A certain forest covers an area of 2300 km^2. Suppose that each year this area decreases by 7.75%. What will the area be after 8 years?Use the calculator provided and round your answer to the nearest square kilometer.
Answers
EXPLANATION:
Given;
We are told that a forest covers an area of 2300 square kilometers.
Next we are told that this forest area decreases by 7.75% each year.
Required:
We are required to calculate the area remaining after 8 years.
Step-by-step solution:
To solve this math problem, take note that what we have is an exponential decay problem. The initial size decreases (decays) at a constant rate every year.
The formula for an exponential growth/decay is given as shown below;
[tex]f(x)=a(1-r)^x[/tex]Where the variables are as follows;
[tex]\begin{gathered} a=initial\text{ }value \\ r=rate\text{ }of\text{ }decay \\ x=number\text{ }of\text{ }years \end{gathered}[/tex]With the values given, we can substitute and we'll have the following;
[tex]f(8)=2300(1-0.0775)^8[/tex][tex]f(8)=2300(0.9225)^8[/tex][tex]f(8)=2300(0.524482495947)[/tex][tex]f(8)=1206.3097...[/tex]Rounded to the nearest square kilometer, we would now have;
ANSWER:
[tex]Area\text{ }after\text{ }8\text{ }years=1206km^2[/tex]Related Questions
Select all the statements below that are true for the following graph
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From the graph given,
It is an absolute function
The following statements are true about the graph
i) The vertex is located at (2, -2)
ii) The graph has two zeros
ii) The range is [-2, ∞)
You'll have to make a series of transformations to make this parabola fit the bridge. Describethem
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The transformations are as follows:
- There is firstly a vertical reflection
- There is a vertex shift from (0,0) to the (-2, 3) position (approximate)
- There is also a horizontal compression of the parabola.
BD is the perpendicular bisector of ac,ac=10and bc=7 find the length of ad and ab
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Since, BD is the perpendicular bisector of AC. So, AD = 1/2(AC) = 5.
Since, BD is the perpendicular bisector of AC and BC is not equal to AC. So, triangle ABC is an isosceles triangle. Therefore, AB = BC = 7.
which of the following describes the area of a circle?
Answers
The area of the circle is given by:
[tex]A=\pi r^2[/tex]So, the area of a circle is basically:
[tex]A=\frac{1}{2}\times2\pi r\times r[/tex]It can be seen as the number of squares inside of the circle
Your friend subtracts to find
44 - 18 = 26. He uses 26+ 18 to check his work. Your
cousin tells him he should use 18 + 26. Who is correct?
Explain how you know.
Answers
Answer:
technically it's both
Step-by-step explanation:
because if you have the answer plus 18 and if it works and you get 44 that will be the answer
grandma has $250000 to invest. she divides her money into two accounts. one account is in ultra-safe treasury bills paying 4% interest, and the other is in riskier corporate bonds paying 6%. if she needs $12,000 per year in income from her investments, how much should she invest in each account
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for the ultra-safe treasury bills:
[tex]\begin{gathered} I_1=PV\cdot r\cdot t \\ I_1=x\cdot0.04\cdot1 \\ I_1=0.04x \\ \text{where:} \\ x=\text{amount 1} \end{gathered}[/tex]For riskier corporate bonds:
[tex]\begin{gathered} I_2=PV\cdot r\cdot t \\ I_2=y\cdot0.06\cdot1 \\ I_2=0.06y \\ \text{Where:} \\ y=\text{amount 2} \end{gathered}[/tex]she needs $12,000 per year, so:
[tex]\begin{gathered} I_1+I_2=12000 \\ 0.04x+0.06y=12000 \end{gathered}[/tex]grandma has $250000 to invest, therefore:
[tex]x+y=250000[/tex]Let:
[tex]\begin{gathered} x+y=250000\text{ (1)} \\ 0.04x+0.06y=12000\text{ (2)} \\ \text{From (1) solve for x:} \\ x=250000-y\text{ (3)} \\ \text{ Replace (3) into (2)} \\ 0.04(250000-y)+0.06y=12000 \\ 10000-0.04y+0.06y=12000 \\ 0.02y=12000-10000 \\ 0.02y=2000 \\ y=\frac{2000}{0.02} \\ y=100000 \end{gathered}[/tex]Replace y into (3):
[tex]\begin{gathered} x=250000-100000 \\ x=150000 \end{gathered}[/tex]Therefore, grandma needs to invest $150000 in ultra-safe treasury bills, and
Find the volume of the rectangular prism O 8 cubic units O 4 cubic units 6 cubic units O 3 cubic units
Answers
Given data:
The given rectangular prism.
