Is 3125 a perfect cube ? If not find the smallest number by which 3125 must be multiplied so that the product becomes a perfect
2 answers:
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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
Answer:
0.42 is closest to the proportion of customer purchase amounts between $14.00 and $16.00
Step-by-step explanation:
Mean =
Standard deviation =
We are supposed to find the proportion of customer purchase amounts between $14.00 and $16.00
P(14<x<16)
Formula :
At x = 14
Refer the z table for p value
P(x<14)=0.1922
At x = 16
Refer the z table for p value
P(x<16)=0.6141
P(14<x<16)=P(x<16)-P(x<14)=0.6141-0.1922=0.42
So, Option C is true
Hence 0.42 is closest to the proportion of customer purchase amounts between $14.00 and $16.00