Answer:
90*
Step-by-step explanation:
Let p be
the population proportion. <span>
We have p=0.60, n=200 and we are asked to find
P(^p<0.58). </span>
The thumb of the rule is since n*p = 200*0.60
and n*(1-p)= 200*(1-0.60) = 80 are both at least greater than 5, then n is
considered to be large and hence the sampling distribution of sample
proportion-^p will follow the z standard normal distribution. Hence this
sampling distribution will have the mean of all sample proportions- U^p = p =
0.60 and the standard deviation of all sample proportions- δ^p = √[p*(1-p)/n] =
√[0.60*(1-0.60)/200] = √0.0012.
So, the probability that the sample proportion
is less than 0.58
= P(^p<0.58)
= P{[(^p-U^p)/√[p*(1-p)/n]<[(0.58-0.60)/√0...
= P(z<-0.58)
= P(z<0) - P(-0.58<z<0)
= 0.5 - 0.2190
= 0.281
<span>So, there is 0.281 or 28.1% probability that the
sample proportion is less than 0.58. </span>
The experimental probability of letter E is: 3/25
Step-by-step explanation:
The given diagram is the number of outcomes for each letter is given
We have to find the total number of outcomes for finding the experimental probability of letter E
So,
Total outcomes = n(S) = 5+12+8+10+6+9 = 50
Number of outcomes for Letter E = n(E) = 6
So the experimental probability will be:

Hence,
The experimental probability of letter E is: 3/25
Keywords: Probability, experimental probability
Learn more about probability at:
#LearnwithBrainly
Answer: The required characteristic polynomial of the given matrix A is 
Step-by-step explanation: We are given to find the characteristic polynomial of the following 3 × 3 matrix A with unknown variable x :
![A=\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right].](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C4%26-3%264%5C%5C-2%260%26-3%5Cend%7Barray%7D%5Cright%5D.)
We know that
for any square matrix M, the characteristic polynomial is given by
where I is an identity matrix of same order as M.
Therefore, the characteristic polynomial of matrix A is
![|A-xI|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right]-x\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\right|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}-x&0&1\\4&-3-x&4\\-2&0&-3-x\end{array}\right] \right|=0\\\\\\\Rightarrow -x(3+x)^2+1(0-6-2x)=0\\\\\Rightarrow (x+3)(-3x-x^2-2)=0\\\\\Rightarrow (x+3)(x^2+3x+2)=0\\\\\Rightarrow x^3+6x+11x+6=0.](https://tex.z-dn.net/?f=%7CA-xI%7C%3D0%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cleft%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C4%26-3%264%5C%5C-2%260%26-3%5Cend%7Barray%7D%5Cright%5D-x%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%5Cright%7C%3D0%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cleft%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-x%260%261%5C%5C4%26-3-x%264%5C%5C-2%260%26-3-x%5Cend%7Barray%7D%5Cright%5D%20%5Cright%7C%3D0%5C%5C%5C%5C%5C%5C%5CRightarrow%20-x%283%2Bx%29%5E2%2B1%280-6-2x%29%3D0%5C%5C%5C%5C%5CRightarrow%20%20%28x%2B3%29%28-3x-x%5E2-2%29%3D0%5C%5C%5C%5C%5CRightarrow%20%28x%2B3%29%28x%5E2%2B3x%2B2%29%3D0%5C%5C%5C%5C%5CRightarrow%20x%5E3%2B6x%2B11x%2B6%3D0.)
Thus, the required characteristic polynomial of the given matrix A is 