Answer:
Mean = 35
Variance = 291.7
Step-by-step explanation:
Data provided in the question:
X : 1, 2, 3, 4, 5, 6
All the data are independent
Thus,
The mean for this case will be given as:
Mean, E[X] = 
or
E[X] = 
or
E[X] = 3.5
For 10 days, Mean = 3.5 × 10 = 35
And,
variance = E[X²] - ( E[X] )²
Now, for this case of independent value,
E[X²] = 
or
E[X²] = 
or
E[X²] = 
or
E[X²] = 15.167
Therefore,
variance = E[X²] - ( E[X] )²
or
variance = 15.167 - 3.5²
or
Variance = 2.917
For 10 days = Variance × Days²
= 2.917 × 10²
= 291.7
The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal, it is obtained by Pythagoras theorem.
Step-by-step explanation:
The given are,
From ΔABC,
AB= 6
BC= 10
AC = x
From ΔDEC,
CD= 28
DE= 21
CE = y
Step:1
Pythagoras theorem from ΔABC,
...............(1)
Substitute the values,
= 
+ 
100 = 36 +
= 100 - 36
= 64
AC = 
AC = 8
AC = x = 8
Step:2
Pythagoras theorem for ΔDEC,
................(2)
From the values,
= 
+ 
= 784 + 441
= 1225
CE = 
CE = 35
CE = y = 35
Result:
The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal.
For x^3-11x^2+33x+45 , we can make it an equation so <span>x^3-11x^2+33x+45=0. Next, we can find out if -1 or -3 is a factor. If -1 is a factor, than (x+1) is factorable. Using synthetic division, we get
x^2-12x+45
___ ________________________
x+1 | x^3-11x^2+33x+45
- (x^3+x^2)
_________________________
-12x^2+33x+45
- (-12x^2-12x)
______________
45x+45
-(45x+45)
___________
0
Since that works, it's either B or D. We just have to figure out when
</span> x^2-12x+45 equals 0, since there are 3 roots and we already found one. Using the quadratic formula, we end up getting (12+-sqrt(144-180))/2=
(12+-sqrt (-36))/2. Since sqrt(-36) is 6i, and 6i/2=3i, it's pretty clear that B is our answer
Answer:
4°
Step-by-step explanation:
All the angles in a triangle add together to equal 180°. We know there are three angles of 20° so let's subtract this.
20° × 3 = 60°
180° - 60° = 120°
Now well divide 120° up among the three angles.
120° ÷ 3 = 40°
Now we know the angles are 40° + 20°, but we need to find the value of x, so divide 40° by 10
40° ÷ 10 = 4°
x = 4°
The equation of the line is y = 3x - 4, so the inequality is y <= 3x - 4.
