Answer:
268 mg
Step-by-step explanation:
Let A₀ = the original amount of caffeine
The amount remaining after one half-life is ½A₀.
After two half-lives, the amount remaining is ½ ×½A₀ = (½)²A₀.
After three half-lives, the amount remaining is ½ ×(½)²A₀ = (½)³A₀.
We can write a general formula for the amount remaining:
A =A₀(½)ⁿ
where n is the number of half-lives
.
n = t/t_½
Data:
A₀ = 800 mg
t₁ = 10 a.m.
t₂ = 7 p.m.
t_½ = 5.7 h
Calculations:
(a) Calculate t
t = t₂ - t₁ = 7 p.m. - 10 a.m. = 19:00 - 10:00 = 9:00 = 9.00 h
(b) Calculate n
n = 9.00/5.7 = 1.58
(b) Calculate A
A = 800 × (½)^1.58 = 800 × 0.334 = 268 mg
You will still have 268 mg of caffeine in your body at 10 p.m.
Answer:
7,000
Step-by-step explanation:
That is a display of the distributive property.
This is shown because when a number is written directly next to a set of parentheses, you must multiply each value inside the parentheses by the number on the outside.
In this case, 5(8-6) means that you must multiply 5 by 8, as well as by -6.
The right side of the equal sign in the given problem shows both of those steps separately, which is why it is a display of the distributive property. The correct answer is A.
Because when the ones add up to 10 or more you will regroup and carry the 1 to the 10's place
Hope this helps:)
The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.
<h3>What is a Rectangle?</h3>
A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).
<h3>What is the Area of a Rectangle?</h3>
The area of a rectangle = (length of rectangle)(width of rectangle).
Given the following parameters for the patio and the bench:
- Length of rectangular patio = x + 20
- Width of rectangular patio = x + 10
- Length of rectangular bench = 6
- Width of rectangular bench = 2
Area to be painted = area of rectangular patio - area of rectangular bench
Area of rectangular patio = (x + 20)(x + 10)
Area of rectangular bench = (6)(2) = 12
Area to be painted = (x + 20)(x + 10) - 12
The answer is: B. A = (x + 20)(x + 10) - 12.
Learn more about the area of rectangle on:
brainly.com/question/25292087
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