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dem82 [27]
3 years ago
13

grain is stored in cylindrical structures called silos which is the best estimate for the volume of a silo with a diameter of 12

.3 feet and a height of 25 feet
Mathematics
1 answer:
zalisa [80]3 years ago
8 0
Volume of a cylinder = base x height
the base is the area of the circle at the bottom. 

To find the area of a circle, you use:
A = πr²
where r is the radius of the circle. 
radius is half of the diameter, so with a diameter of 12.3, (divide that by 2) the radius of the circle is 6.15 feet. 

A = π(6.15)²
A ≈ 118.82 

Since we know the height is 25 feet, we can solve for the area of the cylinder. 

Area of the cylinder = 118.82 x 25 = 2,970.57 feet cubed
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A 5-card hand is dealt from a perfectly shuffled deck. Define the events: A: the hand is a four of a kind (all four cards of one
TiliK225 [7]

In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are \binom44\binom{48}1=48 possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by \binom{13}1=13. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

\dfrac{\binom{13}1\binom44\binom{48}1}{\binom{52}5}=\dfrac{624}{2,598,960}\approx0.00024

There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing \binom41\binom{48}4=778,320 possible hands. Exactly 2 aces are drawn in \binom42\binom{48}3=103,776 hands. And so on. This gives a total of

\displaystyle\sum_{a=1}^4\binom4a\binom{48}{5-a}=886,656

possible hands containing at least 1 ace, and hence B occurs with probability

\dfrac{\sum\limits_{a=1}^4\binom4a\binom{48}{5-a}}{\binom{52}5}=\dfrac{18,472}{54,145}\approx0.3412

The product of these probability is approximately 0.000082.

A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e. P(A\cap B)=P(A)P(B). This happens if

  • the hand has 4 aces and 1 non-ace, or
  • the hand has a non-ace 4-of-a-kind and 1 ace

The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So A\cap B consists of 96 possible hands, which occurs with probability

\dfrac{96}{\binom{52}5}\approx0.0000369

and so the events A and B are NOT independent.

4 0
3 years ago
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589.
KatRina [158]
AB = AU + UB = 20x + 108 + 273 = 20x + 381

\cfrac{AU}{AB} =\cfrac{UV}{BC}    \\  \\  \cfrac{20x+108}{20x+381} =\cfrac{444}{703}   \\  \\ 703(20x+108)=444(20x+381)\\\\14060x+75924=8880x+169164 \\  \\ 14060x-8880x = 169164 - 75924 \\  \\ 5180x = 93240 \\  \\ x=93240/5180 \\  \\ x=18
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Step-by-step explanation:

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What is the coefficient of the c-term of the algebraic expression 14a -72r -c -34d?
8_murik_8 [283]
The coefficient C-term is 1 in problem. The coefficient is the number before the variable of said equation. Example, the coefficient of X for thus problem 4x-4y is 4 the number BEFORE the variable, never variable itself it won’t ever be 4x
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