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
The slope is 1/2 cuz its rise over run
Trust me, it's really easy!
break apart the shape (In 3D, I assume.) there should be 6 breaks apart. The top, bottom, and four sides. After you find the area, (Base x Base x Height for the 4 sides, and Side x Side for the top and the bottom of the figure.) Then you add all of them up, and there's the surface area! If you need more help, message me, I'd be glad to help.
Answer:
Karen (and Devante) walked x feet. They will be toguether after walking 115 feet each.
Step-by-step explanation:
I will assume that you want to know how much karen was walked towards Devante. Since they both travel at the same speed, then if Devante walks x feet, so does Karen.
SInce both of them are traveling in opposite directions, then in order for them to meet they need to walk a total of 230 feet in combination toguether. Since they travel at the same speed, then each one has to travel half that amount, hence each one will travel 230/2 = 115 feet until they meet.
Let's define variables:
x = Rate in $ / hr of the mechanic working 15hr
y = Rate in $ / hr of the mechanic working 5hr
We have the following system of equations:
x + y = 130
15x + 5y = 1400
Solving the system we have:
x = $ 75 / hr
y = $ 55 / hr
Answer:
the rate charged per hour by mechanics was:
x = $ 75 / hr
y = $ 55 / hr
