Populations that can be modeled by the modified logistic equation dP/dt = P(bP – a) can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.0015 and a = 0.44, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes. Initial population is 136 individuals Initial population is 659 individuals
a. Doomsday scenario: Population will exhibit unbounded growth in finite time
b. Population will trend towards extinction There is also a constant equilibrium solution for the population. Find this solution (note that the solution often is not a whole number, and hence unrealistic for population modeling).

The total number of seeds that Josiah would plant would be = nR×S

To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.

Let each row be represented as = nR

Where n represents the number of rows planted by him.

Let the seed be represented as = S

The total number of seeds he planted = nR×S

Therefore, the total number of seeds that was planted Josiah would be = nR×S.

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it's on twitch just search for ninja

Answer:

26 dimes and 52 nickles

Step-by-step explanation:

£293.25

If 1 euro is worth 0.85 pounds, the total of 345 euros is 0.85 times the value of a single euro. This is therefore 0.85 * 345, or £293.25.

The height of the plane is modeled by the linear equation:

height = 3000ft - 2000ft*t

If the rate at which the plane descends is constant, then the height is modeled by a linear equation.

We can write:

height = initial height - rate*time

We know that the initial height is 3000ft, and that the plane descends at ar ate of 2,000ft per minute, then we can write the linear equation:

height = 3000ft - 2000ft*t

Where t is the time in minutes.

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Complete question:

"an airplane 3,000 ft above the ground begin descending at a rate of 2,000 ft per minute​, which will be the height of the plane after t minutes?"

Answer:

Below,

Step-by-step explanation:

a. cos O = adjacent side/hypotenuse

= 88.3/117

= 0.75470

O = 41 degrees.

b. sin O = opposite side/hypotenuse

= 2.4/3.8

= 0.63158

O = 39 degrees

The appropriate critical value is -1.88 and the decision is to fail to reject the null hypothesis.

The null hypothesis (H0) states that the new drug is not superior to the one commonly prescribed. The alternative hypothesis (H1) states that the new drug is superior to the one commonly prescribed. We use the level of significance (α) as 0.03.

Given that:

The test statistic can be calculated using the following formula:

\(Z = (x - np) / \sqrt{(np(1 - p))}\)

Substituting the values, we get:

\(Z = (68 - 100(0.6)) / \sqrt{(100(0.6)(0.4)} )\)

Z = -1.86

The critical value of the z-distribution for a one-tailed test at a 0.03 level of significance is -1.88. Since -1.86 is not less than -1.88, we fail to reject the null hypothesis (H0). Therefore, there is not sufficient evidence to conclude that the new drug is superior to the one commonly prescribed at a 0.03 level of significance.

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The study of hypnosis and its relationship to hysteria was the starting point for the development of psychoanalysis by Sigmund Freud.

The study of hypnosis and hysteria in the late 19th century by Sigmund Freud and his contemporaries led to the development of psychoanalysis, a form of psychotherapy that emphasizes the role of unconscious thoughts and feelings in shaping behavior. Through his work with patients suffering from hysteria, Freud became interested in the idea that psychological conflicts could be traced back to early childhood experiences, and that these conflicts could be resolved through the exploration of unconscious thoughts and feelings. This eventually led to the development of psychoanalysis as a theory and practice for the treatment of psychological disorders.

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In linear equation, If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.

What in mathematics is a linear equation?

To describe the cost of attending n events, create an equation using function notation.

A 10 dollar entrance fee is required each time, and a further 2 dollars must be paid for each unique exhibit that a visitor chooses to visit.

The function, which would depend on n events, is

If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.

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Answer:

0.10 > 0.09  It is greater than. if im wrong plz tell me

Step-by-step explanation:

Answer:

Step-by-step by steo

Total number of students = n(P∪M)=100

                   Number of students who passed in physics= n(P)=55

                   Number of students who passed in maths= n(M)=67

                   Number of students who passed both physics and maths=n(P∩M)

                   ⇒n(P∪M)=n(P)+n(M)−n(P∩M)

                   ⇒100=55+67−n(P∩M)

                   ⇒n(P∩M)=122−100

                   ⇒n(P∩M)=22

Step - 2 : Find number of students who passed only in physics

                   Number of students passed in physics = 55

                   Number of students passed in physics and maths both = 22

                   ∴Number of students passed only in physics = 55−22=33

In the given right-angled triangle, the sine, cosine, and tan of the angle A are: sin A =0.88, cos A = 0.4705, tan A= 1.875

We have a right angles triangle ABC with AC as the hypotenuse and AB and AC as the other two sides.

Given, hypotenuse AC=34, side BC = 30, side AB = 16

∴From the formulae for evaluating sin, cos, and tan of an angle

sin A\(=\frac{opposite}{hypotenuse}= \frac{BC}{AC}=\frac{30}{34}=\frac{15}{17}=0.88\)     (1)

cos A\(= \frac{adjacent}{hypotenuse} =\frac{16}{34}=\frac{8}{17}=0.4705\)          (2)

tan A\(=\frac{OppositeSide}{AdjacentSide}=\frac{30}{16}=\frac{15}{8}=1.875\)           (3)

Thus sin A= 0.88, cos A= 0.4705, tan A= 1.875

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Answer:

141

Step-by-step explanation:

2*3=6

5*9=45

6*15=90

141

Answer:

add all the sides I guess...

Step-by-step explanation:

or you can break that figure into rectangles. then find their areas and later sum up all the areas and you'll have your area of this shape

Answer:

\(x = \frac{1}{4} y^{2} +3y+15\)

Step-by-step explanation:

Solution

As the focus is (7, -6), and

The directrix is x = 5,

so the parabola equation is

\((x-7)^{2}+[y-(-6)]^{2}=(x-5)^{2}\)

\(x^{2}-14x+49+y^{2}+12y+36=x^{2} -10x+25\)

\(4x=y^{2}+12y+60\)

\(x=\frac{1}{4}y^{2}+3y+15\)

{Points to focus distance and directrix are equal, to constitute a parabolic}

The equation of a parabola with a focus at (7, -6) and a directrix at x = 5 is, (x - 7)² = 4y + 24

The standard equation for a parabola with a focus at (p, q) and a directrix at y = k is given by:

(x - p)² = 4a(y - q)

Where a is the distance between the vertex and the focus, and k is the y-coordinate of the directrix.

In this case, the focus is at (7, -6), so p = 7 and q = -6. The directrix is at x = 5, so k = 5. To find the value of a, we need to determine the distance between the vertex and the focus, which is also the distance between the vertex and the directrix.

Since the directrix is a vertical line, the vertex must lie on the horizontal line halfway between the focus and the directrix. Therefore, the vertex has coordinates ((p + k)/2, q), which are ((7 + 5)/2, -6) = (6, -6). The distance between the vertex and the focus (or the directrix) is then |p - k|/2, which is |7 - 5|/2 = 1.

Substituting these values into the standard equation, we get:

(x - 7)² = 4(1)(y + 6)

Simplifying, we get:

(x - 7)² = 4y + 24

This is the equation of a parabola with a focus at (7, -6) and a directrix at x = 5.

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The equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

Given:

(1,-5) with slope m = -1

The standard slope intercept form is y = mx + c.

substitute m = -1 and (1,-5)

-5 = -1(1) + c

-5 = -1 + c

c = -4.

y = mx + c

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

y = -x - 4.

Therefore the equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

Therefore equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

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Answer:

x= 101

Step-by-step explanation:

Exterior angle of triangle states that the exterior angle of a triangle is the sum of the 2 opposite interior angles. This is abbreviated as 'ext. ∠ of ∆'. Thus using the exterior angle theorem,

x°= 64° +37° (ext. ∠ of ∆)

x°= 101°

x= 101

_____

Alternative method:

Let the third angle in the triangle be y°.

Since the sum of the angles in a triangle is 180°,

y° +64° +37°= 180° (∠ sum of ∆)

Simplify:

y° +101°= 180°

y°= 180° -101°

y°= 79°

The sum of the angles on a straight line is 180°.

x° +y°= 180° (adj. ∠s on a str. line)

Substitute y°= 79°:

x° +79°= 180°

x°= 180° -79°

x°= 101°

x= 101

False. The value of the sample mean is not static and can change with different data sets.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

False.

The value of the sample mean is calculated based on the data in the sample, and it can change if the data set from which the sample is drawn changes.

For example, suppose we have a population with a certain mean and take a random sample from that population to calculate the sample mean. If we take a different sample from the same population, we may get a different sample mean. Similarly, if we take a sample from a different population with a different mean, we will get a different sample mean.

Therefore, the value of the sample mean is not static and can change with different data sets.

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The 99% confidence interval for the population proportion is (0.257, 0.583).

(a) The point estimate of the population proportion of plants alive after the first month in the more humid environment is:

point estimate = x/n = 21/50 = 0.42

So, the point estimate is 0.42.

(b) To find the 95% confidence interval for the population proportion, we can use the formula:

confidence interval = point estimate ± z√(point estimate(1-point estimate)/n)

where z is the z-score corresponding to the desired confidence level, n is the sample size, and √ represents the square root.

For a 95% confidence level, z = 1.96 (from a standard normal distribution table).

Plugging in the values, we get:

confidence interval = 0.42 ± 1.96√(0.42(1-0.42)/50)

= 0.42 ± 0.127

= (0.293, 0.547)

So, the 95% confidence interval for the population proportion is (0.293, 0.547).

(c) To find the 99% confidence interval for the population proportion, we can use the same formula but with a different z-score.

For a 99% confidence level, z = 2.58 (from a standard normal distribution table).

Plugging in the values, we get:

confidence interval = 0.42 ± 2.58√(0.42(1-0.42)/50)

= 0.42 ± 0.163

= (0.257, 0.583)

So, the 99% confidence interval for the population proportion is (0.257, 0.583).

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Answer:

c) 12

Step-by-step explanation:

since on the bar graph 12 occurs the most that is the mode so hope this helps!

The particular solution that satisfies the differential equation and the initial condition f(0) = a is: f(x) = -sin(x) + C1x + a.

