biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2,000. the number of fish tripled in the first year. (a) assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years. p
(b) How long will it take for the population to increase to 1000? (Round your answer to two decimal places.)
yr

Answer:

Rotation then translation

Step-by-step explanation:

C on Edg2020

Answer:

c

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

add them all together and and divide by how many they are -thats the meaning of the mean

81+88+69+65+87=390

390divide by 5=78

i divided by 5 becasue there are 5 numbers

Answer:

B

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the right of a units

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

g(x) is f(x) shifted 3 units right and 1 unit up , then

g(x) = (x - 3)² + 1 → B

Answer:

The equation of the blue graph is \(g(x)=(x-3)^{2} +1\). Below is the explanation

Step-by-step explanation:

Given:

   The graph of f(x)=\(x^{2}\)

To find:

    The equation of the transformed graph g(x).

The red graph f(x) is moved right 3 units and up 1 unit to get g(x).

When graph is moved right 3 units , 3 should be subtracted with x.

When graph is moved up 1 unit, 1 is added at the end.

So, our g(x)=\((x-3)^{2} +1\)

The equation of the blue graph is \(g(x)=(x-3)^{2} +1\)

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Answer:

Step-by-step explanation:4

The mean of a binomial probability distribution with p = 0.32 and n = 150 is 48

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success, denoted by p. In the case of a binomial distribution with n trials and probability of success p, the mean, or expected value, is equal to the product of the number of trials and the probability of success, which is np.

In this case, the problem provides the values of p and n, which are p = 0.32 and n = 150, respectively. Therefore, the mean can be calculated by multiplying these two values

μ = np = 150 x 0.32 = 48

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Step-by-step explanation:

1 ounces equal to 28.35 grams

Apply stoichiometry

as in the picture uploaded

Answer:

Increase by 33.33,

Decreased by 25%,

Decreased by 10%,

Decreased by 20%,

9,

66dhs,

Probability is simply how likely something is to happen, so the probability of landing heads up on the next flip is 1/2.

The probability is obtained by dividing the total number of outcomes by the entire number of potential ways an event may occur. Odds are a separate concept from probability. The probability of an event happening is divided by the probability that it won't, and the result is the odds.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value among 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

P(H)= Probability of getting  head while flipping a coin is 1/2

and,

P(T)= Probability of getting  tail while flipping a coin is 1/2

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Answer:

Step-by-step explanation:

If sum of two angles are  90, then they are complementary angles

x = 90 - 51 = 39

Answer: She had left 54% of the money which is $1620.

Step-by-step explanation:

40% of $3000 = $1200

15% of $1200 = $180

$3000 - ($1200 + $180)

$3000 - $1380 = $1620

$1620 is the money she had left.

$1620 is 54% of $3000

She had 54% left of the money.

Hope that helped~!

The MATLAB commands polyfit, polyval and plot data is used .

To determine the cubic fit for the given data using MATLAB commands, we can use the polyfit and polyval functions. Here's the code to accomplish that:

x = [10 20 30 40 50 60 70 80 90 100];

y = [10.5 20.8 30.4 40.6 60.7 70.8 80.9 90.5 100.9 110.9];

% Perform cubic curve fitting

coefficients = polyfit( x, y, 3 );

fitted_curve = polyval( coefficients, x );

% Plotting the data and the fitting curve

plot( x, y, 'o', x, fitted_curve, '-' )

title( 'Fitting Curve' )

xlabel( 'X-axis' )

ylabel( 'Y-axis' )

legend( 'Data', 'Fitted Curve' )

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The complete question is :

Using the curve fitting technique, determine the cubic fit for the following data. Use the MATLAB commands polyfit, polyval and plot (submit the plot with the data below and the fitting curve). Include plot title "Fitting Curve," and axis labels: "X-axis" and "Y-axis."

x = 10 20 30 40 50 60 70 80 90 100

y = 10.5 20.8 30.4 40.6  60.7 70.8 80.9 90.5 100.9 110.9

A frustum is one of two pieces of a double cone divided at the vertex. A double cone is a three-dimensional shape that is created by connecting two cones with their vertices touching.

