Two cyclists begin from the same point and are traveling in opposite directions on a circular bike trail that is 5 miles long. Once cyclist travels at 12 miles per hour, and the other travels at a rate of 18 miles per hour. How far did cyclist A travel?

Therefore, the perimeter of the rug is 22 feet.

Given: Area of the rug = 28 sq ftWidth of the rug = 4 ftWe need to find the perimeter of the rug. The perimeter of the rug is the sum of all its sides. We know the width of the rug which is 4 ft. Let the length of the rug be l. So, the area of the rug is given by: Area of the rug = length × width28 = l × 4l = 28/4 = 7 flow, we have the width and the length of the rug. Let's use option c. Multiplying the length by 4 will give us the perimeter of the rug. The perimeter of the rug = length + width + length + width= 7 + 4 + 7 + 4= 22 therefore, the perimeter of the rug is 22 ft.Explanation: Given, the area of the rug = 28 sq ftWidth of the rug = 4 ft We know that the formula to calculate the area of the rectangle is A = l × w where A is the area of the rectangle, l is the length of the rectangle, and w is the width of the rectangle. Here, A = 28 and w = 4. Therefore, l = 28/4 = 7We have the length and width of the rectangle, we can calculate the perimeter of the rug using the formula for the perimeter of the rectangle, which is given as P = 2(l + w)Putting the values, we get P = 2(7 + 4) = 22.

Therefore, the perimeter of the rug is 22 feet.

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Answer: C. 13/3

Step-by-step explanation:

\(slope=\frac{rise}{run} =\frac{y}{x} =\frac{13}{3}\)

Answer:

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences and engineering disciplines, as well as in non-physical systems such as the social sciences.

Answer:

13/12

Step-by-step explanation:

Hope this helps <3

Answer:

answer is 1 1/12 is the correct answer

Answer: 121°

Step-by-step explanation:

The measure of angle B will be \(121^0\) .

Angle is formed by two rays lie in the plane that contains the rays.

We have,

\(m \angle A =(6x-19)^0\)

Now,

Linear pair angles are those angles whose sum is \(180^0\) .

i.e.

\(m \angle A + m \angle B=180^0\)

So,

\((6x-19)^0 +(11x-22)^0 =180^0\)

Now,

\(17x-41=180\)

\(17x=221\)

\(x=13\)

So,

\(m\angle B=(11x-22)^0\)

Putting value of x;

\(m\angle B=(11*13-22)^0\)

\(m\angle B=(121)^0\)

So, measure of angle B is \(121^0\).

Hence, we can say that the measure of angle B will be \(121^0\) .

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Answer:

I think 2 1/2 for flour and 2 eggs

Answer:

\(f(0)=4\)

\(f(6)=8\)

Step-by-step explanation:

Solution is attached

Answer:

A rhombus is a geometric figure that lies in a plane. It is defined as a quadrilateral all of whose sides are congruent. It is a special type of parallelogram, and its properties (aside from those properties of parallelograms) include:

Its diagonals divide the figure into 4 congruent triangles.

Its diagonals are perpendicular bisectors of eachother.

If all of a rhombus' angles are right angles, then the rhombus is a square.

Answer:yes it does have perpendicular lines

Step-by-step explanation:

Let ABC be the equilateral triangle inscribed in a circle of radius r. The area of the equilateral triangle ABC is:A1 = (sqrt(3) / 4) × (2r)² = (sqrt(3) / 4) × 4r² = sqrt(3) × r²The radius of the circle inscribed in equilateral triangle ABC is r / sqrt(3).

Therefore, the altitude h of the triangle ABC is:h = sqrt(3) / 2 × 2 × r / sqrt(3) = rThe smaller equilateral triangle is ADE, which is inscribed in the region bounded by the base of the equilateral triangle and the lower part of the circle in such a way that the heights of each triangle are on the same line. Let AD = x be the side of the smaller equilateral triangle. The altitude of the smaller equilateral triangle is h – x.The radius of the circle inscribed in the smaller equilateral triangle ADE is (r – h + x) / 2.

The ratio of the area of the shaded region to the area of the smaller triangle is:((1 / 6) × πr² - (sqrt(3) / 4) × x²) / [(sqrt(3) / 4) × x²]Thus, we have the following equivalent ratios:

(sqrt(3) × r²) / [(sqrt(3) / 4) × x²] = ((1 / 6) × πr² - (sqrt(3) / 4) × x²) / [(sqrt(3) / 4) × x²]

After multiplying both sides by 4x² and simplifying, we obtain the following quadratic equation in x:πr² / 6x² - 1 = sqrt(3)After solving the quadratic equation, we obtain the following result:x = r × (2 - sqrt(3))The ratio of the area of the larger triangle to the area of the smaller triangle is:

(sqrt(3) × r²) / [(sqrt(3) / 4) × x²]= 4(2 + sqrt(3)).

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Answer:

P = 2/3 = 0.67

Step-by-step explanation:

Assuming that X1 + X2 = 7

The total number of outcomes such that X1 + X2 = 7 are:

X1 = 3, X2 = 4

X1 = 4, X2 = 3

X1 = 1, X2 = 6

X1 = 6, X2 = 1

X1 = 2, X2 = 5

X1 = 5, X2 = 2

So there are 6 total outcomes such that X1 + X2 = 7

Now, the probability that X1 = 4 is equal to the quotient between the number of outcomes where X1 = 4 (only one outcome) and the total number of outcomes (6)

Then:

p = 1/6

And the probability that X2 = 4 is calculated in the same way, then the probability is:

q = 1/6

Now, the probability that X1 = 4 or X2 = 4 is the sum of both probabilities we've found above, then:

P = p + q = 1/6 + 1/6 = 2/6 = 2/3 = 0.67

Answer:

The first two on the right will not be used

3. goes to 1.

4. goes to 2.

5. goes to 4.

6. goes to 3.

Step-by-step explanation:

The number of red marbles in the bag are 8.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of red marbles in a bag to green marbles is 2:3.

Let the number of red marbles be r and the number of green marbles be g.

r/g =2/3

3r=2g

3r-2g=0 -----(i)

Two red marbles are taken away, the ratio becomes 1:2.

(r-2)/g = 1/2

2r-4=g -----(ii)

Substitute equation (ii) in equation (i), we get

3r-2(2r-4)=0

3r-4r+8=0

r=8

Substitute r=8 in equation (ii), we get

g=2(8)-4

g=12

Therefore, the number of red marbles are 8.

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Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

The solar flux density also referred to as the solar constant is the total amount of energy derived from the sun per unit area per given unit of time. It is considered to be equal to solar luminosity divided by the surface area of a given sphere that has a radius equivalent to the distance between the respective planet from the sun.

using the formula for finding the solar flux density,

solar flux density =  solar luminosity /(4 x π x distance between mercury and the sun)

solar flux density =  3.865 x \(10^{26}\) /(4 x π x ( 5.791 x \(10^{10}\)))

solar flux density = 9.12 x 10⁻³ W/m²

Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

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If we change x by -0.7, we can expect the value of f(x) to decrease by approximately 2.1 units.

Assuming you meant to say "let f be a differentiable function where f(9) = 4 and f'(9) = 3. If we change x by -0.7 and we change y by 0.3, then we can expect the value of f(x) to change by approximately what amount?"

Using the linear approximation formula, we have:

\(Δf(x) ≈ f'(9) Δx\)

where Δx = -0.7 and we want to find Δf(x) when Δy = 0.3.

We can rearrange the formula to solve for Δf(x):

\(Δf(x) ≈ f'(9) Δx\)

Δf(x) ≈ 3(-0.7)

Δf(x) ≈ -2.1

This means that if we change x by -0.7, we can expect the value of f(x) to decrease by approximately 2.1 units. However, this is only an approximation based on the linear behavior of the function near x = 9, so it may not be exactly accurate for large changes in x.

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Answer:

c. plane

Step-by-step explanation:

There are three terms generally considered to be undefined in geometry:- Point, Line, Plane.

A circle is the set of all points in a plane the same distance from a given points (i.e center of the circle)  

The equation correctly uses the value of b to solve for a is tan (22.6)= \(\frac{a}{12}\)

We know that cos  (22.6) =\(\frac{b}{13}\) Rounding the value of b as asked in the problem gives b=12.

According to the right-triangle definition of cosine, b must be the neighboring side to the angle 22.6o and thus the triangle's hypothenuse must be 3.

Then, a is the opposite side of the angle 22.6º therefore using the definition of sine, sin(22.6)= \(\frac{a}{3}\)

Solving for a, we obtain

a=3sin(22.6) =3cos(22.6) tan(22.6)=btan(22.6)=12tan(22.6)

Hence conclusion can be made that tan(22.6)= \(\frac{a}{12}\)

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This question is incomplete. The complete question is:

Triangle ABC is a right triangle and cos(22.6o)=b/13. Solve for b and round to the nearest whole number. Which equation correctly uses the value of b to solve for a? tan(22.6o) = a/13 tan(22.6o) = 13/a tan(22.6o) = a/12tan(22.6o) =12/a

Statistics report that the average successful quitter is able to stop smoking after multiple attempts, usually between 8 to 10 times.  everyone's journey to quitting smoking is unique and may take more or fewer attempts to achieve success.

According to statistics, the average successful quitter is able to stop smoking after attempting to quit 6 to 30 times. This number varies due to individual factors and the methods used for quitting. Remember, persistence is key, and it is never too late to quit smoking for a healthier lifestyle.

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Answer:

depends on what x is

Step-by-step explanation:

Answer:

If this problem is set to zero 1x+34=0 then no.

Step-by-step explanation:

1x+34=0

Step one subtract -34 from both sides.

1x=-34

Step two divided by one.

x=-34

The probability that a cell phone user makes or receives less than 12 calls per day is 0.3971.

To find P(x < 12), we need to standardize the value of 12 using the formula: z = (x - μ) / σ where z = z-score, x = value of interest, μ = mean, and σ = standard deviation.

Substituting the values, we get:

z = (12 - 13.1) / 4.3

z = -0.25581

Using a calculator, we can find the probability that z is less than -0.25581, which is:

P(z < -0.25581) = 0.3971

P(z < -0.25581) = 39.71%.

Full question "Suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. Find P (x <12)".

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A linear perspective drawing of a cube can have a maximum of 2 vanishing points.

What is the cube?

A cube is a three-dimensional solid object with six square faces of equal size. The edges of a cube are equal in length and meet at right angles. Each face is a square and is perpendicular to the opposite face.

The maximum number of apparent vanishing points a linear perspective drawing of a cube can have is 2. In a linear perspective drawing, all parallel lines appear to converge at a single vanishing point on the horizon line. For a cube, all vertical lines are parallel, so they will converge at one vanishing point. All horizontal lines are also parallel, so they will converge at another vanishing point.

Hence, a linear perspective drawing of a cube can have a maximum of 2 vanishing points.

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Answer: The answer is C

Step-by-step explanation:

We are given to find the true solution of the following equation involving logarithms:

We will be using the following properties of logarithms in the solution.

The solution is as follows:

Since we can find the logarithm of a positive integer only, and both the solutions x = 1 and 4 satisfy this condition after substituting in the given equation, so both the solutions are TRUE.

Thus, the correct option is (C).

The true solution to the given equation is x = 1 and x = 4. The correct answer would be an option (C).

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

According to the problem, we will use some of the basic logarithmic properties,

The given equation is as follows:

2log₃(6x) - log₃(4x) = 2log₃(x+2)

Using the property that logₐ(xⁿ) = n logₐx,

log₃((6x)² - log₃(4x) = log₃(x+2)²

Using the property that logₐ(x/y) = logₐx - logₐy,

log₃((6x)²/4x) = log₃(x+2)²

log₃((36x²)/4x) = log₃(x+2)²

log₃(9x) = log₃(x+2)²

Now we can solve for x by setting the expression inside the logarithm equal to 1, which gives:

9x = (x+2)²

9x = x² + 4x +4

x² - 5x + 4 = 0

Solving for x, and we get

x = 1 and x = 4

Thus, the true solution to the equation is x = 1 and x = 4.

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Answer:

y = (x-6)*(x-3)

Step-by-step explanation:

When you plug 6 or 3, y will be 0.

Answer:

\( \tan( \alpha ) = \frac{ \sqrt{1 - { \cos( \alpha ) }^{2} } }{ \cos( \alpha ) } = \: \frac{ \sqrt{0.36} }{0.8} = \frac{0.6}{0.8} \)

Answer:

x = 1

Step-by-step explanation:

Since we have x1 = x2, we can conclude that f(x) = (2x + 1)/(3x) is not one-to-one because different inputs can yield the same output. The function f(x) = (2x + 1)/(3x) is not one-to-one.

A function is considered one-to-one if every element in its domain maps to a unique element in its range. To determine whether f(x) is one-to-one, we need to check if different inputs result in different outputs.

Let's assume x1 and x2 are two different values in the domain of f(x). If f(x1) = f(x2), it would imply that the function is not one-to-one.

Considering f(x) = (2x + 1)/(3x), we can analyze if f(x1) = f(x2) holds true for some x1 ≠ x2.

If we set f(x1) = f(x2), we get (2x1 + 1)/(3x1) = (2x2 + 1)/(3x2). To check if this equation has a solution, we can cross-multiply and simplify:

(2x1 + 1)/(3x1) = (2x2 + 1)/(3x2)

Cross-multiplying gives us:

(2x1 + 1)(3x2) = (2x2 + 1)(3x1)

Simplifying further:

6x1x2 + 3x2 = 6x1x2 + 3x1

From this equation, we can observe that 3x2 = 3x1. Dividing both sides by 3 gives us x2 = x1.

Since we have x1 = x2, we can conclude that f(x) = (2x + 1)/(3x) is not one-to-one because different inputs can yield the same output.

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Answer:

2.8 and 4.4

Step-by-step explanation:

The distance between tick marks is 0.25.

Since the first number is greater than 2.75, we can approximate is as 2.28.

The second number is less than 4.50, we can approximate it as 4.4.

After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-3, -6) and (3, -4). Therefore, option D is the correct answer.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, triangle LMN with vertices L(2, -2), M(6, -3) and N(4, 3).

After clockwise rotation 90° we get

Here, L(2, -2) →L'(-2, -2)

M(6, -3) →M'(-3, -6)

N(4, 3) →N'(3, -4)

Therefore, option D is the correct answer.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$20953.80\\ P=\textit{original amount deposited}\dotfill & \$18000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6 \end{cases} \\\\\\ 20953.80=18000[1+(\frac{r}{100})(6)]\implies \cfrac{20953.80}{18000}=1+\cfrac{6r}{100}\)

\(\cfrac{20953.80}{18000}=\cfrac{100+6r}{100}\implies \cfrac{2095380}{18000}=100+6r\implies \cfrac{11641}{100}=100+6r \\\\\\ \cfrac{11641}{100}-100=6r\implies \cfrac{1641}{100}=6r\implies \cfrac{1641}{600}=r \\\\\\ \cfrac{547}{200}=r\implies \stackrel{\%}{2.735} = r\)

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Answer:

\(\sqrt{\frac{x}{2} }\)

Key:

• \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\)

Step-by-step explanation:

\(\frac{\sqrt{x}}{\sqrt{2}}\\\)

\(\frac{\sqrt{x}}{\sqrt{2}}=\sqrt{\frac{x}{2}}\\\)

\(=\sqrt{\frac{x}{2}}\)