Slope = -1/2 hope that helps.........
Answer:
Mark got 13 more points than Nick did
Step-by-step explanation:
Mark's score in all was: 487
Nick's score in all was: 474
The number -3 written as a logarithm with a base of 2 is log₂(0.125) or log₂(1/8)
<h3>What are logarithms?</h3>
As a general rule, logarithms are mathematical expressions that are written in the form log(x) or ln(x), for natural logarithms
<h3>How to rewrite the number as a logarithm?</h3>
The number is given as:
x = -3
The base of the logarithm is given as:
Base = 2
To rewrite the given number as a base of 2, we take the exponent of the number where the base is 2
This is represented as:
Number =2^-3
Apply the power rule of indices
Number =1/2^3
Evaluate the exponent
Number = 1/8
Evaluate the quotient
Number = 0.125
Hence, when the number -3 is rewritten as a logarithm with base 2, the equivalent logarithm expression is log₂(0.125) or log₂(1/8)
Read more about logarithm at:
brainly.com/question/20785664
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A) Profit is the difference between revenue an cost. The profit per widget is
m(x) = p(x) - c(x)
m(x) = 60x -3x^2 -(1800 - 183x)
m(x) = -3x^2 +243x -1800
Then the profit function for the company will be the excess of this per-widget profit multiplied by the number of widgets over the fixed costs.
P(x) = x×m(x) -50,000
P(x) = -3x^3 +243x^2 -1800x -50000
b) The marginal profit function is the derivative of the profit function.
P'(x) = -9x^2 +486x -1800
c) P'(40) = -9(40 -4)(40 -50) = 3240
Yes, more widgets should be built. The positive marginal profit indicates that building another widget will increase profit.
d) P'(50) = -9(50 -4)(50 -50) = 0
No, more widgets should not be built. The zero marginal profit indicates there is no profit to be made by building more widgets.
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On the face of it, this problem seems fairly straightforward, and the above "step-by-step" seems to give fairly reasonable answers. However, if you look at the function p(x), you find the "best price per widget" is negatve for more than 20 widgets. Similarly, the "cost per widget" is negative for more than 9.8 widgets. Thus, the only reason there is any profit at all for any number of widgets is that the negative costs are more negative than the negative revenue. This does not begin to model any real application of these ideas. It is yet another instance of failed math curriculum material.