Answer:
2. 18-x-x-x = 0
x = 6
3. 35-y-y-y-y-y = 0
x = 7
4. 42-z-z-z-z-z-z = 0
z = 7
Step-by-step explanation:
Answer:
a) 0.997 is the probability that the breaking strength is at least 772 newtons.
b) 0.974 is the probability that this material has a breaking strength of at least 772 but not more than 820
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 800 newtons
Standard Deviation, σ = 10 newtons
We are given that the distribution of breaking strength is a bell shaped distribution that is a normal distribution.
Formula:
a) P( breaking strength of at least 772 newtons)
Calculation the value from standard normal z table, we have,
0.997 is the probability that the breaking strength is at least 772 newtons.
b) P( breaking strength of at least 772 but not more than 820)
0.974 is the probability that this material has a breaking strength of at least 772 but not more than 820.
Answer:
y=14
Step-by-step explanation:
solve for y by simplifying both sides of the equation then insolating the variable
Answer:
y = x + 3 or y = 1x + 3
Step-by-step explanation:
Since we're just going to find the equation (assuming it's slope-intercept form, which is <em>y = mx + b</em>), our jobs will be relatively simple!
Let's start with the first step and identify the y-intercept, which is the easiest step.
That will be (0,3), as the line intercepts the y-axis there.
Next, let's find the slope of the line using or . Just be careful when using that you correctly identify the scale the axis' are using.
For now, I'll use . Let's pick two points... (0,3) and (1,4).
—> =
This will be our slope, 1.
We now have our answer, y = 1x + 3.
Hope that helped!
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.