When the double cone is cut through the vertex, it creates two pieces known as frustums. A frustum has a circular base and a smaller circular top, which are parallel to each other. The height of the frustum is the distance between the two circular bases.

The volume of a frustum can be calculated using the formula V = (1/3)h(a^2 + ab + b^2), where h is the height, a is the radius of the larger base, and b is the radius of the smaller top. Frustums are commonly found in architecture and engineering, such as in the design of buildings and bridges.

A "napped cone" is one of two pieces of a double cone divided at the vertex. When a double cone is bisected through its vertex, it results in two identical, mirror-image napped cones. These geometric shapes have various applications in mathematics, engineering, and design due to their unique properties.

Napped cones share some characteristics with regular cones, such as having a circular base, but their pointed vertex is replaced by a flat plane where the double cone was divided. This creates a shape that is both symmetrical and easy to manipulate for various purposes.

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Answer:

7 minutes

Step-by-step explanation:

okay so lets make blocks = x and neighborhood = y

2x + y =10

2x + 4y = 31

multiply the top equation by -1 so we can single out y

-2x - y = -10

2x + 4y = 31

combine the two equations

3y = 21

since the x's have canceled each other out, just divide both sides by 3 to get a single y

y = 7

Answer: The answer is $13.19.

Step-by-step explanation:

1- Turn the percentage into a decimal by moving the percent sign twice to the left.

2- Multiply the bill by the decimal.

3-youll get 13.185 so you'll round up to 13.19.

hope this helps!!

We need to know about rate of change to solve the problem. The rate of change of population between 2002 and 2004 is -6.098% . The rate of change of population between 2002 and 2006 is -4.88%

The rate of change of something can be calculated by dividing the difference between the final amount and the initial amount by the initial amount. Rate of change is usually calculated as a percentage. We can calculate rate of change of population per year or between any two years. In this question we need to find the rate of change between 2002 and 2004 and also between 2002 and 2006. The initial population in 2002 is 82 and in 2004 it is 77.

rate of change between 2002 and 2004=\(\frac{77-82}{82}\)x100=\(\frac{-5}{82}\)x100=-6.098%

rate of change between 2002 and 2006=\(\frac{78-82}{82}\)x100=\(\frac{-4}{82}\)x100=-4.88%

Therefore the rate of change of population between 2002 and 2004 is -6.098% and the rate of change of population between 2002 and 2006 is -4.88%, the rate of change is negative because the population decreases.

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The required volume of the given composite space figure is 1512 \(cm^3\).

Given that, the rectangular pyramid fits exactly on top of a rectangular prism. The length of the prism is 18 cm, width is 6 cm and height is 9 cm. The length of the pyramid is 18 cm, width is 6 cm and height is 15 cm.

To find the volume of the composite figure formed by the rectangular pyramid on top of the prism, find the volume of prism and pyramid and then add it .

The volume of the prism is given by V1 = length × width × height.

The volume of the pyramid is given by V2 = length × width × height.

The volume of the composite figure is V = V1 +V2.

By using the given data and formula, find the volume of the prism,

Volume of prism V1 = length × width × height.

Volume of prism V1 = 18 × 6 × 9.

Thus, Volume of prism V1 = 972 \(cm^3\) .

By using the given data and formula, find the volume of the pyramid,

Volume of pyramid V2 = (length × width × height)/3.

Volume of pyramid V2 = (18 × 6 × 15)/3.

Thus, Volume of pyramid V2 =  1620/3= 540 \(cm^3\) .

By using above volumes, find the volume of the composite figure.

V = V1 +V2.

V = 972 + 540.

V = 1512 \(cm^3\) .

Hence, the required volume of the given composite space figure is

1512 \(cm^3\)

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Answer:

$840

Step-by-step explanation:

To do this, we can use our formula for solving percents. \(\frac{Part}{Whole}\) = \(\frac{Percent}{100}\)

The part here is $714 because this is only 85% of the original price which is the whole. Our whole in this problem will be x. As for the percent, we will write 85.

We now have \(\frac{714}{x}\) = \(\frac{85}{100}\)

To solve this, we use the rules of a proportion. 714 * 100 = 71,400 and then we will divide that by 85 to find x. x = 840

So, the original price was $840.

Answer:

Step-by-step explanation:

714  is 85%

the full price P is 100%

Using the ratio method

714 /85   =  P/100

TO find P cross multiply

85P = 714*100

85P = 71400

p = 71400/85  = $840

Ans yesterday's price = $840

or

85% of P = 714

.85*P =714

p = 714/.85

p = $840

Answer:

The equation of the line segment to the line segment with end point (4, 4) and (-8, 8) is y = x/3 - 4

Step-by-step explanation:

The coordinates of the given points are;

(4, 4) and (-8, 8)

Therefore;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Where;

y₁ = 4, y₂ = -8, x₁ = 4, x₂ = 8

Therefore, the slope, m of the given line segment = (-8 - 4)/(8 - 4) = -3

The slope of the perpendicular line segment = -1/m = -1/(-3) = 1/3

The mid point of the line segment with endpoint (4, 4) and (-8, 8) is given as follows;

\(Midpoint, M = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )\)

Therefore, the midpoint  = ((4 + 8)/2, (4 + (-8))/2) = (6, -2)

The equation of the perpendicular line segment in point and slope form is given as follows;

y - (-2) = 1/3 × (x - 6)

Which gives;

y + 2 = x/3 - 6/3 = x/3 - 2

y = x/3 - 2 - 2 = x/3 - 4

The equation of the line segment to the line segment with end point (4, 4) and (-8, 8) is y = x/3 - 4

Answer:

(x+6)^2 + (y-8)^2 = 10^2

or

(x+6)^2 + (y-8)^2 = 100

Step-by-step explanation:

Equation of a circle in standard form: (x-h)^2 + (y-k)^2 = r^2

(h,k) represent the center of the circle

h = -6

k = 8

r = the length of the radius

10^2 = 100

The length of the arc shown in red is 5π/4 metre

To find the length of the arc, we need to find the circumference of the circle, which we find with the following formula :

C = 2πr

where r  is the radius which is indicated in the image: .

so the circumference  is:

C = 2π(3)

C = 6π

This is the measure of the entire perimeter of the circle, it is the measure of the 360 ° arc.

Because we only want 30° of that 360 °, we divide the value of the circumference by 360 and multiply po 45:

30/360=0.125 of full circle,

L(arc)=0.125L=5π/4

The length of the arc is 5π/4 m

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Answer:

It is 64. Pls mark me as brainliest.

Step-by-step explanation:

You divide.

576÷9=64

576÷9

9÷9=1

64/1

or

64

There both the same.

Answer:

Reduce 576/9 to lowest terms

The simplest form of  

576 /9 is 64/1

Step-by-step explanation:

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 576 and 9 is 9

Divide both the numerator and denominator by the GCD

576 ÷ 9

9 ÷ 9

Reduced fraction:  

64 /1

Therefore, 576/9 simplified to lowest terms is 64/1.

The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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Answer:

12

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total number of students,

→ 100 students

No. of students were absent & failed,

→ 7 + 10

→ 17 students

No. of students totally passed,

→ 100 - 17

→ 83 students

No. of students passed in Science,

→ 80 students

No. of students passed in Mathematics,

→ 71 students

Then add both science and math,

→ 80 + 71

→ 151 students

No. of students passed in both subjects,

→ 151 - 83

→ 68 students

Therefore, the number of students who passed in both subjects are 68 students.

Total votes were casted in election are 4716

Given: The ratio of votes in favor to votes against in an election is 5 to 4. 2,620 votes are in favor.

To find: The total number of votes cast.

Let the number of votes against is 4x.

Given the ratio of votes in favor to votes against is 5 : 4

Then, the number of votes in favor is 5x.

