(i) The exponential growth model to predict the number of rabbits after 'x' years is [tex]A = 2e^{6.21460809842x}[/tex].
(ii) The number of rabbits at the end of 3 years will be 250000000.
A continuous exponential growth function is of the form [tex]A = Pe^{rt}[/tex], where A is the final amount, which was initially P, growing continuously at the rate of r, after a time of t years.
In the question, we are asked to construct an exponential model to predict the number of rabbits after 'x' years.
We assume the exponential growth model to be a continuous model, of the form [tex]A = Pe^{rt}[/tex], where A is the final amount of rabbits, which was initially P, growing continuously at the rate of r, after a time of t years.
The initial quantity of rabbits, P = 2.
Time, t = x years.
Substituting the values, we get:
[tex]A = 2e^{rx}[/tex] ... (i)
We have been told that after 1 year, the number of rabbits was 1000.
Thus, substituting A = 1000, and x = 1, we get:
[tex]1000 = 2e^{r*1}\\\Rightarrow 1000 = 2e^r\\\Rightarrow e^r = 1000/2 = 500[/tex]
Taking log on both sides, we get:
[tex]log_ee^r = log_e500\\\Rightarrow rlog_ee = log_e500\\\Rightarrow r = 6.21460809842[/tex]
Thus, the rate of growth, r = 6.21460809842.
Substituting r = 6.21460809842 in (i), we get:
[tex]A = 2e^{6.21460809842x}[/tex], which is the required model.
To find the number of rabbits at the end of 3 years, we put x = 3, in the above equation to get:
[tex]A = 2e^{6.21460809842*3}\\\Rightarrow A = 2e^{18.6438242953}\\\Rightarrow A = 2*125000000\\\Rightarrow A =250000000[/tex]
Thus, there would be 250000000 rabbits at the end of 3 years.
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please help urgently
Solving for y:
6y - 2x = 20
6y = 2x + 20
y = [tex]\frac{2x + 20}{6}[/tex]
y = [tex]\frac{2x}{6} + \frac{20}{6}[/tex]
y = [tex]\frac{1x}{3} + \frac{10}{3}[/tex]
Hope it helps!
Answer:
Step-by-step explanation:
6y - 2x = 20
-6 -6
-2x = 20 - 6y
divide both sides by -2
[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{20 - 6y}{-2}[/tex]
Dividing by -2 undoes the multiplication by -2.
[tex]x = \frac{20 - 6y}{ -2}[/tex]
Divide 20 -6 by -2
x = 3y - 10
Or
y = [tex]\frac{10}{3}[/tex]x +[tex]\frac{x}{3}[/tex]
a train started from Howrah to Allahabad and another train started from Allahabad for Howrah at the same time. The two trains reached their destinations in 9 hours
The speed ratio of the two trains is 4:3, that is, for every 4 hours that one train is delayed, the other is delayed 3.
How to find the speed ratio of the trains?To find the speed ratio of the trains we must do the following operation:
V1 = [tex]\frac{x}{t} = \frac{l - x }{9}[/tex]V1 = [tex]\frac{x}{l - x} = \frac{t}{9}[/tex]T = [tex]\frac{t}{9} = \frac{16}{t}[/tex]V2 = [tex]\frac{x}{t} = \frac{x}{12}[/tex]V1 : V2 = [tex]\frac{x}{12}[/tex]:[tex]\frac{x}{16}[/tex]Note: This question is incomplete because there is some information missing. Here is the complete information in:
A train started from Howrah for Allahabad another train started from Allahabad for Howrah at the same time. The two trains reached their destinations in 9hours and 16 hours respectively after they meet each other. Find the ratio of speed of the two trains.
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Find the simple interest.
$2000 at 6% for 6 months
The simple interest is $____
(Round to the nearest cent as needed.)
Answer:
I think it's 120 dollars sorry if i get it wrong but I am sure it is right tell me when you get the right answer byeeee.
A pair of ladders whose lengths are 4.2m and 5.6m are leaned onto a wall such that they reach the same height. The base of the longer ladder is 1.96 further away from the base of the wall then the base of the shorter ladder. The distance of the shorter ladder form the wall is:
Answer:
2.52 m
Step-by-step explanation:
let the height be h m.
let the shorter ladder be x m away from the base of wall.
(x+1.96)²+h²=5.6²
x²+h²=4.2²
subtract
(x+1.96)²-x²=5.6²-4.2²
(x+1.96+x)(x+1.96-x)=31.36-17.64
(2x+1.96)(1.96)=13.72
2x+1.96=13.72/1.96=7
2x=7-1.96=5.04
x=5.04/2=2.52
kerri said that the quotient of 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths /5 do you agree with Kerris reasoning?
Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct
How to interpret Kerris reasoning?The quotient is given as:
4.2/5
Kerris reasoning is that
4.2/5 is approximately 0.8
We start by calculating the actual value of the quotient 4.2/5
Using a calculator, we have:
4.2/5 = 0.84
Approximate to the nearest tenth
4.2/5 = 0.8
This means that Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct
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how do i write 4x+5y=20 in slope intercept form
Answer:
Y=mx+b
Step-by-step explanation:
The answer is y = -4/5x + 4.
We know the general form for slope intercept form is :
y = mx + c
The given equation is in standard form.
4x + 5y = 20
Bring 4x to the other side by subtracting 4x on both sides.
4x + 5y - 4x = 20 - 4x
5y = -4x + 20
Divide 5 on both sides to isolate the variable y.
5y x 1/5 = 1/5 x (-4x + 20)
y = -4/5x + 4
(2) Veena made 5 frocks of the same size out of 14 metres of cloth. How many metres of cloth did she use for each frock? Ans.
Answer:
2.8 metres each
Step-by-step explanation:
14/5
2.8
which equation shows that the Pythagorean identity is true for 0 = 180 degrees? select the equation that is in the form sin^2 0+cos^2 0=1
A. 0^2 + (-1)^2 = 1
B. 1^2 + 0^2 = 1
C. 0^2 + 1^2 = 1
D. (-1)^2 + 0^2 = 1
The equation in the form of the given expression is (0)² + (1)² = 1
Trigonometry identityAccording to some of the trigonometry identity
sin 0 = 0
cos 0 1
Given the expression below
sin^2 0+cos^2 0=1
This can also be expressed as:
(sin0)² + (cos0)² = 1
Substitute
(0)² + (1)² = 1
Hence the equation in the form of the given expression is (0)² + (1)² = 1
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The line 2x + 3y - k = 0 bisects the line segment joining the points A(4, -3) and B(-2, 5). Find the value of k.
Answer:
5
Step-by-step explanation:
The midpoint of segment AB is (1, 1).
Substituting these coordinates into the equation of the line,
[tex]2(1)+3(1)-k=0 \\ \\ 5-k=0 \\ \\ k=5[/tex]
Danni thinks of a number. She subtracts 2 then multiples the result by 8. The answer is the same as subtracting 5 from the number then multiplying by 16. What is the number did Danni think of?
Answer:
8
Step-by-step explanation:
let the number=x
8(x-2)=16(x-5)
divide by 8
x-2=2(x-5)
x-2=2x-10
2x-x=-2+10
x=8
What is the radius and diameter of the following circle?
Radius = cm
diameter= cm
The value of diameter and radius of circle is 7 cm and 3.5cm.
According to the statement
we have given that the a figure of circle and we have to find the radius and the diameter of the circle.
So, We know that the
The radius of a circle runs from its center to its edge, the diameter runs from edge to edge and cuts through the center.
Here from the figure it is clear that the
Diameter of circle = 7cm
and the radius of circle we have to find
So,
Radius of circle = Diameter /2
Substitute the values in it then
Radius of circle = 7cm /2
Radius of circle = 3.5 cm.
So, The value of diameter and radius of circle is 7 cm and 3.5cm.
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The equation 2x = 3y − 5 when written in slope-intercept form
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the problem want us to find:
[tex]\hookrightarrow \text {Slope-intercept form}[/tex]
What is the slope-intercept form:
[tex]\hookrightarrow \text {it is when the function has the y-variable isolated by itself to one side}\\\hookrightarrow \text{and everything else to the other side}[/tex]
Let's apply our knowledge:
[tex]2x =3y-5\\-3y=-5-2x\\y=\frac{2}{3} x+\frac{5}{3}[/tex]
Answer:[tex]y=\frac{2}{3} x+\frac{5}{3}[/tex]
Hope that helps!
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rearrange the equation a = 1/2 b to make b the formula
Answer:
b = 2a
Step-by-step explanation:
a = [tex]\frac{1}{2}[/tex] b ( multiply both sides by 2 to clear the fraction )
2a = b
Answer: b = 2a
Step-by-step explanation:
Original equation
a = (1/2) b
Multiply 2 on both sides
a * 2 = (1/2) b * 2
[tex]\Large\boxed{b=2a}[/tex]
Hope this helps!! :)
Please let me know if you have any quesitons
|x-4| if x>4 please answer
Step-by-step explanation:
if , X>4
---> y= x-4
if , X<4
---> y= -(x-4)
y= 4- X
because , the value of |x-4| is Always positive ....
Write an equation for the function graphed below
f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure. This can be obtained using the formula of f(x) = P(X)/Q(X) by vertical asymptotes and factors of the polynomial.
Write an equation for the function:Let where P(X) and Q(X) are polynomial function.
The function has the following:
From the given graph, we can say that the vertical asymptotes x = - 2 and x = 3, this means that at values of x = -3 or x = 2, the denominator becomes zero and the function becomes undefined.This means that, -3 and 2 are roots of the denominator. Thus, the equation of the denominator is:
⇒ Q(X) = (x + 2)(x - 3)
From the given graph, we can say that the zero is 3, P(X) has the factor (x - 3)
Let a be the leading coefficient of P(X)
⇒ P(X) = a(x - 1)
Now for finding the value of a we can rewrite the equation as,
⇒ f(x) = P(X)/Q(X)
⇒ f(x) = a(x - 1)/[(x + 2)(x - 3)]
⇒ f(0) = a(0 - 1)/[(0 + 2)(0 - 3)]
Since from the graph we can say that the y-intercept is (0, - 2), this means that when x = 0, y = -2, f(0) = - 2
⇒ - 2 = -a/[(2)(- 3)]
⇒ a = - 2 × 2 × 3
⇒ a = - 12
By putting a = -12 in f(x) we get,
⇒ f(x) = 12(x - 1)/[(x + 2)(x - 3)]
Hence f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure.
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Solve:|x-3|=7 pls answer
Answer:
x=10 and x=-4
Step-by-step explanation:
When the absolute value is all by itself on one side of the equation, the next step is to remove the absolute value bars. This will create TWO separate equations.
| x - 3 | = 7
x-3 = 7 This is one of the equations. Just straight up copied the equation but without the bars.
Here is the second equation:
x - 3 = -7
It is the left side copied, without the bars, but the right side has the opposite sign.
Solve these both separately to find the answers.
x-3=7 and x-3=-7
x=10 and x=-4
PLEASE HELP ASAP!
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1 4
Sample 2 1
Sample 3 9
How do the sample statistics compare to the population mean and standard deviation?
The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.
According to the statement
We have given that the A rancher’s herd of 250 sheep grazes over a 40-acre pasture.
And we have to find the how many sheep are grazing on each acre.
So, For this purpose If we assume that the sheep are equally distributed, to see how many sheep there are in each acre we just divide the number of sheep by the number of acres. So,
we have to find the average of number of sheep in per acre.
We know that
The total area of the rancher’s herd = 40 acre
The number of sheep grazes in the land = 250 sheep
Now, we have to find the Average number
Average number of sheep grazed in per acre = 250/40
Average number of sheep grazed in per acre = 6 approx.
So, The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.
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A company makes Japanese-style lunch boxes called bento boxes. Each bento box is a cube with-foot-long edges. The company ships the bento boxes in a container in the shape of a rectangular prism that measures feet by feet by feet. A manager correctly finds the volume of the container using a formula. An employee double-checks the calculation by packing the container full of bento boxes. Use the drop-down menus to explain how both volume calculations compare. Click the arrows to choose an answer from each menu. The manager can find the volume of the container using the formula Choose... The employee correctly determines that the container can be filled with Choose... bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the Choose... of one bento box. The volume found by using the formula is of bento boxes in the container. Y Choose... ▼ the volume of the total number
The volume of a container shows the amount of space that it has inside of it.
The use of bento boxes that has edges that are a foot long and the use of a rectangular-shaped container to ship it would have been more useful if the dimensions were provided.
How to calculate volume?Provided that the dimensions are provided, the formula that can be used to find the volume of a container is:
V = L × W × H
Where:
L= Length
W= Width
H= Height
It is worthy to note that your question is incomplete as you did not include the answer choices for how the manager found the volume of the container and other questions so a general overview was given.
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The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21 bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total numberof bento boxes in the container.
Sue has sourced four wholesalers from where she will buy most of her stock, including arrangements with two suppliers for 30 days credit, while the others are Cash on Delivery (COD).
She has purchased her store fittings and has $15000 of stock (Stock at Valuation - or SAV), with a further $10000 on 30-day credit). The business has an operating cash reserve of $20000.
How many wholesalers require terms of cash on delivery?
The difference between the total number of wholesalers and those that supply on 30-day credit, gives the number that require cash on delivery as 2
How can the question be analyzed to find the required number of wholesalers?The number of wholesalers Sue has sourced = 4
Terms of two suppliers = 30 days credit
Amount of stock Sue has = $15000
Amount of stock on credit = $10000
Operating cash reserve of the business = $20000
Required:
The number of wholesalers that require terms of cash on delivery
Solution:
Given that the number of wholesalers = 4
The number number of suppliers (wholesalers) that supply on 30-day credit = 2
Therefore;
The number of wholesalers that require terms of cash on delivery = 4 - 2 = 2
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2.
David swam 800 m in 20 minutes. Find his average speed in m/min.
Answer:
40 meters a minute
Step-by-step explanation:
800m - 20 min
800/20
40m-1 min
Alicia wanted to lose some weight, so she planned a day of exercising. She spent a total of 3 hours riding her bike and jogging. She biked for 12 miles and jogged for 12 miles. Her rate for jogging was 6 mph less than her biking rate. What was her rate when jogging?
Please answer asap thank you :)
Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:
[tex]v = \frac{12}{t}[/tex]
Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:
[tex]v + 6 = \frac{12}{3 - t}[/tex]
[tex]v = \frac{12}{3 - t} - 6[/tex]
Then:
[tex]\frac{12}{t} = \frac{12}{3 - t} - 6[/tex]
[tex]\frac{12}{3 - t} - \frac{12}{t} = 6[/tex]
[tex]\frac{12t - 36 + 12t}{t(3 - t)} = 6[/tex]
18t - 6t² = 24t - 36
6t² + 6t - 36 = 0
t² + t - 6 = 0
(t + 3)(t - 2) = 0. -> t = 2 hours.
Hence her jogging rate in mph is given as follows:
[tex]v = \frac{12}{2} = 6[/tex]
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As a cold front approaches the weather forecast over the next 5 days calls for the following temperatures In degrees Fahrenheit 12,5,18,8,2 which graph below represents the temperature over this 5 day period
The graph showing the temperature over the 5-day period will look exactly like the attached. On the y-axis, we have the Temperature and the x-axis the number of days.
What is the value of a Graph forecast?Graphs and charts are useful visual aids because they make information accessible and easy to understand.
Therefore, it is not unexpected that print and electronic media frequently employ graphs.
When data is displayed as a graph rather than a table, it can often be easier to understand since the graph might show a pattern or comparison.
What is the interpretation of the graph?The graph shows the forecasted data against the actual data. It is to be noted that the data for the actual 5-day temperatures are made-up to help the analyst understand the differences between the forecasted and the actual data.
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PLEASE HELP FAST (6 1/7 divided by x + 3 5/9) / 4 1/6 = 1 1/3 what is x
Answer:
0.524
Step-by-step explanation:
That is the answer not really sure tho
Asap help with this PLEASE
Answer:
124.5°
Step-by-step explanation:
Let the smallest angle be x. Then, the sum of the angles is an arithmetic sequence with first term x, common difference 7, and 8 terms.
Using the sum of an arithmetic series formula,
[tex]\frac{8}{2}(2x+(8-1)(7))=1080 \\ \\ 4(2x+49)=1080 \\ \\ 2x+49=270 \\ \\ 2x=221 \\ \\ x=110.5[/tex]
So, the third angle is 110.5+14=124.5
In the rectangular prism below, the length of MR is 9 feet, the length of RS is 12 feet, and the length of ST is 5 feet. What is the length of the line
segment drawn from point T to point M?
Answer:
a
Step-by-step explanation:
[tex]\sqrt{9^2 + 12^2 + 5^2}=\sqrt{250}=5\sqrt{10}[/tex]
Calculate the perimeter and area of this shape.
Perimeter =
Perimeter → 25cm
Area → 25.5cm²
Explanation:[tex]perimeter = > 2.5 \times 2 + 5.5 + 3.5 + 6 + 3 + 2 = 5 + 9 + 9 + 2 = 25[/tex]
[tex]area = > 3 \times \frac{1}{2} \times 2 + 3 \times 3.5 + 6 \times 2 = 3 + 12 + 10.5 = 25.5[/tex]
Will mark brainliest!
Answer:
Area under the graph = 6 sq.units
I've shown the complete calculation over the attached page
Select the correct answer. In the given diagram, . Prove: The transversal line intersects two parallel lines m and n with values of corresponding angles are congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6) Statements Reasons 1. given 2. alternate exterior angle theorem 3. ? vertical angles theorem 4. transitive property of congruence Which statement is missing in the proof? A. B. C. D.
Based on the given diagram (see attachment), the statement which is missing in the proof is: D. m∠7 ≅ m∠5.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
From the given diagram (see attachment), we can logically deduce that line m is parallel to line n (m || n) and a transversal line intersects both of them.
Based on these reasons, we can prove the following statements:
m || n (given)m∠1 ≅ m∠7 (alternate exterior angle theorem).m∠7 ≅ m∠5 (vertical angles theorem).m∠1 ≅ m∠7 (transitive property of congruence).In conclusion, we can logically deduce that the statement which is missing in the proof is m∠7 ≅ m∠5.
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Answer:
here you go
Step-by-step explanation:
The perimeter of a football field is 1040 feet. The length of the field is 120 feet less than 3 times the width. What are the dimensions of the field?
Answer:
length: 360 ftwidth: 160 ftStep-by-step explanation:
The perimeter formula and the given relation between length and width can be used to write and solve an equation for the field dimensions.
SetupLet w represent the width of the field. Then (3w-120) is the length of the field, and its perimeter is ...
P = 2(L +W)
1040 = 2((3w-120) +w)
SolutionDividing by 2 and simplifying, we have ...
520 = 4w -120
130 = w -30 . . . . . . divide by 4
160 = w . . . . . . . . . add 30
3w-120 = 3(160) -120 = 360 . . . the field's length
The dimensions of the field are 160 feet long by 360 feet wide.
The radius of a circle is 9.5 cm find the circumference to the nearest tenth
For circumference use C = 2πr because π is the ratio of Circumference to diameter and diameter is 2 x radius.
C = 2 x 3.142 x 9.5 cm ≈ 59.7 cm
Area of a circle is π x r² = 3.142 x (9.5 cm)² ≈ 283.6 cm²
The circumference of a circle with a radius of 9.5 centimeters is about 59.7 centimeters and the area of a circle with radius of 9,5 centimeters is about 283.6 centimeters.