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strojnjashka [21]
3 years ago
7

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.
y=-8x^2+242x-1056
Mathematics
1 answer:
Alex17521 [72]3 years ago
3 0

The equation is that of a parabola, meaning that the maximum (or sometimes minimum) is 1/2 the sum of the solutions found using the quadratic equation.

y = 0 for the 2 solutions to {-b +/- sqrt[b2 - 4ac]} / 2a, where a = -3, b = 152 and c = -1150 from the equation for y. Plug a, b and c into the quadratic formula to get x = 9.2571 and x = 41.4095 as the 2 solutions.

9.2571 + 41.4095 = 50.6666... and the midpoint is 25.3333...

When x = 25.3333..., y = 775.33333.....

To the nearest cent, x=25.33 results in a profit of 775.33.

When x=25.25, Y = 775.31

When x=25.4, Y = 775.32

These are both less than 775.33 when x = 25.33.

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Supposing that the stock increases in 37 days, the 95% confidence interval for the proportion of days JMJ stock increases is: (0.484, 0.7292)

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In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of \alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of \frac{1+\alpha}{2}.

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95% confidence level

So \alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so z = 1.96.  

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6066 - 1.96\sqrt{\frac{0.6066(0.3934)}{61}} = 0.484

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6066 + 1.96\sqrt{\frac{0.6066(0.3934)}{61}} = 0.7292

The ​95% confidence interval for the proportion of days JMJ stock increases is (0.484, 0.7292), in which 0.484 is the lower bound and 0.7292 is the upper bound.

The interpretation is that we are <u>95% sure that the true proportion</u> of all days in which the JMJ stock increases <u>is between 0.484 and 0.7292.</u>

A similar problem is given at brainly.com/question/16807970

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