According to the question, 2,620 votes are in favor.

So, 5x = 2,620x = 2,620/5x = 524

The number of votes against = 4x = 4 × 524 = 2096

The total number of votes cast = votes in favor + votes against= 2620 + 2096= 4716

Therefore, there were 4716 votes cast in the

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Answer: (1) C. 65 + 28H < 250

(2) 6

Step-by-step explanation:

Here is the correct question:

Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an

hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.

Let H represent the whole number of hours that the plumber works.

1) Which inequality describes this scenario?

Choose 1 answer:

A. 28 + 65H < 250

B. 28 + 65H > 250

C. 65 + 28H < 250

D. 65 +28H > 250

2) What is the largest whole number of hours that Anand can afford?​

Since the initial fee charged by the plumber is $65 and an hourly rate of $28, and Anand would like to spend no more than $250. This means that the addition of the initial fee plus the hourly fee based on number of hours worked will have to be less than $250. This can be mathematically expressed as:

= 65 + 28H < 250

That means option C is the correct answer.

Option B and D are incorrect because the greater sign was used but Anand doesn't want to spend more than $250 but the options denoted that he spent more than $250 which isn't correct.

2)'The largest whole number of hours that Anand can afford goes thus:

65 + 28H < 250

28H < 250 - 65

28H < 185

H < 185/28

H < 6.6

Therefore, the largest whole number of hours that Anand can afford is 6.

Answer: The Answer is 65+28H < 250 and the largest amount of hours is 6

Step-by-step explanation:

Answer:

Option A is correct

Step-by-step explanation:

The equation that the first option is talking about would be 5-X=-10

The perimeter of the trapezoid ABFE and the prove that the triangle ΔABC is an isosceles are as follows;

First question;

The perimeter of the trapezoid ABFE is 100 units

Second question;

The sides AB and BC in the triangle ΔABC are congruent, therefore, triangle ΔABC is an isosceles triangle

An isosceles triangle is a triangle that has two sides that have the same lengths.

The specified parameters are;

The segment joining the midpoints of the side \(\overline{AC}\) and \(\overline{BC}\) of the equilateral triangle ΔABC = EF

EF = 2·x + 8 and AB = 7·x - 2

The midsegment theorem applied to the triangle ΔABC indicates that we get;

EF = (1/2) × AB

Therefore; 2·x + 8 = (1/2) × (7·x - 2)

(1/2) × (7·x - 2) = 2·x + 8

7·x - 2 = 2 × (2·x + 8)

7·x - 2 = 4·x + 16

7·x - 4·x = 16 + 2 = 18

3·x = 18

x = 18/3 = 6

x = 6

EF = 2·x + 8

Therefore; EF = 2 × 6 + 8 = 20

EF = 20

AB = 7·x - 2

Therefore; AB = 7 × 6 - 2 = 40

AB = 40

AB = AC = BC (Definition of an equilateral triangle)

Therefore;

AC = BC = AB = 40 (symmetric property)

The midpoints E and F, indicates that we get;

AE = CE and BF = CF

AC = AE + CE and BC = BF + CF (segment addition property)

Therefore; AC = AE + AE = 2 × AE

40 = 2 × AE

AE = 40/2 = 20

BC = 2 × BF

40 = 2 × BF

BF = 40/2 = 20

The perimeter of the trapezoid ABFE, P = AB + BF + EF + AE

P = 40 + 20 + 20 + 20 = 100

Second question

The coordinates of the vertices of the triangle are;

A(1, 2), B(-5, 3), and C(-6, -3)

The lengths of the sides of the triangle found using the distance formula are;

AB = √((-5 - 1)² + (3 - 2)²) = √(37)

BC = √((-6 - (-5))² + (-3 - 3)²) = √(37)

AC = √((-6 - 1)² + (-3 - 2)²) = √(74)

The lengths of the sides AB and BC in the triangle ΔABC are the same, therefore, the triangle ΔABC is an isosceles triangle.

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