A model for the population in a small community after t years is given by P(t)=P0e^kt.
a)If the initial population doubled in 5 years, how long will it take to have tripled its initial population?
b)In addition, if the population of the community is 10,000 in 3 years, what was its initial population?

Answers

Answer 1

[tex]\bf \textit{Amount of Population Growth}\\\\ A=Ie^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}[/tex]

a)

so, if the population doubled in 5 years, that means t = 5. So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

[tex]\bf \textit{Amount of Population Growth}\\\\ A=Ie^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\to &2\\ I=\textit{initial amount}\to &1\\ r=rate\\ t=\textit{elapsed time}\to &5\\ \end{cases} \\\\\\ 2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r \\\\\\ \boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\ \textit{how long to tripling?}\quad \begin{cases} A=3\\ I=1 \end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}[/tex]

[tex]\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t \\\\\\ \cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t[/tex]

b)

A = 10,000, t = 3

[tex]\bf \begin{cases} A=10000\\ t=3 \end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I \\\\\\ 6597.53955 \approx I[/tex]

Related Questions

How many yards equals 765 inches?

Enter your answer, as a decimal.

Answers

The amount of yards that equals 765 inches is 21.25 yards.

One inch equals 0.0277778.
So, in order to see how many yards equals 765 inches, all you have to do is multiply 765 by 0.0277778.
765 * 0.0277778 = 21.25.

The correct answer is 21.25

Determine the slope and y-intercept of the line. y = 8.5x + 6

Answers

the slope is 8.5, the y-intercept is 6, y=mx+b was the original formula and m=slope and b=y-intercept :)

Answer: Slope = 8.5 and y-intercept = 6

Step-by-step explanation:

The intercept form of a linear equation is given by :_

[tex]y=mx+c[/tex], where m( coefficinet of x ) is the slope and c (constant term) is the y-intercept.

The given equation in intercept form : [tex]y = 8.5x + 6[/tex]

Here , the coefficient of c = 8.5

thus , the slope = 8.5

Also, the constant term = 6

Thus, the y-intercept =6

53 freshman were interviewed about the classes they were taking this semester 24 said they were taking science 22 said they were taking math 17 said they were taking English 7 said they were taking both science and math 10 said they were taking both math and English 4 said they were taking both math and English 2 said they were taking all three classes

Answers

The questions are:

How many students are not taking any science, math, or English? AND
How many students are taking exactly one of science, math, or English classes?

This is best answered using a Venn diagram. If you look at the separate areas, you see there are 7 areas.

The common area is the two students who takes the three classes.

4 said they were taking both math and English

4 – 2 = 2 only take math & English

7 said they were taking both science and math

7 – 2 = 5 only take math and science

10 said they were taking both science and English

10 – 2 = 8 only take science and English

17 said they were taking English

17 – (2 + 8 + 2) = 5 take only English

22 said they were taking math

22 – (2 + 5 + 2) = 13 take math

24 said they were taking science

24 – (2 + 8 + 5) = 9 only take science

Adding them all up:

2 + 9 + 13 + 5 + 8 + 5 + 2 = 44

So, 44 students are taking the 3 courses

53 – 44 = 9 students are not taking any of the 3 courses

5 + 13 + 9 = 27 take only 1 of these courses

Write an equation for the translation of y = |x| and the translation is up 4 right 2.

Answers

y = |x-2|+4

it is a negative 2 because you do the inverse

The base of a triangle is 7 inches more than its height. If the area of the triangle is 60 square inches, find the base and height of the triangle.

