Adrian measured a line to be 12.8 inches long. If the actual length of the line is 12.7 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?

The equation for the curve shown in the form y = a cos (k (x - b)). -2, 4π/3, -π/3 y = -2cos (4π/3(x + π/3))

Determine the horizontal shift, period, and amplitude.

Given:

1. The amplitude of a cosine graph is the maximum value of the graph. In this case, the amplitude is -2.

2. The period of a cosine graph is the length of one cycle. In this case, the period is 4π/3.

3. The horizontal shift of a cosine graph is the amount the graph is shifted to the left or right. In this case,

The absolute value of the horizontal shift is less than the period, so the horizontal shift is -π/3.

4. To write the equation of the graph in the form y = a cos (k (x - b)), we can use the information from the previous steps.

We know the amplitude is -2, the period is 4π/3, and the horizontal shift is -π/3. Therefore, our equation is: y = -2cos (4π/3(x + π/3)).

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Answer:

Step-by-step explanation:

i cant but someone can habha

Answer:

4x + y = 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 4 , then

y = - 4x + c ← is the partial equation

to find c substitute (2, 7 ) into the partial equation

7 = - 4(2) + c = - 8 + c ( add 8 to both sides )

15 = c

y = - 4x + 15

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

then

y = - 4x + 15 ( add 4x to both sides )

4x + y = 15 ← in standard form

The transformation that maps polygons JKLM into polygon YXWZ is

Using point M as reference (0, -6)

The transformation rule for reflection 90 deg clockwise is  (x, y) → (y, -x)

M (0 -6) → M' (-6, 0)

Reflection across the x-axis  (x, y) → (x, -y)

M' (-6, 0) → M'' (-6, 0)

Translation by (5, 6)  (x, y) → (x + 5, y + 6)

M'' (-6, 0) → M''' (-6 + 5, 0 + 6) = M'' (-1, 6)

M''' = Z (-1, 6)

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The value of f + g when function f(x) = 3x³- 6x  g(x) = x² + 8x - 9  is 3x³ +x² + 2x - 9.

What is a function?

Function can be defined in which it relates an input to output.

Given functions ,

f(x) = 3x³ - 6x

g(x) = x²  + 8x - 9

So,

f+g = 3x³ - 6x + x²  + 8x - 9

= 3x³ +x² - 6x  + 8x - 9

=  3x³ +x² + 2x - 9

So , f+g  = 3x³ +x²  + 2x - 9

Therefore, The value of f + g when f(x) = 3x³ - 6x  g(x) = x² + 8x - 9  is

3x³  +x² + 2x - 9

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Answer:

For the first question:

A) -9.7 > -18.2

For the second:

A) The temperature is warmer in Minnesota than South Dakota.

Step-by-step explanation:

Hope it helps! =D

3(x+5)-2 is 3x + 13.

Knowing this information, all you have to do is find an equivalent expression to 3x + 13.

I'll see you in class tomorrow.

I'm kind of disappointed.

You were my favorite student too.

(and yes, I do have a secret undercover teacher account.)

x-coordinate of the vertex is time in seconds and y-coordinate of the vertex is the height of the football.

Coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given that Jevonte kicks a football. Its height in feet is given by h = -16t² +48t

where t represents the time in seconds after kick.

We have to find x-coordinate (or t-coordinate) of the vertex is time in seconds and y y-coordinate (or h-coordinate) of the vertex is the height of the football.

Hence, x-coordinate of the vertex is time in seconds and y-coordinate of the vertex is the height of the football.

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Answer:

hope this helps :)

The area of the region bounded by f(x)=(x-8)^2, g(x)=-x-2 and the x-axis is the definite integral of f(x)-g(x) from -2 to 8.

The area of the region bounded by f(x)=(x-8)^2, g(x)=-x-2 and the x-axis is given by the definite integral of f(x)-g(x) from -2 to 8. First, expand f(x) and g(x) to get f(x)=x^2-16x+64 and g(x)=-x-2. Then, subtract g(x) from f(x) to get f(x)-g(x)=x^2-16x+66. This is the equation of the area of the region. To calculate the area, use the definite integral of f(x)-g(x) from -2 to 8. This is equivalent to the integral from -2 to 8 of x^2-16x+66 dx. After integrating, the area is given by the expression (x^3/3)-8x^2+66x from -2 to 8, which is equal to 1176/3 units^2. Therefore, the area of the region bounded by f(x), g(x) and the x-axis is 1176/3 units^2.

