Write the equation of the given circle.
center at origin, r=3

Answer:

x=36

Step-by-step explanation:

you would take 72 divided by 2 to get your answer

Answer:

Step-by-step explanation:

Ok, let's see how much I can do

So I don't know how to label the angles, but let's just say there are 2 angles at point B. One is already given. 72. Since a line is 180. We can find the other angle by subtraction: 180 - 72 = 108

And we can also tell that both angles at point D are equal as they are both represented by 2x.

Now by the looks of it, Line AC and DE are parallel so angle A and both the angles at point D are equal to each other. So triangle ABD is at least an isosceles triangle.  Now because we know it's an isosceles triangle, we can now find the measure of triangle ABD.

72 + 2x + 2x = 180

72 + 4x = 180

4x = 108

x = 27

Answer:

In this equation, we can start by understanding that "x" has a value of 8, as given in the ordered pair. When multiplied by 5, this leads to "40 - 2y = 30". Next, we can subtract 40 from both sides of the equation. This leads us to a value of "-2y = -10". The next step would be to divide both sides by -2 as a way of isolating "y", which leads us to a final value of "y = 5". The final ordered pair would be (8,5).

Answer:

x = -4

Step-by-step explanation:

\(-1 + x = -5\\x = -4\)

In 2020, Harper, Inc. acquired 40% of the outstanding voting stock of Kinman Company for $334,900 in cash.

The book value of Kinman's net assets was $625,000, but there were certain adjustments needed. One of Kinman's buildings was undervalued by $64,750 ($135,550 - $70,800), and there was an undervaluation of $147,500 for the royalty agreement. Harper also purchased inventory from Kinman for $111,000, out of which $18,750 was still held in inventory by the end of the year. Kinman reported a net loss of $51,800 and other comprehensive loss of $26,600 in 2020, but it still paid a $15,000 cash dividend.

To record these transactions, Harper would make the following journal entries in 2020:

1. To record the investment in Kinman's stock:
  Investment in Kinman Company Stock     334,900
  Cash                                                334,900

2. To adjust the building's carrying amount and recognize the related depreciation:
  Investment in Kinman Company Stock     64,750
  Depreciation Expense                                 6,475
  Accumulated Depreciation                      6,475

3. To adjust the undervalued royalty agreement:
  Investment in Kinman Company Stock     147,500
  Royalty Agreement                                      147,500

4. To record the purchase of inventory from Kinman:
  Inventory                                                   111,000
  Investment in Kinman Company Stock     111,000

5. To recognize the equity in Kinman's net loss and comprehensive loss:
  Equity in Net Loss                                         20,720
  Equity in Other Comprehensive Loss        10,640
  Investment in Kinman Company Stock     31,360

6. To record the receipt of the cash dividend:
  Cash                                                15,000
  Dividend Income                                        15,000

In 2021, Kinman reported a net income of $57,200 and paid a cash dividend of $17,000. Harper purchased additional inventory worth $120,000 from Kinman, out of which 70% ($84,000) was sold to outside parties by year-end. Harper would make the following journal entries in 2021:

1. To recognize the equity in Kinman's net income:
  Equity in Net Income                                22,880
  Investment in Kinman Company Stock     22,880

2. To record the receipt of the cash dividend:
  Cash                                                17,000
  Dividend Income                                        17,000

3. To record the purchase of additional inventory from Kinman:
  Inventory                                                   120,000
  Investment in Kinman Company Stock     120,000

4. To eliminate the unrealized profit in inventory:
  Investment in Kinman Company Stock     8,400
  Equity in Net Income                                8,400

Overall, these journal entries reflect the investment in Kinman Company, adjustments for undervalued assets, recognition of income or loss, and dividend payments. The equity method is used to account for the investment, where Harper recognizes its share of Kinman's net income or loss and adjusts the investment account accordingly.

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The antiderivative of the function is F(x) = 4x + 5x^3 + 3x^5 - 12.

