The population size P(t), modeled by a logistic equation, is evaluated from the equation P(t) = 120 cekt +1 = = = a. [15 pts) Find the population at time t = 0 if it observed that x(2) = 10 and x(6) = 20. b. [5 pts) How long will it take for the population size to become five times the initial population?

According to the Mean-Value Theorem, there exists at least one point in the interval where the derivative of the function is equal to the average rate of change of the function over that interval.

The Mean-Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that the derivative of the function at c is equal to the average rate of change of the function over the interval [a, b].

In this case, the function f(x) = 2x^3 - 5x + 7 is a polynomial function, and it is continuous and differentiable for all real values of x. Therefore, we can apply the Mean-Value Theorem to this function. To find the point(s) guaranteed to exist by the theorem, we need to calculate the average rate of change of the function over the interval [a, b] and then find the derivative of the function. By equating the derivative to the average rate of change, we can solve for the value(s) of c.

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Answer: 0.67%

Step-by-step explanation:

Answer: A, B, C.

If the stack of cards are shifted so it is not straight, it still has everything the same.

Answer:

if you have a total of 679 peaches and you split them up into 4 different groups, you will have 169 whole peaches in each but you'll have .75 of a peach left over.

Step-by-step explanation:

=(a+a+a+a+a+a)

= 6a

=(5x+−4x+10x)

= 11x

=(9t+3t+−6t)

= 6t

=(−5j+11j+j)

= 7j

a)= 6a

b)= 11x

c)=6t

d)= 7j

(a) At t = 1.11 s, the distance from the particle to the origin is 3.15 m. (b) The speed of the particle at t = 1.11 s is 1.86 m/s. (c) The magnitude of the acceleration at t = 1.11 s is 0.32 m/s². (a) At t = 3.4 s, the x-coordinate of the particle is 11.56 m. (b) The y-coordinate of the particle at t = 3.4 s is 17.14 m. (c) The speed of the particle at t = 3.4 s is 4.48 m/s.


(a) To find the distance from the particle to the origin, we use the formula for the magnitude of a vector: distance = √(x² + y²). Plugging in the given values at t = 1.11 s, we calculate the distance to be 3.15 m.
(b) The speed of the particle can be found by taking the magnitude of its velocity vector: speed = √(v_x² + v_y²). Plugging in the given values at t = 1.11 s, we calculate the speed to be 1.86 m/s.
(c) The magnitude of the acceleration can be found using the formula: magnitude of acceleration = √(a_x² + a_y²). Plugging in the given values at t = 1.11 s, we calculate the magnitude of the acceleration to be 0.32 m/s².
For the second scenario, the x-coordinate at t = 3.4 s can be found by plugging the given values into x(t) = a*t + b, which gives us 11.56 m. Similarly, the y-coordinate at t = 3.4 s can be found using y(t) = c*t² + d, which gives us 17.14 m. The speed of the particle at t = 3.4 s can be calculated using the same method as in (b), resulting in a speed of 4.48 m/s.

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.

Dimensions of outdoor vegetable garden = 2 m × 2 m

Storm rainfall = 0.8 inches of rain

Time of storm = 1 hr(

a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:

Rainfall flux = (Amount of rainfall) / (Area × Time)

Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:

Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)

Converting inches to meters, we get:

1 inch = 0.0254 m

Therefore,

Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr

Converting the rainfall flux to other units:

In kg/hr:

1 kg of water = 1000 g of water

Density of water = 1000 kg/m3

So, 1 m3 of water = 1000 kg of water

So, 1 m2 of water of depth 1 m = 1000 kg of water

Therefore, 1 m2 of water of depth 1 mm = 1 kg of water

Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr

In lbs/hr:

1 lb of water = 453.592 g of water

So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr

In liters/hr:

1 m3 of water = 1000 L of water

So, 1 m2 of water of depth 1 mm = 1 L of water

Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr

In gallons/hr:

1 gallon = 3.78541 L

So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr

(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.

Volume = Area × Depth.

The area of the garden is 2 m × 2 m.

We need to convert the rainfall amount to meters.

1 inch = 0.0254 m

Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m

Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3

Converting the volume to other units:

In liters:

1 m3 of water = 1000 L of water

Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L

In gallons:

1 gallon = 3.78541 L

Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.

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49.2 calories are in  would that contribute per serving .

What does a calorie mean ?

Carbohydrates provide 4 calories per gram.

              1 gm Carbohydrates = 4 calories

 then 12.3 gm Carbohydrates  = 12.3 * 4

                                             = 49.2 calories

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Answer:

x = 12

Step-by-step explanation:

Use Pythagoras' Thereom

x = L

H = Hypotenuse, L = Length and B = Base

H² = L² + B²

Answer:

8√57/57

Step-by-step explanation:

a² + b² = c²

a² + 8² = 11²

a² + 64 = 121

a² = 57

a = √57

For angle Θ, opp = 8, adj = √57, hyp = 11.

tan Θ = opp/adj = 8/√57 = 8√57/57

Answer:

x = 55°

Step-by-step explanation:

That square box indicates a right angle.

A right angle is 90°.

We know that angle x and the 35° angle are making up this 90° angle together.

So, the equation to show what this ship looks like is the following:

\(x+35=90\)

This is a simple equation, that if we solve, we get:

\(x=55\)

So, x is 55°.

Considering the angle of the ray, it is found that the value of x is of x = 55º.

The ray has an angle of 180º. It is composed by:

Hence:

x + 35 + 90 = 180

x = 180 - 125

x = 55º.

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Erin is 1/2 and Lauren is 6/8 compare them and you get 0.25 or 1/4

BRAINLIEST pls thank you so much

The round of number 371,883 to two significant digits is 370,000.

What are significant figures?

In positional notation, significant figures are digits in a number that are trustworthy and required to denote the amount of something.

For example,

Number 0.00698 contained three significant digits.

Number 102.0094 contains seven significant digits.

As per question,

Number 371,883 contained six significant digits.

Now convert this number to two significant digits as follows:

Number 371,883 rounded to five significant digits is 371,880

Similarly, rounded to four significant digits is 371,800.

Similarly, rounded to three significant digits is 371,000.

and similarly, rounded to two significant digits is 370,000.

Hence, The round of number 371,883 to two significant digits is 370,000.

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Answer:

There are 144 biology books.

There are 228 math books.

Step-by-step explanation:

Let m = the number of math books

Let b = the number of biology books

m + b = 372

m = b + 84   Substitute b + 84 for m in the first equation.

m + b = 372

b + 84 + b = 372  Combine like terms

2b + 84 = 372  Subtract 84 from both sides

2b + 84 - 84 = 372 - 84

2b = 288 Divide both sides by 2

b = 144

There are 144 biology books.

m + b = 372  Substitute 144 for b

m + 144 = 372  Subtract 144 from both sides

m + 144 - 144 = 372 -144

m = 228

There are 228 math books.

Check:

m + b = 372

228 + 144 = 372

372 = 372 Checks

m = b + 84

228 = 144 + 84

228 = 228 Checks

Helping in the name of Jesus.

The probability that Aaron selects a terrier, given Rebecka selects a poodle, is 1/3.

To find the probability that Aaron selects a terrier, given Rebecka selects a poodle, we need to use conditional probability.

First, we need to find the probability that Rebecka selects a poodle. Since there are four poodles out of seven puppies total, the probability that Rebecka selects a poodle is 4/7.

Next, we need to find the probability that Aaron selects a terrier, given that Rebecka has already selected a poodle. Now there are only three poodles and two terriers left in the store, so the probability that Aaron selects a terrier is 2/6 (or simplified, 1/3).

Putting it all together, we can use the formula for conditional probability:

P(Aaron selects a terrier | Rebecka selects a poodle) = P(Aaron selects a terrier and Rebecka selects a poodle) / P(Rebecka selects a poodle)

Since we know that Rebecka selects a poodle, the numerator is just the probability that Aaron selects a terrier given that there are three puppies left in the store. So:

P(Aaron selects a terrier and Rebecka selects a poodle) = (1/3) * (4/7) = 4/21

And we already calculated that P(Rebecka selects a poodle) = 4/7. So:

P(Aaron selects a terrier | Rebecka selects a poodle) = (4/21) / (4/7) = 1/3

Therefore, the probability that Aaron selects a terrier, given Rebecka selects a poodle, is 1/3.

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Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

Answer:

sin 90

Step-by-step explanation:

cos (0)

Using the unit circle, we know that cos 0=1

sin 1 and cos 1  are not equal to 1

sin 90 =1

tan 90 = sin 90/ cos 90 = 1/0 =undefined

Step-by-step explanation:

the area of the full larger circle minus the area of the smaller circle.

the area of a circle is

pi×r²

the radius of the smaller circle is 23.1 yd.

the radius or the larger circle is 23.1 + 7.8 = 30.9 yd.

the area of the larger circle is

pi×30.9² = 3.14 × 954.81 = 2,998.1034 yd²

the area of the smaller circle is

pi× 23.1² = 1,675.5354 yd²

the area of only the ring around the smaller circle is then

2,998.1034 - 1,675.5354 = 1,322.568 yd² ≈

≈ 1,322.57 yd²

or

pi×30.9² - pi×23.1² = pi(954.81 - 533.61) =

= 421.2pi = 421.2 × 3.14 =

= 1,322.568 ≈ 1,322.57 yd²

The error in finding the measure of one exterior angle of a regular polygon lies in using the formula 360°/n, where n is the number of sides of the polygon.

The formula 360°/n is used to find the measure of each exterior angle of a regular polygon. It is based on the idea that the sum of all exterior angles of any polygon is always 360 degrees. However, this formula assumes that the polygon has internal angles of 180°, which is true only for regular polygons.

The error occurs when this formula is applied to a non-regular polygon, as non-regular polygons have varying internal angles. Using the formula 360°/n for a non-regular polygon will give incorrect results because the internal angles are not all equal.

For regular polygons, each exterior angle is indeed 360°/n, and the sum of all exterior angles will be 360 degrees. However, for non-regular polygons, this formula cannot be used, and the measures of exterior angles must be calculated differently based on their internal angles and sides.

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The error in finding the measure of one exterior angle of a regular polygon is they divided 360 by 10 instead of 5.

Given that,

There are a total of 10 exterior angles, two at each vertex, so the measure of one exterior angle is 360°/10 = 36°.

Here, at each vertex there are two angles.

So, there must be 5 vertices and 5 sides.

Then, the measure of one exterior angle = 360°/5

= 72°

Therefore, the error in finding the measure of one exterior angle of a regular polygon is they divided 360 by 10 instead of 5.

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"Your question is incomplete, probably the complete question/missing part is:"

Describe and correct the error in finding the measure of one exterior angle of a regular polygon. There are a total of 10 exterior angles, two at each vertex, so the measure of one exterior angle is 360°/10 = 36°.

The deterministic finite automaton (DFA) M3 for the language L3, where strings have more than 3 'c' symbols and do not end in 'c', is designed with states q0, q1, q2, q3, and q4. Transitions and loops are created to determine acceptance.



To build a deterministic finite automaton (DFA) for the language L3 = {x ∈ {a, b, c}* | x has strictly more than 3 'c' symbols and does not end in 'c'}, we can design the following DFA M3:1. Start with an initial state q0.

2. Create a loop on q0 for 'a', 'b', and 'c' inputs, leading back to q0.

3. From q0, transition to a state q1 on input 'c'. This represents the first 'c' encountered.

4. From q1, create a loop for 'a' and 'b' inputs, leading back to q1.

5. Transition from q1 to q2 on input 'c'. This represents the second 'c' encountered.

6. Similarly, create a loop on q2 for 'a' and 'b' inputs, leading back to q2.

7. Transition from q2 to q3 on input 'c'. This represents the third 'c' encountered.

8. From q3, create a loop for 'a', 'b', and 'c' inputs, leading back to q3.

9. Create a final accepting state q4 and transition from q3 to q4 on 'a' or 'b' inputs.

In this DFA, any string that ends with 'c' or has less than three 'c' symbols will not reach the accepting state q4, hence not belonging to L3.

Therefore, The deterministic finite automaton (DFA) M3 for the language L3, where strings have more than 3 'c' symbols and do not end in 'c', is designed with states q0, q1, q2, q3, and q4. Transitions and loops are created to determine acceptance.

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Answer:

ok so the answer is 28² - 21 to the power of 4

Step-by-step explanation:

Answer:4 × 109

+ 3 × 108

+ 6 × 107

+ 5 × 106

+ 4 × 105

+ 2 × 104

+ 1 × 103

+ 0 × 102

+ 0 × 101

+ 6 × 100

Step-by-step explanation:

Answer:

Ok!

Step-by-step explanation:

if you need help with "expanded form" you can always go to calculatorsoup

The expression (4a³b^4)³ when evaluated is 64a^9b^12

From the question, we have the following parameters that can be used in our computation:

(4a³b^4)³

When expanded, we have

(4a³b^4)³ = 4³ * (a³)³ * (b^4)³

Evaluate the exponents

So, we have the following representation

(4a³b^4)³ = 64a^9b^12

Hence, the solution si 64a^9b^12

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Answer:

Step-by-step explanation:

hello :

r+b=7... (*)

3.75r+2.75b=22.25.... (**)

use (*) :  r = 7 - b

put this value in (**) :

3.75(7 - b)+2.75b =  22.25

26.25 -375b +2.75b = 22.5

-375b +2.75b = 22.5 - 26.25

- b = -3.75

so : b  = 3.75

but : r = 7 - b

r = 7 - 3.75

r = 3.25

Answer:

90 oranges

Step-by-step explanation:

First, find out how many cupfuls are in 3 gallons of juice.

2 cups = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

16 cups = 1 gallon

48 cups = 3 gallons

For every 5 oranges, you get 3 cupfuls of juice.  This gives you the ratio of 5/3.  Multiply 48 cups, which is 3 gallons, by the ratio to find out how many oranges you will need.

48 × 5/3 = 90

You will need 90 oranges for 3 gallons of juice.

Answer:

80 oranges are used to make 3 gallons of juice

Step-by-step explanation:

1 gallon = 8 pint

3 gallons  = 3 * 8 = 24 pint

1 pint = 2 cup full of juice

24 pint = 24 * 2 = 48 cups

Now, we have to find how many 3 cups are in 48. So, 48 ÷ 3 = 16

3 cup of juice is taken form 5 oranges.

Therefore, 16 groups of 3 cups of juice will be taken from 5 *16 = 80 oranges

Answer:

6/12

Step-by-step explanation:

the last one

4/8=6/12!!

Answer:

4 : 8 = 6 : 12

Step-by-step explanation:

4 : 8 = 6 : 12

4 : 8 = 1 : 2

12 : 6 ≠ 1 : 2

10 : 12 ≠ 1 : 2

6 : 20 ≠ 1 : 2

6 : 12 = 1 : 2

4 : 8 = 6 : 12