Tennessee has a population of about 6,495,978. Its territory can be modeled as a trapezoid, as shown in the figure. Each unit on the coordinate grid represents one mile. Find the approximate population density of tennessee. Round to nearest whole number if necessary.
Answers
Answer:
The population density is 150 persons per square mile
Step-by-step explanation:
Firstly, we need to calculate the area of the trapezoid.
Mathematically, the area of a trapezoid is
(a+b)/2 * h
from the grid, we can obtain the lengths
on the x-axis , each line is 40(200/5 thin lines)
on the y-axis, each thin line also is 40(200/5 thin lines)
thus a = (8 * 40) = 320
b = (10* 40) = 400
h = (3 * 40) = 120
Inserting this into the area equation, we have the area of the trapezoid as (320 + 400)/2 * 120 = 43,200 units
since each unit = 1 mile, the area of Tennessee = 43,200 units
The population density is thus ; 6,495,978/43,200= which is approximately 150 persons per square mile
The population density is a number that gives the number of people located within the state.
[tex]\mathrm{The \ population \ density \ is \ approximately}\ \underline{150}\ \frac{persons}{mi.^2}[/tex]
Reasons:
The population of Tennessee = 6,495,978
The dimensions of the trapezoid model of the territory are;
Base length, a = 320
Base length, b = 400
Height of the trapezoid, h = 120
[tex]Area \ of \ the \ trapezoid = \mathbf{\dfrac{a + b}{2} \cdot h}[/tex]
Which gives;
[tex]Area \ of \ the \ trapezoidal \ territory = \mathbf{\dfrac{320 + 400}{2} \times 120 }= 43,200[/tex]
Area of the trapezoidal territory of the state = 43,200 mi²
[tex]The \ ratio \ of \ the \ population \ to \ the \ territory = \dfrac{6,495,978}{43,200} = 150.36986\overline 1[/tex]
Therefore;
[tex]The \ population \ density \approx \underline{150}\ \frac{persons}{mi.^2}[/tex]
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Related Questions
Grant is replacing his aquarium. His old aquarium was in the shape of rectangular prism with a volume of 5,184 cubic inches.
The new aquarium is also a rectangular prism with a length, width, and height that are each 5/8 times as long as the corresponding dimension of his old aquarium. Grant concludes the two aquariums are geometrically similar figures. Which statement is true?
A. The two aquariums are similar, and the volume of the new aquarium is 3,000 cubic inches.
B. The two aquariums are similar, and the volume of the new aquarium is 4,320 cubic inches.
C. The two aquariums are not similar, and the volume of the new aquarium is 3,000 cubic inches.
D. The two aquariums are not similar, and the volume of the new aquarium is 4,320 cubic inches.
Answers
Answer:
The answer is B
Step-by-step explanation:
Which statements are true about surface area and volume? Check all that apply. Volume is labeled with cubic units. Surface area is labeled with cubic units. Volume of a prism is the product of the area of the base and height. Surface area is the sum of the areas of each side. The volume of a prism is One-third the volume of a pyramid.
Answers
We will review each option and see that it corresponds:
-Volume is labeled with cubic units.
True, the units of volume are cubic, since it is distance to the cube.
-Surface area is labeled with cubic units.
False, the units of the area are square, since it is distance squared
-Volume of a prism is the product of the area of the base and height.
True, depending on the base, the volume of the prism is determined, therefore it would be the area of the base by the height.
-Surface area is the sum of the areas of each side.
True, the surface area corresponds to the sum of the lateral areas and the area of the base, that is, the area of each side.
-The volume of a prism is One-third the volume of a pyramid.
False, on the contrary, the volume of a pyramid is one third of the volume of a prism
Answer:
A
C
D
Step-by-step explanation:
Hope you guys have a good day!
One of these pics are proof and the other is to just make you smile :)
You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 555 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.
If you randomly choose your character and tool, what is the probability that you won't be a hobbit or use an umbrella?
