The difference between consecutive terms (numbers that come after each other) in arithmetic sequences is the same. That means you add the same number every time to get the next number. To figure out which choices are arithmetic sequences, just see if the differences are the same.
Choice A) 1, -2, 3, -4, 5, ... -2 - 1 = -3 3 - (-2) = 5 The difference is not constant, so it is not an arithmetic sequence.
Choice B) 12,345, 12,346, 12,347, 12,348, 12,349, ... 12,346 - 12,345 = 1 12,347 - 12,346 = 1 The difference is constant, so it is an arithmetic sequence.
Choice C) <span>154, 171, 188, 205, 222, ... 171 - 154 = 17 188 - 171 = 17 The difference is constant, so it is an arithmetic sequence.
Choice D) </span><span>1, 8, 16, 24, 32, ... 8 - 1 = 7 16 - 8 = 8 </span>The difference is not constant, so it is not an arithmetic sequence. Choice E) <span>-3, -10, -17, -24, -31, ... -10 - (-3) = -7 -17 - (-10) = -7 </span>The difference is constant, so it is an arithmetic sequence.
<em>The smallest number of boats that must be produced to make a profit of $ 75,000 is 10 boats</em>
Step-by-step explanation:
We have this equation
This equation shows the income obtained based on the number of boats sold. We want to know the minimum number of boats that must be sold to obtain $ 75 000.
Then we must equalize the equation to 75 000 and clear b.
3 solutions will be obtained (because it is a polynomial of degree 3), and the lowest value will be taken.
Now we need to solve the equation, for that we seek to factor the polynomial
We divide the equation by -25
We take common factor b
We take out common factor ()
Finally the solutions are:
and
We take the least positive solution (because you can not produce -10 boats)