Question 3 of 10
Find the solution(s) to x2 - 12x + 36 = 0.
A. x = 6 and x = -6
B. x = 6 only
C. x = 4 and x = 9
OD. x = -2 and x = 18
SUBMI

The values of x that make the given vectors orthogonal are xi = 5 and xi = -2.

The dot product of two vectors is equal to zero when the vectors are orthogonal. Thus, to find the values of X such that the given vectors are  orthogonal, we must set the dot product of the two vectors to zero and then solve the resulting equation. The dot product of two vectors is calculated by taking the sum of the product of the corresponding components of the two vectors. In this case, the dot product of the two vectors is calculated as:

(xi + 2xj) • (xi - 5j) = xi2 + 2xixj - 5xi - 10xj

Setting this equal to zero and solving for x, we obtain

xi2 + 2xixj - 5xi - 10xj = 0

Subtracting 2xixj from both sides, we get

xi2 - 5xi - 10xj = -2xixj

Factorizing the left-hand side, we get

(xi - 5)(xi + 2) = -2xixj

Setting the two factors on the left-hand side equal to zero and solving for x, we get

xi - 5 = 0  => xi = 5

and

xi + 2 = 0  => xi = -2

Thus, the values of x that make the given vectors orthogonal are xi = 5 and xi = -2.

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The r-value which suggests a weak negative correlation is B. r = -0.1847.

In statistics, the term "pattern" or "connection" refers to a pattern or relationship between two variables. The degree to which two variables move in opposition to one another is characterized by a negative correlation. For instance, when X and Y are the two variables, a rise in X causes a reduction in Y. Inverse correlation is another name for a negative correlation coefficient. Scatterplots are used to visualise correlation relationships.

We know that the negative correlation weakens as it moves closer to a positive value. From the given values we see that the weakest negative correlation is r = -1847.

Hence, the r-value which suggests a weak negative correlation is B. r = -0.1847.

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   The value of  [tex]P(68 < \bar{X} < 70)[/tex] is  0.759298

What is average/mean ?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Given mean [tex]\mu[/tex]=69.5 , S=3

Consider  [tex]P(68 < \bar{X} < 70)[/tex]

              = P[ (68-69.5)/(3/√20) < ( [tex]\bar{X} -\mu[/tex] )/(S/√n) < (70-69.5)/(3/√20) ]

              =  P ( -2.23607 < Z < 0.74535 )

              = P ( Z< 0.7453) - P(Z < -2.2360 )

              = 0.77197 - 0.01267

              = 0.759298

Hence,  [tex]P(68 < \bar{X} < 70)[/tex] =  0.759298

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height of men in america have a normal distribution with a mean of 69.5  inches and a standard deviation of 3 inches. In a random sample of 20 adult men in the united states find [tex]P(68 < \bar{X} < 70)[/tex]

Answer:

The w-intercept of the line of fit is 2.75, and it means that a kitten who is just born is predicted to weigh 2.75 ounces. This is because the equation of the line of fit is w = 2.75 + 0.2d, where w is the weight of the kitten in ounces and d is the age of the kitten in days. When d = 0, the equation becomes w = 2.75, so the w-intercept is 2.75.

Step-by-step explanation:

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t is the parameter, n is the unit normal vector, and κ is the curvature of the space curve.

To find t, n, and κ for the space curve r(t)=-ti-(a cos h (t/a))j, first calculate the position vector r, which is r(t)=-ti-(a cos h (t/a))j. Then, calculate the derivative of the position vector to find the tangent vector t, which is t=i+(t/a)sin h(t/a)j. Next, calculate the second derivative of the position vector to find the normal vector n, which is n=(-(1/a) sin h(t/a))i+(1/a2)(cos h(t/a))j. Lastly, calculate the curvature κ by dividing the magnitude of the second derivative of the position vector by the square of the magnitude of the first derivative, which is κ=(1/a2)(cos h(t/a))/(1+(t/a) sin h(t/a))2.

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D (2,-3)

Just look where the lines meet

Answer: D IS CORRECT

Step-by-step explanation:

The equation for the tangent line to f(x) = ln(x) at x = 2 is y = 1/2x - 1.

