Answer:
![\large\boxed{4\sqrt{-81}+\sqrt{-25}=41i}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B4%5Csqrt%7B-81%7D%2B%5Csqrt%7B-25%7D%3D41i%7D)
Step-by-step explanation:
![i=\sqrt{-1}\\\\\sqrt{-81}=\sqrt{(81)(-1)}=\sqrt{81}\cdot\sqrt{-1}=9i\\\\\sqrt{-25}=\sqrt{(25)(-1)}=\sqrt{25}\cdot\sqrt{-1}=5i\\\\4\sqrt{-81}+\sqrt{-25}=4(9i)+5i=36i+5i=41i](https://tex.z-dn.net/?f=i%3D%5Csqrt%7B-1%7D%5C%5C%5C%5C%5Csqrt%7B-81%7D%3D%5Csqrt%7B%2881%29%28-1%29%7D%3D%5Csqrt%7B81%7D%5Ccdot%5Csqrt%7B-1%7D%3D9i%5C%5C%5C%5C%5Csqrt%7B-25%7D%3D%5Csqrt%7B%2825%29%28-1%29%7D%3D%5Csqrt%7B25%7D%5Ccdot%5Csqrt%7B-1%7D%3D5i%5C%5C%5C%5C4%5Csqrt%7B-81%7D%2B%5Csqrt%7B-25%7D%3D4%289i%29%2B5i%3D36i%2B5i%3D41i)
Answer:
C
Step-by-step explanation:
related equation
-16t^2 + 32t + 20 = 0
-4t^2 + 8t + 5 = 0
Δ/4 = 16 + 20 = 36
t1 = (-4 + 6)/-4 = -1/2
t2 = (-4 - 6)/-4 = 5/2
-16(t+1/2)(t-5/2)
-16(2t+1/2)(2t-5/2)
-4(2t+1)(2t-5)
Answer:
3(25π/2) + 100 = 217.8097
Step-by-step explanation:
Using the binomial distribution, it is found that:
The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.
For each question, there are only two possible outcomes, either the guess is correct, or it is not. The guess on a question is independent of any other question, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- There are 20 questions, hence
.
- Each question has 2 options, one of which is correct, hence
![p = \frac{1}{2} = 0.5](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%3D%200.5)
The probability is:
![P(X \geq 15) = P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%2015%29%20%3D%20P%28X%20%3D%2015%29%20%2B%20P%28X%20%3D%2016%29%20%2B%20P%28X%20%3D%2017%29%20%2B%20P%28X%20%3D%2018%29%20%2B%20P%28X%20%3D%2019%29%20%2B%20P%28X%20%3D%2020%29)
In which:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 15) = C_{20,15}.(0.5)^{15}.(0.5)^{5} = 0.0148](https://tex.z-dn.net/?f=P%28X%20%3D%2015%29%20%3D%20C_%7B20%2C15%7D.%280.5%29%5E%7B15%7D.%280.5%29%5E%7B5%7D%20%3D%200.0148)
![P(X = 16) = C_{20,16}.(0.5)^{16}.(0.5)^{4} = 0.0046](https://tex.z-dn.net/?f=P%28X%20%3D%2016%29%20%3D%20C_%7B20%2C16%7D.%280.5%29%5E%7B16%7D.%280.5%29%5E%7B4%7D%20%3D%200.0046)
![P(X = 17) = C_{20,17}.(0.5)^{17}.(0.5)^{3} = 0.0011](https://tex.z-dn.net/?f=P%28X%20%3D%2017%29%20%3D%20C_%7B20%2C17%7D.%280.5%29%5E%7B17%7D.%280.5%29%5E%7B3%7D%20%3D%200.0011)
![P(X = 18) = C_{20,18}.(0.5)^{18}.(0.5)^{2} = 0.0002](https://tex.z-dn.net/?f=P%28X%20%3D%2018%29%20%3D%20C_%7B20%2C18%7D.%280.5%29%5E%7B18%7D.%280.5%29%5E%7B2%7D%20%3D%200.0002)
![P(X = 16) = C_{20,19}.(0.5)^{19}.(0.5)^{1} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%2016%29%20%3D%20C_%7B20%2C19%7D.%280.5%29%5E%7B19%7D.%280.5%29%5E%7B1%7D%20%3D%200)
![P(X = 17) = C_{20,20}.(0.5)^{20}.(0.5)^{0} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%2017%29%20%3D%20C_%7B20%2C20%7D.%280.5%29%5E%7B20%7D.%280.5%29%5E%7B0%7D%20%3D%200)
Then:
![P(X \geq 15) = P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.0148 + 0.0046 + 0.0011 + 0.0002 + 0 + 0 = 0.0207](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%2015%29%20%3D%20P%28X%20%3D%2015%29%20%2B%20P%28X%20%3D%2016%29%20%2B%20P%28X%20%3D%2017%29%20%2B%20P%28X%20%3D%2018%29%20%2B%20P%28X%20%3D%2019%29%20%2B%20P%28X%20%3D%2020%29%20%3D%200.0148%20%2B%200.0046%20%2B%200.0011%20%2B%200.0002%20%2B%200%20%2B%200%20%3D%200.0207)
The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.
You can learn more about the binomial distribution at brainly.com/question/24863377
Range of the data = 13
Solution:
To find the range of the given data:
Let us first define what is range.
Range:
The range of the data set is the difference between the highest value and lowest value of the data set.
i. e. Range = Highest value – Lowest value
In the given number line,
Highest value indicated = 115
Lowest value indicated = 102
Range of the data = 115 – 102
= 13
Range of the data = 13
Hence the range of the given data is 13.