5/8 = 5 ÷ 8 = .625
move decimal 2 places to right for %
.625 = 62.5%
Answer:
a) What is the probability that we will pick a blue ball?
there is a 50% chance that urn 1 will be selected and the possibility of a blue ball is 3/4 x 0.5 = 1.5/4
there is also a 50% chance that urn 2 will be selected and the possibility of a blue ball is 2/4 x 0.5 = 1/4
the probability of choosing a blue ball = 1.5/4 + 1/4 = 2.5/4 or 5/8
b) If we picked a blue ball, what is the probability that the selected urn was urn-1?
there are 5 blue balls in total, and 3 of them come from urn 1
c) Suppose we picked a blue ball. If we randomly pick one additional ball from the same urn, what is the probability that we pick a red ball?
there is a 50% chance that urn 1 will be selected, and the possibility of a red ball after a blue ball is 1/3 x 0.5 = 0.5/3
there is also a 50% chance that urn 2 will be selected and the possibility of a red ball after a blue ball is 2/3 x 0.5 = 1/3
the possibility of choosing a red ball after a blue ball = 0.5/3 + 1/3 = 1.5/3 = 1/2
Answer:
153 coins will be there.
Step-by-step explanation:
The number of coin in the bottom row / or last row = 17
The number of coins in the second last row = 16
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The number of coins in the second row = 2
The number of coins in the first row = 1
So the total number of coins = (Number of coin in the first row) + (Number of coins in the second row) + (Number of coins in the third row) + ....... + (Number of coins in the last row / seventeenth row)
Total number of coins = 1+2+3+....+16+17
Total number of coins = ![\frac{17\times(17+1)}{2}=\frac{17\times18}{2}=17\times9=153](https://tex.z-dn.net/?f=%5Cfrac%7B17%5Ctimes%2817%2B1%29%7D%7B2%7D%3D%5Cfrac%7B17%5Ctimes18%7D%7B2%7D%3D17%5Ctimes9%3D153)
(NOTE: Sum of first n natural number =
)
Answer:
<em>11 litres </em>of water will fit inside the container.
Step-by-step explanation:
As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.
Given:
Height of cylinder,
= 15 cm
Diameter of cylinder/ cone, D = 26 cm
Slant height of cone, l = 20 cm
Here, we need to find the volume of container.![\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2](https://tex.z-dn.net/?f=%5C%5CVolume_%7BContainer%7D%20%3D%20Volume_%7BCylinder%7D%2BVolume_%7BCone%7D%5C%5C%5CRightarrow%20Volume_%7BContainer%7D%20%3D%20%5Cpi%20r_1%5E2%20h_1%2B%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r_2%5E2%20h_2)
Here,
![r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm](https://tex.z-dn.net/?f=r_1%3Dr_2%20%3D%20%5Cdfrac%7BDiameter%7D%7B2%7D%20%3D%20%5Cdfrac%7B26%7D%7B2%7D%20%3D13%5C%20cm)
To find the Height of Cylinder, we can use the following formula:
![l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm](https://tex.z-dn.net/?f=l%5E2%20%3D%20r_2%5E2%2Bh_2%5E2%5C%5C%5CRightarrow%20h_2%5E2%20%3D%2020%5E2-13%5E2%5C%5C%5CRightarrow%20h_2%5E2%20%3D%20400-169%5C%5C%5CRightarrow%20h_2%5E2%20%3D%20231%5C%5C%5CRightarrow%20h_2%3D15.2%5C%20cm%20%5Capprox%2015%5C%20cm)
Now, putting the values to find the volume of container:
![Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3](https://tex.z-dn.net/?f=Volume_%7BContainer%7D%20%3D%20%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%2015%2B%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%2015%5C%5C%5CRightarrow%20Volume_%7BContainer%7D%20%3D%20%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%2015%2B%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%205%5C%5C%5CRightarrow%20Volume_%7BContainer%7D%20%3D%20%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%2020%5C%5C%5CRightarrow%20Volume_%7BContainer%7D%20%3D%2010613.2%20%5Capprox%2010613%5C%20cm%5E3)
Converting
to litres:
![10613 cm^3 = 10.613\ litres \approx 11\ litres](https://tex.z-dn.net/?f=10613%20cm%5E3%20%3D%2010.613%5C%20litres%20%5Capprox%2011%5C%20litres)
<em>11 litres </em>of water will fit inside the container.
A & B - the 42 give you the answer so Paul sent the times to the other people thank you