Answer:
Orion's belt width is 184 light years
Step-by-step explanation:
So we want to find the distance between Alnitak and Mintaka, which is the Orions belts
Let the distance between the Alnitak and Mintaka be x,
Then applying cosine
c²=a²+b²—2•a•b•Cosθ
The triangle is formed by the 736 light-years and 915 light years
Artemis from Alnitak is
a = 736lightyear
Artemis from Mintaka is
b = 915 light year
The angle between Alnitak and Mintaka is θ=3°
Then,
Applying the cosine rule
c²=a²+b²—2•a•b•Cosθ
c² =736² + 915² - 2×, 736×915×Cos3
c² = 541,696 + 837,225 - 1,345,034.1477702404
c² = 33,886.85222975954
c = √33,886.85222975954
c = 184.0838184897 light years
c = 184.08 light years
So, to the nearest light year, Orion's belt width is 184 light years
If the number is x, then:
6x+1= (x-1)^2
Now we just need to simplify it
6x+1=(x-1)*(x-1)
6x+1=x^2-2x+1
8x=x^2
8=x
The number is 8.
To check the answer
6*8+1=7^2
49=49
correct :)
Answer:
y=3
Step-by-step explanation:
5y-2(3)=9
5y-6=9
+6 +6
5y=15
/5 /5
y=3
Answer:
a)0.7
b) 10.03
c) 0.0801
Step-by-step explanation:
Rate of return Probability
9.5 0.1
9.8 0.2
10 0.3
10.2 0.3
10.6 0.1
a.
P(Rate of return is at least 10%)=P(R=10)+P(R=10.2)+P(R=10.6)
P(Rate of return is at least 10%)=0.3+0.3+0.1
P(Rate of return is at least 10%)=0.7
b)
Expected rate of return=E(x)=sum(x*p(x))
Rate of return(x) Probability(p(x)) x*p(x)
9.5 0.1 0.95
9.8 0.2 1.96
10 0.3 3
10.2 0.3 3.06
10.6 0.1 1.06
Expected rate of return=E(x)=sum(x*p(x))
Expected rate of return=0.95+1.96+3+3.06+1.06=10.03
c)
variance of the rate of return=V(x)=![sum(x^2p(x))-[sum(x*p(x))]^2](https://tex.z-dn.net/?f=sum%28x%5E2p%28x%29%29-%5Bsum%28x%2Ap%28x%29%29%5D%5E2)
Rate of return(x) Probability(p(x)) x*p(x) x²*p(x)
9.5 0.1 0.95 9.025
9.8 0.2 1.96 19.208
10 0.3 3 30
10.2 0.3 3.06 31.212
10.6 0.1 1.06 11.236
sum[x²*p(x)]=9.025+19.208+30+31.212+11.236=100.681
variance of the rate of return=V(x)=sum(x²*p(x))-[sum(x*p(x))]²
variance of the rate of return=V(x)=100.681-(10.03)²
variance of the rate of return=V(x)=100.681-100.6009
variance of the rate of return=V(x)=0.0801
Answer:
Option (b) is correct.
Step-by-step explanation:
Given: 
We have too choose the correct simplification for the given statement.
Consider
Using property of exponents, 
We have,
Again applying property of exponents 
We have,
Simplify, we have,
we get,
Thus, 
Option (b) is correct.
