Answer:
z * sigma+u = x
Step-by-step explanation:
z = (x-u)/ sigma
z is the z score, u is the mean, sigma is the standard deviation
We need to solve for x
Multiply each side by sigma
z * sigma = (x-u)/ sigma * sigma
z * sigma = x-u
Add u to each side
z * sigma+u = x-u+u
z * sigma+u = x
Answer:
1.) 8.09g ; 2) 206.7 years
Step-by-step explanation:
Given the following :
Half-life(t1/2) of Uranium-232 = 68.9 years
a) If you have a 100 gram sample, how much would be left after 250 years?
Initial quantity (No) = 100g
Time elapsed (t) = 250 years
Find the quantity of substance remaining (N(t))
Recall :
N(t) = No(0.5)^(t/t1/2)
N(250) = 100(0.5)^(250/68.9)
N(250) = 100(0.5)^3.6284470
N(250) = 100 × 0.0808590
= 8.0859045
= 8.09g
2) If you have a 100 gram sample, how long would it take for there to be 12.5 grams remaining?
Using the relation :
N / No = (1/2)^n
Where N = Amount of remaining or left
No = Original quantity
n = number of half-lifes
N = 12.5g ; No = 100g
12.5 / 100 = (1/2)^n
0.125 = (1/2)^n
Converting 0.125 to fraction
(1/8) = 1/2^n
8 = 2^n
2^3 = 2^n
n = 3
Recall ;
Number of half life's (n) = t / t1/2
t = time elapsed ; t1/2 = half life
3 = t / 68.9
t = 3 × 68.9
t = 206.7 years
Number 1 The population of bacteria triples every day.
Answer:
Step-by-step explanation:
As long as the two equations represent the same straight line on the coordinate plane (they overlap), there will be infinite many intersections and infinite number of solutions.
Answer:
Step-by-step explanation:
We are given the two functions:
And we want to find:
So, by substitution, we acquire:
Distribute:
Simplify:
