Differentiation question, please explain :)
The Logistic Law of Population Growth, first proposed by Belgian mathematician
Pierre Verhulst in 1837, is given by [tex]\frac{dN}{dt}= kN-bN^2[/tex], where k and b are constants.
Show that the equation [tex]N= \frac{KN0}{nMN0+(k-bN0)e^{-kt} }[/tex] is a solution of this differential equation (N0 is a constant).

Probability is the ratio of the desired outcomes to all possible outcomes.

If there are no desired outcomes, the ratio is 0 over all possible outcomes, thus 0.

If the event is all possible outcomes, the ratio is all possible outcomes over all possible outcomes, thus 1.

Probability can never be below zero or negative because desired outcomes can never be negative. If an event is impossible that means there are no desired outcomes meaning that probability is zero, thus couldn't fall below

Probability can never exceed 1 as desired outcomes can never be greater than total outcomes.

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Answer:

The statement is not true.

Step-by-step explanation:

[tex]\frac{3}{8} -\frac{2}{7} =\frac{2}{7} -\frac{3}{8}[/tex]

First, let us solve the left side.

[tex]\frac{3}{8} -\frac{2}{7} \\\\\frac{3*7}{8*7} -\frac{2*8}{7*8}\\\\\frac{21}{56} -\frac{16}{56}\\\\\frac{21-16}{56} \\\\\frac{5}{56}[/tex]

And now let us solve the right side.

[tex]\frac{2}{7}-\frac{3}{8} \\\\ \frac{2*8}{7*8}-\frac{3*7}{8*7} \\\\\frac{16}{56}-\frac{21}{56}\\\\\frac{16-21}{56}\\\\\frac{-5}{56}[/tex]

Therefore, it is clear that the left side is not equal to the right side.

∴ Left side ≠ Right side

∴ [tex]\frac{5}{56}[/tex] ≠ [tex]\frac{-5}{56}[/tex]

It depends if you mean

[tex]f(x) = \sin(x^2+2x-1)^2 = \sin^2(x^2+2x-1)[/tex]

i.e. the sine part is getting squared, or

[tex]f(x) = \sin(x^2+2x-1)^2 = \sin\left((x^2+2x-1)^2\right)[/tex]

i.e. the argument to sine is getting squared. I'll assume the first case, since it's fairly common convention to write [tex]g(x)^2 = \bigg(g(x)\bigg)^2[/tex].

Now if

[tex]f(x) = \sin^2(x^2+2x-1)[/tex]

• by the power and chain rules we have

[tex]f'(x) = 2 \sin(x^2 + 2x - 1) \left(\sin(x^2+2x-1)\right)'[/tex]

• using the derivative of sine and the chain rule again we have

[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) \left(x^2+2x-1\right)'[/tex]

• with the power and chain rules we have

[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) (2x+2)[/tex]

Recalling the double angle identity for sine,

[tex]\sin(2x) = \sin(x) \cos(x)[/tex]

we can rewrite the derivative among several other ways as

[tex]\boxed{f'(x) = (2x+2) \sin(2x^2+4x-2)}[/tex]

Answer:

postive

Step-by-step explanation:

im asian

For the graph of a linear function the slope of the line is positive, option A is correct.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Let the line is passing through points (-4, -1) and (0, 0)

m=1/4

The slope value is positive

Hence, for the graph of a linear function the slope of the line is positive, option A is correct.

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Answer: a≈6,1.

Step-by-step explanation:

                                 The sine theorem states:

                                [tex]\boxed {\frac{a}{sinA^0} =\frac{b}{sinB^0}= \frac{c}{sinC^0} }[/tex],             ⇒

[tex]a=\frac{c*sinA^0}{sinC^0}[/tex]

m∡A=180°-(m∡B°+m∡C°)

=180°-(68°+76°)

=180°-144°

=36°.           ⇒

[tex]a=\frac{c*sin36^0}{sin76^0}\\ =\frac{10*sin36^0}{sin76^0} \\\approx6,1.[/tex]

Good luck an' have a nice day!

Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 49 and 69 minutes is 0.8403 = 84.03%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 54, \sigma = 5[/tex]

The relative frequency of classical CDs with playing time X between 49 and 69 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 49, hence:

X = 69:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{69 - 54}{5}[/tex]

Z = 3

Z = 3 has a p-value of 0.9987.

X = 49:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{49 - 54}{5}[/tex]

Z = -1

Z = -1 has a p-value of 0.1584.

0.9987 - 0.1584 = 0.8403.

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The functions that have complex roots are b and d.