Answers

144.5 square cmWhat is the area of the triangle on the flag of Bosnia and Herzegovina?17.5 square unitsDetermine the area of the triangle.58.065 square metersWhat is the area of the triangle?576 square inchesJoseph is painting the flag of Brunei (a country in Southeast Asia) for a geography project at school. How many square inches will he cover with white paint?81 square ftAhmad just bought a used sailboat with two sails that need replacing. How much sail fabric will Ahmad need if he replaces sail A?14 inchesCindy made a triangular shaped sculpture with an area of 63 square inches. The height of the sculpture is 9 inches. What is the base length of the sculpture?80 square kilometersFind the area of the triangle.175 square centimetersFind the area of the triangle.28 square centimetersFind the area of the triangle.78 square metersFind the area of the triangle.9 square milesA wildlife conservation group buys a plot of land. How much land does it buy?1,620 square inchesFind the area of the triangle.1,125 square centimetersFind the area of the triangle.189 square millimetersFind the area of the triangle.132 square metersFind the area of the triangle.35 square centimetersFind the area of the triangle.105 square metersFind the area of the triangle.225 square feetFind the area of the triangle.1 acreYou live on a triangular piece of land with a base of 121 yards and a height of 80 yards. One acre of land is equal to 4840 square yards. Find the area of
your piece of land in acres.16 square feetYour neighbor adds a triangular section to his driveway with a base of 4 feet and a height of 8 feet. What is the area of the new section of driveway?2What is the area of a right triangle 2 cm by 4 cm?15What is the area of a right triangle 6 cm by 5 cm?10What is the area of a right triangle 5 cm by 4 cm?12What is the area of a right triangle 4 cm by 6 cm?1/2 base x heightWhat is the formula for the area of a triangle?6What is the area of a right triangle above?48What is the area of the rectangle above in cm^2?30What is the perimeter of the right triangle above?24How many cm is the perimeter of the triangle above?28What is the perimeter of the rectangle above in cm?Look at the drawing of a triangle within a rectangle. The triangle and the rectangle have the same base, b, and height, h.

If the area of the triangle is 48 square units, what is the total area of sections 1 and 2?48 sq unitsThe base (b) of the triangle is ____units.
The height (h) of the triangle is ____ units.

The area of the triangle is ____square units.3
5
7.5Triangle
Find the area of the triangle.

The area of the triangle is
_____ square units40Renee has a triangular garden with an area of 24 square feet. Which drawing shows Renee's garden?A triangular garden has an area of 9 square yards. Which figure could represent the garden?

James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f). Elapsed Time (seconds) Distance Traveled (feet) 1 6.2 2 12.4 3 18.6 4 24.8 Which of the following equations represents the relationship between the distance traveled and the elapsed ti

Answers

Table

Elapsed Time (seconds) Distance Traveled (feet)

1 6.2

2                                        12.4

3                                        18.6

4                                         24.8

Explanation:

You can check that 6.2 / 1 = 12.4 / 2 = 18.6 / 3 = 24.8 / 4 = 6.2

So, the relationship between the distance traveled and the time elapsed is a constant:

distance traveled / time elapsed = 6.2

n / f = 6.2

=> n = 6.2 f

Answer: n = 6.2 f

Answer:

n = 6.2f

Step-by-step explanation:

Given right triangle def what is the value of sin e

Answers

right triangle
10^2 - 8^2 = 100 - 64 = 36
DF = √36
DF = 6
so
sinE = Opp / Hypo
sinE = 6/10
sinE = 3/5

Answer:

Step-by-step explanation:

From the given triangle DEF, we have

[tex](EF)^{2}=(ED)^{2}+(DF)^{2}[/tex]

[tex](10)^{2}=(8)^{2}+(DF)^{2}[/tex]

[tex]100-64=(DF)^2[/tex]

[tex]DF=6[/tex]

Now, we know that SinE=[tex]\frac{Perpendicular}{Hypotenuse}[/tex], thus

[tex]SinE=\frac{DF}{EF}[/tex]

[tex]SinE=\frac{6}{10}=\frac{3}{5}[/tex]

Therefore, the value of SinE is [tex]\frac{3}{5}[/tex].

Andrew make six dollars an hour +9 dollars an hour for every hour of overtime overtime hours or any hours more than 40 hours for the week create an equation that shows amount of wages earned for working x hours no overtime

Answers

40hours×6($/hour)=$240.

The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is s(t) = -16t2 - 64t + 80, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground? (2 points)
Select one:
a. 256 ft/sec
b. -96 ft/sec
c. 0 ft/sec
d. 112 ft/sec

The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 4. (2 points)
Select one:
a. 24π
b. 16π
c. 64π
d. 20π

