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3 years ago

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4. The ages of a group of tourists on a bus are 3, 6, 9, 11, 15, 26, 27, 30, 30, 31, 32. What is the standard deviation of this

tour group? * a. 10.711 O b. 11.234 O c. 114.726 O d. 126.202

1 answer:

ioda3 years ago

8 0

Answer: b. 11.234

Step-by-step explanation:

used ti84

put in values in list 1

go into 1-var stats

find Sx which is the stand dev for sample

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Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
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$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

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$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
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$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

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