the velocity function (in meters per second) for a particle moving along a line is grven by u(t) : 2t-4, for 0 ( t < 6 (in seconds). what is the total distance traveied by the particle during this interval of tim

Answer:

x = 1

Step-by-step explanation:

2(x - 2)= -2

2x - 4 = -2

2x = 2

x = 1

Answer:

x = 1

Step-by-step explanation:

2(x - 2) = -2

Solve for x

Divide each side by 2

2/2(x - 2) = -2/2

x-2 = -1

Add 2 to each side

x - 2+2 = -1+2

x = 1

The required probability of a sum of 5 or sum of 7 and the first die shows a 3 or the sum of the result is 6 or 8 are 5/18 and 1/18 receptively.

Probability is just the way that logical something is to occur. Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions administered by likelihood is called statistics.

Two fair dice are thrown then the number of  possible way is 6×6 = 36

a) a sum of 5 or sum of 7 :-

The total possible way for dice occurs sum 5 or sum 7 is (1, 4), (2, 3), (3, 2), (4, 1), (1, 6), (2, 4), (3, 4), (4, 3), (5, 2), (6, 1).

So, the total number possible way for dice occurs sum 5 or sum 7 = 10.

Probability = 10/36 = 5/18

Hence, the probability is 5/18.

b) The first dice shows 3 or the sum of the result is 6 or 8 :-

As, first dice shows 3 we have fixed 3 in first dice or results sum is 6 or 8 then second dice possibilities only consist two number either 3 or 5,

So, total possible ways for first dice shows 3 or sum of result is 6 or 8 is (3, 3), (3, 5).

There are only two ways,

Therefore, probability = 2/36 = 1/18

Hence, the probability is 1/18.

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The value of Three less than eight times a number is at least 15 is x≥6

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or explain the overall situation, this is known as an equation.

Given ,

8x

3 less goes to 8x-3

then there is at least 15 which changes to

8x-3≥15

Then solve for x:

add 3 to the sides--> 3x≥15+3

3x≥18

Divide both of the sides by 3

x≥6

Therefore  the value of three less than eight times a number is at least 15 is x≥6

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In any group of 6 people there always at least 3 people who either all know one-another or all are strangers to one-another.

The Pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.

The Pigeonhole principle applies because every person is related to every other person in two ways, either they know the person or they do not.

Given that there is a group of 6 people.

Let us say A,B,C,D,E,F.

Suppose that A has at least three friends. If any two of these three are friends with each other, then together with A, they are a group of three mutual friends. If none of these are friends with each other, then they are a group of three mutual strangers to themselves.

On the other hand, A has fewer than three friends among the other five people, then there must be at least three that are strangers to A. If any two of these are strangers, then together with A, they are a group of three strangers. If none of them are strangers to each other, then they are a group of at least three mutual friends.

Hence it is proved that, in any group of 6 people there are always at least 3 people who either all know one-another or all are strangers to one-another.

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It is difficult to determine the exact volume of a cherry tree without cutting it down, but researchers can use other variables, such as height and diameter, to predict the tree's volume. In a study of black cherry trees

The measurement of how much space an item or substance occupies is called volume. The Allegheny National Forest is occupied by the tree's trunk and branches. Typically, the volume of an object or substance is stated in cubic units, such as cubic feet or cubic metres. The volume variables were looked at in order to comprehend them. Given that it is difficult to quantify without cutting the tree down, the volume of the tree was calculated given its height and diameter. This knowledge may be useful in estimating the potential while looking for them.

Typically, the volume of an object or substance is expressed in cubic units, such as cubic feet or cubic metres. It is determined by multiplying an object's length, breadth, and height.

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A roster of twenty-four players divided into four teams can be represented by the expression 24/4.

Given

24 players total

(4) teams total.

This can be expression as = 24 / 4.

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Answer:

The sale price is 39.99 % off

Step-by-step explanation:

To find the percentage off,

take 49.99 - 30.00 = 19.99

Then divide by 49.99

19.99/49.99

39.9879976

The sale price is 39.99 % off

1 square unit looks like the area of a square with side measuring 1 unit.

According to the question,

We have the following information:

1 square unit

Now, we know that the square units mean that it is the area of the figure. Now, it can be for any figure whether it is a triangle or square or a circle but the measurements of the sides in such a way that the area found using the formulas of the given figure should be 1 square unit.

For example, if the side of the square is 1 unit then the area of the square is 1 square unit.

Hence, 1 square unit looks like the area of a square with side measuring 1 unit.

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Answer:

7/9

Step-by-step explanation:

total: 3+2+4

starbucks or crazy mocho: 3+4

(3+4)/(3+2+4)=7/9

In hypothesis testing, the critical value is option (d) a number that establishes the boundary of the rejection region

The hypothesis testing is defined as the process of collecting the data and using that as inference draw the calculation about the population parameter.

The reject region of the hypothesis testing is defined as the  set of values for the test statistic for which the null hypothesis is rejected.

Therefore, the critical value is  a number that establishes the boundary of the rejection region of the graph

Hence, in hypothesis testing, the critical value is option (d)  a number that establishes the boundary of the rejection region

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Answer:

Unknown

Step-by-step explanation:

What is N? Can you show the numberline?

Answer:

the answer is 8 or more then 8

The system of inequalities did not have any solution, but after reversing the  sign we will get a solution of the system of inequalities.

The inequalities are : y > 2x + 2/3 and y < 2x + 1/3

There is no intersection and no solution to the system since the region above the line y = 2x + 2/3 and the region below the line y = 2x + 1/3, respectively, are the solutions to the inequality y > 2x + 2/3 and y <2x + 1/3, respectively.

Now when the signs are changed we get:

y < 2x + 2/3 and y > 2x + 1/3

The region below the line y = 2x + 2/3 is the solution of the inequality

y= 2x + 2/3, and the region above the line y = 2x + 1/3 is the solution of the inequality y > 2x + 1/3. This implies that the area between the two lines is where the system's solution lies.

Disclaimer: The complete question is :

How will the solution of the system y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?

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Answer:

There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions. 

Step-by-step explanation:

Sample answer

The matching terms and processes are;

1. The nervous system's ability to acquire, retain, and retrieve information- memory

2. Remembering stored information- retrieval

3. Processing information for storage- encoding

4. Retention of information- storage

Given,

The nervous system's capacity for information acquisition, storage, and retrieval is known as memory. Information is processed for storage by encoding, whereas information is remembered from storage through retrieval. Information is retained through storage.

Memory is the process of storing and recalling previously acquired information. The act of storing involves adding new information to the memory, which the brain alters for improved storage. It is easier for the brain to access and bring into conscious mind information that has been encoded.

Information is stored so that it will last throughout time. Modern memory psychology distinguishes between two basic types of memory storage: short-term memory and long-term memory.

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Given question is incomplete. Completed question is here;

Match the terms with their corresponding processes.

a. memory

b. encoding

c. retrieval

d. storage

1. the nervous system's ability to acquire, retain, and retrieve information

2. remembering stored information

3. processing information for storage

4. retention of information

The two numbers are 12 and 26.

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.

Let x and y be the 2 numbers

x+y=38........(1)

8+2x=5y.......(2)

(1) => x=38-y

8+2(38-y)=5y

8+76-2y=5y

84=5y+2y=7y

y=84/7 = 12

when y=12, x=38-y = 38 - 12 = 26

So, the two numbers are 12 and 26.

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The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.

A histogram is a bar graph-like representation of data that groups a range of classes into columns along the horizontal x-axis. The vertical y-axis represents the number count or percentage of occurrences in the data for each column. Columns can be used to visualized as patterns of data distributions.

Lesser the value of n larger the variablity.

Arranging from the least value of n to the naximum value, the order is A, C, B

Therefore, The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.

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Answer:

Step-by-step explanation:

The Subgraph Isomorphism Problem is NP and NP-Hard. Therefore, the subgraph isomorphism problem is NP-Complete.

What is  Subgraph Isomorphism?

In theoretical computer science, the subgraph isomorphism drawback could be a procedure task during which 2 graphs G and H ar given as input, and one should confirm whether or not G contains a subgraph that's similarity to H.

Proof:

Certificate: Let G be a subgraph of G2. We also know the mapping between the vertices of G1 and G.

Verification: We have to visualize if G1 is isomorphous to G or not. (i) Checking if the mapping could be a bijection and (ii) confirming if, for each edge (u, v) in G1, there's a foothold (f(u), f(v)) gift in G takes polynomial time.

Therefore, the Subgraph similarity downside has polynomial time verifiability and belongs to the NP category.

The Subgraph similarity drawback belongs to NP-Hard –A drawback L belongs to NP-Hard if each NP drawback is reducible to L in polynomial time. To prove that the Subgraph similarity drawback (S) is NP-Hard, we have a tendency to associate degreed} scale back an already celebrated NP-Hard drawback to S for a selected instance. If this reduction is feasible in polynomial time, then S is additionally associate degree NP-Hard drawback. Thus, allow us to scale back the ingroup call drawback (C) that is NP-Complete (hence, all the issues in NP will be reduced to C in polynomial time) to the Subgraph similarity drawback. If this reduction is feasible in polynomial time, each NP drawback will be reduced to S in polynomial time, thereby proving S to be NP-Hard.

Proof:

Let us prove that the Clique Decision Problem reduces to the Subgraph Isomorphism Problem in polynomial time.

Let the input to the set call drawback be (G, k). The output is true if the graph G contains a set of size k (a set of size k may be a subgraph of G). Let G1 be a whole graph of k vertices and G2 be G, where G1, G2 ar inputs to the Subgraph isomorphy drawback. we have a tendency to observe that k n, then a set of size k can't be a subgraph of G. The time taken to form G1 is O(k2) = O(n2) [since k]as the range of edges in a very complete graph of size k = kC2 = k*(k-1)/2. G contains a pack of size k, if and as long as G1 could be a subgraph of G2 (since G1 itself could be a subgraph of G2 and each graph is similarity to itself, the results of the Subgraph similarity downside is true. Thus, G1 is similarity to a subgraph of G2). Hence, if the pack call downside is true, the Subgraph similarity downside is true and the other way around. Therefore, the pack call downside will be reduced to the Subgraph similarity downside in polynomial time for a specific instance.

Thus, the Subgraph Isomorphism Problem is an NP-Hard Problem

hence,

The Subgraph Isomorphism Problem is NP and NP-Hard. Therefore, the subgraph isomorphism problem is NP-Complete.

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As per the area of rectangle, the dimensions of the rectangle that maximize the enclosed area is 200 yard.

Area of rectangle:

The standard formula to calculate the are of the rectangle is.

A = l x b

l refers the length

b refers the breadth

Given,

Sienna has 800 yards of fencing to enclose a rectangular area.

Area can be maximized by fencing a square of side 200 yards.

Here we need to find the dimensions of the rectangle that maximize the enclosed area.

Let us consider  x be one of the side and a be the perimeter then the other side would be written as,

=> a/2 - x

And the and area of the rectangle would be

=> x (a/2 - x).

Then the function will be zero when first derivative of the function is equal to zero and second derivative is negative,

So, as per the first derivative is written as,

=> − 2 x + a/2

And this will be zero, when the equation,

=> − 2 x + a/2 = 0 or x = a/4.

Here we have to note that second derivative is − 2.

And then the two sides will be a/4 each that the it would be square.

Therefore, if perimeter is 800 yards and it is a square, one side would be 800/4 = 200 yards.

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The probability of drawing two pink ones if the first marble was not put back before the 2nd drawing is 2/9.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that there are 10 marbles in the bag 2 yellow 3 pink and 5 blue.

First, we need to find the probability of drawing a blue marble on the first draw.

Since there are 5 blue marbles and 10 total, then the probability is;

5⁄10, or 1/2.

Now, we no longer have that blue marble, there are 4 blue marbles and 9 total.

The chances of drawing a blue marble are; 4/9.

Therefore, the chance that both marbles drawn are blue is the chance that the first one is blue times the chance that the second one is blue.

1/2 x  4/9 = 4/18 = 2/9

Hence, the probability of drawing two pink ones if the first marble was not put back before the 2nd drawing is 2/9.

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The research is important for the students because it helps them to have a detailed analysis of everything. When you have a proper in-depth analysis of any topic, the result comes out to be fruitful and also the knowledge is enhanced.

The research is important for the students because it helps them to have a detailed analysis of everything. When you have a proper in-depth analysis of any topic, the result comes out to be fruitful and also the knowledge is enhanced.

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Answer:

139 degrees

Step-by-step explanation:

you just add both the angles together since they share a vertex

The measures of the two complementary angles are 28 and 62 degrees

Complementary angles:

In math, the sum of two angles is equal to 90 degrees, they are called complementary angles.

Given,

Here the two angles are complementary if the sum of their measures is 90.

And we need to find the measures of two complementary angles if one angle is more than 6 times the other angle.

Let us consider A is the measure of the smaller angle and B is the measure of the larger angle.

Here we know that they are complementary 

=> A + B = 90

Here we also know that,

=> 2A + 6 = B

Now, we have to replace B in the first equation with the second equation, then we get,

=> A + 2A + 6 = 90

Now, solve for A:

=> 3A + 6 = 90

=> 3A = 84

Therefore, the value of A is 28

Then the value of B is,

=> 2(28) + 6 = 62

Therefore, the two angles that complementary are: 28 and 62 degrees

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Sum of all positive integers having twice as many digits when written in base  $2$  as they have when written is base $3$ is 10.

This is because the only two integers which fits the constraint are 2 and 8,

2 in base 10 =10 in base 2 = 2 in base 3

8 in base 10 =1000 in base 2 = 22 in base 3.

The result of the expression $a+b$ is 11

This is because the LCM of [1!+2!, 2!+3!, 3!+4!, 4!+5!, 5!+6!, 6!+7!, 7!+8!, 8!+9!] =3,628,800

Which can be written as :  1. 10! = 1 + 10 = 11

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We have given a election data of n voters in an upcoming election in a certain country, where n is a large, even number. There are two candidates, A and B. Thus,

a) Using Normal approximation, the probability of tie the election is φ (1/√n) - φ(-1/√n) in terms of φ

b) Using Talyor expansion, the probability of a tie is approximately c/√n where c = √2/π.

We have given that,

Total number of voters in an election = n where n is large and even .

Number of candidates who elected the election

= 2 = { A,B}

Each voter choose randomly one of both independently.

a) Using Normal approximation we have calculate to the probability of a tie, in terms of Φ.

n is a large even number

let X be a random variable of number of votes

Tie will occur when X = n/2 , here p = 1/2

X ~ Bin (n,1/2) = N (n/2 , n/4)

P(X = n/2) = P(n/2 - 1/2 < X < n/2+1/2)

= P(-1/2/(sqrt(n/4) < Z< 1/2/(sqrt(n/4))

= P(-1/sqrt(n) <Z< 1/sqrt(n))

= φ (1/√n) - φ(-1/√n)

b) Using the Taylor's Expansion in answer of part(a)

φ (x) = 1/√2π ( x - x³/6 + x⁵/40 - x⁷/336+---)

= φ (1/√n) - φ(-1/√n)

= 1/√2π (1/√n - (-1/√n))

= 1/√2π ( 2/√n)

= √2/π ×1/√n = c/√n

where , c = √2/π

Hence, the required probability is c/√n.

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Procedure for regrouping to find sum is as follows as mentioned.

Regrouping is accomplished by forming groups of tens during operations such as subtraction and addition. Regrouping is the process of rearranging numbers into groups based on place value to make operations easier.

This is known as regrouping because you are rearranging numbers into place value to complete the process.

Assume we want to add 18 and 12, which equals 30.

1. It is best to visualise your problem as a grid when regrouping with addition.

              1 2

         +   1 8

2.In this situation, the first addition would be to add 2 and 8, which equals 10. However, there is no place to write 10 on the bottom row. In this case, regrouping is required. To accomplish this, we take the 0 from the 10 and place it in the bottom row, followed by the 1 above our ten's column. Below is an updated grid:          

     1

     12

   +1 8

        0       

3.We must now add up the tens column. In this case, we have three one-digit numbers to add together. This brings us to the correct solution answer, which is 30.

1

1 2

1 8

3 0

Hence, the regrouping is the simplest way to do addition.

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5 types of cubical are: dedicated, Private office, L-shaped, circular, High walled cubicles

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If we consider the function y=2x+1 then the inverse of the function comes to be  y=(x−1)/2.

Each element in the range of an original function f is mapped to its corresponding element in the domain by the inverse function f ⁻¹.

Finding inverse of a function

It is typical to consider the x values as the domain and the y values as the range when considering an equation. The domain and range of f are reversed by the inverse function, f ⁻¹, as was previously mentioned. Flip the x and the y, then solve for y to determine the inverse of a written function.

Find the inverse.

                    y=2x+1

1. Switch the x and y.

                    x=2y+1

2. Then solve the equation for the y value.

                      x−1=2y

                      y=(x−1)/2

The graph of the inverse function is the mirror image to y=x axis

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Answer:

C

Step-by-step explanation:

Denominator can't be 0

Therefore, [tex]x-7\neq 0[/tex]

Adding 7 to both sides gives [tex]x\neq 7[/tex]

Only C corresponds to our answer.

The school cook ordered p packages of hot dog buns for the year-end picnic. Each package contains 8 buns. Write an expression that shows how many hot dog buns were ordered.

order = 8p