Where did the 9/4 come from?
y = x^2 + 3x + 5
= ( x^2+3x ) +5
= (x^2 +3x + 9/4 ) - 9/4 +5
= (x + 3/2)^2 +11/4

( I already asked this question but someone literally answered it with an 'f' so i couldn't get an answer in the end :/ )

Unconstrained population growth equation solved by separation of variables. P = Ce^(Kt). Corrected function found using initial and 5 hour population data. After 10 hours, population is 16,333,333.33.

What is integral ?

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

(a) Solution by separation of variables:

P' = KP

dp/dt = KP => dP/P = K dt

∫(dP/P) = ∫K dt => ln|P| = Kt + C, where C is the integration constant.

P = Ce^(Kt)

(b) Initial population is 3M and after 5 hours the population is 7M.

Using the formula from (a), we have:

Ce^(K5) = 7M => Ce^(K5) = 7*10^6

3M = Ce^(K0) => 310^6 = C

Therefore, the exact function describing the population growth is:

P = 3*10^6 * e^(Kt)

(c) After 10 hours, the population will be:

P = 310^6 * e^(K10)

(d) The population after 10 hours should be exactly 49/3.

Checking with the formula from (c), we have:

P = 310^6 * e^(K10) = 49/3 * 10^6 = 49,000,000 / 3 = 16,333,333.33

Unconstrained population growth equation solved by separation of variables. P = Ce^(Kt). Corrected function found using initial and 5 hour population data. After 10 hours, population is 16,333,333.33.

To learn more about integral visit : brainly.com/question/18125359

#SPJ4

Sum of two numbers is the addition of the numbers.

The number Aesha ends with is 12

sum of 4 and 2

= 4 + 2

= 6

product of 2 and the answer she wrote down, that is, product of 2 and 6

= 2 × 6

= 12

Therefore, the number Aesha ends with is 12

Read more:

https://brainly.com/question/12182305

The statement which is best explained by the alternate exterior angles theorem is ∠1 ≅∠2.

What do you mean by angles?

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

We know that, alternate exterior angles theorem states that, when two parallel lines are cut by a transversal line, the resultant exterior angles are congruent.

∠1 and ∠2 are both alternate exterior angles.

Therefore, the correct answer for the following problem is ∠1 ≅∠2.

To know more about angles, go to link

https://brainly.com/question/11900288

#SPJ4

Answer:

x < -6/25

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-25x + 14 > 20

Step 2: Solve for x

Here we see that any number x less than -6/25 would work as a solution to the inequality.

The probability of getting 3 or fewer successes in 9 independent trials of a binomial probability experiment, where the probability of success in each trial is 0.3, is 0.143 (14.3%). This calculation assumes the trials are independent and the probability of success is constant for each trial.

To compute the probability of x successes in the n independent trials of the experiment, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where (n choose x) represents the number of ways to choose x items from a set of n items and is calculated as:

(n choose x) = n! / (x! * (n-x)!)

where n! represents the factorial of n, which is the product of all positive integers up to and including n.

Using this formula and the given parameters n=9, p=0.3, and x ≤ 3, we can calculate the probability of x successes as follows:

P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

P(x = 0) = (9 choose 0) * 0.3^0 * (1-0.3)^(9-0) = 0.001

P(x = 1) = (9 choose 1) * 0.3^1 * (1-0.3)^(9-1) = 0.009

P(x = 2) = (9 choose 2) * 0.3^2 * (1-0.3)^(9-2) = 0.037

P(x = 3) = (9 choose 3) * 0.3^3 * (1-0.3)^(9-3) = 0.096

Therefore, the probability of x successes in the n independent trials of the experiment, where n=9 and p=0.3, and x ≤ 3, is:

P(x ≤ 3) = 0.001 + 0.009 + 0.037 + 0.096 = 0.143 (rounded to three decimal places)

So, the probability of x successes in the n independent trials of the experiment, where n=9 and p=0.3, and x ≤ 3, is 0.143 (rounded to three decimal places). This means that there is a 14.3% chance of getting 3 or fewer successes in the 9 independent trials of the experiment, where the probability of success in each trial is 0.3.

