The scores of an eighth-grade math test have a normal distribution with a mean Mu = 83 and a standard deviation Sigma = 5. If Di
1 answer:
The missing choices are:
A. z-score = 92 - 83
B. z-score = (92 - 83)/5
C. z-score = 83 - 92
D. z-score = (92 - 83)/92
The expression she would write to find z-score is z-score = ⇒ B
Step-by-step explanation:
The rule of z-score is z = (x -μ)/σ, where
- x is the score
- μ is the mean
- σ is the standard deviation
The scores of an eighth-grade math test have a normal distribution
∵ The mean is 83
∴ μ = 83
∵ The standard deviation is 5
∴ σ = 5
∵ Din’s test score was 92
∴ x = 92
- Substitute all of these values in the formula of z-score
∴ z-score =
The expression she would write to find z-score is z-score =
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Answer:
a)
The combined resistance of a circuit consisting of two resistors in parallel is given by:
where
R is the combined resistance
are the two resistors
We can re-write the expression as follows:
Or
In order to see if the function is increasing in r1, we calculate the derivative with respect to r1: if the derivative if > 0, then the function is increasing.
The derivative of R with respect to r1 is:
We notice that the derivative is a fraction of two squared terms: therefore, both factors are positive, so the derivative is always positive, and this means that R is an increasing function of r1.
b)
To solve this part, we use again the expression for R written in part a:
We start by noticing that there is a limit on the allowed values for r1: in fact, r1 must be strictly positive,
So the interval of allowed values for r1 is
From part a), we also said that the function is increasing versus r1 over the whole domain. This means that if we consider a certain interval
a ≤ r1 ≤ b
The maximum of the function (R) will occur at the maximum value of r1 in this interval: so, at