Answer:
Option 4 - 0.8508
Step-by-step explanation:
Given : A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses.
To find : Estimate the probability of getting at least 20% correct ?
Solution :
20% correct out of 60,
i.e. 
Minimum of 12 correct out of 60 i.e. x=12
Each question has 4 possible answers of which one is correct.
i.e. probability of answering question correctly is 
Total question n=60.
Using a binomial distribution,

![P(X\geq 12)=1-[P(X=0)+P(X=1)+P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)]](https://tex.z-dn.net/?f=P%28X%5Cgeq%2012%29%3D1-%5BP%28X%3D0%29%2BP%28X%3D1%29%2BP%28X%3D0%29%2BP%28X%3D1%29%2BP%28X%3D2%29%2BP%28X%3D3%29%2BP%28X%3D4%29%2BP%28X%3D5%29%2BP%28X%3D6%29%2BP%28X%3D7%29%2BP%28X%3D8%29%2BP%28X%3D9%29%2BP%28X%3D10%29%2BP%28X%3D11%29%5D)
![P(X\geq 12)=1- [^{60}C_0(0.25)^0(1-0.25)+^{60-0}+^{60}C_1(0.25)^1(1-0.25)^{60-1}+^{60-1}+^{60}C_2(0.25)^2(1-0.25)^{60-2}+^{60}C_3(0.25)^3(1-0.25)^{60-3}+^{60}C_4(0.25)^4(1-0.25)^{60-4}+^{60}C_5(0.25)^5(1-0.25)^{60-5}+^{60}C_6(0.25)^6(1-0.25)^{60-6}+^{60}C_7(0.25)^7(1-0.25)^{60-7}+^{60}C_8(0.25)^8(1-0.25)^{60-8}+^{60}C_9(0.25)^9(1-0.25)^{60-9}+^{60}C_{10}(0.25)^{10}(1-0.25)^{60-10}+^{60}C_{11}(0.25)^{11}(1-0.25)^{60-11}]](https://tex.z-dn.net/?f=P%28X%5Cgeq%2012%29%3D1-%20%5B%5E%7B60%7DC_0%280.25%29%5E0%281-0.25%29%2B%5E%7B60-0%7D%2B%5E%7B60%7DC_1%280.25%29%5E1%281-0.25%29%5E%7B60-1%7D%2B%5E%7B60-1%7D%2B%5E%7B60%7DC_2%280.25%29%5E2%281-0.25%29%5E%7B60-2%7D%2B%5E%7B60%7DC_3%280.25%29%5E3%281-0.25%29%5E%7B60-3%7D%2B%5E%7B60%7DC_4%280.25%29%5E4%281-0.25%29%5E%7B60-4%7D%2B%5E%7B60%7DC_5%280.25%29%5E5%281-0.25%29%5E%7B60-5%7D%2B%5E%7B60%7DC_6%280.25%29%5E6%281-0.25%29%5E%7B60-6%7D%2B%5E%7B60%7DC_7%280.25%29%5E7%281-0.25%29%5E%7B60-7%7D%2B%5E%7B60%7DC_8%280.25%29%5E8%281-0.25%29%5E%7B60-8%7D%2B%5E%7B60%7DC_9%280.25%29%5E9%281-0.25%29%5E%7B60-9%7D%2B%5E%7B60%7DC_%7B10%7D%280.25%29%5E%7B10%7D%281-0.25%29%5E%7B60-10%7D%2B%5E%7B60%7DC_%7B11%7D%280.25%29%5E%7B11%7D%281-0.25%29%5E%7B60-11%7D%5D)

Therefore, option 4 is correct.
Answer:
C
Step-by-step explanation: i did this and i think C was the answer
Answer:
tan x = opp / adj = -3/4
Step-by-step explanation:
If sin x = -3/5, then we have the following info as a starting point:
opposite side = -3 (implying that the angle is in either QIII or QIV), and
hypotenuse = 5.
Using the Pythagorean Theorem, we find that x² + (-3)² = 5², where x is the length of the adjacent side. Solving for x², we get x² = 25-9 = 16, so that the adj. side, x, is either +4 or -4.
If cos x > 0, then x must be in either QI or QIV.
If both conditions are satisfied (sin x = -3/5 and cos x > 0), then the angle x must be in QIV.
Then tan x = opp / adj = -3/4.
Answer:
The solved given equation is
.
Step-by-step explanation:
Given equation is 
To solve the given equation:


Multiply the above equation into
on both sides


To sove the equation by using synthetic division method
2_| 1 1 -16 20
0 2 6 -20
___________
1 3 -10 0
Therefore x-2 is a factor
Therefore the quadratic equation is 
(x-2)(x+5)=0
(x-2)=0 or (x+5)=0

Therefore the factors are x-2,x-2,x+5
Therefore the solved given equation is 