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2 years ago

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A producer plans an outdoor concert for the weekend. The cost of the concert is $8,000 which includes advertising, security, pri

nting, tickets, etc. The producer plans to profit $15,000 if all goes well. However, it it rains, the concert will be canceled. The chance of rain is 0.3 according to the weather report. Find the producer’s expected profit.

1 answer:

andrey2020 [161]2 years ago

3 0

Answer: $8,100

Step-by-step explanation:

If it does not rain, the producer stands to make a profit of $15,000.

If it rains, the producer will lose the $8,000 they invested.

The chance of rain is 0.3 which means the chance it does not rain is 0.7.

Producer's expected profit is the weighted average of these outcomes;

= (15,000 * 0.7) + ( -8,000 * 0.3)

= 10,500 + ( - 2,400)

= $8,100

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Alex787 [66]

Answer:

$P = \frac{132000}{12}=11000$

So then P =11000 is the minimum that the least populated district could have.

Step-by-step explanation:

We have a big total of N = 132000 for the population.

And we know that we divide this population into 11 districts

And we have this info given "no district is to have a population that is more than 10 percent greater than the population of any other district"

Let's assume that P represent our minimum value for a district in the population. The range of possible values for the population of each district would be between P and 1.1 P

The interest on this case is find the minimum value for P and in order to do this we can assume that 1 district present the minimum and the other 10 the maximum value 1.1P in order to find which value of P satisfy this condition, and we have this:

$P + 10 (1.1P) = 12 P= 132000$

$P = \frac{132000}{12}=11000$

So then P =11000 is the minimum that the least populated district could have.

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2 years ago

Use lagrange multipliers to find the points on the given surface that are closest to the origin. y2 = 64 + xz

Inessa [10]

The distance between an arbitrary point on the surface and the origin is

$d(x,y,z)=\sqrt{x^2+y^2+z^2}$

Recall that for differentiable functions $g(x)$ and $h(x)$ , the composition $g(h(x))$ attains extrema at the same points that $h(x)$ does, so we can consider an augmented distance function

$D(x,y,z)=x^2+y^2+z^2$

The Lagrangian would then be

$L(x,y,z,\lambda)=x^2+y^2+z^2+\lambda(y^2-64-xz)$

We have partial derivatives

$\begin{cases}L_x=2x-\lambda z\\L_y=2y+2y\lambda\\L_z=2z-\lambda x\\L_\lambda=y^2-64-xz\end{cases}$

Set each partial derivative to 0 and solve the system to find the critical points.

From the second equation it follows that either $y=0$ or $\lambda=-1$ . In the first case we arrive at a contradiction (I'll leave establishing that to you). If $\lambda=-1$ , then we have

$\begin{cases}2x+z=0\\2z+x=0\end{cases}\implies x=0,z=0$

This means $y^2=64\implies y=\pm8$

so that the points on the surface closest to the origin are $(0,\pm8,0)$ .

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2 years ago

The marching band walks 1/15 miles in 1.5 minutes. At this rate, how many minutes will it take to complete 1 mile? Record your a

ipn [44]

Answer:

It will take 22.5 minutes to complete 1 mile

Step-by-step explanation:

From the question,

The marching band walks 1/15 miles in 1.5 minutes

First we will determine the miles cover in 1 minute

If the marching band walks 1/15 miles in 1.5 minutes

then, they will cover $x$ miles in 1 minute

$x = \frac{1/15 * 1}{1.5}\\$

Then,

$x = \frac{1/15 }{1.5}$

$x = 2/45$ miles

∴ 2/45 miles are covered in 1 minute

Now,

If 2/45 miles are covered in 1 minute

Then, 1 mile will be covered in $y$ minute

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$y =\frac{1}{2/45} \\y = \frac{45}{2}\\$

∴ $y = 22.5 minutes$

Hence, it will take 22.5 minutes to complete 1 mile

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2 years ago

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Nostrana [21]

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--------------- = -----------------------------

270 dollars x dollars

using cross products

200 * x = 270 * 300

divide each side by 200

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x =405 dollars

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2 years ago

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convert minutes to hour

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<em>Speed = distance ÷ time</em>

= 6 miles ÷ 0.5 hour

= 12 miles per hour

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1 year ago