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Answer:

10 months

Step-by-step explanation:

30x = 22x + 80

8x = 80

x = 10

The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

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Answer:

the area is 289

Step-by-step explanation:

the formula for calculating the perimeter of a square is the side*4

68/4=17

the formula for calculating tha area is side*side

17*17=289

Answer:

2447.40

Step-by-step explanation:

smart

Answer:

$2447.40

Step-by-step explanation:

Find 5% of average household income to find the savings of your parents in one year.

Savings of your parents in one year: $48,948 x 5/100

Savings of your parents in one year: $48,948 x 0.05

Savings of your parents in one year: $2447.40

Answer:

225/2

Step-by-step explanation:

112R1=225/2

Answer:

23

Step-by-step explanation:

8-2=6

6×3=18

18+5=23

Answer: 23

Step-by-step explanation:

i. The best response function for firm 1 is p1 = (1/3) + (2/3)p2

ii. The best response function for firm 2 is p2 = (1/3) + (2/3)p1

iii. The Nash equilibrium prices are p1 = p2 = 1

iv. The Nash equilibrium profit for each firm is 9.

i. To compute the best response function for firm 1, we need to find the price that maximizes firm 1's profit given the price chosen by firm 2. By differentiating firm 1's profit function with respect to p1 and setting it equal to zero, we can find the best response function: p1 = (1/3) + (2/3)p2.

ii. Similarly, to compute the best response function for firm 2, we differentiate firm 2's profit function with respect to p2 and set it equal to zero: p2 = (1/3) + (2/3)p1.

iii. The Nash equilibrium occurs when both firms choose prices that are best responses to each other. Substituting the best response functions into each other, we find p1 = p2 = 1.

iv. To compute the Nash equilibrium profit for each firm, we substitute the Nash equilibrium prices into their respective profit functions. Firm 1's profit is 9, and firm 2's profit is also 9.

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Driving a personal car would be the most cost-effective mode of transportation for this commute, with a total daily cost of approximately $4.60 ($3.60 for gas + $1 for travel time).

Based on the given information, the most cost-effective mode of transportation for this commute would be to drive a personal car. Taking public transportation or carpooling may be more environmentally friendly options, but they may not save as much money as driving alone.

Assuming an average speed of 60 miles per hour on the highway, the commute would take approximately 20 minutes each way, or 40 minutes round-trip. This means the total cost of travel time for each workday would be $40 ($60/hour x 2/3 hour).

Using a cost calculator such as GasBuddy, we can estimate that the cost of driving 20 miles per day (round-trip) would be around $3.60 per day, assuming an average fuel efficiency of 25 miles per gallon and a gasoline price of $2.50 per gallon.

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The meteorologist needs to analyze approximately 164 air samples to be 80% certain that the error of estimate does not exceed 0.2 ppm.

A meteorologist aiming to estimate the nitrogen dioxide content in the air needs to consider the standard deviation and desired level of certainty. In this case, the known standard deviation is 2 ppm, and the desired certainty is 80%, with an error of estimate not exceeding 0.2 ppm.
To calculate the number of air samples needed, the meteorologist can use the formula:
n = (Z * σ / E)^2
Here, n represents the required sample size, Z is the z-score corresponding to the desired certainty level (80%), σ is the standard deviation (2 ppm), and E is the margin of error (0.2 ppm).
For 80% certainty, the z-score is approximately 1.28. Plugging the values into the formula, we get:
n = (1.28 * 2 / 0.2)^2 = (12.8)^2 ≈ 164
Thus, the meteorologist needs to analyze approximately 164 air samples to be 80% certain that the error of estimate does not exceed 0.2 ppm.

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walking = biking + 1.5 hour

biking speed = 9 mph + walking speed

route = 6 miles

6/w = 6/(w + 9) - 3/2

Solving for w:

108 = -3w^2 - 27w ==> 3w^2 + 27w + 108 = 0 ==> x^2 + 9x + 36 = 0

Answer: Width = 8/20 ÷ 7/8  = 8/20 x 8/7   = 16/35 Therefore, the width will be 16/35 miles. Hope you do great :) !

x in (-oo:+oo)

y = (5/4)*x-(7/4) // - (5/4)*x-(7/4)

y-((5/4)*x)+7/4 = 0

(-5/4)*x+y+7/4 = 0

y-5/4*x+7/4 = 0 // - y+7/4

-5/4*x = -(y+7/4) // : -5/4

x = (-(y+7/4))/(-5/4)

x = 4/5*(y+7/4)

x = 4/5*(y+7/4)

Given:

The functions are

\(f(x)=x\)

\(g(x)=x+8\)

To find:

How the graphs of f and g are related.

Solution:

We have,

\(f(x)=x\)

\(g(x)=x+8\)

Using these functions, we get

\(g(x)=f(x)+8\)                   ...(1)

The translation is defined as

\(g(x)=f(x+a)+b\)                ... (2)

Where, a is horizontal shift and b is vertical shift.  

