Answer: x" = 5.69
Step-by-step explanation:
The graphic solution is attached.
Verifying the solution:
Existence condition: x > 0
2x - 4 = √x + 5
√x =2x - 4 - 5
√x =2x - 9 (²)
x = (2x - 9)²
x = 4x² - 36x + 81
4x² - 36x - x + 81 = 0
4x² - 37x + 81 = 0
Δ = -37² - 4.4.81 = 1369 - 1296 = 73
x = 37 ±√73/8
x' = 3.55
x" = 5.69
checking:
2*3.55 - 4 = 3.1
√3.55 + 5 = 6.88 Its not the same ∴ 3.55 is not a solution
2*5.69 - 4 = 7.39
√5.69 + 5 = 7.39 ∴ it's the only solution
Answer: 0.49
Step-by-step explanation:
The mean= E[x]=1/l= 7.5 min
l=1/7.5 =10/75=2/15
The exponential distribution's probability density function is looking like that:
F(x)= l*e^(-l*x) = 2/15*e^(-2*x/15)
P(0<x<5)= e^(-0*2/15)- e^(-5*2/15)=1- e^(-2/3)= approx 0.49
Answer:
Look below
Step-by-step explanation:
Average means the middle of two numbers.
If the larger number is exactly one more or an odd number more than the smaller, it is possible for a half point to occur.
Answer: Diego has 5 fewer counters.
Step-by-step explanation:
In order to find the answer, you need to find the difference between the amount of counters Dara has compared to Diego.
(Amount Dara has) - (Amount Diego has) = Difference
12 - 7 = 5
Diego has 5 fewer counters
Answer:
67
Step-by-step explanation: Given the quadratic equation $z^2 + bz + c = 0$, Vieta's formulas tell us the sum of the roots is $-b$, and the product of the roots is $c$. Thus,
\[-b = (-7 + 2i) + (-7 - 2i) = -14,\]so $b = 14.$
Also,
\[c = (-7 + 2i)(-7 - 2i) = (-7)^2 - (2i)^2 = 49 + 4 = 53.\]Therefore, we have $b+c = \boxed{67}$.
There are many other solutions to this problem. You might have started with the factored form $(z - (-7 + 2i))(z - (-7 - 2i)),$ or even thought about the quadratic formula.
This is the aops answer :)
