hat is required in order to determine whether or not an object moves?

a reference point
distance
displacement
standard units

Answer:

Option 3

Step-by-step explanation:

33 / 3 + 10 = 21

1.) 5(3 + 5) = 40

2.) 10(1 + 1) = 22

3.) 3(6 + 1) = 21

Answer:

Answer would be 3

Step-by-step explanation:

2(10+1)= 21 and

33 divided by 3 + 10 = 21

If Leona and Fred are friendly competitors in high school. the probability that the scores differ by 5 or more points in either direction is: 0.0771.

Let F = Fred

Let L= Leona

In a situation where F and L are respective score , F -  L is has this distribution N(0, √2² + 2²)

Now let find the Probability

P(Fred score 5 point more than Leona) + P(Leona score 5 point more than Fred)

= P(F-L>5) +P(L-F>5) = P(Z> 5-0/√8) +  P(Z> 0-5/√8)

P(Z>1.7678)+ =P(Z< -1.7678)

=2P(Z>1.7678)

=2(0.03854)

=0.0771

Therefore the probability is 0.0771.

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Answer:

a

Step-by-step explanation:

because printer b has more pictures. to print

Answer:

x = 0, 2π/3, 4π/3, 2π.

Step-by-step explanation:

cos 2x = 2cos^2x - 1 so

2cos^2x - 1 = cos x

2cos^2x - cos x - 1 = 0

(2cosx + 1)(cos x - 1) =0

cos x = -1/2, 1.

When cos x = 1, x = 0, 2π

when cos x = -1/2, x = 2π/3, 4π/3.

In a binomial distribution, the number of ways of arranging all trials to be failures is 1. This means that there is only one way to have all trials result in failures, as each trial can only have one possible outcome - a failure.

1. In a binomial distribution, each trial can result in either a success or a failure. Let's assume that there are n trials in total.

2. To arrange all trials to be failures, we need to ensure that no trial results in a success. Therefore, for each trial, there is only one possible outcome - a failure.

3. The number of ways of arranging all trials to be failures can be calculated using combinations. In this case, we need to select 0 successes from n trials. The number of ways to do this is given by the combination formula: C(n, 0) = 1, where C represents the combination.

Therefore, the number of ways of arranging all trials to be failures in a binomial distribution is given by the combination formula, C(n, k) = n! / (k! * (n-k)!).

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The number of ways of arranging all trials to be failures in a binomial distribution is always 1. This is because there is only one way to have no successes in a set of trials.

Regardless of the number of trials or the probability of success, the number of ways of arranging all trials to be failures in a binomial distribution is always 1.

The number of ways of arranging all trials to be failures in a binomial distribution can be determined using the formula for the binomial coefficient.
The binomial coefficient, often denoted as nCk or n choose k, represents the number of ways to choose k items from a set of n items, without considering their order. In the context of a binomial distribution, n represents the total number of trials and k represents the number of successes (in this case, 0).
To find the number of ways of arranging all trials to be failures, we can use the binomial coefficient formula:
nCk = n! / (k!(n-k)!)
In this case, since we want all trials to be failures, k is equal to 0. Thus, the formula simplifies to:
nC0 = n! / (0!(n-0)!) = n! / (0! * n!) = 1

For example, if we have 5 trials and we want all of them to be failures, there is only one possible arrangement: FFFFF, where F represents a failure.

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Answer:

d-2

Step-by-step explanation:

Answer:

The most important characteristic of a correlation coefficient is the absolute value.

The absolute value of a correlation coefficient represents the strength of the relationship between two variables, regardless of the direction of the relationship. A correlation coefficient can range from -1 to +1, where a value of -1 indicates a perfect negative correlation (i.e., as one variable increases, the other decreases), a value of +1 indicates a perfect positive correlation (i.e., as one variable increases, the other also increases), and a value of 0 indicates no correlation (i.e., there is no relationship between the variables).

The most important characteristic of a correlation coefficient is the absolute value.

The absolute value of the correlation coefficient represents the strength of the relationship between two variables, regardless of its direction. It indicates the degree to which the variables are associated with each other.

By focusing on the absolute value, we can assess the magnitude of the correlation without being influenced by whether it is positive or negative. For example, a correlation coefficient of -0.8 or +0.8 both indicate a strong relationship, while a correlation coefficient of 0 suggests no relationship.

The number of variables included is not a characteristic of the correlation coefficient itself, but rather a consideration in the analysis. One-tailed and two-tailed refer to the type of hypothesis being tested and are relevant in statistical testing. However, the absolute value of the correlation coefficient is crucial in determining the strength of the relationship between variables, making it the most important characteristic to assess in correlation analysis.

