The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2. Which expression is equivalent to this product a
2 answers:
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Answer:
a) The percentage of households in the town with three or more largescreen TVs is estimated as :
The best estimation for the population proportion is :
And that represent the 1.4%.
b) And the 95% confidence interval would be given (0.00370;0.0243).
And the % would be between 0.37% and 2.43%.
Step-by-step explanation:
Data given and notation
n=500 represent the random sample taken
X=7 represent the households with three or more large-screen TVs
estimated proportion of households with three or more large-screen TVs
represent the significance level (no given, but is assumed)
z would represent the statistic (variable of interest)
p= population proportion of households with three or more large-screen TVs
Part a
The percentage of households in the town with three or more largescreen TVs is estimated as :
The best estimation for the population proportion is :
And that represent the 1.4%.
Part b
Yes is possible. We hav that and
so we have the assumption of normality to find the interval.
The confidence interval would be given by this formula
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 95% confidence interval would be given (0.00370;0.0243).
And the % would be between 0.37% and 2.43%.
Answer:
The answer is below
Step-by-step explanation:
A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3 miles.
a) Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.
a) A house is located 5 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?
Answer:
Let the center of the town represent the origin (0,0). Also 1 unit = 1 mile. Since the cell tower is located 3 miles east and 4 miles north of the center of a small town, it is represented by A(3, 4)
The cell tower has a coverage of radius 3 miles. This can be represented by a circle with equation:
(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius. Hence:
(x - 3)² + (y - 4)² = 3²
(x - 3)² + (y - 4)² = 9
The diagram is drawn using geogebra.
b) The house is 5 miles north. It can be represented by y = 5 line.
To find the distance east of the house we have to substitute y = 5 and solve for x, hence:
(x - 3)² + (y - 4)² = 9
(x - 3)² + (5 - 4)² = 9
(x - 3)² + 1 = 9
(x - 3)² = 8
(x - 3) = √8
x - 3 = ±2.83
x = 3 ± 2.83
x = 5.83 or 1.83
Since it is to the east to the cell tower, hence x = 5.83.
Therefore the house is located 5.83 miles to the east of the cell tower
