Given:
The given phrase is 16 seconds faster than Aya’s time.
To find:
The algebraic expression for the given phrase.
Solution:
Let x be the Aya’s time.
16 seconds faster than Aya’s time. It means 16 seconds less than Aya’s time.
We know that a negative sign "-" is used for less than.
16 seconds less than Aya’s time = 
16 seconds faster than Aya’s time =
Therefore, the required algebraic expression is .
Answer:
$110
Step-by-step explanation:
Let a, b, and c represent the earnings of Alan, Bob, and Charles. The problem statement tells us ...
a + b + c = 480 . . . . . . the combined total of their earnings
-a + b = 40 . . . . . . . . . . Bob earned 40 more than Alan
2a - c = 0 . . . . . . . . . . . Charles earned twice as much as Alan
Adding the first and third equations, we get ...
(a + b + c) + (2a - c) = (480) + (0)
3a + b = 480
Subtracting the second equation gives ...
(3a +b) - (-a +b) = (480) -(40)
4a = 440 . . . . . . . . simplify
a = 110 . . . . . . . . . . divide by the coefficient of a
Alan earned $110.
_____
<em>Check</em>
Bob earned $40 more, so $150. Charles earned twice as much, so $220.
The total is then $110 +150 +220 = $480 . . . . as required
Answer:
Null hypothesis; H0: µ ≥ 52 mpg
Alternative hypothesis; Ha: µ < 52 mpg
Step-by-step explanation:
We are told that the newest model gets an average of 52 miles per gallon and that the buyers believe that the average mpg was overstated.
This means the alternative hypothesis will have an average less than 52. Thus;
Null hypothesis; H0: µ ≥ 52 mpg
Alternative hypothesis; Ha: µ < 52 mpg
Let's create this right triangle. We will call it triangle ABC with angle B as the right angle, angle A being the larger of the angles A and C. If the ratio is 5:4, then it is A:C. 5+4 = 9. The measure of the right angle, angle ABC = 90, and 90 divided by 9 is 10. So angle A is 5 * 10 which is 50 degrees, and angle C is 4 * 10 which is 40 degrees. The smallest angle, angle C, is 40 degrees.
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be 
, the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
Let equalize the resulting expression to zero and solve afterwards:
Second Derivative Test
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
The maximum sustainable yield is 202500 swordfishes.