It is important to note that this calculation assumes that the trials are independent and that the probability of success is constant for each trial. If these assumptions are not met, the binomial probability formula may not be appropriate and other methods of probability calculation may need to be used.

Visit to know more about Probability:-

brainly.com/question/13604758

#SPJ11

There are 3,003 different ways to form the committee.

To calculate the number of different ways to form the committee, we can use the concept of combinations. The number of combinations of n objects taken r at a time is given by the formula:

C(n, r) = n! / (r!(n-r)!)

In this case, we have 15 members in the academic senate and we want to form a committee of 5 members. Plugging the values into the formula, we have:

C(15, 5) = 15! / (5!(15-5)!)

= 15! / (5! * 10!)

= (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)

= 3,003

Therefore, there are 3,003 different ways to form the committee of 5 members from the 15 members of the academic senate.

Learn more about committee

brainly.com/question/31624606

#SPJ11

The number of 4-credit classes and 3-credit classes the student can take to complete her degree is 7 and 4 respectively

Total number of class that he need to take = 11 classes

Total credits that he needs = 40 credits

Consider the number of 4 credit scores as x and number of 3 credit scores as y

Then the first equation will be

x + y = 11

x = 11 - y

The second equation will be

4x + 3y = 40

Use substitution method

4(11 - y) + 3y = 40

44 - 4y + 3y = 40

-1y = -4

y = 4

Substitute the value of y in the first equation

x = 11 - y

x = 11 - 4

x = 7

Therefore, he took 7 4-credit classes and 4 3-credit classes

Learn more about substitution method here

brainly.com/question/14619835

#SPJ4

Step-by-step explanation:

\(\angle L\\

\angle GLJ\\

\angle JLG\\

\angle 2\)

Answer:

<L

 <GLJ

< JLG

 <2

Step-by-step explanation:

There are 4 different ways to name this angle

By the vertex  <L

With the sides and vertex  ( vertex in the middle)  <GLJ or < JLG

or by the number in the middle  <2

Answer:

41.41

Step-by-step explanation:

cosA=6/8=3/4

I used a calculator

There are two values of b such that the minimum value of the function is - 1, then the solutions are b₁ = - 2 and b₂ = 2, respectively.

In this problem we know a quadratic equation of the form g(x) = x² + b · x, of which we must determine the value of b such that the y-value of the minimum is - 1. Graphically speaking, quadratic equations are represented by parabolae, which have either a minimum or a maximum know as vertex.

First, we must determine the vertex form of the equation of the parabola:

y = x² + b · x

y = x² + 2 · (b / 2) · x

y + b² / 4 = x² + 2 · (b / 2) · x + b² / 4

y + b² / 4 = (x + b / 2)²

The coordinates of the vertex are (h, k) = (- b / 2, - b² / 4). Then, the y-coordinate of the vertex is:

- b² / 4 = - 1

b² / 4 = 1

b² = 4

b = ± 2

There are two values of b such that the minimum value of the function is - 1, then the solutions are b₁ = - 2 and b₂ = 2, respectively.

To learn more on parabolae: https://brainly.com/question/21685473

#SPJ1

Step-by-step explanation:

\(gradient = \frac{(3 - 6)}{(4 - 5)} \\ = 3 \\ y = mx + c \\ consinder \: (4, \: 3) \\ 3 = (3 \times 4) + c \\ c = - 9 \\ y = mx + c \\ y = 3x - 9\)

The opposite expression of "-2a + 5c" is "5c - 2a".

To rewrite the expression "-2a + 5c" using the guidelines opposite, we will reverse the steps taken to simplify the expression.

Reverse the order of the terms: 5c - 2a

Reverse the sign of each term: 5c + (-2a)

After following these guidelines, the expression "-2a + 5c" is rewritten as "5c + (-2a)".

