Is a quadratic function linear or nonlinear?.

The probability that 2 particles have gone left and 2 have gone right is 0.375, considering four molecules, all starting at the origin, which undergo a 1d random walk, each with a 50% chance of going left or right along the x-axis at each time step.

Probability measures how likely something is to happen. It is calculated mathematically as a fraction, ratio, or percentage. The formula of the favourable outcome over the total outcomes is used to describe probability. The likelihood of flipping a coin heads is one example. Given that there is only one head and two total sides, 50% of the time, a head will land up-side-down.

Given,

4 particles given,

P(left) = 0.5 = P(right)

Possible combinations in total,

2 × 2 × 2 ×2

16

Combinations that are accepted,

RRLL, LLRR, LRLR, RLRL, RLLR, LRRL

Probability of 2 left and 2 right:

= 6/16

= 3/8

= 0.375

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Using Random Experiment of tossing two coin ,

the total number of outcomes of the random experiment is 4 .

Random Experiments:

Specifically, random experiments are the process of observing uncertainties. After the experiment, you will know the result of the random experiment. The results are the results of random experiments.

Sample Space: The set of all possible outcomes is called the sample space. Therefore, in the context of random experiments, the sample space is our universal set.

Random Experiment: Flip a Coin

Sample space , S={Head, Tail} or usually written as {H,T}.

When you repeat a random experiment several times, each is called a trial.

In the coin toss example, each trial is either heads or tails.

we have given a random experiment of tossing two fair coins then,

sample space, S = {HH, HT, TH, TT} = 4

So, the total number of randomized experiment outcomes is 4.

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There are 48 such students who did not know any of the three languages.

Given,

   Since we have given that

   Number of students were taken for survey n(U)= 100

  Number of students who know French n(F) = 30

  Number of students who know German n(G) = 19

  Number of students who know Russian n(R) = 16

 Number of students who know both French and Russian n(F∩ R) = 11

 Number of students who know both German and French n(G ∩ F) = 12

 Number of students who know both Russian and German n(R ∩ G) = 6

Number of students who know all three languages = 4

So, n(F∪G∪R)=n(F)+n(G)+n(R)-n(F∩G)-n(F∩R)-n(G∩R)+n(F∩G∩R)

 n(F∪G∪R)=30+19+16-12-11-6+4

 n(F∪G∪R)=52

 So, the number of students who do not know any of the three languages is

[tex]n ( F ∩ G ∩ R )' = n (U) - n ( F ∩ G ∩ R )\\n ( F ∩ G ∩ R )' = 100- 52\\\\n ( F ∩ G ∩ R )' = 48[/tex]

Hence, there are 48 such students who did not know any of the three         languages.

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The total number of free throws shots Andres made was 8 and the total number of two point shots Andres made was 4.

First, let us understand the variables:

Any number, vector, matrix, function, its argument, set, or one of its elements can be specifically represented by a variable.

Let x and y be the quantity of shorts.

x is the number of attempts at the free throw line.

y is the quantity of two-point attempts.

According to the question, we have;

x + 2y = 16 ............equation 1

x + y = 12    ............equation 2

From equation 2 we can take out the value of x;

x = 12 - y     ............equation 3

substituting the value of x in equation 1, we will get;

(12 - y) + 2y = 16

12 - y + 2y = 16

12 + y = 16

y = 16 - 12

y = 4

putting the value of y in equation 3, we will get

x = 12 - 4

x = 8

Thus, the total number of free throws shots Andres made was 8 and the total number of two point shots Andres made was 4.

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The relation which we see between the orders of the elements of a group and the order of the group is smallest positive power.

G = U(20), order of each element of G = ?

The smallest positive power of an element that gives you your identity is the order of the element in a group. Three instances are covered: complex numbers, a 2x2 rotation matrix, and real number elements of finite order.

G = U(20) = {1,3,7,9,11,13,17,19}

⇒ 3° ≡ 1, 3¹ ≡ 3, 3² ≡ 9, 3³ ≡ 7, 3¹ ≡ 1(20)

∴ order of 3 = 4

7⁴ ≡ 1 (mod 20) → order (7) = 4

9² ≡ 1 (mod 20) → order (9) = 2

11² ≡ 1 (mod 20) → order (11) = 2

13² ≡ 9(mod 20) → 13⁴ ≡ 81(mod 20) → 13⁴ ≡ 1 (mod 20)

⇒ order (13) = 4

order  07 = 4

17 ≡-3(mod 20) ⇒ 17² ≡ yy (mod 20)

⇒ 17⁴ ≡ 81 (mod 20) ≡ 1 (mod 20) ⇒

19 = -1 (mod 20)

19² ≡ 1 (mod 20) ⇒ order (19) = 2

Hence we get the requires answer.

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In 2220 ways the innkeeper can assign the guests to the rooms i.e. Option B is correct.

As per the question,

There are Five friends and Five rooms,

⇒ 0 rooms of 2, 5 rooms of 1

⇒ 1 room of 2, 3 rooms of 1

⇒ 2 rooms of 2, 1 room of 1

Guests can be allotted rooms by the innkeeper as

              1, 1, 1, 1, 1,                 1, 2, 2,             or            1, 1, 1, 2

                                         =   5 × ( 4 2 ) × ( 5 2 ) ( 3 2 )

                                              assign frequencies to rooms

                                         =   5 × 4 × 3! ( 5 2 )

Total number of ways ( N )  =   To assign ( 1, 2, 2 ) + To assign ( 1, 2, 2 )  +      

                                                   To assign ( 1, 1, 1, 1, 1 )

                                              =   5 × ( 4 2 ) × ( 5 2 ) ( 3 2 ) +  5 × 4 × 3! ( 5 2 ) +

                                                   5!

                                              =    5 × ( 4 2 ) × ( 5 2 ) ( 3 2 ) + 120 ( 5 2 ) + 120

                                        N   =    2220 ways    

Therefore, The innkeeper can assign guests to the rooms in 2220 ways with no more than two friends per room i.e. option B is valid.

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The transformation from the parent function f(x) = x³ is a translation to the right by 2 units

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

g(x) = (x − 2)³

To determine the parent function, we leave only the variable in the expression

So, we have

f(x) = x³

Next, we determine the transformation

We have the transformation to be from f(x) = x³ to g(x) = (x − 2)³

This means the function is translated right by 2 units

Hence, the transformation is 2 unit right

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The area of shaded region is 0.171.

Given z-score is z = 0.95.

We have to calculate P(z > 0.95).

We can write this as

P(z > 0.95) = 1 - P(z < 0.95)

From the z-table we know that

P(z < 0.95) = 0.828

We will put this value in above equation, we get

P(z > 0.95) = 1 - 0.828

Therefore

P(z > 0.95) = 0.171.

Z-score tables are very useful in determining the probabilities of normally distributed random variables. The z-score standardizes the normally distributed variable to make any normal distribution fit into the standard normal distribution.

The z-score is calculated using the random variable, the mean, and standard deviation of a particular normal distribution of variables.

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In June 1979, the Pope travelled to Poland for the second time.

 The foundation of the Solidarity trade union, which was a crucial force in the overthrow of Communism in eastern Europe, was reportedly set in motion as a result of this journey, which some historians claim was the most important of all his travels.

John Paul paid visits to Warsaw, Gniezno, Kraków, Nowy Targ, Auschwitz, and Jasna Gora while in Poland. Millions of fans attended the nine-day tour.

His visit to his homeland  drew millions of followers and helped spark a decade-long underground movement against the communist government.

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The correct answer is Probability and non probability sampling procedure.

There are two distinct exits from sampling procedures.

There are two types of sampling: probability sampling and non-probability sampling.

In probability sampling each population has equal and independent chance to comes in the study . There are various types of probability samplings technique exists . These are simple random sampling , stratified random sampling, cluster sampling , systematic random sampling etc.

In non probability sampling the samples are selected on the basis of personal biasness, judgments and preferences. Judgemental sampling , quota sampling, dimensional sampling etc comes under this type of sampling procedure.

So here the correct answer is

Option -E- Probability and non probability sampling procedure.

Except it all other options are wrong.

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Answer: $235.2

Step-by-step explanation:

We just multiply 210 by 12%

which gives us 25.2

Then we just add 25.2 + 210 = 235.2

The 3 types of proofs are the proof by induction, direct proof and the proof by contradiction.

Proof is a logical or mathematical argument that shows that the given statement is true.

Though proofs might later on be proven wrong and/or have exceptions.

The three types of proof are:

(i) Proof by Induction

(ii) Direct Proof

(iii) Proof by Contradiction

Proof by Induction:

Proof by induction is the proof in which we generalize a particular for the entire equation.

In the inductive step we generalize the conclusion from the basis, where we prove the equation for a particular value for the entire theorem or equation.

On solving this, if the answer observed follows the theorem used then it is proven

Proof by Contradiction:

In this type of proof we take a contradicting equation to the one that has to be proven. If this equation when further solved turns out to be false or untrue, the equation is considered proven.

Direct Proof:

In the direct proof we assume that the given equation or theorem, to be proven is correct. We then go on to slow the question with the given assumption. If the on solving the answer comes out to be correct, we say that the theorem has been proven.

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The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

What is the measure of the angle of an isosceles?

Properties of an Isosceles Triangle

The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

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A firm has two plants (X and Y) producing the same product which sells for $12 each. The total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.

To solve the problem, first translate the given problem into equations.

The formula for profit is:

profit = revenue from sales - total cost

total cost = fixed cost + variable cost

revenue = selling price x number of units sold

Let:

x = the number of units sold in plant X

y = the number of units sold in plant Y

From the problem, we can conclude:

Profit X = profit Y

x = y

Profit X = 12x - (5000 + 3x)       (equation 1)

Profit Y = 12 y - (7000 + 2y)      (equation 2)

Substitute y = x into equation 2

Profit Y = 12 x - (7000 + 2x)  

Hence,

12x - (5000 + 3x)  = 12 x - (7000 + 2x)  

3x - 2x = 7000 - 5000

x = 2,000

Therefore, total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.

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The number of degrees of each turn made in the regular hexagonal pond is: 120°.

Altogether is 720°.

A hexagonal shape is a six (6) sided polygon that has 6 interior angles.

The sum of all interior angles of an x-sided polygon can be calculated as:

(n - 2)180.

To find the sum of all the interior angles of the hexagonal pond, substitute the n = 6 into (n - 2)180:

(6 - 2) × 180

= 4 × 180

= 720°

The measure of each interior angle of the hexagonal pond = 720/6 = 120°.

Therefore, it implies that, you made 120 degrees turn at each corner, and altogether, you made 720°.

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Counting from right to left, find the 68th digit of n is 10.

An integer, is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.

The largest integer with exactly 100 digits is the integer that consists of 100 copies of the digit 9.

This integer is equal to 10100 = 10

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The parent graph is the graph of a relatively simple function.

Graph:

Graph refers the diagram that represents the variation of a variable in comparison with that of one or more other variables.

Given,

Here we need to define the parent in a graph.

Parent function refers the simplest form of a given family of functions.

Here by transforming the function in various ways, the graph can be translated, reflected, or otherwise changed.

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the radius of a circle is increasing at a constant rate of 5 meters per second, so the rate of change of the area is [tex]100\pi m/sec^{2}[/tex]  

Divide the y-value change by the x-value change to determine the rate of change. When analyzing changes in observable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.

Suppose the radius of circle be r.

now, [tex]\frac{dr}{dt} = 5 m/sec[/tex]

And, area of circle is [tex]\pi r^{2}[/tex]

[tex]\frac{dA}{dy} = 2\pi r\frac{dr}{dt},[/tex] differentiate both sides with respect to t,

[tex]\frac{dA}{dt} |_{r=10} = 2\pi (10)(5)[/tex]

= [tex]100\pi m/sec^{2}[/tex]

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The required solutions are as follows,
(a) The distance between A and B is 480 KM.
(b) Kenzi drove 60 km more than Jafar.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
a]

1 cm = 200 km,
Distance between A and B = 2.4 cm = 2.4 [200 km]
                                             = 480 km

b]
Jafar drove for (A to B) = 480 km
Kenzi drove for B to C = 2.7 [200] = 540 km
Difference = 540 - 480 = 60km

Thus, the required solutions are as follows,
(a) The distance between A and B is 480 KM.
(b) Kenzi drove 60 km more than Jafar.

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There is not sufficient evidence to claim that the average age of a US adult getting married is different than 27 years old.

μ₀ = 27

h = 30

X = 26

σ = 7

Hypothesis test at α = 0.025

Null & Alternative hypothesis

H₀: μ = 27

Ha: μ = 27

Test statistics = Z

Z= x-μ/(σ/√h)

= 26-27/(7/√30)

Z = -0.78

p-value

p-value from Z-table at |Z|= 0-78,

two-tailed is p-value = 0.4354

decision-

here p-value = 0-4354 > α=0·025 Since we fail to reject H₀ at 2.5%

Hence, there is not sufficient evidence to claim that the average age of a US adult getting married is different than 27 years old.

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The correct formula to calculate monthly mortgage payment on a loan is [tex]M= P\frac{ [R(1+R)^n]}{[(1+R)^n-1]}[/tex]

Where, M is the total monthly payment

P is the total amount of loan

R is the interest rate

N is the total time

The primary advantage of a mortgage loan is that, unlike most other loans, you can get one without giving up ownership of your house to anybody else and at extremely low interest rates. The monthly mortgage repayment is symbolized by the mortgage payment. The standard four components of a mortgage payment are principal, interest, taxes, and insurance. The principal, term, and interest rate of the mortgage loan, as well as other factors, influence the monthly mortgage payment. The monthly mortgage payment can be calculated using the aforementioned formula or a financial calculator online.

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The parts of graph of a rational function is the asymptotes and the intercepts of the graph.

The graph of a rational function is a hyperbola

The asymptote is a line or curve that acts as the limit of another line or curve. For example, a descending curve that approaches but does not reach the horizontal axis is said to be asymptotic to that axis, which is the asymptote of the curve whereas the intercept of the graph is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis

Therefore,  The asymptotes and the intercepts of the graph are the parts of graph in case of a rational function.

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The frog jumped the total length of 11/6m.

If the fractions have the same denominators then their numerators are added keeping the denominators as the same.

For fractions with different denominators the LCM of the denominators are taken then that is divided by the numerators of each fraction and the number obtained is multiplied to each of them to get the equivalent fraction.

Given that,

The length of first jump of the frog is 2/3m.

The length of second jump of the frog is 5/6m.

And, length of third jump of the frog is 1/3m.

Thus, the sum of all the jumps is given as,

2/3 + 5/6 + 1/3

The LCM of denominators is 6. So, the sum becomes,

(2 × 2 + 5 × 1 + 1 × 2)/6

= 11/6.

Hence, total length of the frog's jump is 11/6m.

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If an ankle injury patient is willing to pay for both operation and inspection steps, Value-added time is less than 50% of cycle time

The ankle injury is under 1.5 times as much pressure with each stride .

In an avergae we travel 1000 miles on foot annully.

Over 14.2 million visits to doctors is due to ankle injuries every year.

However only 15% of the total injuries results in fractures.

Therefore, if an ankle injury patient is willing to pay for both operation and inspection steps, the statements which is true is Value-added time is less than 50% of cycle time

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The candidate that would make the company the most money in their first year of employment is Candidate B

The amount of profit that a candidate can make for the company is:

= ( Number of weeks in year x Profit per week ) - Salary for the year

We shall assume 48 working weeks in a year.

The amount of money made by Candidate A would be:

= ( 48 x 3, 000 ) - 80, 000

= $64, 000

The amount of money made by Candidate B is:

= ( 48 x 2, 400 ) - 45, 000

= $70, 200

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The fractional part of the lawn remains uncut = 1/4.

In this question, we have been given a boy is mowing a rectangular lawn 40ft long and 30ft wide.

He has cut all of it except for a rectangle that is 20ft long and 15ft wide.

The area of the rectangular lawn:

40 x 30 = 1200 sq. ft.

And the area of the uncut part of lawn would be:

20 x 15 = 300 sq. ft.

The fractional part of the lawn that remains uncut would be,

300 / 1200 = 1/4

Therefore, 1/4 part  of the lawn  remains uncut.

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The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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The least number of 6th graders who want to take part in both classes is 145.

The intersection of sets A and B is the set of all the elements which are common to both A and B. The intersection of sets is denoted by the symbol '∩'. Hence, we can write the intersection of A and B as A ∩ B.

The number of graders that want to take geometry is 170.

The number of graders that want to take algebra is 175.

A ∩ G= n(A) + n(G) -( AUB)

=175+170-200

= 345-200

= 145

Therefore, the least number of 6th graders who want to take part in both classes is 145.

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