Your yacht sails in the direction S 71° W for 141 miles. It then turns


and sails in the direction N 63º E 213 miles. Find its distance from


the starting point. Round answer to nearest hundredth.

Answer:

\(a_1=2\\a_n=a_{n-1}+(n-1)\,,n>1\)

Step-by-step explanation:

Given: The smaller branches spiral in the pattern \(\{2,3,5,8,...\}\) from a larger limb.

To model: the tree growth with the Fibonacci sequence

Solution:

Take \(a_1=2\)

Let \(a_n\) denotes the \(n^{th}\) term.

\(a_2=3=2+1=2+(2-1)=a_1+(2-1)\\a_3=5=3+2=3+(3-1)=a_2+(3-1)\\a_4=8=5+3=5+(4-1)=a_3+(4-1)\)

So,

\(a_1=2\\a_n=a_{n-1}+(n-1)\,,n>1\)

Answer:

Yes.

Step-by-step explanation:

The pattern in which the branches are growing off the limb is {1, 1, 2, 3, 5, 8, …}, meaning you can use the model with tree growth.

a) 214 in base-five is 1324.

b) 62 in base-five is 222.

c) 8 in base-five is 13.

d) 95 in base-five is 340.

a) To determine the base five representation of 214, we need to   find the largest power of five that  is less than or equal to  214.

In this case, 125 (5³) is the largest power of five   that is less than 214.

Now, we divide 214 by 125 -  

214 ÷ 125 = 1 remainder 89

Next, we divide the remainder, 89, by the next lower power of five, which is 25 (5²) -  

89 ÷ 25 = 3 remainder 14

Finally, we divide the remaining 14 by the lowest power of five, which is 5 itself -  

14 ÷ 5 = 2 remainder 4

Therefore, the base-five representation of 214 is 1324 in base-five.

b) Following the same steps as above -  

62 ÷ 25 = 2 remainder 12

12 ÷ 5 = 2 remainder 2

Hence,  the base-five representation of 62 is 222 in base-five.

c) 8 ÷ 5 = 1 remainder 3

this menas that  the base-five representation of 8 is 13 in base-five.

d) Following the same steps as above -  

95 ÷ 125 = 0 remainder 95

95 ÷ 25 = 3 remainder 20

20 ÷ 5 = 4 remainder 0

Hence, the base-five representation of 95 is 340 in base-five.

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Answer:

   \(\frac{8}{3}\)

Step-by-step explanation:

mean: (22+12+14+14+13+9)=14

|22-14| + |12-14| + ... + |9-14| =16

MAD = 16/6 = \(\frac{8}{3}\)

Answer:

4 : 59

Step-by-step explanation:

Close. But good try

So what is "ratio?"

Well seems like you got 15/59 i think you meant 15:59 right? ratio has a : in it.

But, you see there is only 4 pizzas with pepperoni in it so actually it should be

4 : 59

Good attempt anyways Trying is always better than nothing.

======================================================

Explanation:

Pick two points from the table such as (1,7) and (2,14)

Apply the slope formula.

\((x_1,y_1) = (1,7) \text{ and } (x_2,y_2) = (2,14)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{14 - 7}{2 - 1}\\\\m = \frac{7}{1}\\\\m = 7\\\\\)

This means y = mx+b updates to y = 7x+b

Plug a point like (1,7) into that equation to solve for b.

y = 7x+b

7 = 7*1+b

7 = 7+b

7-7 = b

0 = b

b = 0

We go from  y = 7x+b to  y = 7x+0

That simplifies to the final answer of   y = 7x

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

Check:

Plug x = 2 to get

y = 7x

y = 7*2

y = 14

This shows (2,14) is on the line, and it matches with the table.

I'll let you check the other x values.

Another way to verify is to use a graphing app like GeoGebra or Desmos.

Answer: y+7x

Step-by-step explanation: y equals to 7x because 7x1 is 1 and vice versa.