Answers

b. -96 ft/sec
For the first part, solve the equation you were given to find the time at which the height of the ball is 0. Sos(t) = -16t^2 - 64t + 800 = -16t^2 - 64t + 80
This is a standard quadratic equation that you can solve using the quadratic formula with a = -16, b = -64, and c = 80, so the roots are: 1 and -5.We can ignore the -5 root since that's what the situation would have looked like if we went back in time 5 seconds and launched the ball upwards from the ground. But since we're not doing time travel, the solution of interest is the 1. So the ball hits the ground one second after throwing it.The formula for distance under constant acceleration is d = 1/2 A T^2. That formula accounts for the -16t^2 term, so A is 32. So during that 1 second it takes for the ball to hit the ground, it will be accelerated 1 * 32 = 32 ft/sec. That is added to the initial velocity the ball was given. So at the moment it hits the ground it's going-64 ft/sec - 32 ft/sec = -96 ft/sec.
For the second problem, the key thing to note is "instantaneous rate of change". When you see that phrase you should immediately think "first derivative". So let's calculate the first derivative of the equation given.S(r)=2πrh+2πr^2S'(r)=2πh+4πr
Now substitute the value 4 for r, givingS'(4)=2πh+4π4 = 2πh+16π
And we have a problem. That value isn't one of the available options, so something is wrong. The problem is choice "b" takes into account the increase in surface area for the end caps on the cylinder, but it doesn't take into account the increase in surface area for the side of the cylinder which is what the 2πh term accounts for. Please show this to your teacher.

The instantaneous velocity of the ball when it hits the ground is found by deriving the height function and solving for the time of impact. The instantaneous rate of change of the surface area of a cylinder with respect to its radius when r = 4 is found by differentiating the surface area function and evaluating at r = 4.

The student's question involves two separate parts of physics and calculus related to kinematics and surface area calculations.

Part 1: Instantaneous Velocity of the Ball

The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is given by s(t) = -16t2 - 64t + 80. The instantaneous velocity when the ball hits the ground is the derivative of position with respect to time, s'(t), evaluated at the time t when s(t) = 0 (when the ball hits the ground).

First, we find t by solving -16t2 - 64t + 80 = 0. Then, we find the derivative s'(t) = -32t - 64 and evaluate it at the found time, which gives us the instantaneous velocity.

Part 2: Rate of Change of Surface Area

The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r) = 2πrh + 2πr2. The instantaneous rate of change of the surface area with respect to the radius, when r = 4, is the derivative dS/dr evaluated at r = 4. This is done by differentiating S(r) with respect to r and substituting r = 4 into the resulting expression.

Hi guys can I plz get some help I don't understand and can I plz get the answers so I can get a 4 on this paper thx

Answers

so, Deanna starts with 15 bucks in her pocket, and if she plays 1 game, she then has 15 - 0.75(1), if she plays two games, 15 - 0.75(2), if she plays 3, 15 - 0.75(3), if she plays say "g" amount of games, since each game costs 75 cents, then she would have after "g" games, 15 - 0.75(g) or 15 - 0.75g.

Now, Lise has 13 bucks and her game is 50 cents or $0.50, after say 3 games again she has 13 - 0.5(3) and so on, so after "g" games, she would have 13 - 0.5(g) or 13 - 0.5g.

When with both gals have the same amount?

[tex]\bf \stackrel{Deanna}{15-0.75g}=\stackrel{Lise}{13-0.5g}\implies 15-13=0.75g-0.5g\implies 2=0.25g \\\\\\ \cfrac{2}{0.25}=g[/tex]

and surely you know how much that is, since both quantities equal each other, then after that many games, both girls will have the same amount in their pocket.

Three weeks ago John bought stock at 49 ¼; today the stock is valued at 49 7/8. We could say the stock is performing at which of the following? A. Above par B. Par equality C. On par D. Below par

Answers

To answer this question, we will need to calculated the amount of profit or loss in the stock price.

To so this, we will subtract the original price from the current price as follows:
amount of profit/loss = 49.875 - 49.25 = 0.625

Therefore, the price of the stock increased after 3 weeks.
Based on this, the answer is:
(A) above par

A greeting card company can sell cards for $2.75 each, so the revenue can be calculated using the formula 2.75 Rx . The company’s total cost consists of a fixed overhead of $12,000 plus 35 cents per card, so the total cost can be calculated using the formula 0.35 12000 Cx .

a. Write the algebraic equation needed to determine when the company will break even (when the revenue will equal the cost).

b. Solve the equation from part a.

c. Write the algebraic inequality needed to indicate that the revenue is greater than the cost.

d. Solve the inequality from part c.

e. What does your answer from part d tell you about when the company will make a profit?

Answers

Given that the revenue equation is [tex]R(x)=2.75x[/tex] and the cost equation is [tex]C(x)=0.35x+12,000[/tex]

Part A:

At break-even the cost is equal to the revenue.

Thus, the algebraic equation needed to determine when the company will break even is given by

[tex]R(x)=C(x) \\ \\ \Rightarrow2.75x=0.35x+12,000[/tex]

Part B:

The solution to part A is given as follows:

[tex]2.4x=12,000 \\ \\ \Rightarrow x=5,000[/tex]

Part C:

The algebraic inequality needed to indicate that the revenue is greater than the cost is given by

[tex]R(x)\ \textgreater \ C(x) \\ \\ \Rightarrow2.75x\ \textgreater \ 0.35x+12,000[/tex]

Part D:

The solution to part C is given as follows:

[tex]2.4x>12,000 \\ \\ \Rightarrow x>5,000[/tex]

Part E:

The answer in part D tells us that the the company will make a profit when the produce more than 5000 cards.

What is the answer to this question ?

Answers

Hello there!

The formula to find the area of a trapezoid is:
A = [tex] \frac{a+b}{2} h[/tex]

Since we have everything, we just plug them in :)

A = [tex] \frac{3x+3x+4}{2} (x+2)[/tex]

A = (3x+3x+4)/2 (x) + (3x+3x+4)/2 (2)

A= 3x^2+2x+6x+4

A = 3x^2+8x+4

The correct answer is option A

I hope I helped!
Please feel free to ask me any additional questions about the answer.

A stone is thrown straight up from the edge of a roof, 675 feet above the ground, at a speed of 16 feet per second. A. Remembering that the acceleration due to gravity is -32 feet per second squared, how high is the stone 3 seconds later?

Answers

Final answer:

The stone would be 579 feet high after 3 seconds.

Explanation:

To calculate the height of the stone 3 seconds later, we can use the kinematic equation for position:

h = h0 + (v0 · t) + ((1/2) · a · t2)

where:

h is the final height

h0 = 675 feet is the initial height

v0 = 16 ft/s is the initial velocity

t = 3 seconds is the time

a = -32 ft/s2 is the acceleration due to gravity

Let's plug in the values and calculate:

h = 675 + (16 · 3) + ((1/2) · (-32) · 32)

Solving this equation, we get:

h = 675 + 48 - 144

h = 579 feet

A playground has two poles that are used for games. The first pole is 1.83 m tall. The second pole is 2.172 m tall.

How much taller is the second pole than the first pole?

Enter your answer in the box.
pls help, will matrk brainliest

Answers

The second pole is .342 m taller than the first pole.

Answer:

mark me brainliest plz im a beginner and the answer is .342 becuase the m ok lo, xd

Step-by-step explanation:

Let x be the total number of customers in a one-hour interval and y be the total number of female customers in the same interval. find the joint pmf of x and y.

Answers

The joint PMF of X and Y is [tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \cdot \frac{x!}{y!(x-y)!} \cdot \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad \text{for } y = 0, 1, \ldots, x \text{ and } x = 0, 1, 2, \ldots[/tex]

Distributions of X and Y

X is the total number of customers visiting the store in an hour, which follows a Poisson distribution with mean [tex]\lambda = 10[/tex]

[tex]P(X = x) = \frac{e^{-10} \cdot 10^x}{x!}, \quad x = 0, 1, 2, \ldots[/tex]

Given X = x the number of female customers Y follows a binomial distribution because each customer is independently female with probability [tex]p = \frac{3}{4}[/tex]

[tex]P(Y = y \mid X = x) = \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad y = 0, 1, \ldots, x[/tex]

Joint PMF of X and Y

To find the joint PMF P(X = x, Y = y, we use the law of total probability:

[tex]P(X = x, Y = y) = P(Y = y \mid X = x) \cdot P(X = x)[/tex]

Substitute the expressions for [tex]P(Y = y \mid X = x)[/tex] and P(X = x)

[tex]P(X = x, Y = y) = \left( \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y} \right) \cdot \left( \frac{e^{-10} \cdot 10^x}{x!} \right)[/tex]

Simplify the expression:

[tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}.[/tex]

You purchased 8 pounds 10 ounces of candy from a candy shop. You want to split it equally among 3 classrooms at a local school./7425116/3d9f02b9?utm_source=registration

Answers

they will each get 2 pounds and 7 ounces

If you have 8 punds and 10 oz then we would convert everything into one term/oz.

Since 16 oz are in a pund you would end up with a total of 138 ounces and divide that by 3 and you would get 46.

So each class of the 3 would get 46 ounces/oz.

whats the slope of (-3,-2) and (5,4)

Answers

Hello,

Slope is rise/run, or y/x, and if you are given two pairs of points, this is the equation needed: (y2-y1) over (x2-x1).

Let me plug in the numbers: (4-(-2) over 5-(-3). And that is 6/8, which then is simplified to 3/4. So the slope of those two given points is 3/4. We do not divide or simplify it into a decimal because slope is a fraction, so we leave 3/4 as it is.

Hope this helps, and that my explanation is not too confusing!

May

Hi there! To find the slope, we have to do y2 - y1/ x2 - x1. This means subtracting the first y-coordinate from the second y-coordinate and the first x-coordinate from the second x-coordinate. It would be set up like this: 4 - (-2) / 5 - (-3). When you do this, you get 6/8 or 3/4 in simplest form. There. The slope of the line is 3/4.

Jack has 5 craft sticks he needs four times that number for a project how many craft sticks does Jack need all together

Answers

Solving this problem simply only requires us the knowledge of multiplication.

So we are initially given that there are 5 craft sticks. So if we need four times that amount, that is written as:

5 x 4

Which is equal to 20

So Jack needs 20

Find the derivative of the function y = sin(tan 4x)

Answers

[tex]\bf y=sin[tan(4x)]\implies \cfrac{dy}{dx}=\stackrel{chain~rule}{cos[tan(4x)]\cdot sec^2(4x)\cdot 4} \\\\\\ \cfrac{dy}{dx}=4cos[tan(4x)]sec^2(4x)[/tex]

Please help guys im stuck. THanks

Answers

Angle 3 = 70 ( opposite angles equal each other)

Angle 1 = 90-70 = 20 ( angle 1 plus 70 = 90 )

angle 3 - angle 1 = 70 -20 = 50

Answer is B

A trampoline cost $220 and the sales tax is 6.25% what is the total cost of the trampoline

Answers

you will pay $233.75 when all said and done.

Answer:

$233.75Step-by-step explanation:

If <0 <90 and cos0=11/15 what is the value of sin (90-0)

Answers

check the picture below.

If z = f(x, y), where f is differentiable, and x = g(t) y = h(t) g(1) = 4 h(1) = 7 g' (1) = 5 h' (1) = −3 fx(4, 7) = 4 fy(4, 7) = 7 find dz/dt when t = 1.

Answers

[tex]z=f(x,y)=f(g(t),h(t))[/tex]

By the chain rule,

[tex]\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}[/tex]

but since [tex]z[/tex] is essentially a function of [tex]t[/tex] alone, we can the derivative more succinctly as

[tex]z'(t)=f_x(g(t),h(t))g'(t)+f_y(g(t),h(t))h'(t)[/tex]

[tex]z'(1)=f_x(g(1),h(1))g'(1)+f_y(g(1),h(1))h'(1)[/tex]
[tex]z'(1)=f_x(4,7)(5)+f_y(4,7)(-3)[/tex]
[tex]z'(1)=4(5)+7(-3)[/tex]
[tex]z'(1)=-1[/tex]

Final answer:

The derivative of z with respect to t (dz/dt) when t=1 is -1 using the chain rule for multivariable functions.

Explanation:

This problem uses the chain rule for multivariable functions. Given that z = f(x, y) where x = g(t) and y = h(t), to find dz/dt when t = 1, we apply the chain rule as follows: dz/dt=∂f/∂x *(dx/dt)+ ∂f/∂y * (dy/dt). Here, we have x=g(t), y=h(t), ∂f/∂x = fx(4, 7) = 4, ∂f/∂y = fy(4, 7) = 7, dx/dt = g'(1) = 5, and dy/dt = h'(1) = -3.

Substituting these values in: dz/dt = 4 * 5 + 7 * (-3) = 20 - 21 = -1. Therefore, dz/dt = -1 when t = 1.

Learn more about Chain Rule here:

https://brainly.com/question/34884272

#SPJ2

Lim x → 2 (x3 − 3x + 3) = 5 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1

Answers

[tex]\displaystyle\lim_{x\to2}(x^3-3x+3)=5[/tex]

is to say that for any [tex]\varepsilon>0[/tex], we can find [tex]\delta>0[/tex] that guarantees

[tex]|x-2|<\delta\implies|(x^3-3x+3)-5|<\varepsilon[/tex]

[tex]|(x^3-3x+3)-5|=|x^3-3x-2|[/tex]

Observing that [tex]x^3-3x-2\bigg|_{x=2}=8-6-2=0[/tex], the polynomial remainder theorem tells us that we can factorize the cubic to get

[tex]|x^3-3x-2|=|(x-2)(x^2+2x+1)|=|(x-2)(x+1)^2|=|x-2|(x+1)^2[/tex]

If we assume [tex]0<\delta\le1[/tex], we can set up a corresponding upper bound on the quadratic factor. We start with [tex]|x-2|<\delta[/tex], from which we have

[tex]|x-2|<\delta\le1\implies1\le x-2\le3\implies4\le x+1\le6\implies(x+1)^2\le36[/tex]

Now,

[tex]|x-2|(x+1)^2<36|x-2|<\varepsilon\implies |x-2|=\dfrac\varepsilon{36}[/tex]

which suggests that we can choose [tex]\delta=\min\left\{1,\dfrac\varepsilon{36}\right\}[/tex] to ensure that we arrive at the inequality [tex]|(x^3-3x+3)-5|<\varepsilon[/tex].

So, given [tex]\varepsilon=0.2[/tex], we would have

[tex]\delta=\min\left\{1,\dfrac{0.2}{36}\right\}=\min\left\{1,\dfrac1{180}\right\}=\dfrac1{180}[/tex]

If [tex]\varepsilon=0.1[/tex], we would take

[tex]\delta=\min\left\{1,\dfrac{0.1}{36}\right\}=\min\left\{1,\dfrac1{360}\right\}=\dfrac1{360}[/tex]

Marks brothers is paying a dividend of 56.25 on each share how much will PRH receive in dividends

Answers

Final answer:

To calculate the total dividend PRH will receive, multiply the dividend per share by the number of shares PRH owns.

Explanation:

To calculate how much PRH will receive in dividends, we need to know the number of shares PRH owns. Let's assume PRH owns X number of shares. We can multiply the dividend of $56.25 per share by the number of shares to find the total dividend PRH will receive.

Total Dividend = $56.25 x X

For example, if PRH owns 100 shares, the total dividend will be $56.25 x 100 = $5625.

Final answer:

Without knowing the number of shares PRH owns, we cannot calculate the total dividend payment. With the number of shares, multiply by the dividend per share ($56.25) to get the total dividends. For present value calculations, divide the PDV of profits by the number of shares to get the price per share.

Explanation:

To determine how much PRH will receive in dividends from Marks Brothers, a specific number of shares owned by PRH would be needed. Without this information, we cannot calculate the exact dividend payment to PRH. However, if we had the number of shares, we would multiply that number by the dividend per share, which is $56.25, to find the total dividend payment PRH would receive.

For example, if PRH owns 10 shares, the calculation would be 10 shares × $56.25 per share = $562.50 in total dividends. To understand the calculations surrounding the present value or PDV, consider that a different PDV calculation needs to be done for amounts received at different times. Once the PDV of total profits is calculated, it can be divided by the number of shares to find the price per share. Using the provided example with a total PDV of profits being $51.3 million and 200 shares, the calculation would be $51.3 million / 200 = 0.2565 million or $256,500 per share.

Note that in the real world, expected profits are estimates rather than exact figures, and determining an accurate interest rate is part of that estimation process.

The formula A=P(1+r)t is used to show the total amount owed for a loan with a simple annual interest rate.

Solve for r.

Answers

We are asked to express r in terms of A, P, and t.

We first divide both sides of the equation by t, which gives us

[tex]\displaystyle{ \frac{A}{t}=P(1+r) [/tex],

then, dividing both sides by P, we have

[tex]\displaystyle{ \frac{A}{Pt}=1+r [/tex].

Swap the sides:

[tex]\displaystyle{ 1+r= \frac{A}{Pt}[/tex]

Finally subtracting 1 from both sides gives us

[tex]\displaystyle{ r=\frac{A}{Pt}-1[/tex].

Answer: [tex]r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex]

Step-by-step explanation

Compound interest is the addition of interest to the principal sum of a deposit or a loan.

Let P = principal amount which was taken as a loan then the accumulated amount A is given by

[tex]A=P(1+r)^t[/tex].......(1)

where, r is the rate of simple annual interest in decimal.

t is the time applied for interest.

For solving r divide both sides of equation by P in (1),we get

[tex]\frac{A}{P}=(1+r)^t\\\Rightarrow(\frac{A}{P})^{\frac{1}{t}}=1+r\\\Rightarrow\ r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex].

What can a doctor use to determine a patient's body fat percentage?
Bioelectrical impedance machine
MRI machine
Waist measurement
Weight measurement

Answers

Bioelectrical impedance machine

Bioelectrical impedance machine can be used to determine a patient's body fat percentage

What is Fat percentage?

The body fat percentage of a human or other living being is the total mass of fat divided by total body mass, multiplied by 100

A doctor can use a bioelectrical impedance machine to determine a patient's body fat percentage.

This machine works by sending a small electrical current through the body and measuring how quickly it travels through different types of tissue.

Since fat and muscle have different electrical conductivity, the machine can estimate the amount of fat in the body based on the resistance to the current.

Hence, Bioelectrical impedance machine can be used to determine a patient's body fat percentage

To learn more on Fat percentage click:

https://brainly.com/question/14457888

#SPJ2

Is -2x+3y=6 parallel, perpendicular, or the same line as 2x-3y=9?

Answers

In order to figure this out, you need to get both y's by themselves. Not the most enjoyable thing in the world, but math rarely is. (Make sure to keep them seperate)

3y=2x+6     2x-9=3y
y=(2/3)x+2    y=(2/3)x-3
      Do these have the same slope? (number in front of the x)

If the slope is the same, then they are parallel, if one of them flipped and negative, then they would be perpendicular. That is what perpendicular is.-completely opposite.

Hope this helped. Any questions let me know.

1 mile is equal to 5280 feet. You've walk 0.20 mile on a track. How many feet have you watched?

Answers

0.20 is 1/5 of 1 mile, so a fifth of 5,280 feet would be 1,056

I had that like on my pre test in 5th grade I think that's math right

Other Questions

Which term describes the area behind the membranous lining of the abdominopelvic cavity? Concepts like noble and beggar are not connected with wealth or poverty, but rather with qualities of the inner person. true a gallon of chocolate milk sells for $3.14. a snack-size bottle of chocolate milk sells for 3 cents per ounce. which is a better buy? clarice drove the same distance on each of 4 days. Then on the fifth day she 48 miles more for a total of 828 miles. How many miles did she drive on each of first 4 days? help!Which constitutional power was inspired by the passage below?the passage below is from a historical document."He has kept among us, in times of peace, standing armies without the consent of our legislatures."(Source: U.S. National Archives and Records Administration)A: The President has the power to make treaties with the advice and consent of the Senate.B: Congress has the power to declare war and to raise and support armies.C: The government can house soldiers during times of war and peace.D: The President has the sole power to declare war. Find x if et = 3x+2 and em = 5x What is the solution to the system of equations below? 2x - 5y = 11 and -2x + 3y = -9 A Portuguese man-of-war is an example of ____.A. an anthozoan.B. a sea anemone.C. a hydrozoan colony.D. a large scyphozoan I really need help!!TJ, Max, and Misha are all the same age. The sum of their ages is s years. How old was TJ eight years ago?Thanks! An object's position is given by x(t) = 5 + 10 t 2. what is its acceleration after 5 s If you observed pathological lung sections, record your observations. also record how the tissue differed from normal lung tissue. complete the table below using your answers. The youthful, beardless jesus, depicted in the catacomb of commodilla, holds a book to emphasize his role as Simplest form 1/8 x 20= The relatively faster growth rate of non-european groups is due to a higher birthrate among some of these groups and to greater immigration. a. True b. False What is the domain and range of f(x) = |x + 6|?domain: (negative infinite,infinite); range: f(x) (greater than or equal to) 0domain: x (less then or equal to)-6; range: (negative infinite,infinite)domain: x(greater than or equal to)-6 ; range: (negative infinite,infinite)domain:(negative infinite,infinite) ; range: f(x) (less than or equal to) 0 How did Stalin use propaganda to control the Soviet Union? How did the experiences of the colonies shape Americas political and social ideals The temperature of a sample of water is changed from 10C to 30C. The same change in Kelvin would be A)20 B)100 C)273 D)303 Which three statements would produce the truth value F when p is true and q is false?A. p -> qB. ~p/\~qC. p->~qD. q\/~pC. p/\~qplease help Giorgio memorizes the german poem "the erlking" to recite in his eighth grade german class. he remembers it well for weeks after the presentation, but gradually his ability to recite the poem fades. this is an example of ________, one of the seven sins of memory. Steam Workshop Downloader