Answer:
0.03
Step-by-step explanation:w
standard deviation = ( p(1-p) / n)1/2
p= sample proportion= 55%
n= sample size = 900
standard deviation = ( [55/100] [ 1- 55/100]) / 900)1/2
= (0.55*0.45 / 900)1/2
= 0.0165
margin of error = critical value*standard deviation
[ from graph critical value = 2]
margin of error = 2*0.0165=0.033
Answer: 46 years
Step-by-step explanation:
Let the father's age be x and the son's age be y, then 3 years ago:
Father = x - 3
son = y - 3
Then , from the first statement :
x - 3 = 3 ( y - 3 )
x - 3 = 3y - 9
x = 3y - 9 + 3
x = 3y - 6 .......................................... equation 1
In five years time
father = x + 5
son = y + 5
Then , from the second statement
x + 5 = 2 ( y + 5 )
x + 5 = 2y + 10
x = 2y + 10 - 5
x = 2y + 5 ........................ equation 2
Equating equation 1 and 2 , we have
3y -6 = 2y + 5
add 6 to both sides
3y = 2y + 5 + 6
subtract 2y from both sides
3y - 2y = 11
y = 11
substitute y = 11 into equation 1 to find the value of x
x = 3y - 6
x = 3(11) - 6
x = 33 - 6
x = 27
This means that the father is presently 27 years and the son is presently 11 years.
In four years time
father = 27 + 4 = 31
son = 11 + 4 = 15
sum of their ages in four years time will be
31 + 15 = 46 years
Answer:
4x + 8
Step-by-step explanation:
4(x+2)
4*x + 4*2
4x + 8
Answer:
It is necessary four parameters.
Step-by-step explanation:
Since the augmented matrix of the consistent system has rank equal to three then the number of free variables is (number of unknows)-rank then there are 7-3=4 free variables. This means that are necessary four parameter to specify all solutions.
ANSWER
EXPLANATION
The given function is
We rewrite this function to obtain,
We now compare this function to
We have
This implies that,
The vertex is (2,-11).
The focus is
