If 3b + 4 = 10, then 5b + 4 =
2 answers:
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Answer:
The 95% confidence interval would be given (0.622;0.644).
We are confident (95%) that the true proportion of people that said that they change their nail polish once a week is between 0.622 and 0.644
Step-by-step explanation:
Data given and notation
n=7000 represent the random sample taken
X=4431 represent the people that said that they change their nail polish once a week
estimated proportion of people that said that they change their nail polish once a week
represent the significance level
Confidence =0.95 or 95%
p= population proportion of people that said that they change their nail polish once a week
Solution to the problem
The confidence interval would be given by this formula
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 95% confidence interval would be given (0.622;0.644).
We are confident (95%) that the true proportion of people that said that they change their nail polish once a week is between 0.622 and 0.644
The graph of the pH function can be created by plotting the output of
input values of the hydronium ions, <em>x</em>, in the range 0 < x ≤ 1.
Correct responses:
First part:
Please find attached the graph of the pH function
From the attached graph of the pH function, we have;
- The point where the pH value is 0 is
- The point where the pH value is 1 is
- The pH level if the hydronium ion is raised to 0.50 is approximately <u>0.3</u>
Second part
- Please find attached the graph of the transformations, f(x) + 1, and f(x + 1) of the parent log function.
- The transformation that results in a y-intercept is
, because, at x = 0, f(x + 1) = 0.
First part
The pH function is; f(x) = -log₁₀x
Please find attached the graph of the pH function created with MS Excel
Where;
x = Amount of hydronium ions
f(x) = pH level
When the pH is 0, we have;
-log₁₀x = 0
Which gives;
x = 10⁰ = 1
- When the pH value is 0, the point on the graph is
When the pH value is 1, we have;
-log₁₀x = 1
log₁₀x = -1
x = 10⁻¹ = 0.1
- The point on the graph where the pH value is 1 is
- From the graph, the ideal pH level if the amount of hydronium ions is raised to 0.50 is pH = 0.301029996 ≈ <u>0.30</u>
Second Part
The given transformations are;
f(x) + 1, and f(x + 1)
- <u>The graph of the transformations created with MS Excel is attached</u>
At the y-intercept, x = 0
From the transformation, f(x) + 1, we have;
At x = 0, the transformation = -log₁₀(0) + 1
log₁₀(0) = Does not exist (DNE)
Therefore;
f(x) + 1 = -log₁₀(0) + 1 = DNE
The transformation, f(x + 1), at x = 0, gives;
f(0 + 1) = -log₁₀(0 + 1) = -log₁₀(1) = 0
Therefore;
The function f(x + 1) = -log₁₀(x + 1) is defined at x = 0, and therefore, has a y-intercept
- The transformation that has a y-intercept is
Learn more about the pH values here:
