Answer: Irrational
I'm going to write 'x' in place of "square root of 2" just to save time. Let's consider the possibility that 7-x is rational. I'm going to show there's a contradiction which ultimately concludes that the expression is irrational.
If 7-x was rational, then 7-x = p/q for some integers p,q with q being nonzero. Solve for x to get
7-x = p/q
-x = (pq) - 7
x = -(p/q) + 7
x = 7 - (p/q)
x = (7q/q) - (p/q)
x = (7q-p)/q
So if 7-x were rational, then this forces x to be rational because 7q-p is an integer over q (also an integer). The format is rational = integer/integer. But this is where the contradiction lies. Remember that x is standing in place for "square root of 2", which is an irrational number. There is no way to write sqrt(2) as a ratio of two integers. So x cannot be both rational and irrational at the same time.
Therefore, 7-x must be irrational making 7-sqrt(2) to be irrational as well.
note: sqrt is shorthand for "square root"
another note: adding any rational number to an irrational number will always result in an irrational number.
M = 24
To solve that you divide 42/7 which is 6 then you multiply 4*6 and you get 24
Answer:
There is a 95% probability that the portfolio would not loose more than 30% of its value.
Step-by-step explanation:
The confidence interval for proportions (<em>p</em>) is:
The information provided is:
For 95% confidence level the critical value of <em>z</em> is:
The 95% confidence interval for average annual return is:
The lower limit of the 95% confidence interval is -28%.
This implies that the portfolio would not loose more than 28% of its value.
Thus, there is a 95% probability that the portfolio would not loose more than 30% of its value.
Answer:
Step-by-step explanation:
Equation
3x + 9 + 2x = x - 2x - 3
Solution
Combine all the like terms.
3x+2x+9 = x - 2x - 3
5x + 9 = -x - 3 Add x to both sides of the equation
5x+x +9 = -x+x -3 Combine
6x + 9 = - 3 Subtract 9 from both sides of the equation
6x+9-9 = - 3-9 Combine
6x = -12 Divide both sides by 6
6x/6 = -12/6
x = - 2
Answer x = - 2
Answer:
Explanation:
3. Find LCM of (30, 9):
30 = 2 x 3 x 5
9 = 3 x 3
Thus : LCM(30, 9) = 2 x 3 x 3 x 5 = 90
Therefore, in 90 days he will has both activities again.
4. Determine whether its possible to construct a triangle with the given length.
a.
8 + 9 > 11 (true)
8 + 11 > 9 (true)
9 + 11 > 8 (true)
Thus 8,9 and 11 can be construct as a triangle.
b.
4 + 5.1 > 12.5 (false)
4 + 12.5 > 5 (true)
12.5 + 5 > 4 (true)
Thus, 4, 5.1 and 12.5 cannot be constructed as a triangle.
