Answer:
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Step-by-step explanation:
2.57
The oblique asymptote is y = xThis is a slant asymptote
You can find this by performing polynomial long division. See the attached image for how to do the division. The quotient is the single "x" up at the very top. The remainder is -2 at the very bottom. The oblique asymptote is equal to the quotient.
Step-by-step explanation:
The question above is answered below.
Consecutive numbers are set of numbers that follow one another in ascending or descending order, e.g. 1, 2, 3, 4, 5....
The sum of three consecutive numbers = 72
Let the unknown consecutive numbers be represented by x+1, x+2 and x+3 such that:

Remove the brackets

Collect like terms and simplify


Make 3x subject of formula by subtracting 6 from both sides


To obtain the value of x, divide through by the coefficient of x, which is 3. Hence;


Since x = 22,



The smallest of these numbers is 23.
Check,
23 + 24 + 25 = 72
Answer:
Step-by-step explanation:
x^2 + 11y + y^2 -3x + 11 = 5x +23 - y
First put it into general form by setting the equation to zero and moving all variables to one side.
x^2 + 11y + y^2 -3x + 11 = 5x +23 - y
+y -5x -11 -11
x^2 + y^2 - 8x + 12y = 12
Then solve by completing the square
x^2 - 8x y^2 + 12y = 12
(x - )^2 + (y + )^2 =
Half of 8 is 4
Then square 4 to get 16
Therefore, we plug the 4 into the first parentheses
x^2 - 8x + 16 + y^2 + 12y =12 +16
(x - 4)^2 + (y + )^2 =
Half of 12 is 6
Squared, that would be 36
plug this into the second parentheses
x^2 - 8x + 16 + y^2 +12y + 36 = 12 + 16 + 36
(x - 4)^2 + (y + 6)^2 =
12 + 16 = 28 + 36 = 64
Therefore, the equation of the circle is: (x - 4)^2 + (y + 6)^2 = 64
Which is option D
Question: "A coin is tossed 8 times. Find the probability P(of exactly 6 occurrences of tails)"
Answer:
When we toss a coin we have 50% of probability to get a tail and 50% probability to get heads.
If we toss the coin 8 times, in order to find P(T=6), we need to use the binomial distribution:

where:
n = total number of events
k = number of successes we want
p = probability of success
Therefore:
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= 28 · 0.015625 · 0.25
= 0.109375
Hence, the probability of getting 6 tails out of 8 tosses is D) 10.94%.