The volume of the given prism is,
[tex]\begin{gathered} V=6(\text{volume of a cube)} \\ =\text{ 6(1 cubic-units)} \\ =\text{ 6 cubic-unis} \end{gathered}[/tex]5 Ramon sched 13 -6 She said she thought about taking away and then 3 more from 13. CanRamon do this? Show a diagram and write an equation to show what this solution path would look like
Answers
we know that
14-7=7 --------> given problem
so
we have
14-8
Rewrite the expression
14-(7+1)
14-7-1
Remember that
14-7=7
substitute
7-1
6
we have
12-6=6
so
12-7
rewrite
12-(6+1)
12-6-1
substitute
6-1
5
we have
13-6
13-(3+3)
13-3-3
10-3
7
Frank's rectangular box of toys has a perimeter of 30 inches. The length is twice as long as the width. Which of the following expressions could be a major step in finding the length? A. Length times Width equals AreaB. 2 times Width plus 2 times Width plus Width plus Width equals 30C. Perimeter equals Width plus Width plus Width plus WidthD. 2 times Length equals Width
Answers
From the given problem,
length is twice as long as the width
length = 2 x width
Note that the perimeter is :
[tex]P=2W+2L[/tex]where W and L are the width and length respectively.
Since L = 2W
Perimeter will be :
[tex]\begin{gathered} P=2W+2(2W) \\ P=2W+4W \\ P=6W \end{gathered}[/tex]Perimeter is equal to 30 inches :
[tex]6W=30in[/tex]From the given choices, only B satisfies this condition.
2W + 2W + W + W = 30
6W = 30
Therefore, the answer is B.
Dane is using two differently sized water pumps to clean up flooded water. The larger pump can
remove the water alone in 240 min. The smaller pump can remove the water alone in 400 min.
How long would it take the pumps to remove the water working together?
minutes
Answers
The rate of work obtained from the 240 and 400 minutes it takes for the large and small pumps to remove the water alone respectively, gives the duration it takes for the two pumps to remove the water working together as 150 minutes.
What is the rate of work formula?The rate of work in completing a project is given by the reciprocal of the time it takes to complete the project.
The given parameters are;
The time it takes the larger pump to remove the water, A = 240 minutes
The time it takes the smaller pump to remove the water, B = 400 minutes
The rate of doing work by the larger pump = [tex]\frac{1}{240}[/tex]
The work rate of the smaller pump = [tex]\frac{1}{400}[/tex]
The rate of work of the two pumps combined, [tex]\frac{1}{r}[/tex], is therefore;
[tex]\dfrac{1}{A} +\dfrac{1}{B} = \dfrac{1}{r}[/tex]
Where;
r = The time it takes for the two pumps to remove the water together
Which gives;
[tex]\dfrac{1}{240} +\dfrac{1}{400} = \dfrac{1}{150} = \dfrac{1}{r}[/tex]
∴ r = 150
The time it takes for the two pumps to remove the water together is 150 minutes
Learn more about rate of work here:
https://brainly.com/question/29242115
#SPJ1
Answer: 150 min
(I completed the question)
find the equation of line with points (3, 3) that passes through a slope of 2/3
Answers
hello
the standard equation of a straight line is given as y = mx + b
y = y-coordinate
x = x-coordinate
m = slope
b = intercept
the points given are (3, 3) and the slope = 2 / 3
y = mx + b
y = 3
x = 3
let's substitute in our values and solve for b
[tex]\begin{gathered} y=mx+b \\ 3=\frac{2}{3}(3)+b \\ 3=2+b \\ b=3-2 \\ b=1 \end{gathered}[/tex]since we have the value of the slope, we can simply write the equation from y = mx + b to y = 2/3x + 1
[tex]y=\frac{2}{3}x+1[/tex]this is the equation of the line.
but we can further simplify this by looking for the LCM of the denominators of the independent variables
[tex]\begin{gathered} y=\frac{2}{3}x+1 \\ y=\frac{2x+3}{3} \\ \text{cross multiply both sides} \\ 3y=2x+3 \end{gathered}[/tex]the equation can be rewritten as 3y = 2x + 3
I am thinking of a number. It has two digits. When I reverse the digits and then add the new number to the original number I get 33. What is my number?
Answers
I am thinking of a number. It has two digits. When I reverse the digits and then add the new number to the original number I get 33. What is my number?
Let
the number xy
so
Reverse the digits yx
xy+yx=33
10x+10y=30 ------> equation 1
y+x=3 ----> equation 2
solve the system by graphing
the syste
If a car travels at a speed of 45 mi/h fort hours, then travels 65 mi/h for m hours, what does theexpression 45t +65m represent?The expression represents the (select)
Answers
total distance travelled by the car (option D)
Explanation:
When speed = 45mi/h
time = t hours
when speed = 65mi/h
time = m hours
45t +65m means 45mi/h × t + 65mi/h × m
The formula that relates the speed and the time is distance:
speed = distance/time
distance = speed × time
The distance for the first speed and time = 45mi/h × t hours = 45t
The distance for the second speed and time = 65mi/h × m hours = 65m
The sum of the two distance = distance covered by the car = 45t + 65m
Hence, we can say the expression 45t +65m represents the total distance travelled by the car (option D)
The figure below is composed of squares and semi-circles. Find the perimeter of this shape. Show your work.
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Problem
Solution
For this case we can find the perimeter of the figure with the following operation
[tex]P=(2\cdot4)+\pi(4)+(2\cdot4)+\pi(4)=2\pi(4)+8+8[/tex]Then the final answer would be:
[tex]P=16+8\pi[/tex]I have no clue how to graph inequalities and find the solution
Answers
In the graph we can see two line y=2 and y=x.
Also, we know that there is a system of inequalities and the blue area in the graph represent the solutions for the system.
We can see that the blue area is above the line y=2, thats mean one inequality is:
[tex]y\ge2[/tex]So, any points that y-coordinate is greater than or equal than 2 satisfy the inequality.
Also we can see that the blue area is bellow the line y=x and the line is a dotted line, this last means the inequality do not take take value in the line. So, the second inequation is:
[tex]ySo, the points that satisfy the system of inequalities are above the line y=2 and bellow the line y=x and not touch the line y=x.evaluate the following expression 2 * 1 + 2 * 24/4
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using PEDMAS/ BODMAS
division is executed first followed by multiplication then addition
Given: AB = CB, LABD= LABD= LCBD Prove: LA= LCStatement Reason
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Explanation:
We know that AB = CD and that ∠ABD = CBD because it is given information.
Then, we have that BD = BD because a side is congruent to itself. It is called the reflexive property of congruence.
Now, we can say that ΔABD = ΔBDC by SAS (Side - Angle - Side) because we have two congruent sides and the angle between them is also congruent
Finally, ∠A = ∠C because the corresponding sides of congruent triangles are congruent
Answer:
Therefore, the answer is
In a study of 200 students under 25 years old one-fifth have not yet learned to drive. What percentage can drive?
Answers
12. What is the equation of a circle with center (6,-4) and radius 6?(x - 6)2 + (y + 4)2 = 6(x + 6)2 + (y - 4)2 = 36(x + 6)2 + (y - 4)2 = 6(x - 6)2 + (y + 4)2 = 36
Answers
The equation of a circle with center (h, k) and radius r is given by the following expression:
[tex](x-h)^2+(y-k)^2=r^2[/tex]In this case, the center of the circle is located at (6, -4), and its radius equals 6, then by replacing 6 for h, -4 for k and 6 for r, we get:
[tex]\begin{gathered} (x-6)^2+(y-(-4))^2=6^2 \\ (x-6)^2+(y+4)^2=36 \end{gathered}[/tex]Then, the last option is the correct answer: (x - 6)^2 + (y + 4)^2 = 36
please help me 60 points please show all work this is due in 15 minutes5x-(3x-6)=182(3x-4)=102x+7=5x+16x/3-8=-23x – 6 = -12x/-3=8
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please help me solve this step by step with wrriten explanation. context and words help me
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For the following exercises, determine the least possible degree of the polynomial function shown.
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Solution
To determine the least possible degree of the polynomial function
The function has atmost n - intercepts in the horizontal
The graph turns 4 times in the above curve, hence n = 4
[tex]\begin{gathered} n+1 \\ n=\text{ number of turns} \\ 4+1=5 \end{gathered}[/tex]Therefore the least possible degree of the polynomial = 5
Hence it is a 5 possible polynomial function
ring×heart=hathat×2=heartheart-ring=1/4
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Let's begin by identifying key information given to us:
[tex]undefined[/tex]Please help me with these 2 questions they are both solved problems that go together with one huge problem so please answer both thank you
Answers
1).
r = 11 in
The diameter is twice the radius, so:
d = 2*11 = 22 inches
2).
d = 18 inches
The radius is half the diameter, so:
r = 18/2 = 9 inches
how many people are :9 or younger ?At most 60 years old ?40 to 59 ?
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Given the table represents the ages of people :
We need to find the following:
1. how many people are : 9 or younger ?
As shown in the table : the ages 0 - 9 has a frequency of 8
So, the answer is : 8 people
2. How many people at most 60 years old ?
From the table : the age 60 - 69 the frequency is 10
But there is no information to specify the age 60
The answer is : NEI
3. How many people are : 40 to 59 ?
From the table :
the age 40-49 has a frequency = 9
the age 50-59 has a frequency = 6
So, the answer is 9 + 6 = 15 people
I need help question
Answers
[tex]f(x)=x^2-4x-94[/tex]
The diffrentiated function will be
[tex]2x-4[/tex]RULES FOR DIFFERENTIATION
[tex]\begin{gathered} y=x^n \\ \frac{dy}{dx}=nx^{n-1} \end{gathered}[/tex]Also
[tex]\begin{gathered} y=kx \\ \frac{dy}{dx}=k \end{gathered}[/tex]Also
[tex]\begin{gathered} y=k \\ \frac{dy}{dx}=0 \end{gathered}[/tex]Line Segment AC is 10 centimeters (cm) long, Point M is the midpoint of AC.What will happen to the length of AC if Point A is moved so that the length of AM is squared and the length of MC remains the same?The length of AC will triple.The length of AC will double.The length of AC will be squared.The length of AC will be five times as large.
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We know that AC is 10 centimeters long, and M is the midpoint of AC.
If we move point A as the problem says, we have.
As you can observe, the length of AC is triple.
Hence, the right answer is the first option: The length of AC will triple.Art wants to calculate the diagonal distance across opposite corners of a rectangular parcel. The parcel is 161’ by 326’ . How long is the diagonal measurement?
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Recall that the formula for the length of the diagonal of a rectangle is:
[tex]l=\sqrt[]{a^2+b^2}.[/tex]Where a, and b are the lengths of the sides of the rectangle.
Substituting a=161´, b=326´ in the above formula we get:
[tex]\begin{gathered} l=\sqrt[]{(161^{\prime})^2+(326^{\prime})^2}, \\ l=363.5890537^{\prime}\text{.} \end{gathered}[/tex]Answer: 363.5890537 ´.
Which number line shows the solutions to n -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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The expression
[tex]n<-3[/tex]means "n takes values less than -3 but without taking the 3", for the symbol <.
Then, the number line that shows the solutions of the expression is
Find quotient of 5,433 % 8
Answers
Find the quotient of 5,433 by 8.
8 | 5,433
Divide 54 by 8. The quotient is 6. 6x8 = 48. 54 - 48 = 6.
6
8 | 5433
-48
-------
63
63 by 8 is 7. 7x8 = 56. 63 - 56 = 7.
67
8 | 5433
-48
-------
63
-56
--------
73
73 by 8 is 9. 9x8 = 72. 73 - 72 = 1. The final step is:
679 <== Quotiet
8 | 5433
-48
-------
63
-56
--------
73
-72
-------------
1 <== Remainder