To find the antiderivative F(x) for F′(x) = f(x) = 4 + 15x^2 + 15x^4, and given F(1) = 0, follow these steps,
1. Find the antiderivative of f(x) with respect to x:
F(x) = ∫(4 + 15x^2 + 15x^4) dx

2. Integrate each term separately:
F(x) = ∫4 dx + ∫15x^2 dx + ∫15x^4 dx

3. Calculate the antiderivatives:
F(x) = 4x + (15/3)x^3 + (15/5)x^5 + C

4. Simplify:
F(x) = 4x + 5x^3 + 3x^5 + C

5. Use the given condition F(1) = 0 to find the value of C:
0 = 4(1) + 5(1)^3 + 3(1)^5 + C

6. Solve for C:
C = -12

7. Substitute the value of C back into F(x):
F(x) = 4x + 5x^3 + 3x^5 - 12

The antiderivative is F(x) = 4x + 5x + 3x - 12 as a result.

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Answer:

x=-2

Step-by-step explanation:

The line is vertical and/or undefined and it passes through the point (-2,5).

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

Ans C

m=4/5

X1= -7

Y1 = 9

Y-Y1=m(X-X1)

Y-9=4/5(X-(-7))

Y-9=4/5(X+7)

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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Answer:

  2 times one-half = 1

Step-by-step explanation:

In order to show a property of multiplication, the equation must involve multiplication. There is only one choice that does.

  2 times one-half = 1

__

The multiplicative inverse of a number, multiplied by the number, results in 1, the multiplicative identity element.

Equation C,2 times one-half = 1 shows the inverse property of multiplication. Option C is correct.

A multiplicative inverse is a number whose value is equal to 1 when multiplied by the original number.

The left-hand side of the equation is;

LHS =  2 times one-half

LHS = 2×(1/2)

LHS = 2

The right-hand side of the equation is;

RHS =1

If both LHS and RHS are equal and the RHS value is equal to 1 the RHS is the multiplicative inverse of LHS.

Equation C,2 times one-half = 1 shows the inverse property of multiplication.

Hence, option C is correct.

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The score that separates the top 41% from the bottom 59% is approximately 35.08. To find the score that separates the top 41% from the bottom 59% of scores on an English test with a mean of 33.3 and a standard deviation of 7.1, we need to use the standard normal distribution.

First, we need to find the z-score that corresponds to the top 41% of scores, which can be found using a standard normal distribution table or a calculator. The z-score corresponding to the top 41% is approximately 0.27. We can then use the formula z = (x - μ) / σ to find the corresponding raw score, x, where μ is the mean and σ is the standard deviation. Rearranging the formula gives us x = zσ + μ, which gives us the score that separates the top 41% from the bottom 59%.

In this case, we have z = 0.27, σ = 7.1, and μ = 33.3. Plugging these values into the formula gives us x = 0.27 * 7.1 + 33.3, which simplifies to x = 35.08. Therefore, the score that separates the top 41% from the bottom 59% is approximately 35.08.

This means that if a student scores above 35.08 on the English test, they would be in the top 41% of scores, while if they score below 35.08, they would be in the bottom 59% of scores.

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Answer:

i need more info, like how much r the CDs and the phones

Step-by-step explanation:

Answer:

B=2, C=3, D=4, E=5

More than 50% of the bottles meet the specifications.

To determine the proportion of bottles that meet the specifications, we need to calculate the process capability index (Cpk).

The formula for Cpk is:

Cpk = min((USL - X) / (3* σ), (X - LSL) / (3 * σ))

Given:

USL = 3 + 0.150 = 3.150 ounces

X = 3.042 ounces

σ = 0.034 ounce

So, Cpk = min((3.150 - 3.042) / (3 * 0.034), (3.042 - 2.850) / (3 * 0.034))

   = min(0.108 / 0.102, 0.192 / 0.102)

   = min(1.059, 1.882)

   = 1.059

To determine the proportion of bottles that meet the specifications, we can use the following table:

Cpk Value       Proportion within Specifications

-----------------------------------------------

< 1.00          Poor

1.00 - 1.33     Fair

1.33 - 1.67     Good

> 1.67          Excellent

Since the Cpk value is 1.059, it falls within the range of 1.00 - 1.33, which corresponds to a "Fair" proportion within specifications.

Therefore, slightly more than 50% of the bottles meet the specifications.

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Answer: $36

Step-by-step explanation: 10% of 40 is 4 so 40- 4 is 36

Answer:

x>−7

Explanation:

Let's solve your inequality step-by-step.

−4x<28

Step 1: Divide both sides by -4.

−4x/−4 < 28/−4

x>−7

Answer: x>−7

Answer:

Jason runs faster then his friend.

Step-by-step explanation:

Jason's speed is represented by the equation y = 7x because he runs 7 miles in an hour. If his friend's speed is represented by y = 6x, then his friend runs a total of 6 miles in an hour.

Answer: 72.97 Minutes

Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.

To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.

Relative speed = Speed of car B - Speed of car A

Relative speed = 114 km/h - 77.0 km/h

Relative speed = 37.0 km/h

So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.

To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.

Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours

Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).

Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes

Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.

Hope this helps!

The cost of two oranges is 1.1 dollars.

One Sunday, Cory bought 4 apples and 6 oranges and paid $5.10. Dalia bought 2 apples and 5 oranges and paid $3.65.

Therefore, using equation,

let

x = cost of each apples

y = cost of each oranges

Hence,

4x + 6y = 5.10

2x + 5y = 3.65

Multiply equation(ii) by 2

4x + 6y = 5.10

4x + 10y = 7.3

4y = 2.2

y = 2.2 / 4

y = 0.55 dollars

Therefore,

cost of 2 oranges = 0.55(2) = 1.1 dollars

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Answer:

45,698,09864,58586,96403

Answer:

x = 10, y = 20

Step-by-step explanation:

Form a system of equations:

From the picture at the bottom you can see that vertical angles are equal, so:

\(3x + 2y = 70\)

Then, since the angles all together will add up to 360, you can do

\(3x+2y+9x+y+70+9x+y=360\)

\(21x+4y+70=360\)

subtract 70 from both sides

\(21x + 4y = 290\)

With the equation 3x + 2y = 70, multiply both sides by 2

\(6x+4y=140\)

Subtract the two equations:

\(15x=150\\x=10\)

Plug this into one of the original equations

\(30+2y=70\\2y = 40\\y=20\)

(i) Sketch the waveforms of the resultant AM signals for ka=0.5 and 1.5, respectively. In amplitude modulation (AM), the amplitude of the carrier signal is varied proportional to the instantaneous amplitude of the modulating signal, i.e., the message signal.

The amplitude modulated (AM) waveform is expressed as a product of two functions, i.e., a carrier wave and a message signal. The mathematical representation of an AM signal is as follows:

xAM​(t)={1+ka​m(t)}×cos(20πt).

Here, ka​ is the amplitude sensitivity or modulation index and m(t) is the message signal. For example, when ka​ = 1, it is known as 100% modulation. When ka​ > 1, it is known as over modulation. When ka​ < 1, it is known as under modulation.

The message signal m(t) is assumed to be a rectangular pulse given by m(t)={1,0,​ if −0.2s≤t≤0.2 s otherwise ​The waveform of the resultant AM signal for ka​ = 0.5 is shown below:

Waveform of the AM signal for ka=0.5The waveform of the resultant AM signal for ka​ = 1.5 is shown below:

Waveform of the AM signal for ka=1.5(ii) Discuss whether the message signal can be recovered using the envelop detector for both cases of ka​=0.5 and 1.5, respectively.

The message signal cannot be recovered using the envelope detector in case of overmodulation, i.e., when ka​ > 1. In this case, the carrier is suppressed, and the envelope detector cannot extract the original message signal.The message signal can be recovered using the envelope detector in case of normal modulation, i.e., when ka​ < 1. The envelope detector consists of a diode and a low-pass filter.

The diode rectifies the AM signal, and the low-pass filter smoothens the rectified waveform to obtain the original message signal.

The waveform of the resultant AM signal for ka​ = 0.5 is shown below:The waveform of the resultant AM signal for ka​ = 1.5 is shown below:

The message signal cannot be recovered using the envelope detector in case of overmodulation, i.e., when ka​ > 1. In this case, the carrier is suppressed, and the envelope detector cannot extract the original message signal. The message signal can be recovered using the envelope detector in case of normal modulation, i.e., when ka​ < 1.

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Answer:

14

Step-by-step explanation:

-1+15=14

.................

Santiago needs to invest  50467.3 dollars for the value of the account to reach $81,000 in 16 years at a rate of 3.3%.

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

Given Santiago is going to invest in an account paying an interest rate of 3.3% compounded annually for the value of the account to reach $81,000 in 16 years.

We know the formula of compound interest which is A = P(1 + r/100)ⁿ,

where A = Amount, P = Principle, n = Time in years and r = rate percentage.

∴ 81000 = P( 1 + 3.3/100)¹⁶.

81000 = P( 1 + 0.03)¹⁶.

81000 = P( 1.03)¹⁶.

81000 = P×1.605.

P = 81000/1.605

P = 50467.3 dollars.

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490

472 <490<500

it fits the criteria

The radius of convergence of the given series is infinity.

To find the radius of convergence, we use the ratio test, which involves computing the limit of the ratio of successive terms. Applying the ratio test to the given series, we get:

limit as n approaches infinity of [((n+1)!)^k/(k(n+1))!][k!/(n!)^k][x^(n+1)][(kn)!/k!][n!/(kn)!]*[x^n]

Simplifying the expression, we get:

limit as n approaches infinity of [(n+1)/(kx)]*|x|

Since the limit is infinity, the radius of convergence is infinity. This means that the series converges for all values of x.

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Answer: Greater than or equal to 2.

Step-by-step explanation:

Given

Function is  \(f(x)=2x^2+5\sqrt{x-2}\)

The entity inside a square root is always positive i.e. greater than equal to zero

\(\therefore \ x-2\geq 0\\\Rightarrow x\geq2\)

So, the domain of the function is all real numbers greater than or equal to 2.

The average total time a customer experiences in the service area is 9 minutes. If IKEA reduces to 4 service desks, the average waiting time will become 4 minutes. Yes, IKEA can reduce to 3 service desks.

a. To calculate the average total time a customer will experience in the service area, we need to consider both the waiting time and the processing time.

The average waiting time can be calculated using the M/M/1 queuing model, which assumes that arrivals follow a Poisson distribution and service times follow an exponential distribution. Since we have multiple service desks, we need to use the M/M/c queuing model.

Using the M/M/c model with λ = 0.5 arrivals per minute, μ = 1/6 customers per minute, and c = 5 service desks, we can calculate the average waiting time as:

W = (λ / (c * μ - λ)) * (c / (c - 1)) * (1 / μ)

W = (0.5 / (5 * (1/6) - 0.5)) * (5 / 4) * 6

W = 3 minutes

The average processing time is given as 6 minutes. Therefore, the average total time a customer will experience in the service area is:

Total time = Waiting time + Processing time

Total time = 3 + 6 = 9 minutes

b. If IKEA reduces to 4 service desks, the average waiting time will increase. Using the M/M/c model with λ = 0.5 arrivals per minute, μ = 1/6 customers per minute, and c = 4 service desks, we can calculate the new average waiting time as:

W = (λ / (c * μ - λ)) * (c / (c - 1)) * (1 / μ)

W = (0.5 / (4 * (1/6) - 0.5)) * (4 / 3) * 6

W = 4 minutes

Therefore, the average waiting time would increase from 3 minutes to 4 minutes if IKEA reduces to 4 service desks.

c. It is possible for IKEA to reduce to 3 service desks, but it would result in an increase in the average waiting time. Using the M/M/c model with λ = 0.5 arrivals per minute, μ = 1/6 customers per minute, and c = 3 service desks, we can calculate the new average waiting time as:

W = (λ / (c * μ - λ)) * (c / (c - 1)) * (1 / μ)

W = (0.5 / (3 * (1/6) - 0.5)) * (3 / 2) * 6

W = 6 minutes

Therefore, if IKEA reduces to 3 service desks, the average waiting time would increase from 3 minutes to 6 minutes.

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