1. Start with the equation for a line in slope-intercept form: y = mx + b

2. Substitute in the slope, which in this case is 1/2 since f'(2) = 1/2: y = 1/2x + b

3. Find the y-intercept, which is the point where the line crosses the y-axis. In this problem, we know that f(2) = ln(2), so we can substitute in 2 for x and ln(2) for y in our equation: ln(2) = 1/2(2) + b

4. Using algebra, solve for b: b = ln(2) - 1

5. Substitute b back into our equation to get the final answer: y = 1/2x - 1

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The speed of the truck in km/h at the end of this distance is equal to 81.43 km/h.

The time elapsed is equal to 0.7939 seconds.

In order to determine the speed of the truck in km/h at the end of this distance, we would apply the third equation of motion:

v² = u² + 2as

Where:  

Next, we would convert the value of deceleration in m/s² to km/h² as follows;

Deceleration, a = 6.5 × 60⁴/1000 = -84,240 km/h².

Distance, s = 20/1000 = 0.02 m.

Substituting the given parameters into the third equation of motion, we have;

v² = 100² + 2(-84,240)(0.02)

Speed, v = √(10,000 - 3,369.6)

Speed, v = √6,630.4

Speed, v = 81.43 km/h.

Lastly, we would determine the time by using the first equation of motion:

V = U + at

Time, t = (V - U)/a

Time, t = (100 km/h - 81.43 km/h)/6.5

Time, t = [(100 × 1000/3600) - (81.43 × 1000/3600)]/6.5

Time, t = (27.78 - 22.62)/6.5

Time, t = 5.16/6.5

Time, t = 0.7939 seconds.

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Complete Question:

The driver of a pick up truck going 100 km/h applies the brakes, giving the truck a uniform deceleration of 6.50 m/s^2 while it travels 20.0 m.

a. What is the speed of the truck in km/h at the end of this distance?

b. How much time has elapsed?

The analyst could use the geom_jitter() function to make the points easier to find.

It is difficult for the analyst to distinguish the individual points on the plot because they overlap.

In this question we have been given a data analyst creates a scatterplot with a lot of data points. It is difficult for the analyst to distinguish the individual points on the plot because they overlap.

We need to find a function that could the analyst use to make the points easier to find.

We know that overplotting is caused due to discreteness in smaller datasets.

A function geom_jitter() adds a small random variation to the location of each point, which is a useful way of handling overplotting.

Whereas the function geom_point() adds a layer of points to given plot, which creates a scatterplot.

Therefore, geom_jitter() make the points easier to find.

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The analyst could use the geom_jitter() function to make the points easier to find.

It is difficult for the analyst to distinguish the individual points on the plot because they overlap.

In this question we have been given a data analyst creates a scatterplot with a lot of data points. It is difficult for the analyst to distinguish the individual points on the plot because they overlap.

We need to find a function that could the analyst use to make the points easier to find.

We know that overplotting is caused due to discreteness in smaller datasets.

A function geom_jitter() adds a small random variation to the location of each point, which is a useful way of handling overplotting.

Whereas the function geom_point() adds a layer of points to a given plot, which creates a scatterplot.

Therefore, geom_jitter() makes the points easier to find.

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Answer:

the answers are D and C they both look like triangle T

Answer:

B&F

Step-by-step explanation:

T bottom is 2 squares, side is 3 squares,

so we just need to look for all the shapes with multiples of 2 & 3

Count each, if base is 2 multiple by 2, 3, 4, etc.,

then side must be multiplied by the same

so only B & F satisfy this rule

The corresponding values of x and y is (4, -2), (0, 0) and (2, 10).

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=2x²+x.

substitute the value of x to get the corresponding value of y

When x = -2

y = 2x² + x

= 2(-2)² + (-2)

= 2(4) - 2

= 6 - 2

= 4

(x, y) = (4, -2)

When x = 0

y = 2x² + x

= 2(0)² + 0

= 2(0) + 0

= 0 + 0

= 0

(x, y) = (0, 0)

When x = 2

y = 2x² + x

= 2(2)² + 2

= 2(4) + 2

= 8 + 2

= 10

(x, y) = (2, 10)

Therefore, the corresponding values of x and y is (4, -2), (0, 0) and (2, 10).

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The number of cubes that would be needed to be added to turn the shape into a solid 3x4x4 cuboid would be = 24 cubes.

A cuboid is defined as the type of quadrilateral that has 6 faces, 8 vertices, and 12 edges.

The volume of the cuboid;

volume of the cuboid;= l×w×h

= 3x4x4

= 48cm³

The volume of each cube = 1cm×1cm×1cm

The number of cubes available= 24 cubes

Therefore the remaining cubes = 48-24 = 24 cubes.

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9 kilometers represents the distance from one point to another point. 9 kilometers is equal to 5.59234073013601 miles.

What is the unit of distance?

Any arbitrarily selected and widely used reference standard for length measurement is referred to as a unit of length. The metric system, which is adopted by every nation on earth, is the most widely used in modern times. The American customary units are also in use in the United States.

The S.I. unit of distance is kilometers.

Given that the distance between the two points is 9 kilometers.

1 kilometer is equivalent to 0.621371 miles

9 kilometers is equivalent to 0.621371×9 miles

                                              = 5.59234073013601 miles

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for a uniform probability density function, the height of the function is determined by the constant value that the function takes over the interval of definition, and it is determined by the requirement that the integral of the function over the interval of definition must be equal to

1. The height of a uniform probability density function over an interval [a,b] is given by:

f(x) = 1/(b-a) for a <= x <= b

where b-a is the length of the interval.

A uniform distribution is a continuous probability distribution and connected to the events which are likely to occur equally. A uniform distribution is explained by two parameters, a and b, where a is the minimum value and b is the maximum value.

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The intersection of a triangle's three medians is known as the centroid. It is always inside the triangle since it is the center of mass (or center of gravity).

A triangle's three perpendicular bisectors all meet at this same location. The circumcenter is the location where each perpendicular bisector intersects the other. 1. The circumcenter, or center of the circle, is where the circle is bounded.

Because of this, the circumcenter may be located either inside or outside the triangle. The two points of concurrency that are able to do that are the circumcenter and orthocenter.

An intersection of three or more lines is known as a point of concurrency. The four points of concurrency are the centroid, the orthocenter, the circumcenter, and the incenter. The point of concurrency where a triangle's three medians cross is known as the centroid.

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The three angle bisectors of a triangle are concurrent. Their point of concurrence is called the incenter.

The triangle's three angle bisectors are contemporaneous, which means they cross at the same place.

The incenter is the location where the angle bisectors coincide.

1. The circle's inscribed center is known as the incenter.

2. The incenter is equidistant from the triangle's sides.

More examples of agreement

The centroid is the location where all of a triangle's medians meet.

The triangle's circumcenter is where the perpendicular bisectors of its sides meet.

The intersection of the perpendiculars emanating from the vertices on the opposing sides of a triangle is known as the orthocentre.

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The values in the table do not represent a proportional relationship. The y-values are not a constant multiple of the corresponding x-values.

A proportional relationship exists between two variables when one variable is equal to a constant multiple of the other variable. In the given table, if x increases by 1 unit, the corresponding increase in y is not always the same.

For example, when x increases from 1 to 2, y increases by 2 units (from 3 to 5), but when x increases from 2 to 3, y increases by only 1 unit (from 5 to 6). This lack of a constant ratio between x and y means that the relationship between the two variables is not proportional.

The applicability of proportional relationships depends on the specific problem and the nature of the relationship between the variables being considered. In some cases, a proportional relationship may not be the best model to describe the relationship between variables, and alternative models may be more appropriate.

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The greater angle has a measurement of 152 degrees. The smaller angle has a measurement of 28 degrees.

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles. An angle is formed by joining two rays (half-lines) that have a shared terminal. The latter is referred to as the angle's vertex, while the rays are referred to as the angle's sides, legs, and arms. An angle is a figure in Plane Geometry generated by two rays or lines that share a common endpoint.

Here,

x+y=180

x=y/4-10

y/4-10+y=180

y+4y=190*4

5y=760

y=152°

x=28°

The measure of the larger angle is 152 degree. The measure of the smaller angle is 28 degree.

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The value of the limit is 12.

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.

It is employed in the analysis process and constantly considers how the function will behave at a specific moment.

We can expand the cube:

(2+h)³ = 8+12h +6h²+ h³

Plugging this in,

lim (h->0)8+12h +6h²+ h³-8 / h = lim (h->0) 12h +6h²+ h³ / h

=> lim (h->0) (12h +6h+ h²) = 12

The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals. The upper limit and lower limit for definite integrals are correctly specified.

