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Hoochie [10]
4 years ago
6

In this exercise, we consider strings made from uppercase letters in the English alphabet and decimal digits.

Mathematics
1 answer:
Yuri [45]4 years ago
3 0

Answer:

  • a) 26^2 36^8
  • b) 21\cdot10\cdot36^7
  • c) 5^3 31^7
  • d) 10\cdot 9\cdot 8 \cdot 7 \cdot 26^6

Step-by-step explanation:

We will use the product rule from combinatorics.

  • a) There are 26 letters in the English alphabet, so there are 26 possible choices for the first character and 26 possible choices for the last one. Each one of the remaining eight characters of the string has 36 choices (letters or digits). By the product rule, there are 26\cdot36\cdot 36\cdots 36\cdot 26=26^2 36^8 strings.
  • b) We have 5 possible choices for the first character, it must be some vowel a,e,i,o,u. The second character can be chosen in 21 ways, selecting some consonant. There are 10 possibilities for the last character because only of the digits are allowed. The other seven characters have no restrictions, so each one can be chosen in 36 ways. By the product rule there are 21\cdot 10\cdot 36^7 strings.    
  • c) The third character has 5 possibilities. Repetition of vowels is allowed, so the sixth and eighth characters have each one 5 possible choices. There are seven characters left. None of them are a vowel, but they are allowed to take any other letter or digit, so each one of them can be chosen in 36-5=31 ways. Therefore there are 5^3 31^7 strings.
  • d) Remember that the binomial coefficient \binom{n}{k} is the number of ways of choosing k elements from a set of n elements. In this case, to count all the possible strings, we first need to count in how many ways we can select the four positions that will have the digits. This can be done in \binom{10}{4} ways, since we are choosing four elements from the set of the ten positions of the string. Now, for the first position, we can choose any digit so it has 10 possibilities. The second position has 9 possibilities, because we can't repeat the digit used on the first position. Similarly, there are 8 choices for the third position and there are 7 choices for the fourth. Now, these are the only digits on the string, so the remaining 6 characters must be letters, then each one of them has 26 possibilities. By the product rule, there are 10\cdot 9\cdot 8 \cdot 7 \cdot 26^6 strings.
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Answer:

MP= (-5,7.5 )

Step-by-step explanation:

MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )

MP= (\frac{-7+-3}{2} )(\frac{6+9}{2} ) -7+-3= -10   6+9=15

MP= (\frac{-10}{2} )(\frac{15}{2} ) -10/2=-5 15/2=7.5

MP= (-5,7.5)

8 0
3 years ago
One serving of granola provides 4% of the protein you need daily. You must get the remaining 48 grams from other resources. How
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3 years ago
If (5x−2)^2=ax^2−bx+c, what is the value of a+c^2?
Nostrana [21]

Answer:

41

Step-by-step explanation: u first expand (5x-2)²

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then by comparing it to ax²+bx=c

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3 0
4 years ago
Need help! If someone could help me fill the chart and answer the question, that'd be greatly appricated, it'd be nice if you co
Paul [167]

Answer:

  (Marlins, 6.76×10^5), (Pirates, 9.68×10^5), (Angels, 1.87×10^6), (Cardinals, 1.98×10^6)

  most: Cardinals

Step-by-step explanation:

First, you compare exponents. Higher positive powers are larger. 10^5 < 10^6.

If the exponents are the same, you compare the mantissas. These are compared in the usual way. 6.76 < 9.68, and 1.87 < 1.98.

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8 0
3 years ago
Can someone check my answer? also tell me what property I used.
Semmy [17]
It is not having a definite property it is a way commonly used with algebraic expressions
26 = 8 + x (here, we put x instead of the number we don't know)
you can take 8 to the other side with 26 but it will be minus instead of plus
26 - 8 = ×
18 = x
6 0
3 years ago
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