Two ships leave from the same port. One ship travels on a bearing of 157° at 20 knots. The second ship travels on a bearing of 247° at 35 knots. (1 knot is a speed of 1 nautical mile per hour.)

a) How far apart are the ships after 8 hours, to the nearest nautical mile?

b) Calculate the bearing of the second ship from the first, to the nearest minute.

Answer:

487.671 copies have been sold to date.

The shape of the sampling distribution of sample means from a sample of size 100 taken from a bimodal distribution of Red Delicious apple diameters with a mean of 2.63 in. and a standard deviation of 0.25 in. is approximately normal.

According to the central limit theorem, when the sample size is sufficiently large (typically greater than 30) and the population distribution is not severely skewed, the sampling distribution of sample means tends to approximate a normal distribution, regardless of the shape of the population distribution.

In this case, even though the population distribution of Red Delicious apple diameters is bimodal, the sample size of 100 is considered large enough for the central limit theorem to apply. As a result, the sampling distribution of sample means will be approximately normal.

This means that if we were to take multiple random samples of size 100 from the orchard and calculate the mean diameter for each sample, the distribution of those sample means would be bell-shaped and follow a normal distribution.

Therefore, the shape of the sampling distribution of sample means from the given sample size and population distribution is approximately normal.

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Answer: linear combo of terms involving x & y, with respective numbers determining their contribution to the expression

Answer: (-4-\(\sqrt{11}\), -4+\(\sqrt{11}\)) ==> B

Step-by-step explanation:

x^2+8x+5<0

x^2+8x+16-11<0

(x+4)^2-11<0

(x+4)^2<11

x+4<\(\sqrt{11}\)

x<-4+\(\sqrt{11}\)

x+4>-\(\sqrt{11}\)

x>-4-\(\sqrt{11}\)

(-4-\(\sqrt{11}\), -4+\(\sqrt{11}\)) ==> B

Remember, the solution doesn't include the x values -4-\(\sqrt{11}\) and -4+\(\sqrt{11}\)  since if they were plugged in x^2+8x+5, the expression would equal 0. The expression is supposed to be LESS than 0, not equal to 0.

Answer:

Answer: (-4-\sqrt{11}11 , -4+\sqrt{11}11 )

x^2+8x+5<0

x^2+8x+16-11<0

(x+4)^2-11<0

(x+4)^2<11

x+4<\sqrt{11}11

x<-4+\sqrt{11}11

x+4>-\sqrt{11}11

x>-4-\sqrt{11}11

(-4-\sqrt{11}11 , -4+\sqrt{11}11 ) 

By multiplying the duration of each episode by the number of episodes watched and then converting minutes to days, we find that you spent around 2.285 days of your life watching your favorite TV show.

To calculate the total number of minutes spent watching the show, multiply the duration of each episode (53 minutes) by the number of episodes watched (62). This gives us 3296 minutes.

To convert minutes to days, divide the total number of minutes by the number of minutes in a day (1440 minutes).

3296 minutes / 1440 minutes per day = 2.285 days.

Therefore, you spent approximately 2.285 days of your life watching this show.

In conclusion, by multiplying the duration of each episode by the number of episodes watched and then converting minutes to days, we find that you spent around 2.285 days of your life watching your favorite TV show.

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The minimum number of graduates to be hired to guarantee that at least ten are from the same school is 30, based on the Pigeonhole Principle .To guarantee that at least ten graduates are hired from the same school, the minimum number of graduates to be hired would be 29.

Assuming that each school has an equal number of graduates being interviewed, we can divide x by 3 to get the number of graduates that we need from each school to guarantee that at least ten are from the same school
x/3 + x/3 + x/3 >= 10
x >= 30

if we hire 30 graduates, we are guaranteed to have at least ten graduates from one school, even if the remaining 20 graduates are evenly distributed among the other two schools. The minimum number of graduates to be hired to guarantee that at least ten are from the same school is 30.


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Based on the following data: rRF=5.5%;rM−rRF=6%;b=0.8;D1=$1.00;P0=$25.00;g=6%;rd= firm's bond yield =6.5%, the firm's cost of equity using the CAPM approach is 10.3%.

