Solution :
a). The probability that the student will
the 1st question after the 4th attempt.
P (correct in the 4th attempt)
= ![$(1-0.75)^3 \times 0.75$](https://tex.z-dn.net/?f=%24%281-0.75%29%5E3%20%5Ctimes%200.75%24)
= 0.01171875
b). The probability that the student will
3 questions after 10 total attempts.
P( X = 3) for X = B in (n = 10, p = 0.75)
= ![$C(10,30) \times 0.75^3 \times 0.25^7$](https://tex.z-dn.net/?f=%24C%2810%2C30%29%20%5Ctimes%200.75%5E3%20%5Ctimes%200.25%5E7%24)
= 0.0031
c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :
There are = 6 success, p = 0.75.
Therefore, this is a case of a negative binomial distribution.
![$E(X)=\frac{k}{p}$](https://tex.z-dn.net/?f=%24E%28X%29%3D%5Cfrac%7Bk%7D%7Bp%7D%24)
![$=\frac{6}{0.75}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B6%7D%7B0.75%7D%24)
= 8
So, ![$\sigma = \frac{\sqrt{k(1-p)}}{p}$](https://tex.z-dn.net/?f=%24%5Csigma%20%3D%20%5Cfrac%7B%5Csqrt%7Bk%281-p%29%7D%7D%7Bp%7D%24)
![$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$](https://tex.z-dn.net/?f=%24%5Csigma%20%3D%20%5Cfrac%7B%5Csqrt%7B6%281-0.75%29%7D%7D%7B0.75%7D%24)
= 1.6330
Answer:
Please check the explanation!
Step-by-step explanation:
Given the equation
![f\left(x\right)=-2|x+1|-1](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3D-2%7Cx%2B1%7C-1)
As some of the absolute rules are:
NOW, let us solve!
Let us substitute all the table values
Putting x = -4
∵![\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aabsolute%5C%3Arule%7D%3A%5Cquad%20%5Cleft%7Ca%5Cright%7C%3Da%2C%5C%3Aa%5Cge%200)
![y=-6-1](https://tex.z-dn.net/?f=y%3D-6-1)
![y=-7](https://tex.z-dn.net/?f=y%3D-7)
So, when x = -4, then y = -7
Putting x = -3
![y=-2|-3+1|-1\:](https://tex.z-dn.net/?f=y%3D-2%7C-3%2B1%7C-1%5C%3A)
![y=-4-1](https://tex.z-dn.net/?f=y%3D-4-1)
![y=-5](https://tex.z-dn.net/?f=y%3D-5)
when x = -3, then y = -5
Putting x = -2
![y=-2\left|-2+1\right|-1](https://tex.z-dn.net/?f=y%3D-2%5Cleft%7C-2%2B1%5Cright%7C-1)
![y=-2-1](https://tex.z-dn.net/?f=y%3D-2-1)
![y=-3](https://tex.z-dn.net/?f=y%3D-3)
when x = -2, then y = -3
Putting x = -1
![y=-2\left|-1+1\right|-1](https://tex.z-dn.net/?f=y%3D-2%5Cleft%7C-1%2B1%5Cright%7C-1)
![y=-0-1](https://tex.z-dn.net/?f=y%3D-0-1)
![y=-1](https://tex.z-dn.net/?f=y%3D-1)
when x = -1, then y = -1
Putting x = 0
![y=-2\left|0+1\right|-1](https://tex.z-dn.net/?f=y%3D-2%5Cleft%7C0%2B1%5Cright%7C-1)
![y=-2-1](https://tex.z-dn.net/?f=y%3D-2-1)
![y=-3](https://tex.z-dn.net/?f=y%3D-3)
when x = 0, then y = -3
Putting x = 1
![y=-2\left|1+1\right|-1](https://tex.z-dn.net/?f=y%3D-2%5Cleft%7C1%2B1%5Cright%7C-1)
![y=-4-1](https://tex.z-dn.net/?f=y%3D-4-1)
![y=-5](https://tex.z-dn.net/?f=y%3D-5)
when x = 1, then y = -5
The graph is also attached below.
Let's find the formula for a rectangle:
2L+2W= 90
Now we know the length is equal to 6 more than 2 times the width, let's make the equation.
L=2w+6
Let's plug that in for L in the first equation.
2(2w+6)+2w=90
4w+12+2w
6w+12=90
6w=78
78÷6=13=w
The width is 13, but we need the length. We know the length is equal to 6 more than 2 times the width.
13×2= 26+6= 32
So, the length of the rectangle is 32 ft.
Answer:
∠A = 120°
∠B = 60°
Step-by-step explanation:
Since, ∠A and ∠B form a linear pair.
Therefore,
∠A + ∠B = 180°.....(1)
It is given that:
∠A = 2∠B..... (2)
From equations (1) & (2)
2∠B + ∠B = 180°
3∠B = 180°
∠B = 180°/3
∠B = 60°
So, ∠A = 2∠B = 2*60°
∠A = 120°