We can compare 2 fractions by means of the cross multiplication method. In our case, we have
since 50 is greater than 24 then 10/12 is greater than 2/5:
Answer:
64 cubic metres
Step-by-step explanation:
The triangular pyramid volume formula resembles the volume formula for any other pyramid or cone:
V = A * H / 3
where:
A is the area of the pyramid's base
H is the height from the base to the point
In other words: the volume of a triangular pyramid is one-third of the product of the base area and the pyramid's height.
8 x 6 / 2 to find area of base = 24
x 8 = 192
192 / 3 = 64
Hope this makes sense. If you would like, I can l1nk to a very useful website, or I can explain it further.
- profparis
Answer:
a)P=0.42
b) ![n\geq 297](https://tex.z-dn.net/?f=n%5Cgeq%20297)
Step-by-step explanation:
We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:
![P=\begin{pmatrix}n\\ k\end{pmatrix} p^k(1-p)^{n-k}=\frac{n!}{k!(n!-k!)}p^k(1-p)^{n-k}](https://tex.z-dn.net/?f=P%3D%5Cbegin%7Bpmatrix%7Dn%5C%5C%20k%5Cend%7Bpmatrix%7D%20p%5Ek%281-p%29%5E%7Bn-k%7D%3D%5Cfrac%7Bn%21%7D%7Bk%21%28n%21-k%21%29%7Dp%5Ek%281-p%29%5E%7Bn-k%7D)
a) we have k=2, n=10 and p=0.01:
![P=\frac{10!}{2!(10!-2!)}0.01^2(1-0.01)^{10-2}\\P=\frac{10!}{2!*8!}0.01^2(0.99)^{8}\\P=45*0.01^2(0.99)^8=0.42](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B10%21%7D%7B2%21%2810%21-2%21%29%7D0.01%5E2%281-0.01%29%5E%7B10-2%7D%5C%5CP%3D%5Cfrac%7B10%21%7D%7B2%21%2A8%21%7D0.01%5E2%280.99%29%5E%7B8%7D%5C%5CP%3D45%2A0.01%5E2%280.99%29%5E8%3D0.42)
b) We have,
, Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.
![1-0.99^n\geq 0.95\\0.99^n\leq 1-0.95\\0.99^n\leq 0.05\\n\geq 297](https://tex.z-dn.net/?f=1-0.99%5En%5Cgeq%200.95%5C%5C0.99%5En%5Cleq%201-0.95%5C%5C0.99%5En%5Cleq%200.05%5C%5Cn%5Cgeq%20297)
Answer: Parallelogram is a kind of quadrilateral where as there are some quadrilaterals (like trapezoid , kite, .. ) that do not satisfy the properties of parallelograms.
Step-by-step explanation:
A quadrilateral is a closed polygon having fours sides.
A parallelogram is a kind of quadrilateral having following properties:
Its opposite sides and opposite angles are equal.
The sum of adjacent angles is 180°.
The diagonal of parallelogram bisect each other.
A Trapezoid is also a quadrilateral . It has only one pair of parallel sides. (The other one are not parallel).
So , all quadrilaterals not parallelograms.
Therefore, parallelograms are always quadrilaterals but quadrilaterals are sometimes parallelograms because parallelogram is a kind of quadrilateral where as there are some quadrilaterals (trapezoid , kite, .. ) ) that do not satisfy the properties of parallelograms.
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