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Answer:

60

_

100 * 10=

Step-by-step explanation:

6% so that your answer

For this you will use

FV = PV (1+r)^t

FV = Future Value

PV = Present Value

r = rate

t or n = number of periods

$60 is PV

10% (.10) is rate.

2 years is number of periods.

FV = $60(1.10)^2

FV = $72.60

Answer:

117

Step-by-step explanation:

B=D=63

=>the exterior angle at D = 180-63

Answer: 15kg is equivalent to 33.0693 or 33, for short.

Step-by-step explanation:

33.0693 kilograms, or 33, are equal to 15 kilograms.

A pound is about equivalent to 0.45359237 kilograms. By dividing the specified pound value by 0.45359237, one can convert a pound to kilograms. Remember that 1 kg equals 2.2046 lbs when converting weights.

The weight of a kilogram (kg) is said to be 2.2 times that of a pound. Thus, 2.26 pounds are equal to one kilogram of mass. In light of this, we shall now examine some of the primary variations between the pound and the kilogram. A pound is an imperial unit used to measure bulk or weight.

A weight of 500 pounds exceeds a weight of 200 kilograms because 227 kilograms is greater than 200 kilograms.

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Answer:

Step-by-step explanation:

a branch of mathematics that is concerned with mathematical structures closed under the operations of addition and scalar multiplication and that includes the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations.

The area of the base of the solid is equal to e^-2 - 2.

A base of a solid is the region bounded by y = e^-x, the x-axis, the y-axis, and the line x = 2.

To find the area of the base, we need to find the region that is bounded by y = e^-x, the x-axis, and the line x = 2. The x-axis and the line x = 2 act as boundaries, so we need to find the points where y = e^-x intersects these two lines. The x-axis is at y = 0, so the point of intersection is found by solving the equation:

0 = e^-x

Taking the natural logarithm of both sides, we get:

x = -ln(0) = ∞

The line x = 2 intersects y = e^-x at:

e^-x = 2

Taking the natural logarithm of both sides, we get: -x = ln(2)

And solving for x, we get: x = -ln(2)

So, the area of the base is the region bounded by x = -ln(2), x = 2, and y = e^-x. This can be found by integrating e^-x from x = -ln(2) to x = 2. The result is: A = ∫_{-ln(2)}^{2} e^-x dx = -e^-x |_{-ln(2)}^{2} = e^-2 - e^-(-ln(2)) = e^-2 - e^ln(2) = e^-2 - 2.

Therefore, the area of the base of the solid is equal to e^-2 - 2.

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The pans must be sliced in the following way:

B) 5 pieces are equivalent to the fraction 1/8 of the pan.

The number of pieces in each pan will be equal to the product between the numbers of slices (assuming that the sets of slices are perpendicular)

So, if she wants to have pieces of the same size, she needs to:

Slice the first pan in 10 slices.

Slice the second pan in 4 slices.

Now both of these will have:

10*4 = 40 pieces.

B) There are 40 pieces in each pan, so if she served 5, the fraction is:

5/40 = 1/8

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The sum of the angle measures of a polygon with s sides can be calculated using the formula:

(s - 2) * 180 degrees

We can use this formula to solve for s:

2 = (s - 2) * 180

Dividing both sides by 180:

2 / 180 = (s - 2)

Solving for s:

s = 2 + 2 / 180 = 2 + 1 / 90 = 2 + 1 / 90 * 180 / 180 = 2 + 2 / 3

So the number of sides of the polygon is s = 2 + 2 / 3 = 4 2/3.

Since a polygon must have a whole number of sides, s cannot be a fraction, which means this answer is not a valid solution for the number of sides of a polygon. I don't think the problem as stated does not have a valid solution.

The values of the output for steady-state operation at the two operating points xo = 1 and xo = 2 are y(1)=2.4, y(2)=13.2, and the linearized model for both operating points is y(x)=2.4+5.2(x-1), y(1)=2.4 y(2)= 7.6

The given equation is y=x+1.4x³.

