A limited number system uses base 12. There are at most four integer digits The weights of the digits are 12, 122, 12, and 1. Special names are given to the weights as follows: 12 = 1 dozen, 122 = 1 gross, and 12 = 1 great gross. %3D %3D %3D (a) How many beverage cans are in 6 great gross + 8 gross + 7 dozen + 4? (b) Find the representation in base 12 for 75690 beverage cans.
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- An airline association assigns three-letter codes to represent airport locations. For example, the airport code for Clark, Pampanga, is CPP. Notice that repetition is allowed in forming this code. How many airport codes are possible?A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum ofits digits at even places is either 0 or divisible by 11.For example, for 2547039:(Sum of digits at odd places) - (Sum of digits at even places) = (9 + 0 + 4 + 2) - (3 + 7 + 5) = 0So 2547039 is divisible by 11.But for 13165648:(Sum of digits at odd places) - (Sum of digits at even places) = (8 + 6 + 6 + 3) - (4 + 5 + 1 + 1) = 1212 is not divisible by 11 so 13165648 is also not divisible by 11.Consider a base 26 number system wherein the letters of the alphabet are the digits. That is, A=0, B=1, C=2, … Z=25 in base 10. Use the MAL as a number in the base 26 system, and KHA as another number in the base 26 system.Add these numbers together to obtain the sum in based 26. Example 1 — if your first name is “Peter” and your surname is “Pan”, then add up PET26 and PAN26, and show the sum in base 26.Example 2 — if your first name is “Peter” and your surname is “Pa”, then add up PET26 and PAA26, and show the sum in base 26.
- Given a number n, identify and print which in the given set of numbers are factors of n. Should there be no factors listed in the set of numbers, print "I'm alone". For example, given the number 36 and the set of numbers 2, 3, 5, 7, 12. Only print the numbers which are factors of 36, which are 2, 3, 12. Input The first line contains the number n; The second line contains how many numbers there are in the set of numbers; The third line contains the set of numbers. INPUT: 36 5 2·3·5·7·12 Output The set of numbers that are factors of n separated by a new line in order of appearance. If there are none, print "I'm alone" OUTPUT: 2 3 12To represent an integer value of n in decimal, we need to use ⌈log10(n + 1)⌉ digits . Verify this using n = 35, 1290. Note that for any real number x, ⌈x⌉ is the smallest integer that is greater than x, this means we always round up. For example, ⌈10.3⌉ = 11, ⌈−5.2⌉ = −5. To represent an intege value of n in binary, we need to use ⌈log2(n + 1)⌉ binary digits . Verify this using n = 35, 1290. Use the definition of logarithmic function to show that log2n / log10n = log210A binary number is to be transfromed by appending three 0's to the end of the number. For example , 11101 is transformed to 11101000. Which of the following best dewcribes the relationship between the transformed number and the original.- The transfromed number is 3 times the value of the original number- The transformed number is 4 times the value of the original number- the transformed number is 8 times the value of the original number- The transformed value is 1000 times the value of the original number
- Given that a,b,c,d,e are distinct whole numbers from 1 to 9 inclusive, along with the equalityab=c⋅100+d⋅10+e where c⋅100+d⋅10+e is the largest possible value, find the value ofa+b+c+d+eA number in base 2 (binary) is a number such that each of its digits is 0 or 1. To convert frombinary to decimal (base 10), the digits starting from the right are multiplied by powers of 2(starting at 0) and added. For example, the value in decimal of 10011 is calculated as follows:Evaluate the following Postfix: "4 9 + 8 * 1 - 6 6 + - 13 - 2 /" (All the numbers are in single digit. Everything is separated with a space)* 50.0 49.5 39.5 39 38 76
- A number of the form a + ib, in which i2 = -1 and a and b are real numbers, is called a complex number. We call the real part and b the imaginary part of a + ib. Complex numbers can also be represented as ordered pairs (a, b). The addition and multiplication of complex numbers are defined by the following rules: (a + ib) + (c + id) = (a + c) + i(b + d ) (a + ib) * (c + id) = (ac - bd) + i(ad + bc) Using the ordered pair notation, these rules are written as: (a, b) + (c, d) = ((a + c), (b + d )) (a, b) * (c, d) = ((ac - bd ), (ad + bc)) C++ has no built-in data type that allows us to manipulate complex numbers. Construct a data type, complex Type, that can be used to process complex numbers. Overload the stream insertion and stream extraction operators for easy input and output. We will also overload the operators + and * to perform addition and multiplication of complex numbers. If x and y are complex numbers, we can evaluate expressions such as x + y and x * y.A list of positive and negative numbers are in A2 through A400, and the square root of the absolute value is needed for each cell. Which function typed into B2 and copied through B400 will provide this information? a. =A2^(1/2) b. =SQRT(A2) c. =SQRT(ABS(A$2)) d. =SQRT(ABS(A2))Which of the following sets are equal? A = {x | x^2 − 4x + 3 = 0} B = {x | x^2 − 3x + 2 = 0} C= {x | x ∈ N, x < 3} D= {x | x ∈ N, x is odd, x < 5} E= {1, 2} F = {1, 2, 1} G= {3, 1} H= {1, 1, 3}