Answers
Answer:
There is a 1/3 chance of getting a hobbit, and a 0.1/11 chance of getting an umbrella.
Evaluate the expression 3 x
{10 +1} +5.
Answers
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5.
PEMDAS
Parentheses first
3 x {11} +5.
Then multiply and divide
33+5
38
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5 Following PEMDAS, solve in the parentheses
3 x 11 + 5 Multiply 3 x 11
33 + 5 Add
38
Which of the following is the graph of y = sin(0.5x)?
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 24 pi.
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 2 pi.
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 1 cycle at 8 pi.
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 8 pi.
Answers
Answer: On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 8 pi.
Step-by-step explanation:
The function is y = sin(0.5*x)
We know that sin(0) = 0, so this graph must pass trough the point (0,0)
We know that the maximum of the sin(x) is 1, when x = pi/2. and the minimum is -1 when x = (3/2)*pi
but in our case the function is valuated in 0.5*x
then the maximum is when:
0.5*x = pi/2
x = pi/(2*0.5) = pi
and the minimum is when
0.5*x = (3/2)*pi
x = 3*pi
Now, knowing that sin(2*pi) = 0
The other 0 of the sin is when we have 0.5*x = 2*pi
x = 2*pi/0.5 = 4*pi
this means that in 4*pi we have one cycle, then in 8*pi we have tow cycles.
Then the correct option is:
"On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 8 pi."
Answer:
d
Step-by-step explanation:
one person has corona virus then ten more people catch it how many people have corona virus
Answers
Answer:
11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
1 - Person already infected
10 - People who got the virus
1 + 10 = 11
Cake is shared among Mary, Ann and Susan in the ratio 2 : 5 : 7. If Susan's share is 6 pieces more than twice the share of Mary, find the number of pieces of cake Ann gets.
Answers
Answer:
the answer is 6
Step-by-step explanation:
simple math
Sam is in charge of setting up rooms for parties at a hotel. On Saturday, there are two parties, one with 496 people and one with 784 people. Each table seats 8 people. How many total tables does he need for the two parties?
Answers
Answer:
160
Step-by-step explanation:
add the numbers together then divide by 8
During December,an electronics store saw a 27% increase in video game sales.If the store sold an average of $47,300 in video games during each other month,how much more money did it earn in December for video game sales?
Answers
Answer:
It earned $12,771 more in December.
Step-by-step explanation:
This question can be solved using a rule of three.
During an average month, we have that 100% = 1 is $47,300.
During December, the amount is $x, and it is 100% + 27% = 127% = 1.27. So
1 - $47,300
1.27 - $x
x = 1.27*47,300
x = 60,071
It earned $60,071 in December.
Compared to other months, it earned $60,071 - $47,300 = $12,771 more in December.
what is the median of the following number: 40, 49, 62, 56, 68, 39, 50, 61, 54, 44
Answers
Answer:
52
Step-by-step explanation:
39, 40, 44, 49, 50, 54, 56, 61, 62, 68
39, 40, 44, 49, 50, 54, 56, 61, 62, 68
[tex]\frac{50 + 54}{2}[/tex] = [tex]\frac{104}{2}[/tex] = 52
Answer:
52
Step-by-step explanation:
A small bag of pretzels costs $0.99 and contains 4 ounces. A large bag of pretzels costs $2.99 and contains 15 ounces. Which is the better buy?
Answers
Answer:
$2.99 is the better buy
Step-by-step explanation:
First, find the unit price for each bag of pretzels. This can be found by the formula: (cost/amount). in this case it is (cost/ ounce)
This means:
0.99 bag for 4 ounces means about 25 cents per oz
2.99 bag for 15 oz means about 20 cents per oz
The lower the unit price, the better the buy.
Each ounce is cheaper with the 2.99 bag, therefore it is the better choice.
Consider this right triangle with the given measures.
A triangle has side lengths 5 inches and 12 inches. The hypotenuse is unknown.
What is the length of the hypotenuse?