The values of the output for steady-state operation are:

Now substitute Xo=1 and Xo=2 in given equation:

y(1)=1+1.4(1)³.

y(1)=2.4

y(2)=2+1.4(2)³.

y(2)=13.2

The formula for linearization is:

[tex]y(x)=y(1)+\frac{dy}{dx} |_x_=_1.(x-1)[/tex]

The first derivative of the formula evaluated at x = 1 is:

[tex]\frac{dy}{dx} |_x_=_1=1+4.2(1)^2\\\\\frac{dy}{dx} |_x_=_1=5.2[/tex]

The linearized model is:

y(x)=2.4+5.2.(x-1)

The output at x = 2 is presented below:

y(x)=2.4+5.2.(2-1)

y(2)=7.6

The linearized model offers reasonable approximations for small intervals.

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u in the plane is not spanned by the columns of A.

If u in the plane in spanned by the columns of A, then u can be obtained by the linear combination of the columns of A. That is

(4, -1, 4) = x(2, 0, 1) + y(5, 1, 2) + z(-1, -1, 0)

In matrix form we get

[tex]\left[\begin{array}{ccc}2&5&-1\\0&1&-1\\1&2&0\end{array}\right]\left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}4&-1&4\end{array}\right][/tex]

Determinant of matrix A is

= 2*1*0 + 5*-1*1 + -1*0*2 - -1*1*1 - 5*0*0 - 2*-1*2

= 0 - 5 + 0 + 1 + 0 + 4

= 0

Determinant of matrix A is 0, thus no solutions exist.

So u cannot be spanned by columns of A.

--The question is incomplete, answering to the question below--

"Let u = [tex]\left[\begin{array}{c}4&-1&4\end{array}\right][/tex] and A = [tex]\left[\begin{array}{ccc}2&5&-1\\0&1&-1\\1&2&0\end{array}\right][/tex] . Is u in the plane is spanned by the columns of A? why or why not?"

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function (f-1)(2) = 18 because the derivative of f at a = 2 is 18x2 + 10x.

We can find out how a function is changing at a specific point by looking at its derivative. We are required to calculate (f-1) in this scenario (2). We must first get the derivative of the given function, f(x) = 3x3 + 3x2 + 5x2, in order to perform this. The derivative of each term can be used to achieve this, giving us 9x2 + 6x + 10x. The derivative of f at a = 2 is equal to 18x2 + 10x when this is evaluated at a = 2. Now, by putting the derivative equal to 0 and finding x, we may calculate (f-1)(2). Thus, we obtain x = -1/9. Once this value has been entered, the original method returns (f-1)(2) = 18.

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(a) The probability that a passenger who died was in the third class is 528 / 817.

we can find the probability by using the formula:

P(Third Class | Died) = P(Third Class and Died) / P(Died)

Where,

P(Third Class and Died) = the joint probability of a passenger being in third class and dying

P(Died) = the probability of a passenger dying regardless of class.

We can find P(Third Class and Died) by adding the no. of passengers in third class who died (528) and then dividing by the total no. of passengers (1317)

P(Third Class and Died) = 528 / 1317

Now we can find P(Died) by adding the no. of passengers who died (817) and dividing by the total no. of passengers (1317)

P(Died) = 817 / 1317

By using the values we got, we can find P(Third Class | Died):

P(Third Class | Died) = P(Third Class and Died) / P(Died) = 528 / 817

So, the probability that a passenger who died was in the third class is 528 / 817.

(b) The probability that a passenger survived given they were in first class is 201 / 324

we can find the probability by using the formula:

P(Survived | First Class) = P(Survived and First Class) / P(First Class)

Where,

P(Survived and First Class) = joint probability of a passenger surviving and being in first class.

P(First Class) = probability of a passenger being in first class regardless of survival.

We can find P(Survived and First Class) by adding the no. of passengers in first class who survived (201) and dividing by the total no. of passengers (1317)

P(Survived and First Class) = 201 / 1317

Now we can find P(First Class) by adding the no. of passengers in first class (324) and dividing by the total no.of passengers (1317):

P(First Class) = 324 / 1317

By using the values we got, we can find P(Survived | First Class):

P(Survived | First Class) = P(Survived and First Class) / P(First Class) = 201 / 324

So, the probability that a passenger survived given they were in first class is 201 / 324.

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Answer:

The slope is 7/1

Step-by-step explanation:

The first valid point is at (-1,-4)

The second valid point is at (0,3)

You start at the (-1,-4) and you count up until you get at the same line as the next valid point, then you count over however many times it takes you to get to that point and in your case it would be up 7 over 1 so 7/1 and it is a positive slope

To calculate the kernel, locate the vector subspace in which the homogeneous implicit equations result from the linear transformation formula's component parts being equal to zero.

A function from one vector space to another that respects the underlying (linear) structure of each vector space is called a linear transformation.

A linear operator, or map, is another name for a linear transformation.

The zero transformation and identity transformation are two significant illustrations of linear transformations.

An illustration of a linear transformation is the zero transformation, which is denoted by T(x)=(0) for every x.

Also linear is the identity transformation denoted by T(x)=(x).

Find the vector subspace in which the implicit equations are the homogeneous equations produced when the components of the linear transformation formula are equal to zero in order to compute the kernel.

This is the same as finding the null space of the linear transformation matrix.

Therefore, to calculate the kernel, locate the vector subspace in which the homogeneous implicit equations result from the linear transformation formula's component parts being equal to zero.

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Answer:4

Step-by-step explanation:

4

Answer:

4

Step-by-step explanation:

The volume of the region is 216.6 cubic units.

The volume of a three-dimensional object is the amount of space it occupies. When we rotate a two-dimensional region about a line, we obtain a three-dimensional object called a solid of revolution.

In this case, we are asked to find the volume of the solid of revolution obtained by rotating the region bounded by the curves y = 4x - x^2 and y = x^2 about the line x = 4.

To find the area of each slice, we need to find the radius of the disc.

In this case, the line of rotation is

=> x = 4,

so the radius of the disc at a point (x, y) on the curve is

=> 4 - x.

To find the height of the slice, we need to find the difference in y-values between the two curves at that x-value.

We can set the two curves equal to each other to find the x-values at which they intersect:

=> 4x - x² = x².

Solving for x, we find that x = -2 and x = 2 are the x-values at which the two curves intersect.

These x-values correspond to the y-values -2 and 8, respectively. Therefore, the height of the slice is

=> 8 + 2 = 10.

To find the volume of the solid, we need to integrate the product of the area of the disc and its height over the interval from x = -2 to x = 2.

The area of the disc is given by

=> π * (4 - x)².

Therefore, the volume of the solid of revolution is given by the following integral:

V = π ∫[-2,2] (4 - x)² x 10 dx

Solving this integral, we find that the volume of the solid is approximately 216.6 cubic units

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Amanda could buy more than 4 inches but less than 8 inches of purple wire to make triangle.

For Amanda to make a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Therefore, the minimum amount of purple wire she could buy would be the sum of the lengths of the blue and green wires (4 inches + 8 inches = 12 inches), minus the length of the longest side (which is 8 inches), so 12 inches - 8 inches = 4 inches.

The maximum amount of purple wire she could buy would be the sum of the lengths of the two shorter sides (4 inches + 4 inches = 8 inches).

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The largest possible sample space for a standard deviation is infinity as the number of observations can be infinity.

The standard deviation is a measurement of how much a group of values vary or are dispersed. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean.

There are several mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

The standard deviation is significant because it reveals the degree of dispersion of the values in a particular dataset. Every time we examine a dataset, we look for the following metrics: the dataset's geographic center. The mean and median are the two metrics most frequently used to gauge the "center."

The largest possible sample space for a standard deviation is infinity as the number of observations can be infinity.

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This system of equations has been solved graphically and their solution is equal to the ordered pair (-1, 2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x + 2y = 3     ......equation 1.

-x + 3y = 7     ......equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II and it is given by the ordered pair (-1, 2)

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In this case, the x sampling distribution will be normal, with a mean equal to the population mean (u) and a standard deviation equal to the population standard deviation (a) divided by the sample size squared (n).

The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

Here,

The central limit theorem asserts that, regardless of the form of the underlying population, as the sample size, n, grows, the sampling distribution of x becomes essentially normal, provided n is big enough (usually n >= 30). This is because, regardless of the form of the underlying population, the sum of independent random variables from the same population will tend to become regularly distributed. In this situation, the sampling distribution of x will resemble a normal distribution, with a mean equal to the population mean (u) and a standard deviation equal to the population standard deviation (a) divided by the sample size squared (n).

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