Answer:
Step-by-step explanation:
given a point
the equation of a line with slope m that passes through the given point is
or equivalently
.
Recall that a line of the form
, the y intercept is b and the x intercept is
.
So, in our case, the y intercept is
and the x intercept is
.
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph
. Which means that 
The slope of the tangent line is given by the derivative of the function evaluated at
. Using the properties of derivatives, we get
. So evaluated at
we get 
Replacing the values in our previous findings we get that the y intercept is

The x intercept is

The triangle in consideration has height
and base
. So the area is

So regardless of the point we take on the graph, the area of the triangle is always 2.
Answer:
The probability of selecting a solid black marbles both times;
P = 9/100
Attached is the completed question;
Step-by-step explanation:
Number of solid black marbles = 3
Total number of marbles = 10
The probability of selecting a solid black marble;
P1 = 3/10
With the assumption that the marbles are replaced before next selection.
The probability of selecting a solid black marbles both times;
P = P1 × P1 = 3/10 × 3/10 = 9/100
P = 9/100
There are no 2 consecutive integers which give a product 360360
Answer:

Step-by-step explanation:
![Volume\:of\:cube:V=a^{3} \:(a\:is\:the\:length\:of\:each\:edge)\\\Leftrightarrow a=\sqrt[3]{V} \Leftrightarrow a=\sqrt[3]{729} =9](https://tex.z-dn.net/?f=Volume%5C%3Aof%5C%3Acube%3AV%3Da%5E%7B3%7D%20%5C%3A%28a%5C%3Ais%5C%3Athe%5C%3Alength%5C%3Aof%5C%3Aeach%5C%3Aedge%29%5C%5C%5CLeftrightarrow%20a%3D%5Csqrt%5B3%5D%7BV%7D%20%5CLeftrightarrow%20a%3D%5Csqrt%5B3%5D%7B729%7D%20%3D9)
Answer:
<u>$4800</u>
Step-by-step explanation:
The expected net income is the probability when rains multiplied by net income (profit) summed with the probability of not raining with that days net income multiplied.
First, Chance of rain = 12% = 12/100 = 0.12
Profit/Loss = Income - Cost
Income is 5000
Cost = 9000
So,
Loss = 5000 - 9000 = 4000
Or, Net Income (profit) = - 4000
Now, Change of not raining = 100 - 12 = 88% = 88/100 = 0.88
Profit = Income - Cost
Income = 15,000
Cost = 9000
Net Income (profit) = 15000 - 9000 = 6000
So, we can write the expected net income as:
<u>Expected NI </u>= (0.12)(-4000) + (0.88)(6000) = <u>$4800</u>