To find the particular solution that satisfies the differential equation f''(x) = sin(x) and an initial condition, we need to integrate the equation twice and apply the initial condition.

1. First Integration:

Integrating the differential equation f''(x) = sin(x) with respect to x once gives us:

f'(x) = -cos(x) + C1

where C1 is the constant of integration.

2. Second Integration:

Integrating f'(x) = -cos(x) + C1 with respect to x again gives us:

f(x) = -sin(x) + C1x + C2

where C2 is another constant of integration.

3. Applying the Initial Condition:

To apply the initial condition, we need to use the given information about the problem. Let's say the initial condition is given as f(0) = a, where 'a' is a specific value.

Substituting x = 0 and f(x) = a into the equation, we get:

a = -sin(0) + C1(0) + C2

a = 0 + 0 + C2

C2 = a

Therefore, the particular solution that satisfies the differential equation and the initial condition f(0) = a is:

f(x) = -sin(x) + C1x + a

In this particular case, the initial condition f(0) = a determines the value of the constant C2, which becomes C2 = a. The resulting particular solution incorporates the constant C1 from the first integration and the constant a from the initial condition.

Note that without a specific initial condition or boundary condition, the constants C1 and C2 remain arbitrary and can be adjusted to fit different situations or additional information if provided.

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The value of x in the triangle is equal to: A. 21.

In Mathematics, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the sides are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side).

Note: x is the side opposite to the 60° angle.

The side opposite to the 60° angle, x = 7√3 × √3

The side opposite to the 60° angle, x = 7 × 3

The side opposite to the 60° angle, x = 21 units.

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Answer:

I think it's D

Step-by-step explanation:

Answer:

I think it is C.

Step-by-step explanation:

I think it's C because the 2 is showing how long it took to get to the library.

Answer

The reflection rule for the coordinate of each edge of this triangle is

(x, y) becomes (y, x)

That is, the x-coordinate and y-coordinate change places.

Explanation

For this question, we can see that the original triangle is reflected across the line y = x.

And we know that, when you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. The coordinates, (x, y) after reflection across the line y = x becomes the point (y, x).

So, the reflection rule for the coordinate of each edge of this triangle is

(x, y) becomes (y, x)

That is, the x-coordinate and y-coordinate change places.

Hope this Helps!!!

Answer:

{-1, 2, 47}

Choice B

Step-by-step explanation:

Function is g(x) = x² - 2

Domain is the possible set of x values and range is the set of function values for that domain

Here Domain = {- 2, - 1, 7}. This means these are values for which the function value g(x) exists

(Note this is not the entire domain, only a subset of the domain)

At x = - 2, g(x) = (-2)² - 2 = 4 - 2 = 2

At x = - 1, g(x) = (-1)² -2 = 1 -2 = -1

At x = 7, g(x) = (7)² -2 = 49 - 2 = 47

These are the corresponding range values for the given domain

Both domain and range sets are expressed from lowest to highest so we get range of g(x) as

{-1, 2, 47}

Choice B

Answer:

see below

Step-by-step explanation:

7s + 8s - 6h

7  8 and -6 are coefficients

s and h are variables

We can combine like terms

15s -6h

15 and -6 are coefficients and

s and h are variables

Answer:

Variable Terms:  (Alphabets)

s and h

Constant terms:   (Numbers)

No constants

Coefficient terms:  (Numbers with alphabets)

7 , 8 and -6

Answer:

it's C

Step-by-step explanation:

2y=22............

The volume of the complex figure is determined as 66 ft³ .

The volume of the complex figure is calculated from the summation of volume of the triangle and the volume of the cuboid.

Volume of the cuboid is calculated as follows;

V = 6ft x 2 ft x 3 ft

V = 36 ft³

The area of the triangle is calculated as follows;

A = ¹/₂ x base x height

A = ¹/₂ x 10 ft x 2 ft

A = 10 ft²

The volume of the triangle is calculated as follows;

V = Aw

V = 10 ft² x 3 ft

V = 30 ft³

Total volume = 30 ft³ + 36 ft³ = 66 ft³

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The company survey 307 customers in order to get 98% confidence.

Sample proportion (p) = 0.5 (as no estimate is given)

α = 1 - 92% = 0.08.    Therefore, α/2 = 0.08/2 = 0.04

Z(α/2) = Z(0.04) = 1.751

Estimate = 5% = 0.05

Now, E = Z(α/2) * sqrt (p(1-p)/n)

n = (1.751/0.05)2 * 0.5 * (1-0.5)

n = 307

Hence, the company should survey 307 customers in order to be 98% confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who are over the age of forty.

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Answer:

  c. $350.24, the april balance plus the late fee

Step-by-step explanation:

You want to know the required total payment when the balance being repaid is $325.24 and a late fee of $25 is charged.

Arthur must pay both the balance due and the late fee. The total amount he must pay is ...

  balance + late fee = $325.24 +25.00 = $350.24

Answer:

see below

Step-by-step explanation:

Angle B is 100 degrees because vertical angles are equal

<B and angle X are same side interior angles and since AD and EH are parallel lines same side interior angles are complementary

B + X = 180

100 +x = 180

x = 180-100

x = 80