Answer:
0.2833 = 28.33% probability that a student in the class chosen at random is neither an Actuarial Statistics nor a Data Science major
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, we have that:
There are 300 students.
80 + 5 = 85 are not Actuarial statistics or data science majors. So
![\frac{85}{300} = 0.2833](https://tex.z-dn.net/?f=%5Cfrac%7B85%7D%7B300%7D%20%3D%200.2833)
0.2833 = 28.33% probability that a student in the class chosen at random is neither an Actuarial Statistics nor a Data Science major
Answer: 6 cm
Step-by-step explanation:
Given: The ratio of the areas of two similar parallelograms is 4:9.
To find : The height of the bigger one if the smaller is of height 4 cm.
Let h be the height of the bigger one.
Since the areas of similar figures are proportional to the square of their corresponding sides.
Then, ![\dfrac{4^2}{h^2}=\dfrac{4}{9}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%5E2%7D%7Bh%5E2%7D%3D%5Cdfrac%7B4%7D%7B9%7D)
![\dfrac{16}{h^2}=\dfrac{4}{9}\\\\\Rightarrow\ h^2=\dfrac{9}{4}\times16\\\\\Rightarrow\ h^2=36\\\\\Rightarow\ h= 6\ cm\ \ \ \ \text{[ height cannot be negative.]}](https://tex.z-dn.net/?f=%5Cdfrac%7B16%7D%7Bh%5E2%7D%3D%5Cdfrac%7B4%7D%7B9%7D%5C%5C%5C%5C%5CRightarrow%5C%20h%5E2%3D%5Cdfrac%7B9%7D%7B4%7D%5Ctimes16%5C%5C%5C%5C%5CRightarrow%5C%20h%5E2%3D36%5C%5C%5C%5C%5CRightarow%5C%20h%3D%206%5C%20cm%5C%20%5C%20%5C%20%5C%20%5Ctext%7B%5B%20height%20cannot%20be%20negative.%5D%7D)
Hence, the height of bigger parallelogram = 6 cm
A polynomial with solution
must be a multiple of
. So, your polynomial must be a multiple of
![(x-2)(x+3)(x-1)](https://tex.z-dn.net/?f=%28x-2%29%28x%2B3%29%28x-1%29)
But this is already a cubic polynomial, so it can only be a multiple in a numerical sense:
![p(x)=a(x-2)(x+3)(x-1),\quad a\in\mathbb{R}](https://tex.z-dn.net/?f=p%28x%29%3Da%28x-2%29%28x%2B3%29%28x-1%29%2C%5Cquad%20a%5Cin%5Cmathbb%7BR%7D)
The coefficient
can be found imposing the condition about the y-intercept. The y-intercept is nothing more than the polynomial evaluated at zero:
![p(0)=a(-2)(3)(-1)=6a](https://tex.z-dn.net/?f=p%280%29%3Da%28-2%29%283%29%28-1%29%3D6a)
And we want this to be -12, so we have
![6a=-12\iff a=-2](https://tex.z-dn.net/?f=6a%3D-12%5Ciff%20a%3D-2)
So, your polynomial is
![p(x)=-2(x-2)(x+3)(x-1)](https://tex.z-dn.net/?f=p%28x%29%3D-2%28x-2%29%28x%2B3%29%28x-1%29)
And if you expand it it becomes
![-2 x^3 + 14 x - 12](https://tex.z-dn.net/?f=-2%20x%5E3%20%2B%2014%20x%20-%2012)
3+2.50=P or 5.50
this doesn't matter just trying to get 20 characters
This sequence is:
a(n)=-11(-4)^(n-1)
The sum of the sequence is:
s(n)=-11(1--4^n)/(1--4)
s(n)=-11(1--4^n)/5
so for the first seven terms
s(7)=-11(1--4^7)/5
s(7)=-11(1+16384)/5
s(7)=-11(16385)/5
s(7)=-36047 B.