the speed of a runner increased steadily during the first three seconds of a race. her speed at half-second intervals is given in the table. find lower and upper estimates for the distance that she traveled during these three seconds. ft (smaller value) ft (larger value) t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (ft/s) 0 6.7 9.2 14.1 17.5 19.4 20

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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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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Using Compund interest formula, we can say that total Rs. 67 lakh and sixty thousand is owned by Sunil to the bank after 2 years .

Compound Interest Formulas :

You can also use the principal and interest rate to find compound interest. H. Total interest on principal and accrued interest not repaid within the repayment period. The compound interest formula is:

A = P( 1 + r/100)ᵗ

where A --> amount to pay by person after t years

P --> amount borrowed by person

r ---> rate of interest annually

t-----> time period

We have given that,

The amount borrowed by Sunil for education loan(P) = Rs. 40 lakh

Rate of interest (r) = 30% per annum

Interest is compunded annually.

time period (t) = 2 years

we have to calculate the amount to pay by Sunil after two years .

putting all known values in above formula,

A = 40,00000 ( 1+ 30/100)²

=> A = 40,00000(13/10)²

=> A = 40,00000×13×13/100

=> A = 40,000×169

=> A = 67,60,000

Hence, the amount that Sunil own to bank after two year is 67 lakh sixty thousand.

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As, we get the same results when we double a number and multiply the number by 2.

So, Yes doubling the number is same as multiplying by 2.

Given, the statement

Doubling is same as multiplying by 2.

we have to answer that, is doubling the same as multiplying by 2.

Let a number be, a

now to double the number, we have to add it to itself or to add it twice

= a + a

= 2a

So, on doubling a number we got 2a

Now, on multiplying a number by 2, we get

= a×2

= 2a

As, we can see that we got the same results when we double a number and multiply the number by 2.

So, Yes doubling the number is same as multiplying by 2.

Hence, Yes doubling the number is same as multiplying by 2.

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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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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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The Total Proability will be 297 / 1015

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

Total Number of Regular Soft Drinks = 18

Total Number of Diet Soft Drinks = 12

Total Drinks = 18 + 12 = 30

Probability of selecting Diet Soft Drink in the first two attempt = 12/30 * 11/29 * 18/28 = 2376 / 24360

Probability of selecting Diet Soft Drink in the first and last attempt = 12/30  * 18/29 * 11/28 = 2376 / 24360

Probability of selecting Diet Soft Drink in the second and last attempt = 18/30  * 12/29 * 11/28 = 2376 / 24360

Total Probability = 3 * 2376 / 24360

Total Probability = 2376 / 8120

Total Probability = 297 / 1015

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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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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 recommended daily protein amount to help most exercisers build and maintain muscle tissue is 1.6/kg

During the growth phase, 1.6 to 2.2 grams of protein per kilogram, or 0.7 to 1 gram per pound of body weight, is optimum. Protein consumption can, however, vary substantially across individuals. Your ideal weight and the amount of lean body mass are two variables that affect how much protein is advised. The recommended daily protein intake for a healthy adult is generally considered to be 1.6 g/kg of body weight per day.

A daily protein consumption of more than 1.6 g/kg is not generally supported by studies, however it has been found to be advantageous for lean body mass. Whey protein has typically been utilized in research as a model to compute protein.

Therefore, 1.6/kg of protein per day is suggested for most exercisers to assist them maintain and develop muscle.

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The number of can of soups purchased is 10 and the number of frozen dinner purchased is 10.

What are the linear equations in two variables?

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.

Let 'x' number of cans of soup purchased and 'y' number of frozen dinners purchased.

By the given condition, we can prepare the equations,

              x + y = 15 --------(I)

       200x + 500y = 4500 -----(II)

now from (I), y = 15 - x

Substitute the value of 'y' in the equation (II), we get

              200x + 500(15 - x) = 4500

              200x + 7500 - 500x = 4500

               300x = 3000

                    x = 3000/300

                    x = 10

Put x = 10 in equation (I), we get

                  y = 5

Hence, the number of can of soups purchased is 10 and the number of frozen dinner purchased is 10.

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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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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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The probability of Jack taking 2 red candies is 3/28.

What do you mean by a union in probability?
The letter "U" (union) stands for "or." Specifically, P(AB) represents the probability of that event A or event B occurring. The sample points that are present in both event A and event B must be counted in order to determine P(AUB).

The new probability set made up of all the elements from both sets is created when two sets are joined. When two sets intersect, a new set is created that includes every element from both sets.

Solution Explained:

Given in the question,

A bag contains 3 red and 5 green candies.

Total possibilities is 3 + 5 = 8  

Jack takes a candy at random and eats it  

A/Q there are 3 red candies out of 8, the probability is given by,

P(R) = 3/8

Now there are 2 red candies out of 7, so the probability is given by,

P(R') = 2/7

The probability of both events is given by,

P(2R) = P(R) × P (R') = 3/8 × 2/7 = 3/28

Therefore, the probability of Tim taking 2 red candies is P(2R) = 3/28

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The ratio of students who choose alternative and pop among 30 students is 10:5

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.

Two categories can be used to categorize ratios.

Part to whole ratio is one, and part to part ratio is the other.

The part-to-part ratio shows the relationship between two separate entities or groupings.

Given ,

Alternative =20

Pop = 10

So 20 and 10 both are multiples of 2 by simplifying that

10:5

Therefore the ratio is 10:5

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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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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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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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The relationship between the determinant of a square matrix and the determinant of the matrix multiplied by a scalar is,  the determinant of the matrix multiplied by a scalar is [tex]k^{n}[/tex] times the determinant of a square matrix, det(kA) = [tex]k^{n} D[/tex]

Let A be a square matrix,

And the det(A) = D, equation (1)

If we multiply the square matrix with a scalar k, then the matrix becomes, kA, and its determinant is given as,

det(kA) = [tex]k^{n} D[/tex] , equation (2)

where k is the scalar,

n is the order of the square matrix and

Dis the determinant of the square matrix A.

Thus, the relationship between the determinant of a square matrix and the determinant of the matrix multiplied by a scalar is,  the determinant of the matrix multiplied by a scalar is [tex]k^{n}[/tex] times the determinant of a square matrix.

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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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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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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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Step-by-step explanation:

for that we best use the intercept form of a parabola equation :

y = a(x - p)(x - q)

p and q are the zeroes (x-intercepts) of the parabola.

a is the stretching factor (how wide or how narrow is the curve, and a positive "a" says it is opening upwards, a negative "a" says it is opening downwards).

so, our equation looks like

y = a(x - -2)(x - 5) = a(x + 2)(x - 5)

to get a we use the coordinates of the given point :

-40 = a(3 + 2)(3 - 5) = a×5×-2 = -10a

a = -40/-10 = 4

the equation is then

y = 4(x + 2)(x - 5) = 4(x² -5x + 2x - 10) =

= 4(x² - 3x - 10) = 4x² -12x - 40

The slope of that line through the origin that divides the region bounded is 1.0315

y = 5x - 3x2

5x - 3x2 = 0

x(5 - 3x) = 0

x = 0 , x = 5/3

Area under y = 5x - 3x2 is A = [0 to 5/3] 5x - 3x2 dx

A = [0 to 5/3] 5x2/2 - 3x3/3

A = [0 to 5/3] 5x2/2 - x3

A = 5(5/3)2/2 - (5/3)3 = 125/54

line passing through origin is in the form of y = mx

==> mx = 5x - 3x2

==> 3x2 + mx - 5x = 0

==> 3x2 + x(m -5) = 0

==> x(3x + (m -5)) = 0

==> x = 0 , x = (5 -m)/3

Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108

==> ?[0 to (5 -m)/3] 5x - 3x2 -mx dx = 125/108

==> ?[0 to (5 -m)/3] (5 - m)x - 3x2 dx = 125/108

==> [0 to (5 -m)/3] (5 - m)x2/2 - x3 = 125/108

==> (5 - m)[(5 -m)/3]2/2 - ((5 -m)/3)3 = 125/108

==> (5 -m)3/18 - (5 -m)3/27 = 125/108

==> (5 -m)3/54 = 125/108

==> (5 -m)3 = 125/2

==> (5 -m) = 3.9685

==> m = 5 - 3.9685

==> m = 1.0315

Hence slope of line = 1.0315

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The complete question is given below

There is a line through the origin that divides the region bounded by the parabola y=5x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?

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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True, whole numbers are closed under addition because Any two whole numbers added together result in a whole number. is a whole number as well.

The term "whole numbers" refers to numbers devoid of fractions, which are made up of positive integers and zero. It is denoted by the letter "W," and its corresponding set of numbers are "0," "1, 2, 3,,","5,,"6,,"7,","8,"..." The whole numbers are 0 through 9, then 1, 2, 3, 4, 5, and so on. The set of numbers without fractions, decimals, and negative numbers is known as the "whole number." It consists entirely of positive numbers, even zero.

Given,

Whole numbers are closed under addition

Any two whole numbers added together result in a whole number. is a whole number as well. Therefore, the whole numbers cannot be added.

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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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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 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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There are 40 pupil in a class and 30 of them are girl then  the ratio of girl to pupil is 3:4

If there are 40 pupil in total in the class, and 30 of them are girls, that means there are 10 boys in the class

so the ratio of  girls to pupil is 30: 40

to get simplest form, divide by the greatest common factor. which in this case, is 10

3:4

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