Which statement is true about two ordered pairs that are the same except for the signs of the numbers?

The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.

Hence, The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.

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Answer:

Likely

Step-by-step explanation:

The odds are in favor of it, but it hasn't been proven.

The expression that are equivalent to 10x are 5 * 2x, 2 * 5x, 15x - 5x, 2(5x) and 2 * 5 * x

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

10x

The expression 10x can be rewritten in any of the following ways

5 * 2x

2 * 5x

15x - 5x

2(5x)

2 * 5 * x

There are several other expressions that are equivalent to 10x

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Answer:

Step-by-step explanation

it is true

The volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0) is 25π/12 cubic units.

What is a triangle?

A triangle is a closed geometric shape that is formed by connecting three line segments. These line segments are called sides, and the points where they meet are called vertices. A triangle has three sides, three angles, and three vertices.

To start, let's graph the triangle to get a better understanding of the problem:

(0,3)   *

       |\

       | \

       |  \

       |   \

       |    \

(0,0)   *-----*-----> x

        (5,0)

The height of this slice is given by the line from the point (x,0) to the point (0,3), which has equation y = 3/5 * x + 0. The radius of the semicircle is half the height of the slice, which is given by the equation r = 3/10 * x.

The area of a semicircle is πr²/2, so the volume of this slice is:

V(x) = π * (3/10 * x)² / 2 * dx

To find the total volume of the solid, we need to integrate this expression over the range of x values that covers the entire base of the solid, which is from x=0 to x=5:

V = ∫₀₅ π * (3/10 * x)² / 2 dx

V = π/20 * ∫₀₅ x² dx

V = π/20 * [x³/3] from 0 to 5

V = π/20 * (5³/3)

V = π/4 * (25/3)

V = 25π/12

Therefore, the volume of the solid is 25π/12 cubic units.

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Option(A) is the correct answer is A. 1,335 birds.

To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.

We can use the formula for exponential decay:

N = N₀ * (1 - r/100)^t

Where:

N is the final number of birds after t years

N₀ is the initial number of birds (2,000 in this case)

r is the annual decline rate (2% or 0.02)

t is the number of years (20 in this case)

Plugging in the values, we get:

N = 2,000 * (1 - 0.02)^20

N = 2,000 * (0.98)^20

N ≈ 2,000 * 0.672749

N ≈ 1,345.498

Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.

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Answer:

\(x^{2}\)-6x=-58

Step-by-step explanation:

The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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A square has a perimeter of 24 m and an area of 36m ^ 2 The square is dilated by a scale factor of 3.The perimeter of the dilated figure is 72 m, and the area is \(324 m^2\).

Let's begin by finding the side length of the original square. Since the perimeter of the square is given as 24 m, we can divide it by 4 (as a square has four equal sides) to find the length of each side. Therefore, the original square has a side length of 6 m.

To find the perimeter of the dilated figure, we need to multiply the side length of the original square by the scale factor of 3. So, the new side length of the dilated figure is 6 m * 3 = 18 m. Since the dilated figure is also a square, all its sides are equal. Therefore, the perimeter of the dilated figure is 18 m + 18 m + 18 m + 18 m = 72 m.

To find the area of the dilated figure, we need to square the new side length of 18 m: \(18 m * 18 m = 324 m^2\). Hence, the area of the dilated figure is \(324 m^2.\)

The perimeter of the dilated figure is 72 m, and the area is \(324 m^2\).

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The volume of the cone is 314cm³

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.

The volume of the cone is 1/3πr²h

h²= 13²-5²

h = √169 - 25

h = √144

h = 12 cm

V = 1/3πr²h

V = 1/3 ×3.14 × 5² × 12

V = 942/3

V = 314 cm³

therefore the volume of the cone is 314cm³

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Answer:

The magnitude of the vector is 9.165 and it's direction is 40.6°

Step-by-step explanation:

A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.

Magnitude of vector v is given by

|v| = √6²+7²

= √36+49

= √84

= 9.165

Direction of vector v is obtained by:

\( \tan( \theta) = \frac{x}{y} \)

\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)

\(\theta = {40.6°}\)

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Answer:

7.5 m

10 m

Step-by-step explanation:

i) 30 m ÷ 4 = 7.5m

iii) 30m ÷ 3 = 10m

The numeric values for this problem are given as follows:

The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

For x between -2 and 2, the function is defined as follows:

g(x) = -(x - 1)² + 2.

Hence the numeric value at x = -1 is given as follows:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.

For x at x = 2 and greater, the function is given as follows:

g(x) = 0.5x - 1.

Hence the numeric values at x = 2 and x = 3 are given as follows:

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Answer:

S = [0.2069,0.7931]

Step-by-step explanation:

Transition Matrix:

\(P=\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]\)

Stationary matrix S for the transition matrix P is obtained by computing powers of the transition matrix P ( k powers ) until all the two rows of transition matrix p are equal or identical.

