Need some help on this problem please

(a) P = [tex](56035e^(0.3283t)) / (560 + 35(e^(0.3283t)-1))[/tex] (b) 345 panthers (c) 1.59 years (d) dP/dt = kP(1 - P/560), P(5) ≈ 373 panthers (e) 1.59 years.

(a) The logistic equation that models the population of panthers in the preserve is:

P = [tex](560P0e^{(kt)}) / (560 + P0(e^{(kt)-1}))[/tex]

where P0 is the initial population (35), k is the growth rate constant, and t is the time in years.

To solve for k, we can use the fact that after 2 years the population is 200:

200 =[tex](56035e^(2k)) / (560 + 35(e^{(2k)-1}))[/tex]

Solving for k, we get:

k = 0.3283 (rounded to 4 decimal places)

Therefore, the logistic equation is:

P = (56035e^(0.3283t)) / (560 + 35(e^(0.3283t)-1))

(b) To find the population after 5 years, we substitute t=5 into the logistic equation:

P = (56035e^(0.32835)) / (560 + 35(e^(0.32835)-1))

P ≈ 345 panthers (rounded to the nearest whole number)

(c) To find when the population reaches 280, we can solve the logistic equation for t when P=280:

280 = [tex](56035e^{(0.3283t)}) / (560 + 35(e^{(0.3283t)-1}))[/tex]

Solving for t, we get:

t ≈ 1.59 years (rounded to 2 decimal places)

(d) The logistic differential equation that models the growth rate of the panther population is:

dP/dt = kP(1 - P/560)

Using Euler's method with a step size of h=1, we get:

P(5) ≈ P(4) + hdP/dt(4)

P(4) = 345 (from part b)

dP/dt(4) = k345*(1 - 345/560) = 27.522

P(5) ≈ 345 + 27.522 = 373 panthers (rounded to the nearest whole number)

(e) The panther population is growing most rapidly when the growth rate is at its maximum, which occurs at half the carrying capacity (P=280). We can find the time by taking the derivative of the logistic equation and setting it equal to zero:

dP/dt = kP(1 - P/560)

0 = k280(1 - 280/560)

0.5 = 1 - 280/560

280 = 560/2

So, the panther population is growing most rapidly when P=280, which occurs at half the carrying capacity. Therefore, the time when the population is growing most rapidly is at t=1.59 years (from part c).

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Getting the correct answer in an online school environment can be achieved through a few methods:

Read the course materials carefully: Make sure you understand the material being covered before attempting to answer questions.

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Ask for help: If you are still having trouble finding the correct answer, don't be afraid to reach out to your instructor or classmates for help.

Use additional study materials: Consider using outside study materials such as textbooks, study guides, and online resources to help you better understand the material.

Remember, the key to success in online school is to stay organized, be proactive, and actively engage with the course materials and your classmates. Good luck!

Getting every answer in an online school course depends on several factors, including the format of the course, the resources available, and the instructor's teaching style. Here are some tips that may help:

Utilize course resources: Most online courses provide students with a variety of resources such as textbooks, lectures, discussion forums, and quizzes. Utilize these resources to gain a deeper understanding of the material.

Participate in discussions: Participating in online discussions can be an excellent way to get answers to questions you have about the course material. You can also collaborate with other students to gain a better understanding of the course content.

Ask the instructor: If you're still unsure about a particular topic, don't be afraid to reach out to your instructor for clarification. You can send an email, participate in virtual office hours, or use a discussion forum to ask questions.

Research outside sources: You can also conduct research outside of the course to supplement your understanding of the material. Search for reputable sources, such as academic journals, to gain a better understanding of the course content.

Form a study group: If you're taking the course with other students, consider forming a study group. Studying with others can be an effective way to get answers to questions you have and to collaborate on course assignments.

Remember, the key to getting every answer in an online course is to be an active and engaged learner. Utilize all the resources available to you and don't be afraid to ask for help when needed.

The measure of the angles are

1. 14°

2. 141°

3. 39°

4. 39°

The 4-letter code is DCAA

From the question, we ae to determine the measure of the angles and then the 4-letter code

From the diagram,

m ∠B + m ∠C = 180° (Sum of angles on a straight line)

Then,

1.

9x + 15° + 3x - 3° = 180°

12x + 12° = 180°

12x = 180° - 12°

12x = 168°

x = 168°/12

x = 14°

Thus, D

2.

m ∠B = 9x + 15°

m ∠B = 9(14) + 15°

m ∠B = 126° + 15°

m ∠B = 141°

Thus, C

3.

m ∠C = 180° - m ∠B

m ∠C = 180° - 141°

m ∠C = 39°

Thus, A

4.

m ∠A = m ∠C (Vertically opposite angle)

m ∠A = 39°

Thus, A

Hence, the code is DCAA

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Answer: 3 < c < 13   (choice C or third answer choice)

======================================================

Explanation:

Consider a triangle with sides: a,b,c

Furthermore, we'll have a = 5 and b = 8 as the two known sides.

Due to a modification of the Triangle Inequality Theorem, the third side will have the condition that:

b-a < c < b+a

where b ≥ a must be the case.

----------

Let's plug in those a & b values to determine the range for c.

b-a < c < b+a

8-5 < c < 8+5

3 < c < 13

This points us to Choice C as the final answer.

Answer: 9.43398113206

Step-by-step explanation:

A^2 + B^2 = C^2

5^2 + 8^2 = √89

= 9.43398113206

The surface area Sam needs to paint on the cylinder is  πx² + 2πxy i.e. B.

What exactly is a cylinder?

In geometry, a cylinder is one of the fundamental 3d forms with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.

Because the cylinder is a three-dimensional form, it has two primary properties: surface area and volume. The cylinder's total surface area (TSA) is equal to the sum of its curved surface area and the area of its two circular bases.

The volume of a three-dimensional cylinder is the space it occupies (V).

TSA=2πr²+2πrh, where r is the radius and h is the height.

Now,

Given that the radius of the roof is x feet and the silo is y feet high

Area of roof=πx² and

curved surface area=2πxy

then the surface area Sam needs to paint=πx²+2πxy

Hence,

        The surface area Sam needs to paint on the cylinder is

πx² + 2πxy.

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Exact:  1436.75504cm3

About: 1436.8cm3

pls mark brainliest if correct

The value of a + b + c is 42.

Let's set the arrival time of one of the mathematicians, let's say the first mathematician, to be t minutes after 9 a.m.

The likelihood that a second mathematician will show up while the first one is in the cafeteria is [tex]$ \frac{m}{60}[/tex], since the second mathematician has a [tex]\frac{m}{60} $-hour[/tex] window to arrive while the first is there.

⇒The probability that they arrive during some overlapping time is then [tex]$2\left(\frac{m}{60}\right)\left(1 - \frac{m}{60}\right)$[/tex]. This probability must be equal to 0.4.

⇒So we have the equation [tex]$2\left(\frac{m}{60}\right)\left(1 - \frac{m}{60}\right) = 0.4$[/tex].

⇒Solving for m yields [tex]$m = 24 - 4\sqrt{14}[/tex].

Therefore, the a + b + c = 24 + 4 + 14 =42.

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The midpoint of a line segment is the point located halfway between two endpoints.

Therefore, if the points and have the coordinates (x1, y1) and (x2, y2), respectively, then the coordinates of the midpoint, , are defined as:

[tex]M = (x1 + x2)/2, (y1 + y2)/2[/tex].

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Since we know the coordinates of the two points, we can calculate the slope of the line using the formula:

[tex]m = (y2 - y1)/(x2 - x1).[/tex]

Using the values of x1, y1, x2, and y2, we can calculate the slope of the line. We can then use the coordinates of and to calculate the y-intercept of the line, b.

Once we have determined the slope and y-intercept of the line, we can substitute these values into the equation of a line, y = mx + b, to determine the equation of the line.

The length of the line is equal to the distance between the two points and, for two points with coordinates (x1, y1) and (x2, y2), we can use the distance formula to calculate the length:

[tex]L = √((x2 - x1)^2 + (y2 - y1)^2)[/tex].

Substituting the values of x1, y1, x2, and y2 into this equation will give us the length of the line, which is equal to .

Therefore, the equation of the line and the length of the line are and , respectively.

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If the area to the right of a standard normal random variable z is 0.9803, the value of z is approximately -2.05.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. A normal distribution is a continuous probability distribution that is symmetric and bell-shaped, and it is often used to model many real-world phenomena.

A standard normal random variable, denoted by Z, is a random variable that follows a standard normal distribution. This means that the probability density function of Z is given by:

f(z) = (1/√(2*pi)) * e^(-z^2/2)

where pi is the mathematical constant pi (approximately 3.14159), e is the mathematical constant e (approximately 2.71828), and sqrt() represents the square root function.

The cumulative distribution function (CDF) of Z is given by:

F(z) = P(Z <= z) = integral from -infinity to z of f(x) dx

The CDF gives the probability that a standard normal random variable Z is less than or equal to a given value z.

To find the value of z for a given area under the curve, we use the inverse of the CDF. That is, we find the value of z that corresponds to a given probability or area under the curve. In this case, we were given an area to the right of z, so we first found the area to the left of z by subtracting the given area from 1.

Then, we used a standard normal distribution table or calculator to find the z-value that corresponds to this area. This is often denoted as the "z-score" for the given probability or area.

The z-score is a standardized value that tells us how many standard deviations a given value is from the mean of the standard normal distribution. In this case, a z-score of approximately -2.05 means that the value is 2.05 standard deviations below the mean of the standard normal distribution.

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Profitability ratios is a type of financial ratio shows the combined effects of liquidity, asset management and debt management of a business. So the statement is true.

Financial ratios are calculations used to assess various data to evaluate the company's performance. It is calculated using quantitative data from financial statements. There are mainly four financial ratios

So the statement given is true.

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The required scale factor used to dilate Figure A to make Figure B is 5/4.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges.

The ratio of the volumes of two similar pyramids is equal to the cube of the ratio of their corresponding side lengths. Therefore, the scale factor used to dilate Figure A to make Figure B is equal to the cube root of the ratio of their volumes:

scale factor = cube root of (volume of Figure B / volume of Figure A)

scale factor = cube root of (375 / 192)

scale factor = cube root of (125 / 64)

scale factor = 5/4

Therefore, the scale factor used to dilate Figure A to make Figure B is 5/4.

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The equation of line k is y = x + 1.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ 1 = 1

At data point (-4, -3), a linear equation of this line can be calculated in point-slope form as follows:

y - (-3) = 1(x - (-4))

y + 3 = x + 4

y = x + 1

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The proportion of resistors with resistances less than 90 Ω is 0.125, the mean resistance is 85 Ω, the standard deviation of the resistances is 8.66 Ω, and the cumulative distribution function of the resistances is 1/800x2−80x.

(a) The proportion of resistors with resistances less than 90 Ω is given by the integral of the probability density function f(x) from 80 to 90, which is 0.125.

(b) The mean resistance is given by the following formula:

Mean Resistance = [tex]∫x·f(x)dx[/tex]

Substituting the given equation for f(x) into this formula and integrating, we get the mean resistance to be 85 Ω.

(c) The standard deviation of the resistances is given by the following formula:

Standard Deviation = [tex]√∫(x−Mean Resistance)2·f(x)dx[/tex]

Substituting the given equation for f(x) and the mean resistance into this formula and integrating, we get the standard deviation of the resistances to be 8.66 Ω.

(d) The cumulative distribution function of the resistances is given by the following formula:

[tex]CDF(x) = ∫f(x)dx[/tex]

Substituting the given equation for f(x) into this formula and integrating, we get the cumulative distribution function to be [tex]1/800x2−80x[/tex] (where x is the resistance).

The proportion of resistors with resistances less than 90 Ω is 0.125, the mean resistance is 85 Ω, the standard deviation of the resistances is 8.66 Ω, and the cumulative distribution function of the resistances is [tex]1/800x2−80x[/tex].

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Answer:

28/35 and 25/35

Step-by-step explanation:

To find the equivalent fraction of 4/5 and 5/7 with a common denominator, we can find the least common multiple (LCM) of the two denominators. The LCM of 5 and 7 is 35. So, to get the equivalent fractions with a common denominator of 35, we can multiply both the numerator and denominator of each fraction by the same number so that the denominators become 35:

4/5 becomes 4 x 7/5 x 7 = 28/35

5/7 becomes 5 x 5/7 x 5 = 25/35

So, the equivalent fractions of 4/5 and 5/7 with a common denominator of 35 are 28/35 and 25/35, respectively.

Answer:

Step-by-step explanation:

[tex]\tt 12x=2y+7 \\ y=6-2[/tex]

Substitute y = 6x-2

[tex]\tt 12x=2\left(6x-2\right)+7[/tex]

[tex]\tt 12x=12x+3[/tex]

Cancel 12x from both sides:-

[tex]\tt {0=3}[/tex]

Since the sides are not equal, there's no solution.

___________________

Hope this helps!

The polynomial in standard form is:

F(x) = 2x³ - x² + 5x - 3

Option B is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The standard form of a polynomial is ax³ + bx² + cx + d.

A.

F(x) = -3 - x² + 2x³ + 5x

This is not in standard form.

B.

F(x) = 2x³ - x² + 5x - 3

This is in standard form.

C.

F(x) = -3 + 5x - x² + 2x³

This is not in standard form.

D.

F(x) = 5x + 2x³ - x² - 3

This is not in standard form.

Thus,

F(x) = 2x³ - x² + 5x - 3 is in the standard form.

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Answer:

congruent

Step-by-step explanation:

The opposite sides of a parallelogram are congruent.

We can also determine this from the markings in the diagram.

The part overlapped is showing the acute scalene triangles.

An acute scalene triangle can be defined as a triangle whose angles are less than 90 degrees and all three sides and angles are different in measurement.

Given that, in a graphic organizer, the left circle represents scalene triangles. The right circle represents acute triangles.

Here, we are asked to find that which figure belongs in the part of the organizer where the circles overlap,

In graphic organizers, the overlapped portion shows the common part between other portions.

Therefore, the common in both the triangles will be an acute scalene triangle,

Hence, the part overlapped is showing the acute scalene triangles.

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Answer:

To simplify the given expressions, we can use the property of exponents that states:

x^m * x^n = x^(m+n)

Using this property, we can simplify (x^4) (x^2) as:

(x^4) (x^2) = x^(4+2) = x^6

Similarly, we can simplify (x^3) (x^5) as:

(x^3) (x^5) = x^(3+5) = x^8

Therefore, (x^4) (x^2) and (x^3) (x^5) simplify to x^6 and x^8 respectively.

Answer:

Step-by-step explanation:

It is possible to use the exponents' property, which states:

x(m+n) = x^xm * xn)

This property allows us to simplify (x4) (x2) as follows:

(x^4) (x^2) = x^(4+2) = x^6

Similar to this, we can express (x3) (x5) as:

(x^3) (x^5) = x^(3+5) = x^8

As a result, (x4) (x2) and (x3) (x5) become x6 and x8, respectively.

Option B. 2 K is the correct graph (check the attached image) of parent function after transformation.

In mathematics, a transformation is a function that, typically with some geometrical foundation, maps a set X to itself, i. e. f: X → X. Vector space linear transformations are one example.

A point, line, or geometric figure can be changed in four different ways that are all collectively referred to as transformations. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.

A graph can be altered in three basic ways: by shifting, or compressing, and by flipping. According to the definition of transformation, we can rotate around any point, reflect our image over any line, and translate any vector. These are rigid transformations in which the image is consistent with its pre-image.

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The expression to represent the given scenario is 3x²-7. Therefore, option D is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, the sum of three times the square of a number and -7.

Let the unknown number be x.

Now, the expression is 3x²+(-7)

= 3x²-7

Therefore, option D is the correct answer.

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Answer: the third option

Step-by-step explanation:

Answer: A

Step-by-step explanation:

The change in the position of the minute hand should be matched with the angle made by the change as follows;

The minute hand moves from 2 to 9 = 7π/6 radians

The minute hand moves from 5 to 10 = 5π/6 radians.

The minute hand moves from 3 to 7 = 2π/3 radians.

The minute hand moves from 4 to 6 = π/3 radians.

The minute hand moves from 1 to 4 = π/2 radians.

In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Generally speaking, the angle between numbers that represents the hands on an analog clock is equal to π/6 radians.

When the minute hand moves from 2 to 9, we have:

Difference = 9 - 2 = 7

Angle = 7 × π/6 = 7π/6 radians.

When the minute hand moves from 5 to 10, we have:

Difference = 10 - 5 = 5

Angle = 5 × π/6 = 7π/6 radians.

When the minute hand moves from 3 to 7, we have:

Difference = 7 - 3 = 4

Angle = 4 × π/6 = 4π/6 = 2π/3 radians.

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a) The 95% confidence interval for the mean length of the skulls of this species of bird is (5.35, 6.01) cm.

b) The 95% confidence interval for the true standard deviation of the skull length of the given species of bird is (0.18, 0.40) cm.

(a) To find a 95% confidence interval for the mean length of the skulls of this species of bird, we can use the following formula:

mean ± (t-score * standard deviation / square root of sample size)

Where mean is the sample mean (5.68 cm), standard deviation is the sample standard deviation (0.29 cm), and sample size is the number of skeletons (10).

To find the t-score, we can use the t-distribution table for 9 degrees of freedom (sample size - 1). For a 95% confidence interval, the t-score with 9 degrees of freedom is 1.833.

Plugging in the values, we get:

5.68 ± (1.833 * 0.29 / √(10))

= 5.68 ± 0.33

So the 95% confidence interval for the mean length of the skulls of this species of bird is (5.35, 6.01) cm.

(b) To find a 95% confidence interval for the true standard deviation of the skull length of the given species of bird, we can use the following formula:

standard deviation / √(sample size) * t-score

Where standard deviation is the sample standard deviation (0.29 cm), and sample size is the number of skeletons (10).

To find the t-score, we can use the t-distribution table for 9 degrees of freedom (sample size - 1). For a 95% confidence interval, the t-score with 9 degrees of freedom is 2.306.

Plugging in the values, we get:

0.29 / √(10) * 2.306

= 0.11

So the 95% confidence interval for the true standard deviation of the skull length of the given species of bird is (0.29 - 0.11, 0.29 + 0.11) = (0.18, 0.40) cm.

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Answer:

B.10

Step-by-step explanation:

√2.√10.√5

√2.10.5

√100

√2².5²

2.5

10

Answer:

y = -1/4x + 2

Step-by-step explanation:

First you have to pick 2 points on the line, then you find the slope of the line from those 2 points. The slope formula is m = (y2-y1) / (x2-x1), and filling the variables in with the points (0,2) and (4,1) gives you m = (1-2) / (4-0), which gives you m = -1/4.

Once you have found the slope, you look for the y-intercept which is the point where the x-value is 0, and that is 2 in this graph.

You can then put this information into slope-intercept form, y= mx + b. m represents the slope and b represents the y-intercept. The answer is y = -1/4x + 2

Answer: a) The set W contains the zero vector, since (0,0,0) = (3s,-2s,s) for s = 0.

The set W is closed under addition and scalar multiplication:

If (3s1, -2s1, s1) and (3s2, -2s2, s2) are in W, then their sum, (3(s1 + s2), -2(s1 + s2), (s1 + s2)), is also in W.

If (3s, -2s, s) is in W and c is any scalar, then (3cs, -2cs, cs) is also in W.

The set W has a basis of {(3, -2, 1)}. To see this, we can write any vector in W as a scalar multiple of (3, -2, 1). For example, (3s, -2s, s) = s(3, -2, 1). The dimension of the set W is 1.

b) The set W contains the zero vector, since (t-2,0,6-3t) = (t-2,0,6-3t) for t = 2.

The set W is closed under addition and scalar multiplication:

If (t1 - 2, 0, 6 - 3t1) and (t2 - 2, 0, 6 - 3t2) are in W, then their sum, ((t1 + t2) - 2, 0, 6 - 3(t1 + t2)), is also in W.

If (t - 2, 0, 6 - 3t) is in W and c is any scalar, then (ct - 2c, 0, 6c - 3ct) is also in W.

The set W has a basis of {(1, 0, -3)}. To see this, we can write any vector in W as a scalar multiple of (1, 0, -3). For example, (t - 2, 0, 6 - 3t) = t(1, 0, -3) - 2(1, 0, -3). The dimension of the set W is 1.

c) The set H contains the zero vector, since (2b, a, 3b) = (0,0,0) for b = 0 and a = 0.

The set H is closed under addition and scalar multiplication:

If (2b1, a1, 3b1) and (2b2, a2, 3b2) are in H, then their sum, (2(b1 + b2), a1 + a2, 3(b1 + b2)), is also in H.

If (2b, a, 3b) is in H and c is any scalar, then (2cb, ca, 3cb) is also in H.

The set H has a basis of {(2,1,3)}. To see this, we can write any vector in H as a scalar multiple of (2,1,3). For example, (2b, a, 3b) = b(2,1,3) + a(0,1,0). The dimension of the set H is 2.

d) The set H contains the zero vector, since (−b + 2c, b, 4c) = (0,0,0) for b = 2c.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the product of the factors 3.78 and 9.2, we simply multiply them together:

3.78 × 9.2 = 34.776

Therefore, the product of the factors 3.78 and 9.2 is 34.776.