question a circle has a radius of 21 inches. what is the length of the arc intercepted by a central angle that measures 4π7 radians? express the answer in terms of π . enter your answer in the box.

The image of the vector (1, -3, 0) under the linear transformation T is (-4, -5, 8).

The linear transformation T: R³ → R³, defined by T(1, 0, 0) = (-1, 4, 2), T(0, 1, 0) = (1, 3, -2), and T(0, 0, 1) = (0, 2, -2), can be used to find the image of the vector (1, -3, 0) under T.

To find the image of the vector (1, -3, 0) under the linear transformation T, we can use the linearity property of the transformation. Since T is a linear transformation, we can express any vector v = (x, y, z) as a linear combination of the standard basis vectors (1, 0, 0), (0, 1, 0), and (0, 0, 1).

The given information states that T(1, 0, 0) = (-1, 4, 2), T(0, 1, 0) = (1, 3, -2), and T(0, 0, 1) = (0, 2, -2). Using these values, we can express (1, -3, 0) as a linear combination:

T(1, -3, 0) = T(1, 0, 0) - 3T(0, 1, 0) + 0T(0, 0, 1)

           = (-1, 4, 2) - 3(1, 3, -2) + 0(0, 2, -2)

           = (-1, 4, 2) - (3, 9, -6) + (0, 0, 0)

           = (-1 - 3 + 0, 4 - 9 + 0, 2 + 6 + 0)

           = (-4, -5, 8)

Therefore, the image of the vector (1, -3, 0) under the linear transformation T is (-4, -5, 8).

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Answer:

82°

Step-by-step explanation:

(8x-7)=(x+16)

x+16+x=180

2x+16=180

2x=180-16

2x=164

2x/2=164/2

x=82°

Answer:

Answer is 0

Step-by-step explanation:

-6x-6=x²-5x-6

-6(x+1)=(x+1)(x-6)

-6=x-6

x=0

(a) The ball's height when it leaves the child's hand is 3 feet.

(b) The maximum height of the ball is 3.5625 feet.

(c) The ball strikes the ground approximately 32 feet away from the child.

The ball strikes the ground approximately -16 + 32√(22) feet away from the child in the forward direction.

(a) To find the height of the ball when it leaves the child's hand, we need to determine the value of y when x is zero. Plugging x = 0 into the equation y = -1/16x^2 + 2x + 3, we get:

y = -1/16(0)^2 + 2(0) + 3

y = 3

Therefore, the ball is 3 feet high when it leaves the child's hand.

(b) The maximum height of the ball can be found by finding the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, the equation is y = -1/16x^2 + 2x + 3, so a = -1/16 and b = 2. Plugging these values into the formula, we get:

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

x = -16/32

x = -1/2

To find the corresponding y-coordinate, we substitute this value back into the equation:

y = -1/16(-1/2)^2 + 2(-1/2) + 3

y = -1/16(1/4) - 1 + 3

y = 1/64 - 64/64 + 192/64

y = 129/64

Therefore, the maximum height of the ball is 129/64 feet.

(c) The ball strikes the ground when its height is zero. To find the distance from the child where this occurs, we set y = 0 and solve for x:

0 = -1/16x^2 + 2x + 3

This equation can be solved using various methods such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula here:

x = (-2 ± √(2^2 - 4(-1/16)(3)))/(2(-1/16))

x = (-2 ± √(4 + 3/2))/(2(-1/16))

x = (-2 ± √(11/2))/(2(-1/16))

x = (-2 ± √(11/2))/(-1/8)

x = (-2 ± 4√(22))/(1/8)

Since we're interested in the positive value of x (the ball strikes the ground in the forward direction), we take the positive square root and simplify:

x = (-2 + 4√(22))/(1/8)

x = 8(-2 + 4√(22))

x = -16 + 32√(22)

Therefore, the ball strikes the ground approximately -16 + 32√(22) feet away from the child in the forward direction.

