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2 years ago

The profit (in thousands of dollars) of a company is given by P(x) = -8x2 + 32x + 14.

Mathematics

1 answer:

andre [41]2 years ago

5 0

Answer:

Step-by-step explanation:

The profit (in thousands of dollars) of a company is given by the function:

$\displaystyle P(x) = -8x^2+32x+14$

And we want to find the maximum profit of the company.

Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex. Recall that the vertex of a quadratic is given by:

$\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

Find the x-coordinate of the vertex. In this case, a = -8, b = 32, and c = 14. Hence:

$\displaystyle x=-\frac{(32)}{2(-8)}=\frac{32}{16}=2$

To find the maximum profit, substitute this value back into the function. Hence:

$\displaystyle P(2) = -8(2)^2+32(2) + 14 = 46$

Therefore, the maximum profit of the company is 46 thousand dollars.

Our answer is C.

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The population of a pigeons in a city is 100 and is growing exponentially at 20% per year. Write a function to represent the pop

NikAS [45]

Answer:

p(t) = 100×1.0153^(12t)
1.53% per month

Step-by-step explanation:

In general, the function will be written ...

p(t) = (initial value)×(growth factor)^t

where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...

growth factor = 1 + growth rate

Here, the growth rate is given as 20% per year, so the growth factor per year is ...

1 +20% = 1.20

The initial value is given as 100, so we can write the exponential function as ...

p(t) = 100×1.20^t

The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.

p(t) = 100×(1.20^(1/12))^( 12t)

p(t) = 100×1.0153^(12t) . . . . population exponential function

This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...

1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change

5 0

2 years ago

Read 2 more answers

if the eggs in a basket are removed 2 at a time, 1 egg will remain. if the eggs are removed 3 at a time, 2 eggs will remain. if

Yanka [14]

The least number of eggs that could be in the basket is 119.

Multiple of the number:

The multiple is the numbers you get when you multiply a certain number by an integer.

Given,

If the eggs in a basket are removed 2 at a time, 1 egg will remain.

If the eggs are removed 3 at a time, 2 eggs will remain.

If the eggs are removed 4, 5, or 6 at a time, then 3, 4, and 5 eggs will remain, respectfully.

But if they are taken out 7 at a time, no eggs will be left over.

Here we need to find the least number of eggs in the basket.

Let the number of eggs in the basket be N.

We know that,

if the eggs in a basket are removed 2 at a time, one eggs will remain.

So N is 1 less than a multiple of 2, so

=> N=2A-1

If they are removed 3 at a time, 2 eggs remain.

So N is 2 more, and therefore 1 less than, a multiple of 3, so

=> N=3B-1

If the eggs are removed 4...at a time, then 3...eggs remain,

So N is 3 more, and therefore 1 less than, a multiple of 4, so

=> N=4C-1

Similarly,

For 5,

=> N = 5D - 1

For 6,

=> N = 6E - 1

So, if they are taken out 7 at a time, no eggs will be left over.

So,

N => 7F

Where A,B,C,D,E, and F are any positive integer.

Therefore,

N = 2A-1 = 3B-1 = 4C-1 = 5D-1 = 6E-1 = 7F

Add 1 to all those:

N+1 = 2A = 3B = 4C = 5D = 6E = 7F+1

Through this,

N + 1 = 7F + 1

has to be a common multiple of 2,3,4,5,6.

So, the LCM of 2,3,4,5,6 is 60.

So N+1 is a multiple of 60 which means N is 1 less than a multiple of 60.

So we find the least multiple of 60 that is 1 more than a multiple

of 60.

The multiples are, 60, 59, ....but 59 is not a multiple of 7.

The next multiple of 60 is 120.

1 less than 120 is 119, and sure enough, 119 is a multiple of 7.

So,

=> 119 = 17*7.

Therefore, the least number of eggs that could be in the basket is 119.

To know more about Multiple here

brainly.com/question/5992872

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4 0

1 year ago

Someone please tell me the answers to this please I beg you

Wittaler [7]

1) 216
2) 203
3) 315
4) 256
5) 576
6) 440

7 0

3 years ago

Which of the following could lead to a misleading graph?

natima [27]

Answer:

The intervals on the y-axis are inconsistent.

Step-by-step explanation:

The x- and y-axes start at 0 - this is what graphs normally start with - it is out of the norm to not start at 0.

The intervals on the y-axis are inconsistent - this can cause a problem - we humans tend to judge a graph on height, so changing some of the intervals can mess up a human's actions based on the graph,for example people might think more positively or negatively of a brand or company, and even a totally different view.

The intervals on the y and x-axis are different - they can be different for particular reasons, for example a company might want to put time intervals in months on the x-axis and revenue in dollars on the y-axis - sometimes it is just necessary.

Differing heights are used on a bar graph - this allows us to compare data - without it we would not be able to do much with it.

3 0

3 years ago

Hacksaw’s Boats of St. Lucia takes tourists on a daily whale/dolphinwatch cruise. Their brochure claims an 80% chance of siting

Fittoniya [83]

Answer:

The probability you see a dolphin or a whale on both days is 0.64

Step-by-step explanation:

Consider the provided information.

It is given that the brochure claims an 80% chance of siting a dolphin or a whale.

The provided claims can be written as: 80% or 0.80

Let say first day you see a dolphin or a whale and same happen on the next day.

Thus, the probability is:

0.80 × 0.80 = 0.64

Probability of see them on both days is 0.64

Hence, the probability you see a dolphin or a whale on both days is 0.64

5 0

3 years ago