To find the expected value of your gain in each prize, subtract the price of the ticket from the prize:

If the prize is $500: $500 - $2 = $498
If the prize is $250: $250 - $2 = 248
If the prize is $160: $160 - $2 = $73

But if you did not win any cash prize, you do not have any gain because
0 cash prize - $2 ticket = -$2 which is a loss

5 0

2 years ago

Find the minimum and maximum values of the function subject to the given constraint. (if an answer does not exist, enter dne.) f

nata0808 [166]

Via Lagrange multipliers:

$L(x,y,\lambd)=x^2y+x+y+\lambda(xy-5)$
$L_x=2xy+1+\lambda y=0$
$L_y=x^2+1+\lambda x=0$
$L_\lambda=xy-5=0$

$\underbrace{10}_{2xy}+1+\lambda y=0\implies \lambda=-\dfrac{11}y$
$xy=5\implies y=\dfrac5x\implies\lambda=-\dfrac{11}5x$

$\impliesx^2+1+\left(-\dfrac{11}5x\right)x=0\implies x^2=\dfrac56\implies x=\pm\sqrt{\dfrac56}$
$xy=5\implies y=\pm\sqrt{30}$

At these points, we get local minima of $f\left(\pm\sqrt{\dfrac56},\pm\sqrt{30}\right)=\pm2\sqrt{30}$ .

- - -

Another way to do this is to make $f(x,y)$ a function independent of $y$ , which is made possible by the constraint.

$xy=5\implies y=\dfrac5x$
$\implies f(x,y)=f\left(x,\dfrac5x\right)=F(x)=6x+\dfrac5x$
$\implies F'(x)=6-\dfrac5{x^2}=0\implies x=\pm\sqrt{\dfrac56}$

and so on.

8 0

3 years ago

Which is the graph of a quadratic equation that has a positive discriminant? On a coordinate plane, a parabola opens up. It goes

irina [24]

Answer:

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

zzz [600]

A two-way table is such that has two categorical variables and as such, the data are presented in rows and columns.

The correct row and column headings for the given dataset are: