a sailing ship stopped at several islands, releasing one mating pair of goats onto each one. on the smallest island, the limited food supply could only support a total of 1500 goats. if their per capita growth rate is 0.5 per year, how many years will it take before the goat population on the smallest island reaches 1000?
Answers
After 6 years the population of goats on the small island reaches 1000.
What is per capita growth rate?It is the rate of increases of population per individual in the population. The term related to time period and entire population.
How to calculate the time to reach the maximum populationgiven, initial population of goat on the smallest island, N° =2,
after t years the population of goats on this island, N= 1000
the maximum goat carrying capacity of this island, K= 1500
per capita growth rate, r = 0.5 per year
now, we use logistic growth equation, dN/dt = r×N[(K-N)/K]
dN/dt = 0.5×1000{1500-1000)/1500}
dN/dt= 166.67
∫dN/166.67 = ∫dt
by integrating both sides
N/166.67 = t+c , where c is the
integration constant
at time t=0, N°=2
c= 0.012
N/166.67 =t+0.12
as N=1000 , t= 5.99 years
hence, after 6 years the population of goat on the island reaches 1000.
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Related Questions
Question below plz answer it fast!
Answers
Answer:
The answer is 49 .
Step-by-step explanation:
Do i need to explain ?
2. Colleen ordered a set of beads. She received 76 beads, and 50% of them were purple. How many purple beads did Colleen receive!
Answers
Math:
76 divided by 2 = 38.
A polling company has been hired to determine the approval rating for a local member of Congress. The company completed the poll by creating a survey and instructing representatives to stand outside a mall to give the survey to departing shoppers. The polling representatives were also instructed to take responses only from participants who were male. Then, the polling company published a report which put the congressperson's approval rating at 79%. Why could this sample be biased?
A. The representatives of the company were male.
B. The representatives of the company only gave the survey to a select group, as opposed to a wider, more representative sample.
C. The survey questions were biased toward the congressperson's opponent.
D. The mall was outside the congressperson's local area.
Answers
Answer:
The answer is B. The sample was biased because the survey was only given to a select group (the males). An unbiased sample would be a large group of random people (all genders included).
Answer:
B
Step-by-step explanation:
It is wat is is my boy
What are the Examples of Adding Fractions with Unlike Denominators
Answers
2/3 + 1/4 = 11/12
Fractions are very important in many areas such as math, physics, engineering, chemistry and many more, understanding how to add fractions with unlike denominators is a fundamental skill that will help you in many aspects of your life.
Adding fractions with unlike denominators can be a bit tricky, but with the right understanding and techniques, it's definitely doable.
When we add fractions with unlike denominators, we need to first find a common denominator. A common denominator is a number that is a multiple of both denominators. Once we have a common denominator, we can add the fractions as usual by adding the numerators and keeping the denominator the same.
Here are a few examples of adding fractions with unlike denominators:
2/3 + 1/4
We can find a common denominator by finding the least common multiple (LCM) of 3 and 4. The LCM of 3 and 4 is 12.
So, we can convert 2/3 to 8/12 by multiplying the numerator and denominator by 4.
We can convert 1/4 to 3/12 by multiplying the numerator and denominator by 3.
Now we can add the fractions by adding the numerators: 8/12 + 3/12 =
1/5 + 2/7
We can find a common denominator by finding the least common multiple (LCM) of 5 and 7. The LCM of 5 and 7 is 35.
So, we can convert 1/5 to 7/35 by multiplying the numerator and denominator by 7.
We can convert 2/7 to 10/35 by multiplying the numerator and denominator by 5.
So, we can convert 3/4 to 9/12 by multiplying the numerator and denominator by 3.
We can convert 1/3 to 4/12 by multiplying the numerator and denominator by 4.
Now we can add the fractions by adding the numerators: 9/12 + 4/12 = 13/12
So, 3/4 + 1/3 = 13/12
It's important to note that when adding fractions, it's also important to simplify the final result if possible.
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A common at-home workout that features high-intensity cardio, strength-building exercises, and focuses on total body fitness might be:____.
Answers
A common at-home workout that features high-intensity cardio, and strength-building exercises, and focuses on total body fitness might be a 21-day or 60-day "challenge". Thus, the correct option is C.
Body fitness may be defined as an ability of a person to perform daily physical activities with normal performance, endurance, and strength. This fitness assists the individual in the regulation of disease, fatigue, and stress and reduced inactive behavior.
People who performed high-intensity cardio, and strength-building exercises, in their home and focus on total body fitness must be actively involved in the 21-day or 60-day "challenge".
A 21-day or 60-day "challenge" would be self-selected by an individual in order to maintain their overall physical fitness.
Therefore, the correct option for this question is C.
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What is the Consistency Ratio of the GEAR Matrix? This question is related to BIKE and not fruit..So please use BIKE MATRIX.
What is the CR of Criteria?
Answers
A CR less than or equal to 0.1 is considered acceptable, indicating a consistent set of judgments in comparing the criteria. If the CR is greater than 0.1, it is advised to revise the pairwise comparisons to improve consistency.
The Consistency Ratio (CR) in the context of the GEAR Matrix (which is related to bikes, not fruit) measures the level of consistency in judgments made when comparing criteria in a decision-making process, such as the Analytic Hierarchy Process (AHP). To calculate the CR for the Criteria in the GEAR Matrix, follow these steps:
1. Determine the pairwise comparison matrix by comparing the importance of each criterion against the others.
2. Calculate the weights of each criterion by normalizing the columns and finding the average for each row.
3. Multiply the pairwise comparison matrix by the weight vector to obtain a new vector.
4. Divide each element of the new vector by its corresponding weight to obtain the Consistency Vector.
5. Calculate the average of the Consistency Vector to get the Consistency Index (CI).
6. Divide the CI by the Random Index (RI) for the specific matrix size (this value can be found in AHP literature) to obtain the Consistency Ratio (CR).
A CR less than or equal to 0.1 is considered acceptable, indicating a consistent set of judgments in comparing the criteria. If the CR is greater than 0.1, it is advised to revise the pairwise comparisons to improve consistency.
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A circle is centered at O. The tangent to the circle at P is extended to Q. Line segment QS intersects the circle at R. Given that OS = 2, SR = RQ = 3, and PQ = 6, find the radius of the circle.
Answers
The radius of the circle will be \(\sqrt{22}\).
In our question, we shall first extend QRS to the circle's point T.
According to the power of a point.
\(QP^{2}\) = QR*QT
\(6^{2}\) = 3*QT
QT = 12
Since QR = 3, RT = 9.
Since RS = 3, ST = 6.
Draw OT and OR, creating a triangle(TSO) and triangle(RSO).
OT and OR are radii, Let the radius be r.
Use the Law of Cosines on these two triangles.
OT2 = \(r^{2}\) = \(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)
OR2 = r2 = \(3^{2}\) + \(2^{2}\) - 2*3*2*cos(RSO)
Since these are equal:
\(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO) = \(3^{2}\) + \(2^{2}\) - 2*3*2*cos(RSO)
40 - 24*cos(TSO) = 13 - 12*cos(RSO)
Since angle(RSO) is supplementary to angle(TSO), cos(RSO) = - cos(TSO)
40 - 24*cos(TSO) = 13 + 12*cos(TSO)
27 = 36*cos(TSO)
0.75 = cos(TSO)
Since \(OT^{2}\) = \(r^{2}\) = \(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)
\(r^{2}\) = 40 - 24*0.75
\(r^{2}\) = 22
r = \(\sqrt{22}\)
Hence the radius of the given circle will be \(\sqrt{22}\).
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Which statements about the location of the point are true? Check all that apply.
The point is in the first octant.
The x-coordinate is 5.
The y-coordinate is positive.
The point lies below the xy plane.
The point lies to the right of the x-plane.
Answers
The statements about the location of the point that are true include:
The point is in the first octant.The x-coordinate is 5.The y-coordinate is positive.How to explain the informationThe point (5, 5) is in the first octant, has a positive x-coordinate, and a positive y-coordinate. It lies above the xy plane and to the right of the x-plane. Therefore, the following statements are true:
The point is in the first octant.
The x-coordinate is 5.
The y-coordinate is positive.
The point lies above the xy plane.
The point does not lie below the xy plane, so the statement is false:
The point lies below the xy plane.
The point does not lie to the left of the x-plane, so the statement is false.
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What is the solution to this system of equations?
y=1/3x+4
y=1/6x+3
Answers
All questions pertain to the simple (two-variable) linear regression model for which the population regression equation can be written in conventional notation as: Y₁ =B₁ + B₂X₁+1, equation I where Y, and X, are observable variables, ₁ and ₂ are unknown (constant) regression coefficients, and u, is an unobservable random error term. The Ordinary Least Squares (OLS) sample regression equation corresponding to regression equation (1) is Y=A₁ + A₂X₁ + ₁ equation 2 where , is the OLS estimator of the intercept coefficient ₁. A₂ is the OLS estimator of the slope coefficient , is the OLS residual for the i-th sample observation, and N is sample she (the number of observations in the sample). a) State the Ordinary Least Squares (OLS) estimation criterion (5 marks] b) Derive the OLS normal equations from the OLS estimation criterion. [10 marks]
Answers
The OLS estimation criterion states that the OLS estimators for the regression coefficients are chosen to minimize the sum of squared residuals, and the OLS normal equations are derived by setting the partial derivatives of the sum of squared residuals with respect to the coefficients equal to zero.
a) The Ordinary Least Squares (OLS) estimation criterion states that the OLS estimators for the regression coefficients, A₁ and A₂, are chosen to minimize the sum of the squared residuals, given by the equation:
min Σ(yᵢ - A₁ - A₂xᵢ)²
b) To derive the OLS normal equations, we differentiate the OLS estimation criterion with respect to A₁ and A₂, and set the derivatives equal to zero.
Taking the partial derivative with respect to A₁:
∂/∂A₁ Σ(yᵢ - A₁ - A₂xᵢ)² = -2Σ(yᵢ - A₁ - A₂xᵢ) = 0
Taking the partial derivative with respect to A₂:
∂/∂A₂ Σ(yᵢ - A₁ - A₂xᵢ)² = -2Σxᵢ(yᵢ - A₁ - A₂xᵢ) = 0
These equations are known as the OLS normal equations. Solving them simultaneously will give us the estimators A₁ and A₂ that minimize the sum of squared residuals.
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Tina needs to mix 2 gallons of water with one cup of iced tea mix to make the tea. Tina only has a 1 cup measure. How many cups of water does she need to make the iced tea?
A 4 cups
B 8 cups
C 16 cups
D 32 cups
Answers
Tina will need 32 cups of water to make the iced tea.
Determine If The Triangles Are Similar.If They Are,Choose The Reason Why.
Answers
Answer:
because they all have 3 corners
Each step in a procedure to solve this equation is shown. Find where the first error occurs. Given: 2(x - 4) = 8x + 16
step 1: 2x-8=8x+16
step 2: 10x-8=16
step 3: 10x=24
step 4: x=2.4
In which given step is the first error made?
a. From the Given to Step 1
b. From Step 1 to Step 2
c. From step 2 to Step 3
d. From Step 3 to Step 4
I'll give the right person brainlist!
Answers
Answer:
b
Step-by-step explanation:
It is B because he makes the error of adding 8x to 2x instead of subtracting 8x from 2x.
How is i 4 equal to 1?
Answers
The given expression is a complex expression and we can prove the given expression equal to 1 by using definition.
What is i in complex number?a+ib, often known as the generic form of complex numbers, is how complex numbers are expressed. In the complex numbers a+ib form, a represents the real component of the number, b represents the imaginary part, and i is defined as√(-1). Complex numbers can take a variety of shapes.
Write the general form of complex number.z=a+bi is the general form of complex number
As by definition
i^2=-1
So
i^4=(i^2)^2
=(-1)^2
=1
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find the $1314^{\text{th}}$ digit past the decimal point in the decimal expansion of $\dfrac{5}{14}$.
Answers
The $1314^\text{th}$ digit past the decimal point is 2.
To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.
The long division of $\frac{5}{14}$ is as follows:
```
0.35 <-- Quotient
-----
14 | 5.00
4.2 <-- Subtract: 5 - (14 * 0.3)
-----
80 <-- Bring down the 0
70 <-- Subtract: 80 - (14 * 5)
-----
100 <-- Bring down the 0
98 <-- Subtract: 100 - (14 * 7)
-----
20 <-- Bring down the 0
14 <-- Subtract: 20 - (14 * 1)
-----
60 <-- Bring down the 0
56 <-- Subtract: 60 - (14 * 4)
-----
40 <-- Bring down the 0
28 <-- Subtract: 40 - (14 * 2)
-----
120 <-- Bring down the 0
112 <-- Subtract: 120 - (14 * 8)
-----
80 <-- Bring down the 0
70 <-- Subtract: 80 - (14 * 5)
-----
...
```
We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.
Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.
So, the $1314^\text{th}$ digit past the decimal point is 2.
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write an equation of a line in slope intercept form that passes through (3,-2) and the slope is 1/6 then convert to standard form
Answers
Answer:
slope-intercept form: \(y=\frac{1}{6} x-\frac{5}{2}\)
standard form: \(x-6y=15\)
Step-by-step explanation:
To write an equation for the line with the only point as (3,-2) and the slope is \(m=\frac{1}{6}\) we use the slope-intercept formula \(y=mx+b\)
To convert an equation that is in slope-intercept form with fractions you have to multiply the denominator of each fraction on both sides of the slope-intercept form equation.
198.16 X 10 pls help
Answers
Answer:
1981.6
Step-by-step explanation: :))
Answer:
Step-by-step explanation:
Move the decimal point one side to the right when multiplied by 10
198.16 X 10 = 1981.6
8. Find (f+g)(x) if f(x) = 4x² - 5x and g(x) = 3x² + 6x - 4.
Answers
\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)
Here we go ~
\(\qquad \sf \dashrightarrow \: (f + g)(x)\)
\(\qquad \sf \dashrightarrow \: f(x) + g(x)\)
\(\qquad \sf \dashrightarrow \: (4 {x}^{2} - 5x) + (3 {x}^{2} + 6x - 4)\)
\(\qquad \sf \dashrightarrow \: 7 {x}^{2} + x - 4\)
if the diameter of a cone is 19 yd and the height is 13 yd . What is the volume?
Answers
If the diameter of a cone is 19 yd and the height is 13 yd, the volume of this cone is equal to 1,228 cubic yard.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
V represents the volume of a cone.h represents the height.r represents the radius.Radius = diameter/2 = 19/2 = 9.5 cm.
Substituting the given parameters into the volume of a cone formula, we have the following;
V = 1/3 × πr²h
V = 1/3 × 3.14 × 9.5² × 13
Volume, V = 1,228 cubic yard.
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PLEASE HELP ME I WILL MARK BRAINLIEST
Answers
Answer:the answer is solid B
Step-by-step explanation:
Oh your on edmentum I hate it there is so much work but I can help I'm a math master I'm top 3 smartest at math in my whole school.
Identify the shape that is graphed from the points:
A (4, 6)
B (4, 7)
C (8, 6)
D (8, 7)
Answers
Answer:
Rectangle
Step-by-step explanation:
It's a rectangle because opposite sides are parallel as you can see , it has 4 right angles , and it has 4 sides .. it's not a square because in a square all sides are equal
An animal shelter currently has 40 cats in it. Next month they expect the number of cats to increase by 15% over the number this month. Which of the following is the number of cats they expect next month? Show how you found your answer.
Answers
Answer:
46 cats
Step-by-step explanation:
40x15%
Ages of students 17,18,19,20,21,22
Number of students 2x,3x,4x-1,x,x-2,x-3.
The table above shows ages of 42 students in a class.
find the value of x
Answers
Answer:
x=4Step-by-step explanation:
total number of students=42
2x+3x+4x-1+x+x-2+x-3=42
12x-6=42
12x=42+6
12x=48
x=48/12
x=4
T/F: an example of a weight used in the calculation of a weighted index is quantity consumed in a base period.
Answers
False. The quantity consumed in a base period is not an example of a weight used in the calculation of a weighted index.
In the calculation of a weighted index, a weight is a factor used to assign relative importance or significance to different components or categories included in the index. These weights reflect the contribution of each component to the overall index value. The purpose of assigning weights is to ensure that the index accurately reflects the relative importance of the components or categories being measured.
An example of a weight used in a weighted index could be market value, where the weight is determined based on the market capitalization of each component. This means that components with higher market values will have a greater weight in the index calculation, reflecting their larger impact on the overall index value.
On the other hand, the quantity consumed in a base period is not typically used as a weight in a weighted index. Instead, it is often used as a reference point or benchmark for comparison. For example, in a price index, the quantity consumed in a base period is used as a constant quantity against which the current prices are compared to measure price changes.
Therefore, the statement that the quantity consumed in a base period is an example of a weight used in the calculation of a weighted index is false.
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Question 4: Optimization (25 points) Find the maximum and minimum of the following functions over the indicated interval: f(x)=−2x−1 over [−3,5]f(x)=x3−4x+10 over [−10,10]f(x)=xx2+1 over [1,4] Question 1: Inverse Functions ( 25 points) Find the inverse function of the following functions: - y=7x+4 - y=x−2x+1 - y=ex+5 - y=x3+2 Question 2: Concave/Convex Functions (25 points) Are the following functions convex or concave? Why?: - f(x)=x2−2x+2 - f(x)=5x31 - f(x)=3x3+2x+1 Question 3: Derivative of Functions ( 25 points) Differentiate the following functions with respect to x : - f(x)=6x5−2x15 - f(x)=x−23x−5 - f(x)=x5x+1 - f(x)=(x2+x+1)5ln(x+1)
Answers
The maximum value is 5 and the minimum value is -11.The maximum value is approximately 13.84 and the minimum value is -1040. The maximum value is approximately 0.8 and the minimum value is -0.333.
1. For f(x) = -2x - 1 over [-3, 5]:
- Take the derivative of f(x) with respect to x: f'(x) = -2.
- Set f'(x) equal to zero and solve for x: -2 = 0. There are no solutions, so there are no critical points.
- Since the interval is finite, we evaluate f(x) at the endpoints:
- f(-3) = -2(-3) - 1 = 5.
- f(5) = -2(5) - 1 = -11.
- Therefore, the maximum value is 5 and the minimum value is -11.
2. For f(x) = x³ - 4x + 10 over [-10, 10]:
- Take the derivative of f(x) with respect to x: f'(x) = 3x² - 4.
- Set f'(x) equal to zero and solve for x: 3x² - 4 = 0.
- x = 2/√3 or x = -2/√3.
- Since the interval is finite, we evaluate f(x) at the endpoints and critical points:
- f(-10) = -10³ - 4(-10) + 10 = -1040.
- f(-2/√3) ≈ 8.16.
- f(2/√3) ≈ 13.84.
- f(10) = 10³ - 4(10) + 10 = 960.
- Therefore, the maximum value is approximately 13.84 and the minimum value is -1040.
3. For f(x) = x/(x^2 + 1) over [1, 4]:
- Take the derivative of f(x) with respect to x: f'(x) = (x² + 1 - 2x²) / (x² + 1)².
- Set f'(x) equal to zero and solve for x: (x²+ 1 - 2x²) / (x² + 1)² = 0.
- x² + 1 - 2x² = 0.
- -x² + 1 = 0.
- x² = 1.
- x = ±1.
- Since the interval is finite, we evaluate f(x) at the endpoints and critical points:
- f(1) = 1 / (1² + 1) ≈ 0.333.
- f(-1) = -1 / (1² + 1) ≈ -0.333.
- f(4) = 4 / (4² + 1) ≈ 0.8.
- Therefore, the maximum value is approximately 0.8 and the minimum value is -0.333.
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can someone pls help me solve this
Answers
Using the congruency statement, select which statements are true.
Triangle W X Y is congruent to triangle E F G.
Segment W X is congruent to segment F G
Segment W Y is congruent to segment E G
Angle X is congruent to angle F
Angle G is congruent to angle W
what' s the answer? hurryyy
Answers
Answer:
Angle X is congruent to angle F
I hope it helps.
Answer:
B and C IT CORRECTCORRECT
Step-by-step explanation:
While driving at an average
velocity of 15.6 m/s down the
road, a driver slams on brakes to
avoid hitting a squirrel. The car
stops completely in 4.2 seconds.
What is the average acceleration
of the car?
Answers
The average acceleration is -3.71m/s². Any procedure where the velocity varies is referred to as acceleration.
What is acceleration ?Any procedure where the velocity varies is referred to as acceleration. There are only two ways to accelerate: changing your speed or changing your direction, or changing both. This is because velocity is both a speed and a direction.According to Newton's second law, a body's acceleration is the end outcome of all the forces that have been applied to it. The frequency at which a body's velocity changes is referred to as acceleration, a vector quantity.A vehicle accelerates in the direction of travel when it begins at a stop and moves at increasing speeds in a straight line.A linear acceleration is the acceleration of the car in the direction it is moving, and it causes the passengers to feel a force pushing them back into their seats. The acceleration that is used when shifting direction is known as radial acceleration.acceleration = change in velocity / Time taken
a = 0 - 15.6 / 4.2
= -15.6 / 4.2
= -3.71
The average acceleration is -3.71m/s²
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I need help with number one step by step quickly
Answers
Answer:
64
Step-by-step explanation:
We know that m<ABC is bisected. Hence, m<ABD = m<DBC.
Using the substitution property of equality, we can conclude that
8x - 14 = 2x + 10
Next, we shall solve for x, which is, and substitute 6 into one of the two equations. The correct answer is 32.
By multiplying 32 by 2, we shall arrive at the final answer, 64.
1/4 divided by 2 and 1/4 divided by 3
Answers
Answer:
1/4/2=1/8 1/4/3=1/12
"The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed."
Answer:
1/8 ; 1/12
Step-by-step explanation:
1/4 / 2 = 1/8
1/4 / 3 = 1/12