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faust18 [17]
2 years ago
7

A company that manufactures vehicle trailers estimates that the monthly profit for selling its midsize trailer is represented by

function p, where t is the number of trailers sold. p(t)= -25t^3+625t^2-2500t Use the key features of function p to complete these statements. The company makes a profit when it sells _____trailers. The maximum profit of approximately $____ occurs when it sells approximately____ trailers.
Mathematics
2 answers:
lapo4ka [179]2 years ago
6 0

Answer:

The answer is below

Step-by-step explanation:

The profit equation is given by:

p(t)= -25t³+625t²-2500t

The maximum profit is the maximum profit that can be gotten from selling t trailers. The maximum profit is at point p'(t) = 0. Hence:

p'(t) = -75t² + 1250t - 2500

-75t² + 1250t - 2500 = 0

t = 2.3 and t = 14.3

Therefore t = 3 trailers and t = 15 trailers

p(15) = -25(15³) + 625(15²) - 2500(15) = 18750

Therefore the company makes a maximum profit of approximately $18750 when it sells approximately 15 trailers.

Korolek [52]2 years ago
3 0

Answer:

See below

Step-by-step explanation:

Since t is number of trailers, the domain includes only those values greater than 0.

On the relevant domain, the graph crosses the x-axis at the points (5,0) and (20,0). Between these points, the value of p(t) is positive. So the company makes a profit when it sells between 5 and 20 trailers.

On the positive interval between these points, the graph reaches a relative maximum when t roughly equals 14 and p(t) roughly equals $19,000.

So the maximum profit of approximately $19,000 occurs when it sells approximately 14 trailers.

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ZanzabumX [31]

Answer:

1/4

Step-by-step explanation:

The maximum sum of the two cubes is 6 + 6 = 12

The multiples of 4 until 12 are: 4, 8 and 12.

each cube has 6 possible values, so two cubes have a total of 6 * 6 = 36 possible results

We can have a sum of 4 with the pairs (1,3), (2,2), (3,1).

We can have a sum of 8 with the pairs (2,6), (3,5), (4,4), (5,3), (6,2)

We can have a sum of 12 with the pair (6,6)

So we have a total of 9 pairs that satisfy our condition over a total of 36 possibilities, so the probability is 9 / 36 = 1/4

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3 years ago
Let D = {-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36} Determine which of the following statements are true and which are false. a)
morpeh [17]

Answer:

\forall x\in D if x is odd then x> 0 is true statement.

\forall x\in D if x is odd then x> 0 is true statement.

\forall x\in D if x is even then x≤0 is false statement.

\forall x\in D If the ones digit of x is 2, then the tens digit is 3 or 4 is true statement.

\forall x\in D if the ones digit of x is 6, then the tens digit is 1 or 2 is false statement.

Step-by-step explanation:

Consider the provided information.

D = {-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36}

Part (A) \forall x\in D if x is odd then x> 0

Here only even numbers are less than 0 that means the statement is true.

\forall x\in D if x is odd then x> 0 is true statement.

Part (B) \forall x\in D if x is less than 0 then x is even.

Here only even numbers are less than 0 that means the statement is true.

\forall x\in D if x is odd then x> 0 is true statement.

Part (C) \forall x\in D if x is even then x≤0

Here we can see that 16, 26, 32, 36 are even number and also greater than 0. Thus the statement is false.

\forall x\in D if x is even then x≤0 is false statement.

Part (D) \forall x\in D If the ones digit of x is 2, then the tens digit is 3 or 4.

There is only one number whose ones digit is 2. i.e. 32 also the tens digit of the number 32 is 3. Which makes the above statement true.

\forall x\in D If the ones digit of x is 2, then the tens digit is 3 or 4 is true statement.

Part (E) \forall x\in D if the ones digit of x is 6, then the tens digit is 1 or 2.

Numbers having ones digit 6 are: 16, 26 and 36

Here, the tens digits are 1, 2 and 3 which is contradict to our statement. Hence the provided statement is false.

\forall x\in D if the ones digit of x is 6, then the tens digit is 1 or 2 is false statement.

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