The table shows the population and land area, in square miles, of
County
four counties in New York State at the turn of the century. Which county had the greatest population density?
Broome
Dutchess
Niagara
Saratoga
2000
Census Population
200,536
280,150
219,846
200,635
2000
Land Area (mi2)
706.82
801.59
522.95
811.84
(1) Broome
(3) Niagara
(2) Dutchess
(4) Saratoga
To find the population density, we need to divide the population by the land area. We can do this for each county:
Broome: 200,536 / 706.82 = 283.8 people per square mile
Dutchess: 280,150 / 801.59 = 349.7 people per square mile
Niagara: 219,846 / 522.95 = 420.4 people per square mile
Saratoga: 200,635 / 811.84 = 247.2 people per square mile
Therefore, Niagara County had the greatest population density. Answer: (3) Niagara.
On the set faxes, triangle ABC
Вороватоено то она и в т
ho images of triansle 1BC, are graphed her a sequence of rigid motions identify which sequence of rigid motions maps MABC onto 41 B'C
And then maps A'B'C' onto 14"3" c«
1)a rotation followed by another rotation
2)a translation followed by a reflection
b)a reflection followed by a translation
4)a reflection followed by a rotation
Without a visual representation of the set faxes, it is difficult to determine the exact sequence of rigid motions required to map one triangle onto another. However, here are some general things to consider:
- Rigid motions include translations, rotations, and reflections. These are transformations that preserve distance and angles.
- To map one triangle exactly onto another, we need to perform a sequence of rigid motions that takes each vertex of the original triangle to its corresponding vertex in the new triangle.
- Because a triangle has three vertices, we need to know the correspondence between each vertex of the original triangle and each vertex of the new triangle.
- The order of the rigid motions matters, since performing them in a different order could produce a different result.
Based on these considerations, we can eliminate answer choices 1 and 3, since they suggest a single rotation or translation followed by a different type of transformation, which is unlikely to map one triangle exactly onto another. This leaves answer choices 2 and 4, which involve a combination of rigid motions that could potentially map one triangle onto another.
However, without more information, it is impossible to determine which answer choice is correct. We would need to know the specific directions and magnitudes of each rigid motion to determine the exact sequence required to map MABC onto 41 B'C and A'B'C' onto 14"3" c.
dhlidaegal swimmine дос сто ополнов- тре рос із піона вите рол и,
diameter of 6;
ad svand a height of 12 inches. The poo wis tiled with waters.
2
amas hotel. Determine and state the volume of the water in the pool. die
3
nearest cubic foot.
gallon, the number of gallons of water in the pool.
One cubic foot equals 7.48 gallons of water. Determine and state, to the nearest
First, we need to find the volume of the pool. The pool is in the shape of a cylinder with a diameter of 6 feet and a height of 12 inches, which is equivalent to 1 foot. The radius, which is half the diameter, is 3 feet. The formula for the volume of a cylinder is:
V = πr^2h
Plugging in the values, we get:
V = π(3 ft)^2(1 ft)
V ≈ 28.27 cubic feet
Next, we can convert the volume from cubic feet to gallons. We know that one cubic foot equals 7.48 gallons of water. Multiplying the volume by this conversion factor, we get:
V ≈ 28.27 ft^3 x 7.48 gal/ft^3
V ≈ 211.73 gallons
Therefore, the volume of water in the pool is approximately 28.27 cubic feet or 211.73 gallons, to the nearest cubic foot/gallon.
To determine the county with the greatest population density, we need to calculate the population density for each county using the formula: population density = population / land area.
Let's calculate the population density for each county:
1) Broome County: population density = 200,536 / 706.82 = 283.93 people per square mile
2) Dutchess County: population density = 280,150 / 801.59 = 349.30 people per square mile
3) Niagara County: population density = 219,846 / 522.95 = 420.37 people per square mile
4) Saratoga County: population density = 200,635 / 811.84 = 246.97 people per square mile
From the calculations, we can see that Niagara County has the highest population density with 420.37 people per square mile. Therefore, the answer is (3) Niagara.