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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20 substandard?
A girl has 25 plants in all, 8 of them are tomatos. She has 10 more bean plants than pepper plants. How many pepper plants does she have?
Euler''''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.
By the method of completion of squares show that the equation 4x 2 +3x +5 = 0 has no real roots. Ans: 4 x 2 +3 x +5=0 ⇒ x 2 + 3/4 x + 5 = 0 ⇒ x 2 + 3/4 x +
calculate x+2+y=4
a conical hole drilled in a circular cylinder of height 12 and radius 5cm the height and radius of cone are also same find volume
# In a two-digit, if it is known that its unit''s digit exceeds its ten''s digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the
Example of Decimal to Fraction Conversion: Example: Convert 18.82 to a mixed number. Solution: Step 1: 18.82 is 18 and 82 hundredths. 18.82 = 18(8
A golf ball has a diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate the total surface area which is exposed to the surroundings assuming that the d
Evaluate following. ∫ 0 ln (1 + π ) e x cos(1-e x )dx Solution The limits are little unusual in this case, however that will happen sometimes therefore don't get
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