Answer:

if 8:00 is in the 24 hr clock then it is 08:00 am

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

The maximum rate of change of f at the point (0, 4) is 28, and it occurs in the direction of the vector (28, 0).

To find the maximum rate of change of the function f(x, y) = 7 sin(xy) at the point (0, 4), we need to compute the gradient vector ∇f(x, y) and evaluate it at the given point.

The gradient vector ∇f(x, y) of a function f(x, y) is given by the partial derivatives with respect to x and y:

∇f(x, y) = (∂f/∂x, ∂f/∂y)

Taking the partial derivatives of f(x, y) = 7 sin(xy):

∂f/∂x = 7y cos(xy)

∂f/∂y = 7x cos(xy)

Now, let's evaluate the gradient vector at the point (0, 4):

∇f(0, 4) = (7(4)cos(0), 7(0)cos(0))

= (28, 0)

The maximum rate of change of f at the point (0, 4) occurs in the direction of the gradient vector ∇f(0, 4) = (28, 0). The magnitude of this vector represents the maximum rate of change, and the direction is given by the direction of the vector.

The magnitude of the gradient vector is √(\(28^{2}\) + \(0^{2}\)) = √(784) = 28.

Therefore, the maximum rate of change of f at the point (0, 4) is 28, and it occurs in the direction of the vector (28, 0).

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Answer:

( 14 , 0 )

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*x+6*y-(42)= Pull out like factors :

  3x + 6y - 42  =   3 • (x + 2y - 14)

Equations which are never true:   Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

Answer:

x = 13

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )

x = \(\sqrt{169}\) = 13

The Laplace inverse of the given function, F(s) = (s^2 + s + 1) / (s^2 + 4s + 3), can be obtained by performing partial fraction decomposition.

By factoring the denominator, we get F(s) = (s^2 + s + 1) / [(s + 1)(s + 3)]. Applying partial fraction decomposition, we express F(s) as A/(s + 1) + B/(s + 3), where A and B are constants.

By equating numerators, we find A = 1 and B = -1. Therefore, the Laplace inverse of F(s) is f(t) = e^(-t) - e^(-3t). This means that the original function F(s) corresponds to an inverse Laplace transform those results in a decaying exponential function with two different rates, indicating a system with distinct time constants.

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Answer:

70°

Step-by-step explanation:

The sum of the interior angles is 180.  Subtract the 40 that you know about and you have 140.  Since the two sides are equal, the angles opposite them are equal.  140/2 = 70

Answer:

i think it is y = -4/5x + 4

Step-by-step explanation:

4x + 5y = 20

Subtract 4x on both sides

5y = -4x + 20

Divide 5 on both sides

y = -4/5x + 4

\(solution \\ - 25 + 4y = 35 \\ or \: 4y = 35 + 25 \\ or \: 4y = 60 \\ or \: y = \frac{60}{4} \\ y = 15\)

Hope it helps...

Good luck on your assignment....

The equation for the circle on the graph is:

(x - 2)^2 + (y + 2)^2 = 9

First, we know that the general circle equation can be written as:

(x - a)^2 + (y - b)^2 = R^2

That is the equation of a circle centered at the point (a, b) that has a radius of R units.

In the image, we can see that the center is at (2, -2) and it has a radius of 3 units, then we can rewrite the general equation to get:

(x - 2)^2 + (y - (-2))^2 = 3^2

Now we can simplify that equation so we get:

(x - 2)^2 + (y + 2)^2 = 9

That is the equation for the circle.

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The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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Answer:

-6 is the rate of change per year

Step-by-step explanation:

The amount in dollars decrease by 6 every year.

It went from $27 to $21 to $15 and finally to $9.

Hope I helped you!!

It will cost $312 to replace the glass in the window.

By multiplying the window's area by the tinted glass' price per square foot, we can figure out how much it will cost to replace the window's glass.

Looking at the plan, we can see that the window is in the shape of a rectangle. We need to find the length and width of the window to calculate its area.