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An area of mathematics that studies how competing parties interact is known as "game theory."

Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.

Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.

The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.

Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.

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Step-by-step explanation:

Divide the 12 by the 3 and you get 4 so multiply the 2 by 4 and you got your answer. Hope this helps.

Answer:

The correct answer is x= - 3

Step-by-step explanation:

Answer:

-2/5

Step-by-step explanation:

Answer:

x = -2/5 or -0.4

Step-by-step explanation:

The non-permissible replacement of the variable in a certain expression is the value of x that will make the denominator of the expression zero.

=============================================================

Then,

⇒ 5x + 2 = 0

⇒ 5x = -2

⇒ x = -2/5 or -0.4

The pigeonhole principle guarantees that at least 1 pair of students (or possibly more) were born on the same day of the week.

The pigeonhole principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must have more than one pigeon.

Applied to this problem, there are 7 days of the week (pigeon holes) and 54 students (pigeons) enrolled in the two hybrid classes.

Therefore, the maximum number of students that can be born on different days of the week is 7 (one student born on each day), leaving 47 students that must share a day of the week.

Thus, the pigeonhole principle guarantees that at least 1 pair of students (or possibly more) were born on the same day of the week.

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a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

To write a rational number as a decimal, you need to divide the numerator by the denominator. Let's go through each option to determine which decimal is repeating or terminating.

a. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

b. 0: This decimal is also terminating because there are no numbers after the decimal point. The rational number is 0.

c. 0.16 overbar: This decimal has a line over the 16, indicating that it is repeating. The rational number is 0.161616...

d. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

So, to summarize:

a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

.

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The equation of the polynomial is P(x) = (x - 4)(x - 6)(x + 3)²

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zeros 4 and 6 is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x - (-3))² * (x - 4) * (x - 6)

This gives

P(x) = (x - 4)(x - 6)(x + 3)²

Hence, the equation is P(x) = (x - 4)(x - 6)(x + 3)²

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(a)  T satisfies both additivity and homogeneity so it is a linear operator.

(b) A basis for ker(T) is { (2, -1, 0) }.

(c)  The determinant of the linear operator T is -6.

(a) To show that T is a linear operator, we need to demonstrate two properties: additivity and homogeneity.

Additivity:

Let u, v be vectors in R³ and c be a scalar. We need to show that T(u + cv) = T(u) + cT(v).

T(u + cv) = (<u + cv, (1, 2, 3)>, <u + cv, (4, 5, 6)>, <u + cv, (7, 8, 9)>)

= (<u, (1, 2, 3)> + c<v, (1, 2, 3)>, <u, (4, 5, 6)> + c<v, (4, 5, 6)>, <u, (7, 8, 9)> + c<v, (7, 8, 9)>)

= (<u, (1, 2, 3)>, <u, (4, 5, 6)>, <u, (7, 8, 9)>) + c(<v, (1, 2, 3)>, <v, (4, 5, 6)>, <v, (7, 8, 9)>)

= T(u) + cT(v)

This shows that T is additive.

Let v be a vector in R³ and c be a scalar.

We need to show that T(cv) = cT(v).

T(cv) = (<cv, (1, 2, 3)>, <cv, (4, 5, 6)>, <cv, (7, 8, 9)>)

= c<v, (1, 2, 3)>, c<v, (4, 5, 6)>, c<v, (7, 8, 9)>

= c(<v, (1, 2, 3)>, <v, (4, 5, 6)>, <v, (7, 8, 9)>)

= cT(v)

This shows that T is homogeneous.

Since T satisfies both additivity and homogeneity, it is a linear operator.

(b)

T(v) = (<v, (1, 2, 3)>, <v, (4, 5, 6)>, <v, (7, 8, 9)>) = (0, 0, 0)

From the first component, we have <v, (1, 2, 3)> = 0.

From the second component, we have <v, (4, 5, 6)> = 0.

From the third component, we have <v, (7, 8, 9)> = 0.

These equations represent three planes in R³ passing through the origin, and the intersection of these planes will give us the kernel of T.

Solving these equations, we find that the solution is the span of the vector (2, -1, 0).

Therefore, a basis for ker(T) is { (2, -1, 0) }.

(c)

The determinant of the linear operator T.

T(v) = (<v, (1, 2, 3)>, <v, (4, 5, 6)>, <v, (7, 8, 9)>)

To find the determinant of T, we can write T as a matrix and compute its determinant.

T can be written as the following matrix:

\(\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]\)

det(T) = 1(45 - 48) - 2(36 - 42) + 3(32 - 35)

det(T) = -3 - 12 + 9

det(T) = -6

Therefore, the determinant of the linear operator T is -6.

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Let T: R³ -->R³ be a map from the Euclidean inner product space R to itself defined by T(v)=(<v, (1,2,3)>, <v,(4,5,6)>, <v, <(7, 8, 9)> ) for all vectors VE R³. (a) Show that T is a linear operator. (2 marks) (b) Find a basis of ker(T). (2 marks) (c) Find det(T). (2 marks)

Answer:

2 Height ft and 6.75 length ft

Step-by-step explanation:

You just decrease it to 1:16

so, 34:108 is 2:6.75 to be about the same size as 1:16

Answer:

B

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

So the ladder is 4 feet from the wall and 18 feet tall. This can translate to negative 4 spaces on the x-axis and 18 spaces on the y-axis. The slope of a line is rise over run which is 18/4 or 4.5

I hope the answer is right and I hope I helped. Have fun with the rest of your math :)

Answer:

30°

Step-by-step explanation:

\( \sin \theta = \frac{1}{2} \\ \\ \sin \theta = \sin 30\degree \\ \\ \theta = 30 \degree\)

Answer:

6x - 8

Step-by-step explanation:

Distribute 1/2 to all terms within the parenthesis:

1/2(12x - 16) = (12x - 16)/2

12x/2 = 6x

-16/2 = -8

6x - 8 is your answer.

~

We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.

Given that,

The number is either 1-digit or 2-digit.

In the case of 1-digit, the only 1-digit primes are 3 and 7, for a total of 2 primes.

In the case of 2-digit, We have the following combinations of numbers: 13, 16, 17, 36, 37, 67, 76, 73, 63, 71, 61, 31. Out of these 12 numbers, it is easier to count the composites: 16, 36, 76, and 63 for a total of 4 composites, which we subtract from the original 12 numbers to yield 12-4=8 prime numbers.

Thus, We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.

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Let's transform the equation into slope intercept form first ~

that is ~

now, equate the equation with general equation of line in slope intercept form (that is : y = mx + c) where, m = slope of the line and c = its y - intercept.

So, we get the value of m (slope) as ~

where as the value of c (y - intercept) is ~

I hope it helps ~

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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The probability that the spinner will land on a number that is not between 22 and 30, inclusive is 0.62

The given parameters are

Spinner = 1 to 50

This means that

Sections = 50

There are 31 sections that are not between 22 and 30, inclusive

This means that the probability is

P = 31/50

Evaluate

P = 0.62

Hence, the probability that the spinner will land on a number that is not between 22 and 30, inclusive is 0.62

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Dave has $11 and he buys a book for $8 but he spends an equal amount of money on 2 cards. Let's model this problem with an inequality.

x = $ spent on one card.

2x + $8 ≤ $11

Let's subtract $8 from both sides.

2x ≤ $3

Divide both sides by 2

x ≤ $1.5

Dave can spend at most $1.5 on each card.

The equation that models this scenario is: \(c(x) = -2x^2 + 16x + 168\).

Given:

Average number of students per session = 14

Fee per session = $12

For every $2 increase in the fee.

Let x be the number of $2 fee increases.

So, the fee for each session is $12 + ($2 x) as there is a $2 increase for each x.

and, the average reduces by 1 for each $2 increase then the average number of students per session is 14 - x.

Now, the revenue generated

\({\text} Revenue (c(x)) =\) \({\text} Fee per session * Average number of students per session\)

Substituting the values of fee per session = 12 + 2x and Average= 14- x into above formula as:

\(c(x) = (12 + (2 x)) * (14 - x)\)

Expanding and simplifying the equation:

\(c(x) = (12 + 2x) * (14 - x)\)

\(c(x) = 168 - 12x + 28x - 2x^2\)

\(c(x) = -2x^2 + 16x + 168\)

Therefore, the equation is: \(c(x) = -2x^2 + 16x + 168\)

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Th question attached here seems to be incomplete, the complete question is:

Type the correct answer in each blank. Use numerals instead of words. If necessary, use / for the fraction bar(s). John hosts an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. He estimates that for every $2 increases in the fee, the average number of students reduces by 1. Complete the equation that models this scenario, where c(x) is the revenue generated and x is the number of $2 fee increases.

c(x) =_x^2 +_x+_

Answer:

Step-by-step explanation:

its correct [hope this helped]