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Answer:

B = (1,3)

Step-by-step explanation:

(- 7 + x)/2 = -3

-7 + x= -3 * 2

x = -6 + 7

x = 1

(1 + y)/2 = 2

1 + y = 2*2

y = 4 - 1

y = 3

Answer:

Answer is 120

Step-by-step explanation:

180*(6-2)/6

120

Answer:

Step-by-step explanation:

Assuming that 23 is the first term

4823

25th term of arithmetic sequence is 4,823

Given arithmetic sequence:

23, 223, 423, 623,...

Find:

25th term of arithmetic sequence

Computation:

First term a = 23

Common difference d = A2 - A1

Common difference d = 223 - 23

Common difference d = 200

Number of term n = 25

So,

An = a + (n - 1)d

A25 = 23 + (25 - 1)(200)

A25 = 23 + (24)(200)

A25 = 23 + 4,800

A25 = 4,823

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The required 99% confidence interval representing the true proportion of all college students owns a car lies between the range of 0.3253 and 0.4283.

Sample size n = 319

Students who own a car represents the number of successes x = 120  

Confidence interval =  99%

True proportion p of all college students who own a car.

The formula for the confidence interval for a population proportion is,

p1± zα/2 × √(p1(1-p1)/n)

where p1 is the sample proportion,

zα/2 is the z-score corresponding to the desired level of confidence interval 99%.

First, we find the sample proportion,

p1 = x/n

    = 120/319

    ≈ 0.3768

z-score corresponding to a 99% confidence level.

This is a two-tailed test,

Split the alpha level evenly between the two tails.

α/2 = (1 - 0.99) / 2

     = 0.005,

The z-score that encloses 0.005 in each tail of the standard normal distribution.

Using a standard normal table ,

zα/2 = 2.576.

Substituting the values into the formula, we get,

p1 ± zα/2 × √(p1(1-p1)/n)

= 0.3768 ± 2.576×√(0.3768(1-0.3768)/319)

= 0.3768 ± 0.0515

99% confidence interval for the true proportion p of all college students who own a car is,

0.3253 ≤ p ≤ 0.4283

Therefore, 99% confidence interval that the true proportion of all college students who own a car lies between 0.3253 and 0.4283.

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Answer:

- 1/4 ( 1 + 2y)

Step-by-step explanation:

The possible endpoints are (-3, 6) and (8, -5).

The distance between two points of a line is given as:

Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

We have,

The coordinates of the endpoints are (a, b) = \((x_1, y_1)\) and (-3, -5) = \((x_2, y_x)\).

The distance between the two endpoints is 11 units.

Now,

Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

11 = \(\sqrt{(-3 - a)^2 + (-5 - b)^2}\)

Squaring both sides.

11² = (-3 - a)² + (-5 - b)²

121 = (-3 - a)² + (-5 - b)²

If we take a = -3 and b = 6

121 = (-3 + 3)² + (-5 - 6)²

121 = 0 + (-11)²

121 = 121

or

If we take a = 8 and b = -5

121 = (-3 - 8)² + (-5 + 5)²

121 = (-11)² + 0

121 = 121

Thus,

(-3, 6) and (8, -5) are the possible endpoints.

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The measure of the angle D and F can be calculated form the total measure of the Angle of the triangle that is 180.

In the triangle DEF, F is 120 degree and F is 4/3rd of E. A straight angle is just a straight line which is where it gets its name. the sum of a triangles angles 180. It is proved by angular defect and triangles area. The angle sum of a triangle will always be equal to 180°. The angle sum of a quadrilateral is equal to 360°, and a triangle can be created by slicing a quadrilateral in half from corner to corner. Since a triangle is essentially half of a quadrilateral, its angle measures should be half as well.

Angle F = 120 degree

F= 4/3 E

E= 90 degree

The sum of the angle is 180. so,

D + E + F = 180

Putting all the values we can find the measure of angle D and Angle E.

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The correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.

To determine which angles are congruent in circle D, we need to analyze the given information about the measures of minor arcs. Since minor arcs are measured in degrees, we can use the following properties:

1. When two arcs are congruent, their corresponding central angles are also congruent.

2. The measure of a central angle is equal to the measure of its intercepted arc.

Given these properties, let's examine the answer choices:

A) EDH and FDG: We cannot determine their congruency based solely on the measures of the minor arcs.

B) FDE and GDH: These angles have the same intercepted arc, so they are congruent.

C) GDH and EDH: The intercepted arcs for these angles are different, so they are not congruent.

D) GDF and HDG: These angles have the same intercepted arc, so they are congruent.

Therefore, the correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.

