Answer:
6
Step-by-step explanation:
First, simplify the exponents:
2*(3^6*3*-5)
2*((3*3*3*3*3*3)*(1/3*3*3*3*3))
2*(729*0.00411522633)
Then solve from there:
2*2.99999999457
5.99999998914
Since there is only whole numbers and a fraction present, im assuming you have to round:
5.99999998914
6
6 is your answer
Hope this helps!
Answer:
The Answer is 76.
Step-by-step explanation:
Given the normal distribution " 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable'', we can see that exemplary employees are top 10% rated employees.
We have the formula for normal distribution:
z=(X-M)÷σ
where z is the <em>minimum z-score </em>for top 10% employee, X is the <em>minimum </em>score for top 10% employee, M is the <em>mean</em> of the score distribution, σ is the <em>standard deviation</em> of the score distribution.
The z-score we are looking for is the value "a" that separates the highest 10% from the lowest 90% i.e. P(z≤a)=0.90
If we look at z-table, corresponding value for a is 1.28155
We can now put the values in the formula:
1.28155=
So X=(1.28155×20)+50=75.631
Therefore minimum score for exemplary employee is 76.
Answer:
Step-by-step explanation:
Begin by squaring both sides to get rid of the radical. Doing that gives you:

Now use the Pythagorean identity that says
and make the replacement:
. Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:
and then simplify to

Factor out the common cos(x) to get
and there you have your 2 trig equations:
cos(x) = 0 and 1 - cos(x) = 0
The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at

The second equation simplifies to
cos(x) = 1
Again, look to the unit circle and find where the cos of an angle is equal to 1. That occurs at π only.
So, in the end, your 3 solutions are

Answer:
Length = 45 m
Width = 185 m
Step-by-step explanation:
Given:
Perimeter of rectangular rug = 460 m
width of the rug is five meters more than 4 times the length
To find:
Width and length of rug = ?
Solution:
Let the length =
m
As per given statement,
Width =
m
Formula for perimeter of a rectangle = 

Width =
m
Width = 
So, the answer is:
<em>Length = 45 m</em>
<em>Width = 185 m</em>
<em></em>
Answer:
a. 0.689
b. 0.8
c. 0.427
Step-by-step explanation:
The given scenario indicates hyper-geometric experiment because because successive trials are dependent and probability of success changes on each trial.
The probability mass function for hyper-geometric distribution is
P(X=x)=kCx(N-k)C(n-x)/NCn
where N=4+3+3=10
n=2
k=4
a.
P(X>0)=1-P(X=0)
The probability mass function for hyper-geometric distribution is
P(X=x)=kCx(N-k)C(n-x)/NCn
P(X=0)=4C0(6C2)/10C2=15/45=0.311
P(X>0)=1-P(X=0)=1-0.311=0.689
P(X>0)=0.689
b.
The mean of hyper-geometric distribution is
μx=nk/N
μx=2*4/10=8/10=0.8
c.
The variance of hyper-geometric distribution is
σx²=nk(N-k).(N-n)/N²(N-1)
σx²=2*4(10-4).(10-2)/10²*9
σx²=8*6*8/900=384/900=0.427