Answer:
B. (-3, 1), (6,2), (8,3), (6,4), (3, 5)
Step-by-step explanation:
This relation is not a function because the number 6 repeats twice.
mercury : 5.8 • 107 = 620.6
Venus : 1.1 • 108 =118.8
620.6 - 118.8 = 501.8
so Venus is about 501.8 kilometers from then sun then mercury
We have the function:
f(x) = 3x / (x + 7)
(a)
We rename the function as: f(x) = y
Then:
y = 3x / (x + 7)
Taking the inverse:
1/y = (x + 7) / 3x
1/y = x/3x + 7/3x
1/y = 1/3 + 7/3x
Solving for x:
1/y - 1/3 = 7/3x
1/x = 3/7y - 1/7 = (3 - y) / 7y
Taking the inverse:
x = 7y / (3 - y)
Then, the inverse function of f is:
f ⁻¹(x) = 7x / (3 - x)
(b)
We know that the division by 0 is undefined in real numbers. From the function f, we have a division by 0 if x = -7, so the domain should be:
Dom_f = {x| x ≠ -7}
For the range, we know that x = -7 is a vertical asymptote of the function f, so this means that the graph never passes across x = -7, but it tends to it on infinity. Then, the range of f is:
Ran_f = All the real numbers
For f ⁻¹(x), we see that for x = 3 there is a division by 0, so this is an asymptote of the function. Then, the domain of f ⁻¹ is:
Dom_f ⁻¹ = {x| x ≠ 3}
Again, as there is an asymptote, the range is:
Ran_f ⁻¹ = All the real numbers
Answer:
82.31% of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Approximately what percentage of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter?
This is the pvalue of Z when X = 5.4 subtracted by the pvalue of Z when X = 4.2. So
X = 5.4
has a pvalue of 0.9842
X = 4.2
has a pvalue of 0.1611
0.9842 - 0.1611 = 0.8231
82.31% of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter