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Answer: 17500 miles

Step-by-step explanation:

The system of equation have 0 = 0, so this system must have infinitely many solutions.

The system of equations are:

-x(1) + 3x(2) - 2x(3) = 4,

-x(1) + 4x(2) − 3x(3) = 5,

-x(1) + 5x(2) - 4x(3) = 6

An approach for resolving networks of linear equations is called Gaussian elimination, commonly referred to as row reduction. It comprises of a series of operations carried out on the relevant coefficients matrix.

[tex]\left [ \begin{matrix}-1 &3 & -2\\ -1 &4 &-3 \\ -1&5 & -4\end{matrix} \right ]\begin{bmatrix}x(1)\\ x(2)\\ x(3)\end{bmatrix}=\begin{bmatrix}4\\ 5\\ 6\end{bmatrix}[/tex]

The matrix is in the form of

[A][X] = [D]

To solve the matrix we represent the matrix in the form of [A : D]

Now writing the augmented matrix

[tex]\left [ \left.\begin{matrix}-1 &3 & -2\\ -1 &4 &-3 \\ -1&5 & -4 \end{matrix}\right| \begin{matrix}4\\5 \\6 \end{matrix}\right ][/tex]

Now solving the matrix

R(2)→R(2) - R(1) and R(3)→R(3) - R(1)

[tex]\left [ \left.\begin{matrix}-1 &3 & -2\\ 0 &1 &-1 \\ 0&2 & -2 \end{matrix}\right| \begin{matrix}4\\1 \\2 \end{matrix}\right ][/tex]

R(1)→R(1) - R(3)

[tex]\left [ \left.\begin{matrix}-1 &1 & 0\\ 0 &1 &-1 \\ 0&2 & -2 \end{matrix}\right| \begin{matrix}2\\1 \\2 \end{matrix}\right ][/tex]

R(3)→R(3) - 2R(2)

[tex]\left [ \left.\begin{matrix}-1 &1 & 0\\ 0 &1 &-1 \\ 0&0 & 0 \end{matrix}\right| \begin{matrix}2\\1 \\0 \end{matrix}\right ][/tex]

Now we can see that the last every elements are zero, which shows

0 = 0

So the system of equation have infinitely many solutions.

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The complete question is:

Attempt to solve the system

-x(1) + 3x(2) - 2x(3) = 4,

-x(1) + 4x(2) − 3x(3) = 5,

-x(1) + 5x(2) - 4x(3) = 6,

using gaussian elimination and explain why this system must have infinitely many solutions.

The value of the modulus function is g ( x ) = | x | - 4

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the absolute value function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = | x |   be equation (1)

Now , the function f ( x ) is shifted vertically down by 4 units

Down by d units: y = f(x) - d

Substituting the values in the equation , we get

Let the translated function be represented as g ( x )

g ( x ) = f ( x ) - 4

On simplifying the equation , we get

g ( x ) = | x | - 4

Hence , the transformed function is g ( x ) = | x | - 4

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The triangles in this problem are similar.

Similar triangles share these two features:

For this problem, we have that the side lengths are proportional, as:

3/6 = 4/8 = 5/10 = 0.5.

(same ratio, applying the trigonometric ratios we would find them to have the same angle measures).

However, the triangles in this problem are not congruent, as they have different side lengths.

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At the end of 2018, the world population was approximately 7.53 billion people. This figure is calculated by taking the total population at the end of 2017, 7.4 billion people, and multiplying it by the population growth rate of 1.07%..

This means that the world population increased by approximately 130 million people in 2018. This population growth rate is consistent with the average growth rate of the world population over the last decade. While the population growth rate has been decreasing over the past few decades, it is still relatively high at 1.07%.

The high population growth rate is primarily due to high fertility rates in developing countries and a longer life expectancy in developed countries. This means that more people are born and fewer people die each year. As a result, the total population of the world increases each year.

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Answer:

8/100

Step-by-step explanation:

first we will find the value of 10^-2

to find negative exponents we turn into a fraction like this

1/10^2

and simplify

1/100

0.01

now to find 64^1/2

we use the formula pictured below

(2√64)^1

8^1

8

and now we multiply

8x0.01

0.08

turn it into a fraction

8/100

hopes this helps

The radius of the cone is given by the equation r = 4 inches

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Surface area of the cone = πrl

where l = √ ( b² + r² )

Given data ,

Let the radius of the cone be represented as r

Now , the equation will be

The volume of the cone = 64π inches³

The height of the cone h = 12 inches

So , Volume of Cone = ( 1/3 ) πr²h

Substituting the values in the equation , we get

64π = ( 1/3 )π r² ( 12 )

Divide by π on both sides of the equation , we get

64 = 4r²

Divide by 4 on both sides of the equation , we get

r² = 16

Taking square roots on both sides of the equation , we get

r = 4 inches

Therefore , the value of r is 4 inches

Hence , the radius of cone is 4 inches

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The integrating factor is x³, and the general solution is y = x⁹/12 + C/x³. When putting y(1) = 9, the initial value problem's solution is y = x⁹/12 + 107/12x³.

Now, the equation given to us is:

[tex]y' + 3x^{-1}y = x^8\\[/tex]

Since the equation is not seperable by variables, therefore we have to use the integrating factor method (IF Method).

The ordinary linear differential equations are represented in the following general form:

y’ + P y=Q or dy/dx + P(x) y = Q(x)

Integrating factor is defined as the function which is selected in order to solve the given differential equation. It is most commonly used in ordinary linear differential equations of the first order.

When the given differential equation is of the form;

dy/dx + P(x) y = Q(x)

then the integrating factor is defined as:

μ = [tex]e^{\int{Px} \, dx }[/tex]
where P(x) (the function of x) is a multiple of y and μ denotes integrating factor.

For this equation, the Integrating Factor is:

IF = [tex]e^{3\int{\frac{1}{x} }\, dx }[/tex] = x³

Multiplying both sides of the equation by the IF,

μy' + μ3x^{-1}y = μx^8

x³y' + 3x²y = x¹¹

On solving it, we get the general solution as:

y = x⁹/12 + C/x³

We know that the initial value is y(1) = 9

Substituting y = 9 when x = 1 in the general value,

9 = 1/12 + C/1

C = 9 - 1/12 = 107/12

Therefore, the particular solution is

y = x⁹/12 + 107/12x³

Thus, the integrating factor is x³, and the general solution is y = x⁹/12 + C/x³. When putting y(1) = 9, the initial value problem's solution is y = x⁹/12 + 107/12x³.

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The magnitude of the net force Fnet on the negative charge due to all other charges is 1102.5 N. So, correct option is (a).

Forces are caused by interactions between objects, and they can result from a variety of sources, such as gravitational attraction, electromagnetic interactions, and friction. Forces can be balanced, meaning that the sum of all forces acting on an object is equal to zero, or they can be unbalanced, meaning that the sum of all forces is not equal to zero. Unbalanced forces cause changes in an object's velocity and acceleration, and they can result in changes in an object's position, direction, and speed.

In physics, forces play a central role in our understanding of the world and the laws of motion. They are used to describe the behavior of objects in motion and to analyze the interactions between objects. The study of forces and the interactions between objects is known as mechanics, and it forms the foundation of classical physics.

Overall, the concept of force is a fundamental and important idea in physics and is used to describe and understand the behavior of objects in motion and the interactions between objects.

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(1)a total of 28  ways the student can select 3 writing implements

2)A total of 25 ways the selection be made if no more than one ballpoint pen is selected.

For the first question, the student has three different types of writing implements and thus three different ways to make a selection. The student can choose any combination of three pencils, three ballpoint pens, or three felt-tip pens. This is known as a combination problem and can be solved using the combination formula. The combination formula, which is often written as "n choose k" (where n is the number of objects and k is the number of objects to be selected), can be used to calculate the total number of possible combinations.

In this case, the student has 4 pencils, 3 ballpoint pens, and 1 felt-tip pen, so the combination formula would be (4 choose 3) + (3 choose 3) + (1 choose 3). This simplifies to 28, meaning that there are 28 possible ways the student can select 3 writing implements.  

For the second question, the student is limited to selecting no more than one ballpoint pen. Since the student can only select one ballpoint pen, the combination formula would now be (4 choose 3) + (2 choose 3) + (1 choose 3). This simplifies to 25, meaning that there are 25 possible ways the student can select 3 writing implements without selecting more than one ballpoint pen.

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