when u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin. T/F

The x value when the y value equals 12 is calculated to be 31

From the problem the equation is deduced to be : x = 2y + 7

When y = 12,

we can substitute this value into the equation to find the corresponding x value:

x = 2(12) + 7

x = 24 + 7

x = 31

Therefore, the x value when the y value equals 12 is 31.

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Answer: 10 yards is equivalent to 30 feet.

Step-by-step explanation:

In 30 feet, there are 10 yards. Therefore 3 feet are equal to 1 yard. To precisely calculate the length in feet, divide 4 yards by 3.

Add three to the total number of yards.

Add 10 to 3 since 3 feet are equivalent to 1 yard.

10 × 3 = 30.

10 yards equal 30 feet.

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Answer:

1/4=0.25

Step-by-step explanation:

The probability that both students pick the same tire is (1/4) * (1/4) = 1/16

The probability of the first student picking a specific tire is 1 in 4, or 1/4. The probability of the second student also picking that same tire is also 1 in 4. To find the probability that both students pick the same tire, we need to multiply the probabilities of each event.

So, the probability that both students pick the same tire is (1/4) * (1/4) = 1/16. This means that the chance of both students picking the same tire is 0.0625 or 6.25%.

To summarize, there are four possible tires that could have gotten a flat, and two students are asked to identify the tire. If each student randomly chooses a tire, the probability that both students will pick the same tire is 1 in 16, or 0.0625. This means that the chance of both students picking the same tire is low, and the likelihood of them choosing different tires is much higher.

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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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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 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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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 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 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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Answer: 17500 miles

Step-by-step explanation:

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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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 given inequality states that the value of x is greater than 3 and less than or equal to 4.

3 ≥ x > 4

Given inequality: 3 < x ≤ 4

Negating the given inequality:

1. Negate the inequality symbol:

3 ≥ x

2. Negate the comparison operator:

3 ≥ x > 4

The given inequality states that the value of x is greater than 3 and less than or equal to 4. When we negate this inequality, we get that the value of x is greater than or equal to 3 and greater than 4. This means that the fully simplified negation of 3 < x ≤ 4 is 3 ≥ x > 4.

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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 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]

The complete table of values is

x  1   2   3  4

y  4  7  10  13

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

y = 3x + 1

Set the variable x from 1 to 4

So, we have

y = 3 * 1 + 1 = 4

y = 3 * 2 + 1 = 7

y = 3 * 3 + 1 = 10

y = 3 * 4 + 1 = 13

When represented on a table of values, we have

x  1   2   3  4

y  4  7  10  13

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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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(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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The exponential Function is  y(t) = 1500 [tex]e^{-0.0.325t[/tex].

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

An exponential function is defined by the formula f(x) = [tex]a^x[/tex], where the input variable x occurs as an exponent.

Given:

Forest covered the area of = 1500 Km²

Now, the area is decreased by 3.25%

So, the exponential Function to represent the situation

y(0)= 1500 km², r = -3.25% = - 0.0325

y(t) = A [tex]e^{rt[/tex], and A = y(0) = 1500

so, y(t) = 1500 [tex]e^{-0.0.325t[/tex]

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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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Answer: C. 12000(1.05)^n < 20000

Step-by-step explanation:

When it says that the tuition is increasing at a rate of 5%, it means that you add 1

1+0.5= 1.05

Everything else is the same so you just add 1 to 0.5 and that is the answer.

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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The tangent line on the curve x = 3t² + 5 , y = t³ - 7 have a slope as 1/2 at the point (8, -6).

The Tangent Line to a curve at a specific point is calculated  by the derivative of the curve at that point.

The Slope of the tangent line at a point (x₀, y₀) is given by the derivative of the curve at that point, denoted as f'(x₀).

The curve x = 3t² + 5 , y = t³ - 7 ,

we have to find the value of t such that the slope of the tangent line at that point is 1/2.

we first find the derivative of y with respect to x, which is given by:

⇒ dy/dt = 3t² and dx/dt = 6t

Using chain rule to find the derivative of y with respect to x:

⇒ dy/dx = dy/dt × dt/dx = (3t²)/6t = t/2

Next, we equate derivative to 1/2 and solve for t ;

⇒ t/2 = 1/2

⇒ t = 1

So, the point where the tangent line has slope 1/2 is

⇒ (x, y) = (3t² + 5, t³ - 7)

⇒ (8, -6).

Therefore , the point is (8,-6) .

The given question is incomplete , the complete question is

At what point on the curve x = 3t² + 5 , y = t³ - 7 , does the tangent line have slope as "1/2" ?

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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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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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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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A running shoe manufacturer randomly selects 386 of its shoes for quality assurance and finds that 3. 12% of these shoes are found to be defective. The number of successes (defective shoes) is 12

The number of defective shoes can be calculated by multiplying the percentage of defective shoes (3.12%) by the total number of shoes selected (386).

(3.12/100) * 386 = 12

So, the number of successes (defective shoes) is 12

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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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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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