Answer:
The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.
Step-by-step explanation:
Let
, for
.
represents the temperature of the water, measured in degrees Celsius, and
is the number of salmon swimming upstream to spawn, dimensionless.
We compute the first and second derivatives of the function:
(Eq. 1)
(Eq. 2)
Then we equalize (Eq. 1) to zero and solve for
:

And all roots are found by Quadratic Formula:
, 
Only the first root is inside the given interval of the function. Hence, the correct answer is:

Now we evaluate the second derivative at given result. That is:


According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.
Answer:
Check the explanation
Step-by-step explanation:
Following table shows the calculations:
Delta, X Southwest , Y X^2 Y^2 XY
45.96 38.76 2112.3216 1502.3376 1781.4096
46.8 45.41 2190.24 2062.0681 2125.188
47.93 15.7 2297.2849 246.49 752.501
51.78 49.58 2681.1684 2458.1764 2567.2524
52.17 44.34 2721.7089 1966.0356 2313.2178
47.36 18 2242.9696 324 852.48
Total 292 211.79 14245.6934 8559.1077 10392.0488
Sample size: n =6
Now



The coefficient of correlation is :

Answer:
Selling price= $580
Step-by-step explanation:
eGiving the following information:
Buying price= $400
Mark-up percentage= 45% = 0.45
<u>The manager applies a mark-up equivalent to 45% of the buying price. First, we need to determine how much is 45% of the cost.</u>
Mark-up= buying price* Mark-up percentage
Mark-up= 400*0.45
Mark-up= $180
<u>Now, the selling price:</u>
Selling price= 400 + 180
Selling price= $580
Let x be the number. x + 5 = 2x. 5 = x because you isolate for x by moving it to the right side, meaning you’d have to subtracts 1 x from 2x
20/10=2.
14/7=2.
2 dollars per pound.