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Lesechka [4]
3 years ago
10

Four cards are shuffled and placed face down in front of you. Their faces (hidden) display the four elements: water, earth, wind

, and fire. You are to turn the cards over one card at a time until y ou either win or lose. You win if both the water and earth cards are turned over. You lose if the fire card is turn ed over. What is the probability of winning?
Mathematics
1 answer:
Licemer1 [7]3 years ago
5 0

Answer:

probability of winning is\frac{2}{3}

Step-by-step explanation:

As it is given , 4 cards are available,  there are 4!  mean total possible way of ordering is 24  

following are the cases of loosing

1) first card is fire.

Thus there are 3! = mean 6 possible ways for particular ordering  to occur.

2) If wind is first card and Fire is second. Then, There are 2! = 2 ways to occur.

Hence, the probabiIity of losing is given as  = \frac{6+2}{24}=\frac{1}{3}

therefore probality of winning is 1 -\frac{1}{3}

probality of winning is\frac{2}{3}

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I will give lots of points please help
aalyn [17]

Answer:

a)  81π  in³

b)  27  in³

c)  divide the volume of the slice of cake by the volume of the whole cake

d)  10.6%

e)  see explanation

Step-by-step explanation:

<h3><u>Part (a)</u></h3>

The cake can be modeled as a <u>cylinder </u>with:

  • diameter = 9 in
  • height = 4 in

\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in

\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}

\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}

<h3><u>Part (b)</u></h3>

\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}

<h3><u>Part (c)</u></h3>

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}

<h3><u>Part (d)</u></h3>

Probability is approximately 10.6%  (see above for calculation)

<h3><u>Part (e)</u></h3>

If the four slices of cake are cut and passed out <em>before </em>anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, <u>until the marble is found</u>.  So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

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Please help me understand
nalin [4]

Answer:

  (x +2)(2x +1)

Step-by-step explanation:

The factors are the set of tiles down the left side: x + 1 + 1 = (x +2), and the set of tiles across the top: x + x + 1 = (2x +1)

Your factored form is shown in choice D:

  (x +2)(2x +1)

_____

<em>Additional comment</em>

The point of this sort of diagram is to show you how the factors work together to give you the product. Each tile in the middle of the figure represents the product of the tile on the top line and the tile in the left column.

The product of x and x is x².

The product of 1 and x is x.

The product of 1 and 1 is 1.

The product of the two factors is the sum of all the tiles in the middle of the diagram: 2x² +5x +2.

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