Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6
Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1
(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1
Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x
Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2
Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2
Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144
Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0
The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0
Divide both sides by -4:
(x - 9) (x - 4) = 0
Split into two equations:
x - 9 = 0 or x - 4 = 0
Add 9 to both sides:
x = 9 or x - 4 = 0
Add 4 to both sides:
x = 9 or x = 4
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct
The solution is:
Answer: x = 9
Answer:
48
Step-by-step explanation:
Answer:
Step-by-step explanation:
Since the amount of soft drink dispensed into a cup is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = amount in ounce of soft drink dispensed into cup.
µ = mean amount
σ = standard deviation
From the information given,
µ = 7.6oz
σ = 0.4 oz
a) The probability that the machine will overflow an 8-ounce cup is expressed as
P(x > 8) = 1 - P(x ≤ 8)
For x = 8,
z = (8 - 7.6)/0.4 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.84
P(x ≤ 8) = 1 - 0.84 = 0.16
b) P(x< 8) = 0.84
c) when the machine has just been loaded with 848 cups, the number of cups expected to overflow when served is
0.16 × 848 = 136 cups
Answer:
AA similarly is correct....
Answer: the lines on the outside mean absolute value and the absolute value of -3 is 3
Step-by-step explanation:
