If the first and second terms of a geometric sequence are 3 and 12, what is
the expression for the value of the 24th term of the sequence?

If P(t) is the size of a population at time t , the differential equation describes linear growth in the size of the population is [tex]\frac{dP}{dt}=200[/tex]

The differential equation is is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point.

dy/dx = f(x)

Here “x” is an independent variable and “y” is a dependent variable

According to the question,

Size of population at t time = P(t)

Also given ,The differential equations have a linear growth in the size of the population.

So, The degree of the variable must be one. And the equation of the population will be quadratic.

Therefore , dP/dt = 200 tells us the rate change of population with respect to time.

A derivative of linear function is constant .

Hence , option B is correct.

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The solutions of given function;

(a) k = -12

(b) f'(3) = 0

(c) f'(x) = 0

Given info,

A function f is defined for all real numbers and has the following three properties:

[tex]f(1)=5 \quad f(3)=21 \quad f(a+b)-f(a)=k a b+2 b^{2}f(1)\\[/tex]

for all real numbers a and b where k is a fixed real number independent of a and b.

To find,

(a) Use a = 1 and b = 2 to find k.

[tex]f(a+b)-f(a)=k a b+2 b^{2}f(1)[/tex]

f(1 + 2) - f(1) = k(1 * 2) + 2 * 2² * f(1)

f(3) - f(1) = 2k + f(1) * 8

21 - 5 = 2k + 8 * 5

16 = 2k + 40

-2k = 24

k = -12

(b) Find f'(3).

f(3) = 21

f'(3) = d/dx(21) = 0

(c) Find f'(x) for all real x.

f'(x) = 0

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The probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999

1) Using by the central limiting theorem:

We know the formula for the z-score for the normal distribution is given by:

z = (x - μ) /( ρ√n)  

Follows normal distribution with mean 0 and the variance of 1.

Where

x is the  sample mean,

μ is the  population mean,

ρ denotes population standard deviation

n = sample size

The required probability is

P(z < 0.5/[0.4/√ 10])

= P(z < 3.95)

P = 0.9999

Therefore the probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999 .

Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.

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The correct option b. 0.004629 for  the probability of observing a 1 three times in a row.

Probability of an event = (Number of favorable events) /   (total number of event).

P(B) = (Event B) / (total number of event).

The number of times the dice are rolled has no bearing on the outcome of the roll.

The likelihood of receiving 1 is 1/6.

The likelihood of obtaining 1 three times in a row is equal to the likelihood of getting 1 the first time, the second time, and the third time.

Receiving 1 three times in succession has a probability;

= 1/6 x 1/6 x 1/6

= 1/216.

As a result, there is a 0.463% chance that you'll get 1 three times in a row.

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Yes, the given curves are orthogonal.

In mathematics, an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally.

Given equation is,

x²+y²=ax

Differentiating,

2x+2yy'=a

y' = (a-2x)/2y = m1

Again,

x²+y²=by

Differentiating,

2x+2yy'=by'

y' = -2x/(2y-b) = m2

For both curves are orthogonal, we have

m1*m2 = -1

(a-2x)/2y*-2x/(2y-b)  = -1

-2ax+4x² = -4y²+2yb

4(x²+y²) = 2ax+2yb

Since, ax = (x²+y²)

by = (x²+y²)

Then,

4(x²+y²) = 2(x²+y²) +2(x²+y²)

4(x²+y²) = 4(x²+y²)      (true)

Hence, the above response is appropriate.

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The case in which the triangle can be drawn are

the triangle is most effective viable while the sum of aspects is exactly extra than the 0.33 side.

This hassle is primarily based totally at the triangle inequality assets which states that if the sum of lengths of any aspects of a triangle is extra than the 0.33 side, then it's miles viable to attract a triangle. The indoors angles rule states that the 3 angles of a triangle need to identical 180°. As you may see below, the 3 perspective measurements of obtuse triangle ABC upload to 180°.

Even, if there may be a single pair now no longer enjoyable the circumstance, the triangle will now no longer be viable.The sum of the lengths of aspects needs to be extra than the 0.33 side. If the given lengths fulfill this circumstance then most effective it's miles viable to assemble a triangle.

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An writing format called R Markdown (. Rmd) makes it simple to create dynamic documents, presentations, and reports with R.

It mixes R code chunks that are embedded and run so that their result can be included in the final document with the basic grammar of R markdown, a simple plain text format. The following are some benefits of utilizing R markdown: explicitly connects your data, R code, and output to produce a workflow that is completely reproducible. You can include ALL of the R code that was used to explore, summarize, and analyze your data in a single, simple-to-read document.

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Applying the distance formula, the length of the bike path as shown in the coordinate plane is approximately 28 feet.

To find the distance between two points that are on a coordinate plane, the formula used is the distance formula which is given as:

d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

Point G on the coordinate plane is at (20, 20), while point E is at (0, 0):

Therefore:

E (0, 0) = [tex](x_1, y_1)[/tex]

G (20, 20) = [tex](x_2, y_2)[/tex]

Plug in the values into the distance formula:

EG = √[(20 − 0)² + (20 − 0)²]

EG √[(20)² + (20)²]

EG = √(400 + 400)

EG = √800

EG ≈ 28 feet

The length of the bike path would be approximately 28 feet.

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The required distance between point on the ground and foot of the tower.

On the off potential for success that an individual has and peers down at an item, the angle of depression is the point between the level view and the item. Geometry can be utilized to take care of issues that utilization a point of rise or sorrow.

Height of  the tower = 43 ft

And angle of depression = 63 degree

we know that

tan(theta) = P/B

P is height of tower, B distance between tower and point on the ground.

tan(63)= 43/B

B = 43/tan(63)

B = 43/1.96 = 21.93 = 22 ft approx.

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The nearest foot, on the building does the ladder reach is 7.1 ft

Because of Pythagorean Theorem.

Since the ladder is leaning against a building it makes 10ft the hypotenuse, (c).

Additionally, they give you one of the bases = 7ft, (a)

So in order to find the other base you must plug in what you already know.

= [tex]10^{2} = 7^{2} + b^{2}[/tex]

Which equals to 100= 49 + [tex]b^{2}[/tex]

Then you have to subtract 49 on both sides ending up with

[tex]b^{2}[/tex] = 51.

Then you have to square root on both sides and we will get [tex]\sqrt{51}[/tex].

Which is around 7.1 ft.

Hence the answer is the nearest foot, on the building does the ladder reach is 7.1 ft

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If the is lets say 5 years old, in 2 years, she will be 5 + 2 = 7 years old, and in 10 years 5 + 10 = 15 years old

so age in the future is the present age + how many years from now she will be

in this example the present age is 5 years old , if you replace that 5 with an x, the age in 10 years will be x + 10

Out of the choices provided, the density curve for a continuous and a random variable ''x'' has all the properties, which have been listed above. Therefore, the option D holds true.

A density curve can be referred to or considered as the smooth curve, which is used for the purpose of representation of shape of a variable's distribution, which is easily identified through the properties that it contains. A density curve can be used for the purpose of graphical representation, such as a histogram.

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take any negative value of x suppose x= -1,-2 ....etc then it makes sence and it is valid cube

What are types of expressions?

There are three kinds of expressions: An arithmetic expression evaluates to a single arithmetic value. A character expression evaluates to a single value of type character. A logical or relational expression evaluates to a single logical value.

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the probability  that a randomly selected when the IQ is lower than 136 is 0.9641

Given that

The mean is 100

The standard deviation is 20

We need to find out the probability when the IQ is lower than 136

So,

z value equivalent to 136 = (136 - 100)  ÷ 20 = 1.8

Now  

p (z < 1.8) = 0.9641

hence, the probability when the IQ is lower than 136 is 0.9641

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Natural numbers known as prime numbers can only be divided by one (1) and by the number itself.

In the given question we have to explain about the prime number.

Natural numbers known as prime numbers can only be divided by one (1) and by the number itself. In other terms, prime numbers are positive integers greater than one that only have the number itself and the number's first digit as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are only a few examples.

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Answer:

a. parameter

Step-by-step explanation:

A parameter is any descriptive measure of a population characteristic.

The probability of all 3 selected were rated excellent is 1/114 and the probability of one from each category was selected, is 7/114.

In the given question,

In a certain department, 5 employees received excellent ratings, 14 received good ratings, and 1 received a marginal rating.

So total number of employees = 5+14+1 = 20

If 3 employees in this department are randomly selected to complete a form for an internal study of the firm, then we have to find the probability that the following occurs.

The following occurs given below:

(a) We have to find the probability of all 3 selected were rated excellent.

5 employees who got excellent rating. So the selection of 3 employees from 5 employees who got excellent rating is:

selection of 3 employees from 5 employees = [tex]^5C_{3}[/tex]

Using, [tex]^nC_{r}=\frac{n!}{r!(n-r)!}[/tex]

selection of 3 employees from 5 employees = [tex]\frac{5!}{3!(5-3)!}[/tex]

selection of 3 employees from 5 employees = [tex]\frac{5!}{3!2!}[/tex]

selection of 3 employees from 5 employees = [tex]\frac{5\times4\times3!}{3!\times2\times1}[/tex]

selection of 3 employees from 5 employees = 5×2

selection of 3 employees from 5 employees = 10

Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140

Probability of 3 employees who got excellent rating

P(E) = 10/1140

P(E) = 1/114

(b) We have to find the probability of one from each category was selected.

One candidate selected from excellent category = [tex]^5C_{1}[/tex] = 5

One candidate selected from marginal category = [tex]^1C_{1}[/tex] = 1

One candidate selected from good category = [tex]^{14}C_{1}[/tex] = 14

Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140

The probabilty of one from each category = (5*1*14)/1140

The probabilty of one from each category = 70/1140

The probabilty of one from each category = 7/117

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The equation of a line perpendicular to p(t) = 3t + 4 and passing through the point (3, 1) is: P(t) = -1/3 + 1

Given:

p(t) = 3t + 4

point (3,1)

To find this out, we must use the slope perpendicular to 3

perpendicular slopes are the slope's reciprocal's negative, which in this case it is -1/3

to find the line with the points (3,1), we simply use the equation y = -1/3x + b and then plug them in

1 = -1/3(3) + b

1 = -1 + b

b = 2

the y intercept is 2 and so we can write the equation like this:

P(t) = -1/3t + 2

Hence we get the required equation of a line.

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The population of interest in Kristen's investigation is the students at her high school.

The specific group of people or items that a researcher is researching in a given study  is known as the population of interest. This group may be categorized according to factors like age, gender, employment, geography, or a particular health condition. The target audience for the study is the population of interest, and this demographic is generally the one to which the study's findings are applied. Identifying the population of interest is a crucial phase in the research process because it allows the researcher to focus on a specific group and develop meaningful findings that are applicable to that group.

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Alicia have to pay $10,000 and her insurance will pay $10,500.

What is limit of coverage in insurance?

This limit is the most the insurer will pay for sums as damages because of bodily injury or property damage included within the products-completes operations hazard during the policy period.

Given that Alicia has a collision deduction of $500 and a bodily injury coverage limit of $50,000.

And there is a verdict to compensate the injured person for $40,000

Therefore Alicia have to pay

$50,000-$40,000 = $10,000

And her insurance will pay

$10,000 + $500 = $10,500

Hence Alicia have to pay $10,000 and her insurance will pay $10,500.

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Answer:

a function is like f(X)=2x+6 where X can be anything , you just substitute in the number u have been given

Step-by-step explanation:

other examples could include

f(X)=X+1

or they can start with

g(X)=3x+7

h(X)=4-3x

and there are inverse functions witch can be found be rearranging the function

example if substituteing a function

if

f(X)= 2x+1

f(3)=2(3)+1

f(3)=6+1=7

Hope this helps

The agile frameworks that have in common are:

Self-organized teams can better adapt to business requirements with a lightweight strategy.

All agile frameworks use iterative and incremental development and have a set, defined iteration duration. They also all take a lightweight approach that enables self-organized teams to better adapt to business needs. It's a term for methods used in software development.

What is the Agile cycle?

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention.

Hence,

The agile frameworks that have in common are:

Self-organized teams can better adapt to business requirements with a lightweight strategy. All agile frameworks use iterative and incremental development and have a set, defined iteration duration. They also all take a lightweight approach that enables self-organized teams to better adapt to business needs. It's a term for methods used in software development.

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Answer:

[tex]\sqrt{178}[/tex] or 13.3 rounded to the nearest tenth

Step-by-step explanation:

The solution for the given expression is a⁴b³/cd × c²/a⁴b⁵ = c/b²d.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The given algebraic expression is as below,

a⁴b³/cd × c²/a⁴b⁵

It can be simplified  by using the rules of exponent as follows,

a⁴b³/cd × c²/a⁴b⁵

= a⁴b³ c²/(cd × a⁴b⁵)

= b³ c²/b⁵cd

= c²/b²cd

= c/b²d

Hence, the given expression can be simplified as c/b²d.

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Answer:

A triangle in which each angle is less than 90 degrees is called an acute angled triangle.

Step-by-step explanation:

The way fuel consumption of a car change as its speed increases represents a relationship that is curved with higher at extremes when scatter plot is constructed. It shows fuel efficiency is high at moderate speeds.

What is scatter plot?

A scatter plot is a type of mathematical diagram using Cartesian coordinates to demonstrate values for typically two variables for a set of data.

Main body:

In the given case, the scatter plot shows a relationship between the speeds of a car and fuel consumption.

The curved relationship which is high on extreme and low in the middle. As the car speed increases from 10km/h to 60 km/h, the fuel consumption decreases. As the car speed increases from 60km/h to 150khm/h, the fuel consumption increases. Hence, the fuel consumption is lowest at 60km/h and its generally low for moderate speeds – 40 km/hr to 100 km/h. It can be deduced that fuel efficiency (which pertains to how well a vehicle uses fuel) is high for moderate speeds.

Hence, at moderate speeds best performance is achieved.

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The five rules of congruence theorem are described below.

The sign for congruence is ≅ and we compose △ABC≅△DEF. ∠A relates to ∠D, ∠B compares to ∠E, and ∠C relates to ∠F. Side Stomach muscle relates to DE,BC compares to EF, and AC relates to DF.

Side-Side-Side(SSS):Corresponding sides of two triangles are equal, then triangles are congruent.

Side-Angle-Sid(SAS):Corresponding two sides and one angle are equal, then triangles are congruent.

Angle-Side- Angle(ASA):One side and two angles are equal, then triangles are congruent.

Angle-Angle-Side(AAS):Corresponding conductive two angles and one side are equal, then triangles are congruent.

Right angle- Hypotenuse-Side(RHS): assuming the hypotenuse and side of one right-calculated triangle are equivalent to the hypotenuse and the comparing side of another right-calculated triangle, the two triangles are consistent.

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The relation between the given function is X cannot repeat itself.

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of a varying quantity depends on another quantity.

We have given that the functions table.

We need to determine which relation is a function.

The relation between the function, that is;

X cannot repeat itself

Hence, the option C is correct.

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A polynomial is a function with two or more terms that have positive integer exponents. The terms can be constants and/or have variables. They are separated by either addition or subtraction signs.

fundamental coefficients are the numbers written in front of the variable with the maximum important exponent. just like ordinary coefficients, they may be fine, terrible, real, or imaginary further to whole numbers, fractions, or decimals. for instance, inside the equation [tex]-7x^4[/tex] +[tex]2x^(3-11)[/tex], the very satisfactory exponent is four.

The degree of the polynomial is the best strength of the variable that takes location in the polynomial. the number one time period is the time period containing the very high-quality energy of the variable: the term with the very wonderful degree.

In a polynomial, the principal term is the term with the very first-rate electricity of x. for instance, the principal term of 7+x−3x² is −3x². the principal coefficient of a polynomial is the coefficient of the primary term. within the above instance, the primary coefficient is −3.

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The next step of marshall should be divide both sides of the equation by 5.

Given:

Marshall is writing an equivalent equation to solve for x. what should be his next step.

5 + 4 y = 8.

5+4y-4y = 8-4y

5x = 8 - 4y

To solve for x:

The correct step is:

divide by 5 on both sides

5x/5 = 8-4y / 5

x = 8/5 - 4y/5

x = 1/5(8-4y).

Therefore The next step of marshall should be divide both sides of the equation by 5.

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