Answer:
a) margin of error ME = 5.77
b) Margin of error becomes smaller
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-ME
Where margin of error ME = zr/√n
a)
Given that;
Mean = x
Standard deviation r = 25
Number of samples n = 72
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
ME = 1.96(25/√72)
ME = 1.96(2.946278254943)
ME = 5.774705379690
ME = 5.77
b)
For n = 89
ME = 1.96(25/√89)
ME = 1.96(2.649994700015)
ME = 5.193989612031
ME = 5.19
5.19 is smaller than 5.77 in a) above. So,
Margin of error becomes smaller
If you didn't go in a straight line, you will not reach 30 miles but however 30 miles, in general, going at a pace of 75mph it would take you 1 through 1 hour and a half.
Answer:
see explanation
Step-by-step explanation:
Using sum to product identities
cos x - cos y = - 2sin(
)sin(
) = 2sin( )sin(
)
cos x + cos y = 2cos( )cos( )
Note that
sin10° = sin(90 - 10)° = cos80°
Thus
← cancel 2 from numerator/ denominator
= 
× 
= tan45° × tan35° { tan45° = 1 ]
= 1 × tan35°
= tan35° ← as required
408 round to the nearest tenth: 410