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

\(a=0,b=8\)

It means, the graph of f is translated 8 units up to create the graph of g.

Therefore, the correct option is B.

Answer:

Step-by-step explanation:

Remove the brackets. Watch out for that minus sign. It affects all three terms in the right bracket.

(-3f - 4g + 9) - (2 - 6f + 5g)

-3f - 4g + 9 - 2 + 6f - 5g

+3f - 9g + 7 is your answer.

Answer:

3f−9g+7

Step-by-step explanation:

(−3f−4g+9)−(2−6f+5g)

To find the opposite of 2−6f+5g, find the opposite of each term.

−3f−4g+9−2−(−6f)−5g

The opposite of −6f is 6f.

−3f−4g+9−2+6f−5g

Subtract 2 from 9 to get 7.

−3f−4g+7+6f−5g

Combine −3f and 6f to get 3f.

3f−4g+7−5g

Combine −4g and −5g to get −9g.

3f−9g+7

From the information given, the value of b if YH = 12b - 4.5, MV = 17b +0.75, and MW-WH = 13.25 is 0. 59

Algebraic expressions are simplify defined as expressions that are composed of terms, variable, coefficients, factors and also constants.

They also seen as expressions involving arithmetic operations such as;

From the information given, we have that;

MW-WH = 13.25.

Where;

Now, to determine the value of b, substitute the values into the equation

17b +0.75 + 12b - 4.5 = 13. 25

collect like terms

17b + 12b = 13.25 + 4. 5 - 0. 75

add or subtract like terms

29b = 17

Make 'b' the subject of formula by dividing both sides by 29, we have;

29b/29 = 17/29

Divide through

b = 0. 59

Thus, the value of b is 0. 59

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The function after transformation is G(x) = -5 ln (x+6) is the correct answer.

The correct answer is an option (C)

Here, the function is f(x) = ln x

A function f(x) is stretched vertically by a factor of 5.

As we know for a vertical stretch, we need to multiply the whole function by the factor of stretching.

If the stretching factor is m, then after stretching the function becomes

⇒ m × f(x)

Here, stretching factor m = 5

So the transformed function would be,

G(x) = 5 f(x)

⇒ G(x) = 5 ln x

Now, function is reflected across the x-axis, so the function becomes

⇒ G(x) = -5 ln (x+6)

Then the function is shifted by 6 units left, so after translation the function becomes

⇒ G(x) = -5 ln (x+6)

Thus, we can conclude that the function f(x) = ln x after transformation would be G(x) = -5 ln (x+6) is the correct answer.

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Answer:

a)0

b)-27

Step-by-step explanation:

I simplified it u just combine the like terms

the rest should be easy

Answer:

C. 20 x 4 = 1/5Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

4/20=.02 so its not A

1/5 divided by 4 is .05

So that leaves C

I hope this helps :)

Step-by-step explanation:

r=3/2=(4.5)/3=3/2

it is geometric, so we will use this equation:

a(n)=a1*(r)^(n-1)

and we have a(1)=2 , r=3/2    

So  explicit formula:

a(n)=2*(3/2)^(n-1)

hope this helps

Answer: B

Step-by-step explanation:

on edge warm-up

The required solution of given polynomial equation is \(x+1-\frac{8}{2x+5}\) .

Given polynomial equation is \(2x^{2}+7x-3\) which is to be divided by \(2x+5\)

In case of division of polynomials we Long division method to calculate final value of the given equation.

For solving given equation let us start from;

\(\frac{2x^{2} +7x-3}{2x+5}\) = \(x+\frac{2x-3}{2x+5}\)

\(x+\frac{2x-3}{2x+5}\) = \(x+1 +\frac{-8}{2x+5}\)

\(x+1-\frac{8}{2x+5}\)

The final solution for given equation is \(x+1-\frac{8}{2x+5}\)

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Equation represents the comet's orbit \(\frac{x^{2} }{100} -\frac{(y-6)^2}{64} =1\), So correct option is C.

A coordinate plane, also known as a Cartesian plane, is a two-dimensional surface that is used to graph points, lines, and shapes. It is named after the mathematician René Descartes, who is credited with inventing the system in the 17th century.

The coordinate plane is divided into four quadrants by two perpendicular lines called the x-axis and y-axis. The point where the two axes intersect is called the origin and is assigned the coordinates (0,0). The x-axis runs horizontally and is used to measure values along the horizontal (or "x") direction, while the y-axis runs vertically and is used to measure values along the vertical (or "y") direction.

Each point on the coordinate plane can be represented by an ordered pair of numbers, called coordinates, that indicate its position in relation to the x- and y-axes. The coordinates of a point are written as (x, y), where x is the point's distance from the y-axis and y is the point's distance from the x-axis.

The equation that represents the comet's orbit is:

\(\frac{x^{2} }{100} -\frac{(y-6)^2}{64} =1\)

This is the standard equation for a hyperbola in the center form, where the center is at (0,6), the distance between the center and the vertex is 8 and the distance between the center and the focus is 2.

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The domain of the function is R - {m} and the range of the function is (-∞, ∞).

We are given a function f: R−{n}→R defined by f(x) = (x-n)/(x-m), where m ≠ n.

To find the domain of the function, we need to consider the values of x for which the denominator (x-m) is zero. Since m ≠ n, we have m - n ≠ 0, and therefore the function is defined for all x except x = m.

Therefore, the domain of the function is R - {m}.

To find the range of the function, we can consider the behavior of the function as x approaches infinity and negative infinity. As x approaches infinity, the numerator (x-n) grows without bound, while the denominator (x-m) also grows without bound, but at a slower rate. Therefore, the function approaches positive infinity.

Similarly, as x approaches negative infinity, the numerator (x-n) becomes very negative, while the denominator (x-m) also becomes very negative, but at a slower rate. Therefore, the function approaches negative infinity.

Thus, we can conclude that the range of the function is (-∞, ∞).

In summary, the domain of the function is R - {m} and the range of the function is (-∞, ∞).

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Answer:

y <  \(\frac{1}{3}\) x - 2

Step-by-step explanation:

Slope of the line m = \(\frac{-4+1}{-6-3}\) = \(\frac{1}{3}\)

y + 1 = \(\frac{1}{3}\) (x - 3)

y = \(\frac{1}{3}\) x - 2

Points (9, 1) and (- 4, 7) are not solutions, then

1 < \(\frac{1}{3}\) (9) - 2

7 < \(\frac{1}{3}\) (- 4) - 2

Thus, the inequality is y <  \(\frac{1}{3}\) x - 2  

Answer:

The answer is 80°

Step-by-step explanation:

Here, we know that the sum of all interior angles of hexagon is equal to 720°

So,

x + x + 140 + 140 + 140 + 140 = 720

2x + 560 = 720

2x + 560 – 560 = 720 – 560

2x = 160

2x/2 = 160/2

x = 80°

Thus, The value of x is 80°

For Verification

x + x + 140 + 140 + 140 + 140 = 720

80 + 80 + 140 + 140 + 140 + 140 = 720

720 = 720

L.H.S = R.H.S

Hence Verified!

-TheUnknownScientist 72

The correct scientific notation for the number 0.00050210 is 5.0210 x 10^(-4).

Here's a step-by-step explanation:

1. To convert a decimal number to scientific notation, we need to move the decimal point until we have a number between 1 and 10. In this case, we need to move the decimal point 4 places to the right to get 5.0210.

2. Next, we determine the power of 10 by counting the number of places we moved the decimal point. In this case, since we moved it 4 places to the right, the power of 10 is -4.

3. Finally, we write the number in the form of "a x 10^n", where "a" is the number between 1 and 10 (5.0210 in this case), and "n" is the power of 10 (-4 in this case).

So, the correct scientific notation for 0.00050210 is 5.0210 x 10^(-4).

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Question- The correct scientific notation for the number 0.00050210 is: a. 5.0210 x 10° b. 5.021 x 10 c. 5.021 x 10 d. 5.0210 x 10 e. None of the choices listed are correct.

The scientific notation for 0.00050210 is 5.0210 x 10^-4. It was calculated by moving the decimal point 4 places to the right, resulting in 5.0210, and then multiplying by 10 to the power of -4.

The given number is 0.00050210. We're trying to express it in scientific notation which is a shorthand way to write numbers that are either very large or very small by representing them as the product of a number (between 1 and 10) and a power of ten.

First, let's consider the number 0.00050210. We shift the decimal point 4 places to the right until we have a number that is between 1 and 10. So, we get 5.0210. Then, we multiply by 10 to the power of minus the number of places we moved the decimal (in this case, -4) to write the scientific notation.

So, the scientific notation of 0.00050210 is 5.0210 x 10^-4.

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Answer:

CDW stocks a broad selection of office furniture, supplies, and accessories from computer stands to cleaning wipes, paper shredders and monitor stands.

Step-by-step explanation:

If sofia has a collection of 200 coins, 40 coins represent 20% of Sofia's collection.

To find out how many coins represent 20% of Sofia's collection, we need to first calculate what 1% of her collection is.

To do this, we can divide the total number of coins by 100:

1% of Sofia's collection = 200 coins ÷ 100 = 2 coins

Now that we know that 1% of her collection is 2 coins, we can find 20% by multiplying 2 by 20:

20% of Sofia's collection = 2 coins × 20 = 40 coins

Therefore, 40 coins represent 20% of Sofia's collection.

To find out what percentage a different number of coins represents, we can use the same method. For example, if we want to know what percentage 30 coins represent, we can divide 30 by 2 (since 2 coins represent 1%), which gives us 15%.

So, 30 coins represent 15% of Sofia's collection.

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The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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