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The null hypothesis is a common statistical theory that contends that there is no statistically significant association between any two sets of a single observed variable.

The hypothesis suggests no two given sets make any significance meaning until and unless they are proven wrong.

As given in the example,

The group of answer choices the (population) mean amount of time reading and sending e-mails daily is greater than 60 minutes and the (population) mean amount of time reading and sending e-mails daily is equal to 60 minutes.

You can see in one set the amount of reading and sending e-mails is more than 60 minutes and in other one the amount of time reading and sending e-mails is equal to 60 minutes which doesn't make any sense if you consider them both in a single set of information.

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Answer:

x=2 y=0

Step-by-step explanation:

Answer:

A is true

B is false

C is true

D is true

E is false

The sag in the cable for problem 5/160 is approximately 24.4 meters.

To solve the problem of finding the sag in a cable, we can use the catenary equation. The equation is given by:

y = a cosh(x/a)

For problem 5/159, we were given a cable weighing 25 N/m and spanning a distance of 160 m. We can find the tension in the cable by using the formula:

T = wL/2

Substituting in our values, we get:

T = (25 N/m)(160 m)/2 = 2000 N

Now we can solve for a by using the formula:

a = T/(w*g)

where g is the acceleration due to gravity. Substituting in our values, we get:

a = (2000 N)/((25 N/m)*9.81 m/s^2) ≈ 8.13 m

Finally, we can find the sag at the midpoint of the cable (x = L/2) by plugging into the catenary equation:

y = a cosh(x/a) = (8.13 m) cosh(80 m/8.13 m) ≈ 24.6 m

Therefore, the sag in the cable is approximately 24.6 meters.

For problem 5/160, we are given a similar situation but with a shorter span of 159 meters. Using the same method as above, we find that:

T = (25 N/m)(159 m)/2 = 1987.5 N

a = (1987.5 N)/((25 N/m)*9.81 m/s^2) ≈ 8.06 m

y = a cosh(x/a) = (8.06 m) cosh(79.5 m/8.06 m) ≈ 24.4 m

Therefore, the value obtained is approximately 24.4 m.

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Answer:

See the answers below.

Step-by-step explanation:

1. A. 13-ounce box is better to buy.

2. B. Gas station candies bars are cheaper.

3. D. x=40

4. A. x=12

Best Regards!

Given:

A bird was sitting 16 feet from the base of an oak tree and flew 20 feet to reach the top of the tree.

To find:

The length of the tree.

Solution:

A bird was sitting 16 feet from the base of an oak tree.

Vertical distance between bird and base = 16 feet

Then the bird flew 20 feet to reach the top of the tree.

Now, the vertical distance between bird and base = (16+20) feet

So, length of the oak tree is it the sum of 16 feet and 20 feet.

\(\text{Length of the oak tree}=16+20\) feet

\(\text{Length of the oak tree}=36\) feet

Therefore, the length of the oak tree is 36 feet.

The equilibrium constant (Kc) for the reaction ni₂⁺ + 6nh₃ is [Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆.

The given reaction is:

Ni₂+ + 6NH₃ ⇌ [Ni(NH₃)₆]²⁺

The equilibrium constant (Kc) for this reaction can be obtained by the formula given below

[Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆

The equilibrium constant (Kc) for the reaction ni²⁺ + 6nh₃ is given as

[Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆

Thus, the equilibrium constant (Kc) for the reaction ni²⁺ + 6nh₃ is [Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Translation right 6 units adds 6 to every x-coordinate. Rotation 90° CW is the transformation (x, y) ⇒ (y, -x). The sequence of transformations gives ...

  (x, y) ⇒ (y, -x-6)

Then the coordinates of the transformed figure are ...

  P(-3, 7) ⇒ P'(7, -3)

  Q(4, 12) ⇒ Q'(12, -10)

  R(4, -2) ⇒ R'(-2, -10)

  S(-3, -7) ⇒ S'(-7, -3)

The acceleration components of point D are, ax = 3.6 m/s², ay = 6.4 m/s², az = -1.14 m/s²

At the instant shown, the shaft and plate rotates with an angular velocity of 19 rad/s and angular acceleration of 9 rad/s2. The given diagram is shown below. Angular velocity (w) = 19 rad/sAngular acceleration (α) = 9 rad/s²Plate dimension AB = 0.6 m, BC = 0.2 m, CD = 0.4 m, DA = 0.3 m, AE = 0.3 m and EF = 0.4 m.

Determine the wocl and Dsea of Enter the ", y, and Z components of the velocity separated by commas vec m/sThe velocity components for point D can be calculated using the following formula.Vd = R x wWhere R is the position vector of D relative to the origin.

According to the given diagram, the position vector of point D relative to the origin is, R = 0.2i + 0.4j + 0.3kThe velocity of point D can be calculated as follows.Vd = R x w = 0.2i + 0.4j + 0.3k x 19The cross product of R and w can be calculated as follows.i j k 0.2 0.4 0.3 0 19 0 = [(0.4 × 0) - (0.3 × 19)] i - [(0.2 × 0) - (0.3 × 0)] j + [(0.2 × 19) - (0.4 × 0)] kVd = -5.7i + 6.8kThus, the velocity components of point D are, Vx = -5.7 m/s, Vy = 0 m/s, Vz = 6.8 m/s

Determine the acceleration of point D located on the corner of the plate at this instant. Enter the, y, and Z components of the velocity separated by commas vec m/sThe acceleration components of point D can be calculated using the following formula.aD = R x α + w x (w x R)Where R is the position vector of D relative to the origin.

According to the given diagram, the position vector of point D relative to the origin is, R = 0.2i + 0.4j + 0.3kThe acceleration of point D can be calculated as follows.aD = R x α + w x (w x R) = (0.2i + 0.4j + 0.3k) x 9 + 19 x (19 x (0.2i + 0.4j + 0.3k)) = (0.4k - 0.3j) x 9 + 19 x (0.4 x (0.4j - 0.3k))aD = 3.6i + 6.4j - 1.14k.

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Answer:

=-3.5

Step-by-step explanation:

Subtract  38.5  from both sides of the equation then Simplify, lastly you Add  

9

to both sides of the equation

Karen is correct because

Step-by-step explanation:

10 to the 3rd power is 1000 and 560.9 divided by 1000 is 0.5609

Answer:

There's no options

Step-by-step explanation:

Answer:

Options please

Step-by-step explanation:

The value of the trigonometry function sin (2θ) would be 24/25. Hence option B is true.

Given that;

The trigonometry function is,

tan θ = 3/4

Where, 0 ≤ θ ≤ 2π

Now by using the trigonometry formula, we get;

If tan θ = 3/4

Then, By using the trigonometry formula,

sin θ = 3/5

And, cos θ = 4/5

Therefore, the value of sin (2θ) is,

sin (2θ) = 2 sin (θ) cos (θ)

            = 2 × 3/5 × 4/5

            = 24/25

Therefore, the value of sin (2θ) is 24/25. So, the correct option is B.

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The angle theta lies in the third quadrant where sin is negative. Given tan theta = 3/4, we use the Pythagorean identity to find the value of sin theta, which results in approximately - 24/25.

The angle theta is located in the third quadrant, where sin is negative. Given tan theta = 3/4, we can use the Pythagorean identity to find the value of sin theta.

Since tan theta = opposite/adjacent (y/x), we can use this to form a right triangle in the third quadrant. The opposite side (y) would be -3 (since y is negative in the third quadrant) and the adjacent side (x) would be -4 (x is also negative in the third quadrant.)

Using the Pythagorean theorem (x^2 + y^2 = r^2), we find that the hypotenuse (r) is 5.

Sin theta is defined as opposite/hypotenuse (y/r). Given y is -3 and r is 5, sin theta is -3/5, which is approximately - 24/25.

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Answer:   Therefore, the answer is:

a) ONE TRIANGLE

b) The sides 4 cm, 6 cm, and 9 cm can form a single triangle.

Step-by-step explanation:

a) There is exactly ONE TRIANGLE that can be constructed with sides measuring 4 cm, 6 cm, and 9 cm.

b) To determine the number of triangles that can be formed from three given sides, we can use the triangle inequality theorem which states that the sum of any two sides of a triangle must be greater than the third side.

Let's check if the given sides satisfy this inequality:

4 cm + 6 cm > 9 cm (True)

4 cm + 9 cm > 6 cm (True)

6 cm + 9 cm > 4 cm (True)

Since all three inequalities are true, we can conclude that a triangle can be formed using these three sides.

Now, let's determine if there is only one possible triangle that can be formed or if there are more than one. To do this, we can use the fact that the largest side of a triangle must be smaller than the sum of the other two sides. If this is not the case, then it's not possible to form a triangle.

In this case, the largest side is 9 cm. Let's check if it's smaller than the sum of the other two sides:

4 cm + 6 cm = 10 cm (True)

Since 9 cm is smaller than the sum of the other two sides, we can conclude that it's possible to form a triangle, but there is only one possible triangle that can be formed.

Answer:

Step-by-step explanation:

a lot of dancers go to Rio de Janeiro to attend the Carnival

The formula to calculate the geometric mean of two numbers is the square root of their product.

So in this case, the geometric mean can be calculated as follows:

Geometric Mean = √(8 * 12) = √96 = 10

The growth factors for the population of Chattanooga in the past two years have a geometric mean of 10.

The geometric mean is a measure of central tendency that is used to describe the average growth rate of a set of numbers. It is especially useful when working with data that represents exponential growth or decay, such as population growth or the rate of return on an investment. Unlike the arithmetic mean, the geometric mean takes into account both the size and the direction of growth. This makes it a better measure of central tendency for data that is not symmetrically distributed.

In the case of population growth, the geometric mean can be used to determine the average annual growth rate over a given period of time. For example, if the population of a city grows by 8% in one year and then by 12% the following year, the average annual growth rate over the two years can be estimated using the geometric mean.

It is important to note that the geometric mean is always smaller than the arithmetic mean for the same set of numbers, and it can be a better representation of the underlying growth trend in some cases.

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A rule that could represent this dilation of a hexagon on a coordinate grid with the origin as the center is: (x, y) → (kx, ky), where k is the dilation factor (0 < k < 1) for creating a smaller hexagon.

The rule that could represent this dilation is to multiply the coordinates of each vertex of the original hexagon by the scaling factor (the factor by which the hexagon is being dilated) and the distance from the origin. Since the origin is the center of the dilation, the distance from the origin to any point on the hexagon remains constant. Therefore, the rule for dilating a hexagon with the origin as the center of dilation can be written as:
New Vertex = Scaling Factor x Distance from Origin x Old Vertex

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The rule that represents the dilation of the hexagon with the origin as the center of dilation is:
\((x\prime, y\prime) = (xr, yr)\)
r is the ratio of the side lengths of the image to the pre-image, and (x, y) are the coordinates of a point on the pre-image.

A hexagon means to scale it up or down in size while maintaining its shape.

The hexagon will be made smaller.

The center of the dilation is the origin, which means that the hexagon will be scaled equally in all directions from the center.
To find the rule that represents this dilation, we can use the formula for dilation.

The formula for dilation is:
\((x\prime, y\prime) = k(x, y)\)
(x, y) are the coordinates of a point on the pre-image (the original hexagon), \((x\prime, y\prime)\) are the coordinates of the corresponding point on the image (the smaller hexagon), and k is the scale factor.
The center of dilation is the origin, which means that the coordinates of the center of the pre-image and the image are both (0, 0). Since the hexagon is being scaled down, the scale factor k must be less than 1.
To find the value of k, we need to know the ratio of the side length of the image to the side length of the pre-image. Let's say that the side length of the pre-image is s, and the side length of the image is \(s\prime\).

The scale factor k can be found using the formula:
\(k = s\prime / s\)
Since the hexagon is being scaled down, we know that\(s\prime < s.\)

Let's say that the ratio of the side lengths is r, where:
\(r = s\prime / s\)
Then we can rewrite the formula for k as:
\(k = r / 1\)
The center of dilation is the origin, the coordinates of each point on the pre-image are equal to the length of their respective sides.

The vertices of the pre-image using the following coordinates:
A = (0, s)
\(B = (s\sqrt 3/2, s/2)\)
\(C = (s\sqrt 3/2, -s/2)\)
\(D = (0, -s)\)
\(E = (-s\sqrt3/2, -s/2)\)
\(F = (-s\sqrt3/2, s/2)\)
The coordinates of the corresponding vertices on the image, we can substitute these coordinates into the formula for dilation:
\(A\prime = k(0, s) = (0, rs)\)
\(B\prime = k(s\sqrt3/2, s/2) = (s\sqrt3/2 r, s/2 r)\)
\(C\prime = k(s\sqrt3/2, -s/2) = (s\sqrt3/2 r, -s/2 r)\)
\(D\prime = k(0, -s) = (0, -rs)\)
\(E\prime = k(-s\sqrt3/2, -s/2) = (-s\sqrt3/2 r, -s/2 r)\)
\(F\prime = k(-s\sqrt3/2, s/2) = (-s\sqrt3/2 r, s/2 r)\)

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Answer:

Step-by-step explanation:

its 2.82, a little further forward, 82% of the way to number 3

Check the picture below.

Answer:

No

Step-by-step explanation:

f(x)= 4/-x-2

inverse

f-1(x)= -4/x-2

Answer: The one on the bottom right.

Step-by-step explanation:

Symmetry is basically like a mirror. The line of symmetry is the exact point where it starts to reflect.

A symmetrical shape can also be folded onto itself equally.

Looking at the photo, the picture on the bottom right is the left part of the figure.