1. 52 + 122 =c2
2. 25 + 144 =c2
3. 169=c2
c=
Answers
Answer:
c=13
Step-by-step explanation:
You then square root both sides of the equation and the square root of 169 is 13.
Hope this helps! :)
Answer:
c is 13
Step-by-step explanation:
trust me bro
A commercial airplane travels 5,000 feet east and then ascends 3,000 feet from its starting point in the sky. Upon noticing a severe storm system on the horizon, the pilot decides to return to the starting point. A) how much distance does the plane have to travel to turn back? B) at what angle would the plane need to travel to return to its starting point. (1,000 feet = 1 unit)
Answers
Answer:
A) 5830.95 B)59.04
Step-by-step explanation:
Solve for the hypotenuse of 5,000 and 3,000
Use tangent to find the angle
tanx = 5,000/3,000
x=59.04
The distance the plane has to travel to turn back is 5830.95 km.
The angle would the plane need to travel to return to its starting point is 59.04°
How to find the distance?Solve for the hypotenuse of 5,000 and 3,000
Use tangent to find the angle
tanx = 5,000/3,000
x = 59.04
Height is the size of an object in the vertical course and distance is the measurement of an object from a specific factor in the horizontal route.
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A bottle contains 3 red marbles, 5 blue marbles and 2 green marbles. If a single marble is drawn from the bottle at random, what is the probability that the marble is green?
Answers
Answer:
1/5
Step-by-step explanation:
There are 3+5+2 = 10 marbles in the bottle
P(green) = number of green marbles/ total
= 2/ 10 = 1/5
Help please will give brainliest
Answers
Answer:
A
Step-by-step explanation:
Answer no clue if u remember me but we was friends like last year over the summer. i found one our old conversations on here. j wanted to say hi and check in :)
Step-by-step explanation:
I really need help on this, please help out
Answers
Answer:
x+y= idk
Step-by-step explanation:
sorry i need the points
Answer:
15
Step-by-step explanation:
so you know that the hypotenuse for the triangle with "x"'s is 5 square root two, and because we know that the triangle is an isoceles triangle we know the other two side are equal and as a result x=5. Now for the next triangle it is 5 square root 2 on both sides and that is also an isoceles triangle and y is the hypotenuse so it 5 square root 2 times square root 2 which just becomes 2 so then it is 5 times 2 which is 10. So Y=10 and X=5 so X+Y=15.
Which set of three angles could represent the interior angles of a triangle?
A:199, 709, 910
B:470, 120, 310
C:50°, 20° 20°
D:250, 250, 100%
Answers
Answer: B
Step-by-step explanation:
Find mZA.
Note that mZA is acute. Round to the nearest degree.
5
10
B
28°
Answers
A cylinder and it’s dimensions are diameter 8.4cm and height 10.9cm. Which measurement is closest to the lateral surface area of the cylinder in square centimeters
Answers
Answer:
287.64
Step-by-step explanation:
2πrh is the formula you use for the lateral surface area.
to get radius, we know its half of the diameter so 4.2.
plug them in and you get your answer :)
Today, everything at a store is on sale. The store offers a 20% discount.If the regular price of an item is x dollars, what is the discount price in dollars? Type the correct expression in the box below.
Answers
Answer:
0.80x dolllars
Step-by-step explanation:
20% discount of the total amount is
0.20 * x dolllars
So if you start with x dollars you need to subtract the discount to get the new (lower ) price.
x - (0.20 * x) dolllars
1* x - 0.20 * x
x * 1 - 0.20 * x
x * ( 1 - 0.20 )
x * ( 0.80 )
0.80x dolllars
Huixian needs 171 pens , 63 pencils and 27 erasers into identical gift bags so that each item is equally distrusted among the gift bags . Find the number of each item in a gift bag
Answers
Answer:
57 pens per bag
21 pencils per bag
9 erasers per bag
Step-by-step explanation:
Here, we are to distribute a specific portion of each of the items in each of the gift bags.
What we must take into consideration is that the number of items per gift bag must be equal.
Thus, what we do is to divide the total number of each item by 3 to get exactly the number of each items that would be in each of the gift bags
For the pens, we have 171/3 = 57 pens per bag
For the pencils, we have 63/3 = 21 pencils per bag
For the erasers, we have 27/3 = 9 erasers per bag
Alex surveyed his classmates to determine who has been surfing and who has been snowboarding. Let A be the event that a classmate HAS snowboarded and let B be the event that a classmate HAS surfed.
If Alex picked a classmate at random, what is P(B/A) ?
A. 4/21
B. 3/4
C. 4/25
D. 25/28
Answers
Answer:
surburu
Step-by-step explanation:
Answer:
B. [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
I got this question correct. :)
A: SnowboardedB: SurfedP(B|A) = P(A and B) / P(A)P(Surfed|Snowboarded) = P(Surfed and Snowboarded) / P(Snowboarded)
Amount surfed and snowboarded: 36Total amount snowboarded: 48P(B|A) = [tex]\frac{36}{48}[/tex] = [tex]\frac{3}{4}[/tex]
Apologies for lack of explanation, but I think this will do it.
hi I need some help...
-6y + 17 = 3y -10
Answers
Answer:
y=3
Step-by-step explanation:
Solve by subtracting
[tex]-6y + 17 = 3y -10\\-6y=3y-27\\-9y=-27\\[/tex]
Divide.
[tex]-9y=-27\\y=-27/-9\\y=3[/tex]
Answer:
3
Step-by-step explanation:
Please help! Very confused
Answers
Answer:
a
Step-by-step explanation:
Frankie was practicing for a 5 kilometer race his normal time is 31 minutes and 24 seconds but yesterday he took 29 minutes and 50 seconds how much time came of his normal time
Answers
Answer: 1 minute 34 seconds
Step-by-step explanation:
From the question, Frankie was practicing for a 5 kilometer race and his normal time is 31 minutes and 24 seconds but yesterday he used 29 minutes and 50 seconds. To calculate how much time came of his normal time, we are going to find the difference between the yesterday's time and normal time. This will be:
31 minutes 24 seconds - 29 minutes 50 seconds = 1 minute 34 seconds
What is the value of r in the equation?
Negative 1.5 (4 minus r) = negative 12
–6
–4
4
6
Answers
Answer:
The answer is -4
Step-by-step explanation:
that would be because that is the answer
the correct answer is B.) -4
Stephanie has 4,500 in her savings account. If it earns 6% interest every month how much money does Stephanie have her bank account after 3 months?
Answers
Answer:
5,310
Step-by-step explanation:
6% of 4,500 is 270
270×3 is 810
810+4,500=5,310
Chloe purchased 4 apps online. She paid 6% in sales tax. Her total cost was $4.24. What was the price of each app, not including the sales tax?
Answers
The price of each app was $1.
Can someone please help me? I keep losing points...
CORRECT ANSWERS ONLY PLEASE!!!!
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
Answer:
$93,996
Step-by-step explanation:
i = prt
i = ($53,712)(.15)(5)
i = $40, 284
$40, 284 + $53,712
$93,996
Answer:
$92996
Step-by-step explanation:
Using the given formula :
I = P × R × T
I = 53712 × 15/100 × 5
I = $40284
He has = 40284 + 53712 = $93996
You have 4 tickets to the movies and can take 3 of four friends, Mike, Tom, Eddie, and Chris. If chosen randomly, what is the probability that you will take Mike, Tom, and Chris?
Answers
Answer:
Hello!
You have to find the probabilities of these happening
To pick Mike the first time is a 1 /4 chance
To pick Tom after Mike is a 1 / 3 chance since you picked mike
To pick Chris after Tom is a 1 / 2 chance since there are only two friends left
To find the probability of these happening in a row you multiply them
1/4 * 1/3 * 1/2 = 1/24
The answer is 1/24
Hope this helps!
-Brinks
