Answer:
option A: 0.2357
Step-by-step explanation:
P( less than 1.76 or greater than 2.39) = P(X < 1.76) + P( X > 2.39)
P(X < 1.76) = 0.0126 (as per the excel output)
P(X < 2.39) = 0.7769
Hence P( X> 2.39) = 1- 0.7769 = 0.223
P( less than 1.76 or greater than 2.39) = P(X < 1.76) + P( X > 2.39) = 0.0126 + 0.223 = 0.2357
P( less than 1.76 or greater than 2.39) = 0.2357
Solve for m:
1/sqrt(8) = 4 (m + 2)
Rationalize the denominator. 1/sqrt(8) = 1/sqrt(8)×(8^(1 - 1/2))/(8^(1 - 1/2)) = (8^(1 - 1/2))/8:
(8^(1 - 1/2))/8 = 4 (m + 2)
Combine powers. (8^(1 - 1/2))/8 = 8^((1 - 1/2) - 1):
8^((1 - 1/2) - 1) = 4 (m + 2)
Put 1 - 1/2 over the common denominator 2. 1 - 1/2 = 2/2 - 1/2:
8^(2/2 - 1/2 - 1) = 4 (m + 2)
2/2 - 1/2 = (2 - 1)/2:
8^((2 - 1)/2 - 1) = 4 (m + 2)
2 - 1 = 1:
8^(1/2 - 1) = 4 (m + 2)
Put 1/2 - 1 over the common denominator 2. 1/2 - 1 = 1/2 - 2/2:
8^(1/2 - 2/2) = 4 (m + 2)
1/2 - 2/2 = (1 - 2)/2:
8^((1 - 2)/2) = 4 (m + 2)
1 - 2 = -1:
8^((-1)/2) = 4 (m + 2)
1/sqrt(8) = 1/sqrt(2^3) = (1/sqrt(2))/2:
(1/sqrt(2))/2 = 4 (m + 2)
Rationalize the denominator. 1/(2 sqrt(2)) = 1/(2 sqrt(2))×(sqrt(2))/(sqrt(2)) = (sqrt(2))/(2×2):(sqrt(2))/(2×2) = 4 (m + 2)
2×2 = 4:
(sqrt(2))/4 = 4 (m + 2)
(sqrt(2))/4 = 4 (m + 2) is equivalent to 4 (m + 2) = (sqrt(2))/4:
4 (m + 2) = sqrt(2)/4
Expand out terms of the left hand side:
4 m + 8 = sqrt(2)/4
Subtract 8 from both sides:
4 m + (8 - 8) = (sqrt(2))/4 - 8
8 - 8 = 0:
4 m = (sqrt(2))/4 - 8
Put each term in (sqrt(2))/4 - 8 over the common denominator 4: (sqrt(2))/4 - 8 = (sqrt(2))/4 - 32/4:
4 m = (sqrt(2))/4 - 32/4
(sqrt(2))/4 - 32/4 = (sqrt(2) - 32)/4:
4 m = (sqrt(2) - 32)/4
Divide both sides by 4:
Answer: m = (sqrt(2) - 32)/(4×4)
Answer:
11 > n > 4
Step-by-step explanation:
Given any two sides of a triangle, we now that the sum of such sides MUST be greater than the measure of the remaining side. This is, given the three sides a, b and c, it must be that:
a + b > c
a + c > b
b + c > a
For our case:
7 + 4 > n (1) ---> 11>n
7 + n > 4 (2)
4 + n > 7 (3)
The 1 inequality says that the n side MUST be less than 11.
Now, pick the (3) inequality and subtract 4 in both sides:
4 + n -4 > 7 - 4
n > 3
So, the n side must be grater than 3.
Thus, the solution is:
11 > n > 3
As we are working with integers we now that the grater integer larger than 3 is 4, and the greater integer less than 11 is 10. So, the side must be equal or greater to 4 and equal or less than 10:
10 >= n >= 4
Answer:
250000000000000000000000
Step-by-step explanation:
do 5*5 and ignore all the 0's
5*5=25
now add ALL the 0's
250000000000000000000000
hope this helps!
Answer:
x^3/4.
Step-by-step explanation:
√︎(x) • ∜︎(x)
= x^1/2 * x^1/4
= x^3/4.