Let's assume the length of the window is L feet and the width is W feet.

From the plan, we can see that the length of the window is 4 units and the width is 3 units.

Therefore, L = 4 feet and W = 3 feet.

The area of a rectangle is given by the formula: A = L * W

Substituting the values, we have: A = 4 feet * 3 feet = 12 square feet.

Now, we need to multiply the area of the window (12 square feet) by the cost per square foot of the tinted glass ($26 per square foot) to find the total cost.

Total cost = Area of window * Cost per square foot

Total cost = 12 square feet * $26 per square foot

Total cost = $312

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sin ( x − 5 π 3 ) sin(x-5π3) in terms of sin ( x ) sin(x) and cos ( x ) cos(x) can be rewritten as ( x − 5 π 3 )

We can use the identity for the sine of the difference between two angles:

sin ( a − b ) = sin a cos b − cos a sin b

where a = x and b = 5π/3:

sin ( x − 5 π 3 ) = sin x cos ( 5 π 3 ) − cos x sin ( 5 π 3 )

Since cos (5π/3) = -1/2 and sin (5π/3) = -√3/2, we have:

sin ( x − 5 π 3 ) = sin x ( − 1 2 ) − cos x ( − √ 3 2 )

Using the identity sin (π/3) = √3/2 and cos (π/3) = 1/2, we can write:

sin ( x − 5 π 3 ) = − 1 2 sin x + √ 3 2 cos x

Therefore, we have expressed sin ( x − 5 π 3 ) in terms of sin x and cos x.

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Using the angle subtraction formula for sine, we can rewrite sin (x - 5π/3) as sin x cos (5π/3) - cos x sin (5π/3). Simplifying further, we know that cos (5π/3) = -1/2 and sin (5π/3) = √3/2. Substituting these values, we get:

sin (x - 5π/3) = sin x (-1/2) - cos x (√3/2)

Therefore, we can rewrite sin (x - 5π/3) in terms of sin x and cos x as:

sin (x - 5π/3) = -1/2 sin x - √3/2 cos x
To rewrite sin(x - 5π/3) in terms of sin(x) and cos(x), you can use the angle subtraction formula for sine, which is:

sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

In this case, A = x and B = 5π/3. Apply the formula:

sin(x - 5π/3) = sin(x)cos(5π/3) - cos(x)sin(5π/3)

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The slope of the points (-1,4) and (5,-5) is -1.5 and the graph is attached below.

Slope of the line:

The slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line.

Formula,

m = (y2-y1)/x2-x1)

Given,

Points are (-1,4) and (5,-5)

Now we need to find the slope of the line and we have to plot it.

Apply the given values on the formula, then we get,

m = (-5-4)/5-(-1)

m = -9/6

m = -3/2

m= -1.5

Now we have to plot the graph for it

To graph the line going through the two points, we plot the two points and then draw a line through the points,

Then we get the graph like the following:

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Answer:

B) add (-7) to both sides

Step-by-step explanation:

If you wanna get or find a easier way to solve this you would have to subtract 7 to both side or from 18 and then you'll get your answer.

Answer:

Cone: 100ft^3

Sphere: 200ft^2

Step-by-step explanation:

Firstly, the volume of a cone is 1/3 of the volume of the cylinder. It's literally in the formula:

\(V_{cone} = \frac{h \pi r^2}{3}\\\textrm{As you can notice, }\pi r^2\textrm{ is the area of the base, like in the cylinder formula}\\\)

So we can just instantly tell that the volume of the cone is 100feet^3.

Not for the sphere - we can assume that if the height is the same, it's equal to two radiuses, or simply - to the diameter. Let's use the formula for the volume of a sphere, but substitute one of the radiuses with \(\frac{h}{2}\)

\(V_{sphere} = \frac{4\pi r^3}{3} = \frac{2\pi r^2 h}{3} = \frac{2h\pi r^2}{3} = 2\cdot V_{cone}\)

So we can instantly tell that the volume of the sphere is 200feet^3

Answer:

283

Step-by-step explanation:

The unconditional mean of the series, yt, is 0.6. This means that if we were to simulate the time series over a very long period of time, we would expect the average value of the series to converge to 0.6.