Transition matrix P raised to the power 2 (at k = 2)

\(P^{2} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]\)

\(P^{2} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right]\)

Transition matrix P raised to the power 3 (at k = 3)

\(P^{3} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]\)

\(P^{3} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]\)

  \(P^{3} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right]\)

Transition matrix P raised to the power 4 (at k = 4)

\(P^{4} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]\)

\(P^{4} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]\)

\(P^{4} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right]\)

Transition matrix P raised to the power 5 (at k = 5)

\(P^{5} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]\)

\(P^{5} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]\)

\(P^{5} =\left[\begin{array}{ccc}0.2069&0.7931\\0.2069&0.7931\end{array}\right]\)

P⁵ at k = 5 both the rows identical. Hence the stationary matrix S is:

S = [ 0.2069 , 0.7931 ]

The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.

The z-score formula is:

z = (x - μ) / σ

where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For the lower bound of 93, the z-score is:

z = (93 - 105) / 20 = -0.6

For the upper bound of 117, the z-score is:

z = (117 - 105) / 20 = 0.6

Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:

normalcdf(-0.6, 0.6, 0, 1)

This gives us a probability of 0.6827.

Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

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Using it's concept, it is found that the probability that the next trial will result in a 2 and 4 is given by:

A. \(\frac{3}{10}\).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In an experimental probability, the number of outcomes are taken from previous trials.

In this problem, the table states that of 20 trials, 6 resulted in either (2,4) or (4,2), hence the probability is given by:

p = 6/20 = 3/10.

Which means that option A is correct.

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By taking the product between the combinations of possible groups fo men and women we will see that the number of different committees is:

392

For a set of N elements, the number of different sets of K elements that can be formed is:

C(N, K) = N!/(K!*(N - K)!)

Here we have 8 men and 7 women, and we want to make a committee of 5 men and 6 women

Then the total number of different committees is given by the product between the different sets of 5 men and the different sets of 6 women, these are:

for men:

C(8, 5) = 8!/( 5!*(8 - 5)!) = (8*7*6)/(3*2*1) = 56

for women:

C(7, 6) = 7!/(6!*(7 - 6)!) = 7

Then the total number of different committees is:

C = 56*7 = 392

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We have found that: AB = (BD/2) * (XZ/AY) and we can solve for BD:

BD = 2 * AB * AY / XZ

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Since BD is a median of triangle ABC, it divides side AC into two equal parts. Let's label the midpoint of AC as M. Similarly, YW is a median of triangle XYZ and it divides side XZ into two equal parts, with the midpoint labeled as N.

Since AABC~AXYZ, we know that the corresponding sides are proportional. Thus,

AB/AX = AC/AY = BC/BZ

Since AB = BC (given that B is a vertex of both triangles), we have:

AB/AX = AC/AY

We can rewrite this equation as:

AB/AC = AX/AY ----(1)

Since BD is a median of triangle ABC, we have:

BD = 1/2 AC ----(2)

Similarly, since YW is a median of triangle XYZ, we have:

YW = 1/2 XZ ----(3)

From equation (1), we have:

AB/AC = AX/AY

Multiplying both sides by AC, we get:

AB = AX * (AC/AY)

Now, using equation (2), we can substitute AC/2 for BD:

AB = AX * BD/AY

Finally, using equation (3), we can substitute XZ/2 for YW:

AB = (BD/2) * (XZ/AY)

Therefore, we have found that:

AB = (BD/2) * (XZ/AY)

Hence, we can solve for BD:

BD = 2 * AB * AY / XZ

Note that we need to know the actual values of AB, AY, and XZ to find BD.

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Answer:

Step-by-step explanation:

To find the value of sec(145°), we first need to find its reference angle in the range 0° to 90°. The reference angle is the acute angle between the terminal side of the given angle and the x-axis.

To find the reference angle of 145°, we can subtract the nearest multiple of 90° (which is 90° itself) from 145°:

reference angle = 145° - 90° = 55°

Now we can use the definition of the secant function:

sec(θ) = 1/cos(θ)

To express sec(55°) in terms of secant of a positive acute angle, we need to find the cosine of 55°. We can use a scientific calculator to get:

cos(55°) ≈ 0.5736

So we have:

sec(145°) = 1/cos(145°) = 1/cos(55°) ≈ 1.742

Therefore, sec(145°) can be written in terms of the secant of a positive acute angle as sec(55).

Answer:

y = 3x + 1

Step-by-step explanation:

Since we know the Graph is Parallel to y = 3x + 11, we know that the "mx" portion of the equation is 3x since only the "b" would be different.

Then we just substitute in the point and to find b.

4 = 3(1) + b

b = 1

y = 3x + 1  is the answer

Answer:

1.Many pairs of triangles designed into a building, for example as roof ends, would be congruent, so the roof beam and the top edges of the walls are horizontal.

2.The congruent triangle is used in most of the building that are design to stay in bad conditions and Strong winds for Example the Sydney Bridge.

3.in real life two triangles are rarely exactly congruent. However they are crucial in the construction of large man-made structures. This is because a triangle is the most stable shape and the congruence is needed to create even surfaces.

Answer:

22

Step-by-step explanation:

So if you have f(x) = x^2 - 3, then all you have to do is plug in x = -5 into the equation. This would be (-5)^2 - 3 = 25 - 3 = 22.

I hope that makes sense!

Answer:

30 kg of dough

Step-by-step explanation:

you have to figure out how much dough he made in an hour. so divide the total hours by to the amount of dough. you then multiple the total hours by the amount of dough per hour.

27/9=3

3*10= 30

Answer:

1+2

Step-by-step explanation:

By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

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