal to 0.

x−1=0 or x+9=0

x=1 or x=−9

8 0
3 years ago
Which fraction represents the decimal 0.8888...?
suter [353]

Answer: The decimal 0.88888.... represented by the fraction \dfrac{8}{9}

Step-by-step explanation:

Since we have given that

0.888888....

So, Let x = 0.88888....=0.\bar{8} -----(1)

Now, multiply by 10 on both sides, we get that

10x=8.8888.....=8.\bar{8}----------(2)

Now, Subtracting (1) from (2), we get that

10x-x=8.\bar{8}-0.\bar{8}\\\\9x=8\\\\x=\dfrac{8}{9}

Hence, the decimal 0.88888.... represented by the fraction \dfrac{8}{9}

8 0
3 years ago
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Paul can choose to be paid $50 for a job or he can be paid 12.50 per hour. Underwhat circumstances should he choose the hourly w
Advocard [28]
Option 1: $50
Option 2: $12.50 per hour.

50 ÷ 12.50 = 4

Paul can choose the hourly wage if he works more than 4 hours.
For example, he works 5 hours.

12.50 x 5 hours = 62.50

$62.50 is higher than the fixed rate of $50. Thus, hourly wage is the better option.
8 0
3 years ago
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