To find the unconditional mean of the series, yt, we need to consider what happens when the time series is allowed to run indefinitely. In other words, we want to know what the long-term average value of the series is likely to be.

To do this, we can use the concept of stationarity. A stationary time series is one where the statistical properties of the series do not change over time. In this model, we can see that the mean of the series is constant over time, since the intercept term, 0.3, does not depend on any past or future values of the series or the error term. Therefore, we can assume that the series is stationary, and we can use the equation for the mean of a stationary AR(1) process to find the unconditional mean:

μ = c / (1 - φ)

where μ is the unconditional mean, c is the intercept term, and φ is the coefficient on the lagged value of the series. In this case, we have c = 0.3 and φ = 0.5, so we can plug these values into the equation and get:

μ = 0.3 / (1 - 0.5) = 0.6

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The unconditional mean of the series is 0.6.

The unconditional mean of the series can be found by taking the expectation of both sides of the given model:

E(yt) = E(0.3 + 0.5yt-1 - 0.4εt-1 + εt)

= 0.3 + 0.5E(yt-1) - 0.4E(εt-1) + E(εt)

Since the error process is zero mean, we have E(εt) = 0 for all t. Also, since the model does not depend on time explicitly, we can assume that E(yt) = E(yt-1) = μ, where μ is the unconditional mean of the series. Substituting these values, we get:

μ = 0.3 + 0.5μ - 0.4E(εt-1) + E(εt)

= 0.3 + 0.5μ

Solving for μ, we get:

μ = 0.3 / (1 - 0.5) = 0.6

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Answer:

/13=3.60

(a)^2+(b)^2=(c)^2

(6)^2+(3.60)^2=(c)^2

36+13=(c)^2

49=(c)^2

c= /49

c=7

Step-by-step explanation:

pythagorean theorem is (a)^2+(b)^2=(c)^2

then replace it with the given values

inverse of square is squareroot

Answer:

third side is 7 units

Step-by-step explanation:

Hi there!

the Pythagorean theorem is given as a²+b²=c², where a and b are legs (the sides that make up the right angle) and c is the hypotenuse (side that is opposite to the right angle, or in this case, the third side)

we are given the lengths of the 2 legs, and we need to find the hypotenuse

a=6

b=√13

c=unknown value

square the values of a and b, add them together, and set that to equal c squared

or in other words:

6²+(√13)²=c²

36+13=c²

(because 6*6=36; √13*√13=13)

49=c²

√49=√c²

7=c

therefore the hypotenuse is 7 units

Hope this helps!

Answer:

She worked for 4 hours

Step-by-step explanation:

150-10=140

140/35=4

The standard deviation of returns is 0.0665 when a person is holding stock and there are three possible outcomes.

To calculate the expected return, we multiply the probability of each state by its corresponding return and sum them up:

Expected return = (20% * 18%) + (55% * 9%) + (25% * -5%)

Expected return = 0.20 * 0.18 + 0.55 * 0.09 + 0.25 * (-0.05)

Expected return = 0.036 + 0.0495 - 0.0125

Expected return = 0.073

The expected return is 7.30%.

To calculate the standard deviation of returns, we need to find the variance first. The variance is calculated as the weighted sum of squared deviations from the expected return:

Variance = (20% * (18% - 7.30%)^2) + (55% * (9% - 7.30%)^2) + (25% * (-5% - 7.30%)^2)

Variance = 0.20 * (0.1077)^2 + 0.55 * (0.0177)^2 + 0.25 * (-0.123)^2

Variance = 0.00232 + 0.000173 + 0.001903

Variance = 0.004423

The standard deviation is the square root of the variance:

Standard deviation = √(0.004423)

Standard deviation = 0.0665

Therefore, the value obtained is 0.0665.

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