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Answer:

7. 78

8. 169

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

cherry street is 85 yards, while orange dr. and peach ave. is 113 yards, meaning that cherry st. is 28 yards faster

Step-by-step explanation:

85 x 85) - (77 - 77) = 1296

square root of 1296 is 36

77 + 36 = 113

113 - 85 = 28

this means that cherry st. is 28 yds faster

using the Pythagorean Theorum

hope i helped

-lvr

Answer:

sine=opposite/hypotenuse

sine=6/10

sine=0.6

sine^-1 0.6

=36.87

Complete question :

At a certain bus station, 47% of all arrivals are late. Suppose a random

sample of 12 bus arrivals is examined. Using the binomial function, give the probability of ;

Atleast 8 late arrivals 2) At most 4 late arrivals

Answer:

P(x >= 8) = 0.1411 ;

P(x ≤ 4) = 0.2570

Step-by-step explanation:

Using the binomial probability distribution relation :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

p = 47% = 0.47

1 - p = 0.53

n = 12

A.)

Atleast 8 late arrivals

P(x >= 8) :p(x = 8)+p(x =9)+p(x=10)+p(x=11)+p(x=12)

Using a binomial distribution calculator to save computation time :

P(x >= 8) = 0.141096

P(x >= 8) = 0.1411

B.)

P(x ≤ 4) = p(x=0)+p(x=1)+p(x=2)+p(x=3)+p(x=4)

Using a binomial probability calculator ;

P(x ≤ 4) = 0.25697

P(x ≤ 4) = 0.2570

Answer:

$2,550.20

Step-by-step explanation:

just took the test and got it right!

Answer:

C - 18 pi

Step-by-step explanation:

edge

Answer:

5/18

108

A sector has an area of 30π in.2. The radii containing the sector form an angle of 100°. What is the area of the circle?

The ratio of the angle of the sector to the entire circle is

✔ 5/18

.

Area of the sector = StartFraction n degrees over 360 degrees EndFraction (pi) (r squared). 30 pi = StartFraction 100 degrees over 360 degrees EndFraction (pi) (r squared). (StartFraction 18 over 5 EndFraction) 30 pi = (pi) r squared.

The area of the entire circle is

✔ 108

Pi in.2

Given point: (5, -3)Given equation of the line: y = x + 2We are supposed to find the equation of the line passing through the point (5, -3) that is parallel to the line y = x + 2.

First, we need to find the slope of the given line y = x + 2. Here, the slope is 1 as the coefficient of x is 1.Now, a line parallel to this line will also have the same slope. Therefore, the slope of the required line is also 1.Now we have the slope and the point (5, -3) that the line passes through. Using the point-slope form of the equation of a line, we can find the equation of the line that passes through the given point and has the given slope.So, the equation of the line passing through the point (5, -3) that is parallel to the line y = x + 2 is:y - (-3) = 1(x - 5)This can be simplified to obtain the equation in the slope-intercept form:y = x - 8Thus, the equation of the line is y = x - 8.

To find the equation of a line parallel to the line y = x^2 and passing through the point (5, -3), we need to determine the slope of the given line and then use it to construct the equation.

The slope of the line y = x^2 can be determined by taking the derivative of the equation with respect to x. In this case, the derivative is:

dy/dx = 2x

Since the derivative represents the slope of the original line, we know that the slope of the line y = x^2 is 2x. To find the slope of the parallel line, we use the fact that parallel lines have the same slope.

Therefore, the slope of the parallel line is also 2x.

Now, using the point-slope form of a linear equation, we can write the equation of the parallel line:

y - y1 = m(x - x1)

where (x1, y1) is the given point (5, -3) and m is the slope.

Plugging in the values, we have:

y - (-3) = 2x(x - 5)

Simplifying further:

y + 3 = 2x^2 - 10x

Rearranging the equation to the standard form:

2x^2 - 10x - y - 3 = 0

So, the equation of the line passing through the point (5, -3) and parallel to the line y = x^2 is 2x^2 - 10x - y - 3 = 0.

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We have to find the equation of the line passing through the point [tex]$(5,-3)$[/tex] that is parallel to the line [tex]$y=x+2$[/tex].

Therefore, the equation of the line passing through the point [tex]$(5,-3)$[/tex] and parallel to the line [tex]$y=x+2$[/tex] is:

[tex]$y=x-8$[/tex].

As we know, the parallel lines have the same slope. Therefore, the slope of the line passing through the point (5,-3) will be the same as the slope of the line y=x+2.

Thus, we can write the slope-intercept form of the equation of the line y = mx + b as follows:

y = mx + b ------(1)

Here, m is slope of the line, b is y-intercept of the line. For the line y=x+2, slope of the line is:

m=1

Now, we will find the value of b for the line y = mx + b passing through the point (5,-3).

[tex]$$-3=1\times5+b$$$$[/tex]

[tex]b=-8$$[/tex]

Therefore, the equation of the line passing through the point (5,-3) and parallel to the line y=x+2 is:

y=x-8

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Answer:

since it is Right angled isosceles triangle it's base side are equal

by using Pythagoras law

x²+x²=1²

2x²=1

x=√{1/2}or 0.707 or 0.71

Answer:Yes

Step-by-step explanation:

Answer:

WOAH!!!!

Step-by-step explanation:

Thx for sharing that!

Mark as brainlist plssss.

Answer:

Wow

Step-by-step explanation:

Answer:

5 2/6

Step-by-step explanation:

you have to mutiply

Answer:

90 degrees

Step-by-step explanation:

The three angles of a triangle always add up to 180 degrees, so knowing this, all three of the measures given should add up to 180.

First, you need to solve for x:

S(x+10) + R(2x+60) + T(50+x) = 180

Add up all of the like terms:

10 + 60 + 50 = 120

x + 2x + x = 4x

So now you are left with 4x + 120 = 180

And solve for x:

4x/4 + 120/4 = 180/4

x + 30 = 45

x + 30-30 = 45-30

x = 15

Now that we have the value of x, plug it into the measure given for angle R:

(2x+60)

= (2(15)+60)

= (30 + 60)

= 90

So the measure of angle R is 90 degrees.

I hope this helped! :)

Answer:

Step-by-step explanation:

Use the Pythagorean Theorem. The hypotenuse, 14  square should be equal to the sum of x squared + 10 squared.

14^2 = 196

10^2 = 100.

So, 196 = 100 + x^2

[tex]x = \sqrt{96}[/tex]  

the solution of system of linear equations is x = 27/2, y = 21/2, z = -1/2

To solve the system of linear equations using the Gaussian Elimination Method with Partial Pivoting, we'll perform the following steps:

Step 1: Set up the augmented matrix for the system of equations.

Step 2: Perform row operations to eliminate variables below the main diagonal.

Step 3: Back-substitute to find the values of the variables.

Let's proceed with the calculations:

Step 1: Augmented matrix setup

The augmented matrix for the system of equations is:

[ 0.5  -0.5   1 |  1 ]

[-0.5   1   -0.5 |  4 ]

[  1   -0.5  0.5 |  8 ]

Step 2: Row operations

[ 0.5  -0.5   1 |  1 ]

[-0.5   1   -0.5 |  4 ]

[  1   -0.5  0.5 |  8 ]

R₂ -> R₂ + R₁

[ 0.5  -0.5   1 |  1 ]

[0   0.5   0.5 |  5 ]

[  1   -0.5  0.5 |  8 ]

R₃ -> R₃ - 2R₁

[ 0.5  -0.5   1 |  1 ]

[0   0.5   0.5 |  5 ]

[  0   0.5  -1.5 |  6 ]

R₃ -> R₃ - R₂

[ 0.5  -0.5   1 |  1 ]

[0   0.5   0.5 |  5 ]

[  0   0  -2 |  1 ]

The new augmented matrix after the row operations is:

[ 0.5  -0.5   1 |  1 ]

[0   0.5   0.5 |  5 ]

[  0   0  -2 |  1 ]

Step 3: Back-substitution

Now, we'll back-substitute to find the values of the variables. Starting from the last row, we can directly determine the value of z:

-2z = 1

z = - 1/2

Substituting z = - 1/2 into the second equation, we can find the value of y:

0.5y + 0.5z = 5

0.5y + 0.5(-1/2) = 5

y = 21/2

0.5x - 0.5y + z = 1

0.5x - 0.5(21/2) + (-1/2) = 1

x = 27/2

Therefore, the solution of system of linear equations is x = 27/2, y = 21/2, z = -1/2

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Answer:

False

True

True

Step-by-step explanation:

Multiplying add exponents

Divide subtract exponents

Exponent multiply exponents

The statement and reason for each equation is written below:

Multiplication law is a law of indices that governs the multiplication of variable. if they are of the same base they add up their powers.

Division law is also a law of indices that governs division of variables, and it states that for every division the  bases are equal we subtract their powers

In conclusion, The statement and reason for each equation is written above.

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Answer:

Large number =52

small number =13

Step-by-step explanation:

4x + x =65

5x=65

x=13

4x=52

.186915888

that is the answer

if I meant 2.675 divided by .5 it is 5.35

Answer:

you can use a calculator but, its 0.1869158878504672897196261682243

Step-by-step explanation:

a) The  scatter diagram is shown below.

b) The estimated regression equation for the given data is given as [tex]y = 5.47 + 1.18x[/tex].

c) When x = 6, the estimated value of y is approximately 12.65.

d) T

e) The sample correlation coefficient is approximately 0.8107.

f) In this case, the standard error of the estimate is approximately 5.10.

g) Without these details, it is not possible to conduct the t-test.

Scatter diagram is a visual representation of data points plotted on a Cartesian coordinate system. It is used to display the relationship between two variables.

a) To develop a scatter diagram, plot the given data points (xi, yi) on a graph, where xi represents the values of the independent variable and yi represents the values of the dependent variable. The  scatter diagram is shown below.

b) To develop the estimated regression equation, we need to find the equation of the line that best fits the data points. This line represents the relationship between the independent variable (x) and the dependent variable (y). The estimated regression equation is given by:

y = a + bx

where "a" represents the y-intercept and "b" represents the slope of the line.

Using statistical methods such as least squares regression, the estimated regression equation can be calculated. In this case, the estimated regression equation is:

y = 5.47 + 1.18x

c) To predict the value of y when x = 6, substitute x = 6 into the estimated regression equation:

y = 5.47 + 1.18(6)

y = 12.65

Therefore, when x = 6, the estimated value of y is approximately 12.65.

d) The percentage of the total sum of squares accounted for by the estimated regression equation is given by the coefficient of determination (R-squared). It represents the proportion of the total variation in the dependent variable (y) that can be explained by the independent variable (x) through the estimated regression equation.

In this case, the coefficient of determination (R-squared) is 0.6563, or approximately 65.63%. This means that the estimated regression equation can account for about 65.63% of the total variation in the dependent variable.

e) The sample correlation coefficient (r) measures the strength and direction of the linear relationship between the two variables. In this case, the sample correlation coefficient is approximately 0.8107, indicating a strong positive linear relationship between the variables.

f) The standard error of the estimate measures the average distance between the observed data points and the predicted values from the regression equation. In this case, the standard error of the estimate is approximately 5.10.

g) To test for a significant relationship using the t-test, you would need additional information such as the sample size and the significance level (α) specified in the question. Without these details, it is not possible to conduct the t-test.

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Answer:

x= -2635

Step-by-step explanation:

2 - 2197 - 10 x 44 = x

2- 2197 - 440 = x

-2635 = x

Answer:

x= -2635

Step-by-step explanation:

2 - 2197 - 10 x 44 = x

2- 2197 - 440 = x

-2635 = x

Answer:

Similar by: SAS

ΔPKM ~ ΔLQM

Yes, the triangles PMK and LMQ are similar by SAS similarity statement.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The triangles PKM and triangle LMQ are the similar triangles.

If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent

Both the triangles have a common angle M and two sides are proportional

∠LMQ = ∠PMK

The sides are proportional

LM/PM = QM/KM

The triangles are similar

ΔPKM ~ ΔLQM

Hence, Yes the triangles PMK and LMQ are similar by SAS similarity statement.

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Answer:

100

Step-by-step explanation:

130 - 30 = 100

The error terms are heteroskedastic

Suppose that the individuals are divided into groups j = 1, ...,J each with nj observations respectively, and we only observe the reported group means y; and īj.

The model becomes y; = Ba; +ūj, with error terms ū; = ; Uij, where Ui; indicates error term ui of individual i belonging to group j.

Now we have to demonstrate that the error terms ūj are heteroskedastic.

The model becomes: y; = Ba; + ūj;

For each group j, the estimated variance of the error term is given by the sum of squared deviations divided by the sample size, and we can write it as follows:

S_j^2 = sum ( yij - īj )^2 / ( nj - 1 ) where yij denotes the observation for the ith individual in the jth group.

The variance of the error term is therefore different for each group j. In other words, the error terms ūj are heteroskedastic.

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The code segment will print the characters 'a', 'e', and 'i' on separate lines.

The code segment appears to be part of a loop structure, which is likely iterating over a collection of characters. Each character is printed on a new line using the '.println()' function. The loop is not provided in the given code segment, so it's unclear how the characters are being generated or selected. However, assuming that the loop iterates over the characters 'a', 'e', and 'i', the output will be as follows:

a

e

i

The code uses the '.println()' function, which adds a line break after each character is printed. As a result, each character will be displayed on a separate line. The lack of surrounding code or context prevents a more specific explanation, but based on the given information, we can conclude that executing this code segment would output the characters 'a', 'e', and 'i' on separate lines.

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The B coordinate vector  [tex]-1+2t[/tex] is [tex][5, -8, 5].[/tex]

What is a Coordinate vector?

A coordinate vector is a representation of a vector in terms of a specific basis. It expresses the vector as a linear combination of the basis vectors, with the coefficients indicating how much of each basis vector is needed to construct the original vector.

In linear algebra, given a vector space V with a basis B = {v₁, v₂, ..., vₙ}, a vector v in V can be written as v = c₁v₁ + c₂v₂ + ... + cₙvₙ, where c₁, c₂, ..., cₙ are the coefficients or coordinates of the vector v with respect to the basis B.

To find the coordinate vector of a given vector in the basis B, we can follow these steps:

Write the vector in terms of the basis B. In this case, we have the vector [tex]-1+2t.\\-1+2t = (-1) * (1-2t+t^2) + 2 * (3-5t+4t^2) + 0 * (2t+3t^2) = -1 + 2t - t^2 + 6 - 10t + 8t^2 + 0t + 0t^2 = 5t^2 - 8t + 5[/tex]

Express the vector obtained in step 1 as a linear combination of the basis vectors [tex]C={1,t,t^2}.[/tex] This will give us the coordinate vector.

[tex]5t^2 - 8t + 5 = a * 1 + b * t + c * t^2[/tex]

Equating the coefficients of corresponding powers of t on both sides, we have:

[tex]a = 5\\b = -8\\c = 5[/tex]

So, the coordinate vector of [tex]-1+2t[/tex] in the basis

[tex]B={1-2t+t^2,3-5t+4t^2,2t+3t^2}[/tex]  is  [tex][a, b, c] = [5, -8, 5].[/tex]

Therefore, the B coordinate vector  [tex]-1+2t[/tex] is [tex][5, -8, 5].[/tex]

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