Let's break down the steps:

Reverse the order of the terms

We simply switch the positions of the terms -2a and 5c to get 5c - 2a.

Reverse the sign of each term

We change the sign of each term to its opposite.

The opposite of -2a is +2a, and the opposite of 5c is -5c.

Therefore, we obtain 5c + (-2a).

It is important to note that the expression "5c + (-2a)" is equivalent to "-2a + 5c".

Both expressions represent the same mathematical relationship, but the rewritten form follows the guidelines opposite by reversing the order of terms and changing the sign of each term.

For similar question on opposite expression.

https://brainly.com/question/3426818  

#SPJ8

The length of the arc of the curve from point P to point Q. y = 1/2 x^2, P (−7, 49/2) , Q (7, 49/2) is (50)7 + 1/2 in (√50 + 7/√50 - 7).

The core of calculus in mathematics is the concept of functions. The unique types of relations are the ones with functions. Mathematical functions are represented as a rule that, for each input x, produces a distinct result. Mathematicians refer to a function as being mapped or transformed. Typically, letters like f, g, and h are used to indicate these functions. The collection of all the values that the function is capable of accepting is referred to as the domain. The entire set of values that the associated function's output produces is known as the range. A function's co-domain is the collection of values that could be used as its outputs. Let's explore the world of arithmetic functions.

Given

Function

y = x²/2

Differentiate with respect to x

dy/dx

= d/ dx x²/2

= 1/2 d/dx x²

= 1/2 2x

= x

Squaring both sides,

(dy/dx)² = x²

Adding 1 on both sides,

1 + (dy/dx)² = 1 + x²

√1 + (dy/dx)² = √1 + x²

The length of the curve is given by,

S = ∫₋₇⁷ √1 + (dy/dx)² dx

S = ∫₋₇⁷ √1 +x² dx

Let

I = ∫ √1 + x²dx

Take x = tan∅

dx/d∅ = d/d∅ tan∅

= sec²∅

dx = sec²∅/d∅

Substitute x = tan∅ and dx = sec²∅ d∅

I =

∫√1 + tan²sec²d∅

∫ √sec²∅sec²d∅

∫ sec∅ sec² ∅d∅

Substituting,

∫₋₇⁷ √1 + x²

(1/2 (√1+x²)x + in (√1+x² + x )₇⁻⁷

(1/2(√50)7 + in(√50 + 7) - 1/2(√50)(-7) + in(√50 -7))

1/2((√50)(7) + In(√50 + 7) + (√50)7 + In(√50 - 7)

1/2(2(√50)7 + In(√50 + 7/ √50 - 7

(50)7 + 1/2 in (√50 + 7/√50 - 7)

The length of the arc of the curve from point P to point Q. y = 1/2 x^2, P (−7, 49/2) , Q (7, 49/2) is (50)7 + 1/2 in (√50 + 7/√50 - 7).

To learn more about function, visit:

https://brainly.com/question/28303908

#SPJ4

These are the corresponding snapshots of memory after each set of statements have been executed.The value of x becomes 2 and the value of z becomes 2.

To answer this question, we need to understand how memory works in a computer. Whenever we declare a variable, it is assigned a memory location, and whenever we assign a value to it, that value is stored in that memory location. The corresponding snapshot of memory is the state of memory after each set of statements has been executed.
So, let's look at the given statements and their corresponding snapshots of memory:
1. int x1; x1 = 3+4
In this statement, we are declaring a variable x1 of type integer and assigning it the value 3+4, which is 7. Therefore, the corresponding snapshot of memory would look like this:
| Variable | Memory Location | Value |
|----------|----------------|-------|
| x1       | 1000           | 7     |
2. int x(1), z(5); x = __z = __z = z/++x;
In this statement, we are declaring two variables x and z of type integer and assigning the value 1 to x and 5 to z. Then, we are dividing z by the pre-incremented value of x and assigning the result to both x and z.
The pre-increment operator increases the value of x by 1 before it is used in the division. Therefore, the value of x becomes 2 and the value of z becomes 2.
So, the corresponding snapshot of memory would look like this:
| Variable | Memory Location | Value |
|----------|----------------|-------|
| x1       | 1000           | 7     |
| x        | 1004           | 2     |
| z        | 1008           | 2     |
In summary, the corresponding snapshots of memory after executing the given set of statements are:
1. x1 = 7
| Variable | Memory Location | Value |
|----------|----------------|-------|
| x1       | 1000           | 7     |
2. x = 2, z = 2
| Variable | Memory Location | Value |
|----------|----------------|-------|
| x1       | 1000           | 7     |
| x        | 1004           | 2     |
| z        | 1008           | 2     |
Therefore, these are the corresponding snapshots of memory after each set of statements have been executed.

To know more about corresponding visit :

https://brainly.com/question/29207897

#SPJ11

Answer: The final answer is:\(`I = -2π / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

Explanation: We have to use contour integration to evaluate the integral cos20 -do, [. a²+6²-2abcose where b> a > 0.

Let \(f(z) = cos(20 - z) / [a² + b² - 2abcos(z - 6)] .\)

The denominator in the integral looks like\(cos(z - 6) = Re(e^(i(z-6)) ).\)

Therefore, we have \(cos(20 - z) = Re(e^(i(20 - z)))\)

Thus, we can write the integral as follows: `I = ∮ |z|=1 f(z) dz `

By Cauchy's Residue Theorem, the integral of f(z) over any closed curve in the complex plane is equal to `2πi` times the sum of residues of f(z) at its poles within the curve.

If we use the parametrization \(`z = 6 + b/a + re^(it)`\) with `0 <= t <= 2π`, then the integral becomes:

\(`I = -i ∫ 0^{2π} dt (a² + b² - 2abcos(t) ) / [ a² + b² - 2abcos(t) + 2ib(asin((r/a)sin(t-θ))]`\)

This integral can be computed using the residue theorem. If we define

\(`g(z) = 1 / [ a² + b² - 2abcos(t) + 2ib(asin((r/a)sin(t-θ))]`,\)

then the residue of g(z) at `z = 6 + b/a + i(asin((r/a)sin(t-θ))` is given by:

\(`Res(g, z) = lim_{z->6+b/a+i(asin((r/a)sin(t-θ)))} (z - (6 + b/a + i(asin((r/a)sin(t-θ))))) g(z) / [a² + b² - 2abcos(t)]`\)

We can compute this residue using L'Hopital's Rule.

After some algebraic manipulation, we can show that the residue is:\(`Res(g, z) = -1 / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

Hence, by the residue theorem, we have: \(`I = -2πi / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

Therefore, the final answer is:\(`I = -2π / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

To know more about Cauchy's Residue Theorem visit :

https://brainly.com/question/31058232

#SPJ11

Answer:

t = 4, 9

Step-by-step explanation:

Hi there!

f(t) = t² - 13t + 36

Let f(t) = 0:

0 = t² - 13t + 36

Factor the equation:

0 = t² - 4t - 9t + 36

0 = t(t - 4) - 9(t - 4)

0 = (t - 9)(t - 4)

The zero-product property states that if the product of two numbers is zero, then one of the numbers is equal to zero. Therefore, either (t - 9) or (t - 4) is equal to zero:

t - 9 = 0

t = 9

t - 4 = 0

t = 4

Therefore, the zeros of the function are 4 and 9.

I hope this helps!

Answer:

Alternate exterior angles: <2 and <7

Interior angles same transversal: <4 and <6

Corresponding angles: <4 and 8

Vertical angles: <6 and <7

Step-by-step explanation:

Answer:B)  5

Step-by-step explanation:

The expected number of people who will drop out due to either relapse or moving away is 10 + 6 = 16. However, taking into account the standard deviations, it is 16 +/- 5.

To find the expected number of people who will drop out due to either relapse or moving away, we need to add the expected number of people who will drop out due to relapse (10) and the expected number of people who will drop out due to moving away (6).

Expected number of people who will drop out due to either relapse or moving away = 10 + 6 = 16.

However, we also need to take into account the standard deviations for each of these groups. To do this, we can use the square root of the sum of the variances (SD squared) for each group, squared.

Variances:
- Relapse: 4 squared = 16
- Moving away: 3 squared = 9

Square root of the sum of the variances:
- sqrt(16 + 9) = 5

Therefore, the expected number of people who will drop out due to either relapse or moving away, taking into account the standard deviations, is 16 +/- 5.

This means that we can expect anywhere between 11 and 21 people to drop out due to either relapse or moving away during the two-year cohort study.

More on standard deviation: https://brainly.com/question/8889532

#SPJ11

I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

Answer:

Number one is Linear, Number two is Exponential, and Number three is quadratic

Step-by-step explanation:

Answer: 50%

Hope this helps!

The value of x is 24

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

2/10 = 3/(x-9)

Do cross multiplication

2(x-9) = 10*3 = 30

2x-18=30

2x=30+18=48

x=48/2=24

So, the value of x is 24

To learn more about the solution of an equation from the given link

https://brainly.com/question/22688504

#SPJ1

Answer:

-82

Step-by-step explanation:

84/21=4

-25x4=-100

-3x-6=18

-100+18=-82

the discriminant is:

D = (-1)^2 - 4*(-2)*6 = 49

We have a positive discriminant, which means that we have two real solutions.

For the general quadratic equation, the discriminant is:

a*x^2 + b*x + c = 0

The discriminant is:

D = b^2 - 4ac

In this case, the quadratic equation is:

6*x^2 - x - 2 = 0

Then we have:

a = 6, b = -1, c = -2

Replacing that in the discriminant equation:

D = (-1)^2 - 4*(-2)*6 = 49

We have a positive discriminant, which means that we have two real solutions.

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

The calculated number of times you would expect to roll a three or a six is 32 times

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

Cube = 96

In a cube, we have the following probability equation

P(3 or 6) = 1/6 + 1/6

When the sum is evaluated, we have

P(3 or 6) = 2/6

So, when the die is rolled 96 times, we have

Expected value = 2/6 * 96

Evaluate the products

Expected value = 32

Hence, the expected number of times is 32

Read more about expected value at

https://brainly.com/question/15858152

#SPJ1

Since the school chooses 3 randomly selected athletes from each of its sports teams, this is a B. Stratified Random Sample.

In this case, since the school chooses 3 randomly selected athletes from each of its sports teams, it means the stratified random sample is used.

Read related link on:

https://brainly.com/question/10585424

Answer:

400000

Step-by-step explanation:

The required rate for water being poured into the cup when the water level is 9 cm = 40.5π cm³/sec

For given question,

We have been given the height of a conical paper cup i.e., h = 10 cm

and the radius of a conical paper cup r = 10 cm

The cup is being filled with water so that the water level rises at a rate of 2 cm/sec

We need to find the rate at which water being poured into the cup when the water level is 9 cm

We know that the volume of the cone is \(V=\frac{\pi r^2 h}{3}\)

We can relate h and r as we know that the slope = h/r

                                                                                  = 10/5

                                                                                  = 2

Now, we make the volume a formula in a single variable

\(\Rightarrow V=\frac{\pi (\frac{h}{2} )^2 h}{3}\\\\\Rightarrow V=\frac{\pi h^3}{12}\)

Differentiating above equation with respect to time,

\(\Rightarrow V'=\frac{3\pi h^2 h'}{12} \\\\\Rightarrow V'=\frac{\pi h^2 h'}{4}\)

Substituting values,

\(\Rightarrow V'=\frac{\pi \times 9^2\times 2}{4}\\\\\Rightarrow V'=40.5\pi~~cm^3/sec\)

Therefore, the required rate for water being poured into the cup when the water level is 9 cm = 40.5π cm³/sec

Learn more about the volume of cone here:

https://brainly.com/question/1984638

#SPJ4

it A

Step-by-step explanation: