The cost, in millions of dollars, for a company to manufacture x thousand speed boats is given by the function c(x) = 3x2 - 30x + 175. find the number of speedboats that must be produced to minimize the cost.

  5000

Step-by-step explanation:

In vertex form, the cost function is ...

  C(x) = 3(x² -10x) +175 = 3(x² -10x +25) +175 -3(25)

  C(x) = 3(x -5)² +100

The vertex is at x=5, so the cost function will be minimized when 5000 speed boats are produced.

See the corrections below;

1. Synthetic Plant Creates Fuel from Sunlight

British scientists might have solved one of chemistry’s most difficult issues: the creation of a synthetic leaf.

2. Researchers at the Occidental Research Bureau have struggled for three decades to produce a man-made leaf able to absorb CO₂ from the atmosphere and convert it into chemical energy. Yet now it seems that they have at long last achieved their goal.

3. “Everyone in the bureau is responsible for this success,” said Professor Giles Smiley, the chief scientist leading the research efforts. The staff’s attitude has been faultless.

Explanation:

In making sentences, the writer should ensure that there is harmony between the subjects and the verb in the sentences. In the first sentence above, the plural verb 'have' agrees with the plural subject, 'British Scientists'. In the second sentence also, the plural subject, 'Researchers' also agrees with the plural verb, 'have'.

In the last sentence, the collective pronoun, 'everyone' matches with the singular verb, 'is'. Staff is also a collective pronoun. When acting as a single unit, in this case describing their attitude, a singular verb in this case, 'has' is used.