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3 years ago

Find volume and surface area

Mathematics

1 answer:

Nadya [2.5K]3 years ago

7 0

This is a right solid meaning that the area of the base doesn't change at all as you go up the shape. To find the volume of a right solid, multiply the area of the base times the height.

height      area of base                                                  Volume
    v                  v                                                                v
    7 x (4 x 2 + 3 x 2 + 3 x 2) = 7 x (8 + 6 + 6) = 7 x 20 = 140 cm^3

To find aurface area we must add together the areas of the two bases, which we learned were 20 as well as the back of the shape and the other three faces facing towards us.

bases        back                     faces
     v               v
(20 x 2) + (10 x 7) + (4 x 7) + (3 x 7) + (3 x 7) = 40 + 70 +28 + 21 + 21

Add these together to find your surface area of 180 cm^2

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Step-by-step explanation:

At a local restaurant there are six rooms total; 1 is a "high roller" room and other 5 are normal rooms.

There are 6 waitresses working at the local restaurant.

The room assignments are made by fair random selection such that each waitress has an equal probability of being in the "high roller" room.

This implies that a waitress can be assigned any of the six rooms with probability, $\frac{1}{6}$ .

The tip earned by the waitress working in the "high roller" room is $200 and that for other rooms is $75.

So, the distribution of tips earned is as follows:

X: $200 $75 $75 $75 $75 $75

P (X): $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{6}$

The expected value of a random variable is given by:

$E(X)=\sum x\cdot P (X)$

Compute the expected amount earned by a waitress per evening as follows:

$E(X)=\sum x\cdot P (X)$

$=(200\times \frac{1}{6})+(75\times \frac{5}{6})\\\\=\frac{575}{6}\\\\=95.8333\\\\\approx 95.83$

Thus, the expected amount earned by a waitress per evening is $95.83.

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