Complex roots are the imaginary root of polynomial functions. The complex roots are represented as α = a + ib, and β = c + id.

When the quadratic equation has a discriminant value less than zero will have imaginary roots.

Out of the given functions, a ,b, c, and d, the function with complex roots are b and d.

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Answer:

b &d is correct. i just took the test. :)

Step-by-step explanation:

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial is x³- 7x² - 6x + 72.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

The polynomial using the given information can be made as shown below.

Given the zeros of the polynomial are -3, 4, and 6.

P(x) = (x+3)(x-4)(x-6) = x³- 7x² - 6x + 72

To check the end behaviour of the function, the graph of the function can be plotted as shown in the below image.

Hence, the polynomial is x³- 7x² - 6x + 72.

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The possible values of x be  4.8, 5.6 and 6.4.

The statement of equality between two expressions consisting of variables and/or numbers.

Given:

5x -4y = 24

when y=0

5x = 24

x = 4.8

when y=1,

5x= 28

x= 5.6

when y=2,

5x= 32

x= 6.4

Hence, the possible values of x is 4.8, 5.6 and 6.4.

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

Explanation:

When going from f(x) to f(x-3), we replaced x with x-3.

Doing this shifts the xy axis 3 units to the left since each x input is three units smaller than before. If we had the f(x) curve fixed in place while the axis moves like this, then it gives the illusion of the curve moving 3 units to the right.

The +4 at the end adds 4 to each y coordinate to shift things 4 units up.

Answer:

I'm pretty sure the answer is 4

Step-by-step explanation:

Because SQ is 4 and it looks like QT is the same length

The ship traveled 80 miles in 4 hours while the submarine traveled 75 miles in 5 hours.

Based on the information provided, we can logically deduce that the ship is initially 80 miles away from its destination. Thus, f(x) would be equal to 0, if it traveled 80 miles and 0 miles away from its destination:

f(x) = 80 - 20x

0 = 80 - 20x

20x = 80

x = 80/20

x = 4 hours.

By critically observing the graph (see attachment) for the submarine's voyage, we can logically deduce the following:

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If [tex]t[/tex] and [tex]r[/tex] are inverse proportional to one another, then for some constant volume [tex]V[/tex] we have

[tex]V = tr[/tex]

It takes 45 min to empty a tank containing at 300 gal/min, so the tank contains

[tex]V = (45\,\mathrm{min}) \left(300\dfrac{\rm gal}{\rm min}\right) = 13500\,\mathrm{gal}[/tex]

of liquid.

If it's emptied at 500 gal/min, it would take

[tex]13500\,\mathrm{gal} = t \left(500\dfrac{\rm gal}{\rm min}\right) \implies t = \boxed{27\,\mathrm{min}}[/tex]

Answer:

4x + 3y = 12

Step-by-step explanation:

Answer:

4x + 3y = 12

Step-by-step explanation:

At x-intercept, y = 0.

∴ When we substitute y = 0 into the equation, x should equal 3.

• 1st equation:     3x + 4(0) = 12  ⇒  x = 4       ❌

• 2nd equation:  4x + 3(0) = 7    ⇒  x = 7/4    ❌

• 3rd equation:   3x + 4(0) = 7    ⇒  x = 7/3    ❌    

• 4th equation:   4x + 3(0) = 12   ⇒  x = 3       ✅

This means the 4th option is the correct one.

To check, we can replace x = 0 into the 4th equation to see if the y-intercept value comes out to be 4:

4(0) + 3y = 12    ⇒    y = 4     ✅

The angle for which the sine value is 0.6691 is found to be 42°.

What is the sine value?

A trigonometric function called sin x, where x is the angle under discussion stands for the sine of an angle. The sine function is the proportion between the perpendicular and hypotenuse of a right-angled triangle. In other words, the hypotenuse and its value change as the angle changes, and it is the ratio of the side opposite to the angle under discussion. In the study of physics, sound and light waves are represented by the sine function.

When the angle between a right-angled triangle's base and hypotenuse changes, the sine's value changes.

[tex]sin^{-1}(0.6691)[/tex]=41.99°≈42°

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Answer:

The third one of the first question.

√(x₂-x₁)² + (Y2 − 1)²

√(7-4)² + (11− 7)²

√(3)² + (4)²

√(9)+ (16)

√(25) = 5

Thus, CD = 5

Hope this helps!

The student product is 81936 greater than the correct product

The student was suppose to multiply 4552 by 157 but instead he multiplied 4552 by 175.

Therefore, let's find how much his product is greater than the correct product.

incorrect product = 4552 × 175 = 796600

Correct product = 4552 × 157 = 714664

Therefore,

difference = 796600 - 714664 = 81936

Therefore, his product is 81936 greater than the correct product.

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The required equation of the line is y = 5

The equation of a perpendicular line to a line in point-slope form is expressed as:

y-y1 = -1/m(x-x1)

m is the slope

(x1, y1) is any point on the line

Determine the slope

Slope = -3-3/2-2

y = ∞

Since there is no slope, hence the equation of the line will be in the form y = b

where b is the y-coordinate of the point. Hence the required equation of the line is y = 5

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Answer:

  x ≈ 0.499

Step-by-step explanation:

The value of x can be found by undoing the operations done to it.

The operations done to the variable are ...

We undo these operations in reverse order:

  7e^(2x) + 10 = 29 . . . . given

  7e^(2x) = 19 . . . . . . . . . subtract 10

  e^(2x) = 19/7 . . . . . . . . . divide by 7

  2x = ln(19/7) . . . . . . . . take the natural logarithm

  x = (ln(19/7))/2 . . . . . . divide by 2

The rounded result is ...

  x ≈ 0.499

We will see that the bison is faster, by 9.9 miles per hour.

We know that the deer's speed is:

D = 30 mi/h

The bison's speed is:

B = 3,520 ft/min.

We want to convert the second speed to miles per hour, then we can use:

1 hour = 60 min

1 mile = 5289 ft

So, to get the speed in miles per hour, we need to multiply by 60 and divide by 5289, we will get:

B = 3,520 ft/min = 3,520*(60/5289) mi/h = 39.9 mi/h

So we can see that the bison is faster, by 9.9 miles per hour.

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Answer:

Step-by-step explanation:

Can 10 people be divided into two groups with a ratio of 1 : 2?

Explain.

10 : 3 = 3.33

or 10 : 3 = 9 remaining 1

since it is not possible to divide a person into three parts, your answer is no

Answer:

Step-by-step explanation:

Answer:

Hence, 0.00000103 can be expressed as [tex]$1.03 \times 10^{-6}$[/tex].

Step-by-step explanation:

- Given 0.00000103

- Move the decimal point so that the factor is greater than or equal to 1 but less than 10 .

- Then count n and write no. as a product with a power of 10 .

Step 1 of 1

Consider 0.00000103,

1.03

Decimal has moved 6 places to right.

The power will be negative as the original no. is less than 1 .

[tex]$$\begin{array}{r}1.03 \times 10^{-6} \\0.00000103=1.03 \times 10^{-6}\end{array}$$[/tex]

the quotient will be:

[tex](f/g)(x) = \frac{|x + 20|}{x + 1}[/tex]

with x ≠ -1

For two functions f(x) and g(x), the quotient:

(f/g)(x) is equal to f(x)/g(x).

Here we have:

[tex]f(x) = |x + 20|\\\\g(x) = x + 1[/tex]

Taking the quotient, we get:

[tex](f/g)(x) = \frac{|x + 20|}{x + 1}[/tex]

Where we also need to add the restriction that x must be different than -1, as we can divide by zero.

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Answer:

$6.40

Step-by-step explanation:

let d be the cost of 1 doughnut and b the cost of 1 burger.

set up 2 equations and solve for b

9b + d = 31.3 → (1)

6b + 3d = 26.7 → (2)

multiplying (1) by - 3 and adding to (2) will eliminate d

- 27b - 3d = - 93.9 → (3)

add (2) and (3) term by term to eliminate d

- 21b + 0 = - 67.2

- 21b = - 67.2 ( divide both sides by - 21 )

b = 3.2

then

cost of 2 burgers = 2 × $3.20 = $6.40

Mean (m) = 498

Standard deviation (σ) = 12

Sample size (n) = 86

The probability that the sample mean would differ from Population mean by less than 494.7 watts

P(m - s < Z < m + s)

P(498-494.7 < Z < 498+ 494.7)

Using the Z formula :

Zscore = (x - m) / (σ/√n)

x = 498 - 494.7 = 3.3 , x = 498 + 494.7 = 992.7

Z = (3.3 - 498) / (12/√86) = -383.48

P(Z < -383.48)

Z = (992.7 - 498 ) / (12/√86) = 383.48

P(Z<383.48)

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Answer:

A , B, D

Step-by-step explanation:

YX is the segment joining points Y and X and is defined (A)

∠ XYZ is the angle between XY and YZ and is defined (B)

∠ YXZ is the angle between YX and XZ

However there is no segment joining XZ ← not defined

YW is the segment joining points Y and W and is defined (D)