The answer is 44 if I’m not mistaken
We have been given prism J and prism K have the same volume. A cube J with height 10, length 4 and width 3 A right angled triangular prism K with breadth 10, height 3 and width w. We are asked to find width w of the prism K.
We will use formulas of volume of cuboid and volume of triangular prism.
![\text{Volume of cuboid}=\text{Length}\times \text{Width}\times \text{Height}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20cuboid%7D%3D%5Ctext%7BLength%7D%5Ctimes%20%5Ctext%7BWidth%7D%5Ctimes%20%5Ctext%7BHeight%7D)
![\text{Volume of cuboid}=4\times 3\times 10](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20cuboid%7D%3D4%5Ctimes%203%5Ctimes%2010)
![\text{Volume of cuboid}=120](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20cuboid%7D%3D120)
![\text{Volume of triangular prism}=\frac{1}{2}\text{Base length}\times \text{Height}\times \text{Width}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20triangular%20prism%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctext%7BBase%20length%7D%5Ctimes%20%5Ctext%7BHeight%7D%5Ctimes%20%5Ctext%7BWidth%7D)
![\text{Volume of triangular prism}=\frac{1}{2}\times 10\times 3\times w](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20triangular%20prism%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%2010%5Ctimes%203%5Ctimes%20w)
![\text{Volume of triangular prism}=5\times 3\times w](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20triangular%20prism%7D%3D5%5Ctimes%203%5Ctimes%20w)
![\text{Volume of triangular prism}=15\times w](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20triangular%20prism%7D%3D15%5Ctimes%20w)
Now we will equate both volumes as we are told that prism J and prism K have the same volume.
![15\times w=120](https://tex.z-dn.net/?f=15%5Ctimes%20w%3D120)
![\frac{15\times w}{15}=\frac{120}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B15%5Ctimes%20w%7D%7B15%7D%3D%5Cfrac%7B120%7D%7B15%7D)
![w=8](https://tex.z-dn.net/?f=w%3D8)
Therefore, the width w of prism K is 8 units.
Answer:
![\frac{1}{32 m^{15} n^{35}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B32%20m%5E%7B15%7D%20n%5E%7B35%7D%7D)
Step-by-step explanation:
![(2m^3n^7)^{-5}](https://tex.z-dn.net/?f=%282m%5E3n%5E7%29%5E%7B-5%7D)
= ![2^{-5} m^{-15} n^{-35}](https://tex.z-dn.net/?f=2%5E%7B-5%7D%20m%5E%7B-15%7D%20n%5E%7B-35%7D)
= ![\frac{1}{2^{5} m^{15} n^{35}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%5E%7B5%7D%20m%5E%7B15%7D%20n%5E%7B35%7D%7D)
=
Answer:
a ) 0.9
<em>Expected number of bower-birds that have bowers featuring reflective decor</em>
<em> μ = 0.9</em>
Step-by-step explanation:
<u><em>Explanation:-</em></u>
Given Sample size 'n' = 20
Given data A population consists of twenty bower-birds, six of which have bowers featuring reflective decor.
<em>probability of success </em>
![p = \frac{x}{n} = \frac{6}{20} =0.3](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7Bx%7D%7Bn%7D%20%3D%20%5Cfrac%7B6%7D%7B20%7D%20%3D0.3)
Given three of the bower-birds are randomly sampled with replacement from this population.
So we will choose sample size 'n'= 3
Let 'X' be the random variable in binomial distribution
Expected number of bower-birds that have bowers featuring reflective decor
<em> μ = n p</em>
= 3 × 0.3
=0.9
<u><em>conclusion:-</em></u>
<em>Expected number of bower-birds that have bowers featuring reflective decor</em>
<em> μ = 0.9</em>
2x+57+61=180
2x+118=180
2x=62
X=31