Answer:
never
Step-by-step explanation:
Set the whole expression = to 0 and solve for x.
3x^(5/3) - 4x^(7/3) = 0. Factor out x^(5/3): x^(5/3) [3 - 4x^(2/3)] = 0
Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.
In the latter case, 4x^(2/3) = 3.
To solve this: mult. both sides by x^(-2/3). Then we have
4x^(2/3)x^(-2/3) = 3x^(-2/3), or 4 = 3x^(-2/3). It'd be easier to work with this if we rewrote it as
4 3
--- = --------------------
1 x^(+2/3)
Then
4
--- = x^(-2/3). Then, x^(2/3) = (3/4), and x = (3/4)^(3/2). According to my 3 calculator, that comes out to x = 0.65 (approx.)
Check this result! subst. 0.65 for x in the given equation. Is the equation then true?
My method here was a bit roundabout, and longer than it should have been. Can you think of a more elegant (and shorter) solution?
The 68 - 95 - 99.7 rule, gives the basis to solve this question.
It says that for a normal distribution 95% of the results are between the mean minus 2 standard deviations and the mean plus 2 standard deviations.
Here:
mean = 64.5 inches,
standard deviaton = 2.5 inches
mean - 2 standard deviations = 64.5 inches - 5 inches = 59.5 inches
mean + 2 standard deviations = 64.5 inches + 5 inches = 69.5 inches
Then, the answer is that 95% of women range approximately between 59.5 inches and 69.5 inches.
Answer:
Rectangle A's length = 22 ft., Rectangle B's length = 44 ft.
Step-by-step explanation:
Since we know that the length of Rectangle B is twice the length of Rectangle A, we know that 2*(3x + 7) = Rectangle B's length.
We must set this equation to the dimensions already given for Rectangle B, which gives us 2(3x + 7) = 2 (5x - 3).
Using the distributive property gives us 6x + 14 = 10x - 6 and solving for x gives us x = 5.
We must plug five into the original dimensions to find that the lengths of Rectangles A and B are 22 feet and 44 feet respectively.
Answer: C
Step-by-step explanation:
992/4=165
846/6=141
165+141=306
(992/4) + (846/6) = 306 total calories consumed