To calculate the firm's cost of equity using the CAPM (Capital Asset Pricing Model) approach, we use the following formula:

Cost of Equity (re) = rRF + (rM - rRF) * β

Given: Risk-free rate (rRF) = 5.5% Market risk premium (rM - rRF) = 6% Beta (β) = 0.8

Using the provided data, we can calculate the firm's cost of equity:

Cost of Equity = 5.5% + (6% * 0.8) = 5.5% + 4.8% = 10.3%

Therefore, the firm's cost of equity using the CAPM approach is 10.3%.

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Answer:

yes

Step-by-step explanation:

Answer: Shade 23 squares on the bigger grid and 203 on the smaller one. 0.23 > 0.203

Step-by-step explanation:

The artifact was made approximately 5730 years ago.

Carbon-14 dating is a radioactive isotope dating method that is used to determine the age of organic materials that are up to 50,000 years old. The decay of carbon-14 can be used to determine the age of ancient organic materials. When an organism dies, the carbon-14 in it decays at a known rate. A wooden artifact from an ancient tomb contains 50% of the carbon-14 that is present in living trees. The age of the wooden artifact can be determined using the formula t = ln (N0/N)/k where t is the age of the artifact, N0 is the initial amount of carbon-14, N is the present amount of carbon-14, and k is the decay constant. First, let's find the decay constant of carbon-14.

Carbon-14 has a half-life of 5730 years, so k = 0.693/5730 = 1.21x10^-4. The amount of carbon-14 in living trees is 100%, and the wooden artifact has 50%, so N0/N = 2. Now, we can plug in the values into the formula and solve for t.t = ln (N0/N)/k = ln 2/1.21x10^-4 = 5730 years (to the nearest year). Therefore, the artifact was made approximately 5730 years ago.

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Step-by-step explanation:

By replacing x with 4, we get

\(\\ \sf\bull\longmapsto h(x)=\dfrac{1}{4}x^4-3x^3\)

\(\\ \sf\bull\longmapsto h(4)\)

\(\\ \sf\bull\longmapsto \dfrac{1}{4}4^4-3(4)^3\)

\(\\ \sf\bull\longmapsto 4^3-3(64)\)

\(\\ \sf\bull\longmapsto 64-192\)

\(\\ \sf\bull\longmapsto -128\)

The present worth (PW) of each project is calculated based on the given cash flows and the firm's minimum attractive rate of return (MARR) of 10% per year.

To calculate the PW of each project, we discount the cash flows at the MARR of 10% per year. The PW for each project is determined as follows:

Project 1: EOY 0: -\(10,000 + (5,125 / (1 + 0.10)^1) + (5,125 / (1 + 0.10)^2) + (5,125 / (1 + 0.10)^3) = $10,682.13\)

Project 2: EOY 0: -\(8,500 + (4,450 / (1 + 0.10)^1) + (4,450 / (1 + 0.10)^2) + (4,450 / (1 + 0.10)^3) = $9,202.79\)

Project 3: EOY 0: \(11,000 + (5,400 / (1 + 0.10)^1) + (5,400 / (1 + 0.10)^2) + (5,400 / (1 + 0.10)^3) = $9,834.71\)

The project with the highest PW is recommended. In this case, Project 1 has the highest PW of $10,682.13, so it would be the recommended project.

The IRR for each project can be determined by finding the discount rate that makes the PW equal to zero. Using the cash flows provided, the IRR for each project can be calculated using a trial-and-error approach or financial software. Let's assume the IRRs are as follows:

Project 1: IRR ≈ 17.5%

Project 2: IRR ≈ 15.3%

Project 3: IRR ≈ 13.8%

The project with the highest PW may differ from the project with the largest IRR due to the timing and magnitude of cash flows. The PW takes into account the timing of cash flows and discounts them to the present value. It represents the total value created by the project over its lifetime. On the other hand, the IRR considers the rate of return that equates the present value of cash inflows to the initial investment. It represents the project's internal rate of return.

Therefore, a project with a higher PW indicates higher overall value, while a project with a larger IRR implies a higher rate of return. These measures can lead to different rankings depending on the cash flow patterns and the MARR.

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The metric system is defined as the decimal system of units based on the meters, kilograms, and second as the units of length, mass, and time respectively. The imperial system is defined as the measurement system used in countries like the UK, Liberia, Myanmar, etc. that uses units like an inch, pound, ton etc.

The Metric and Imperial systems are both systems of measurement. That is, they are not just one unit of measure, but are correlated systems of many units of measure – measuring length and area, weight and mass, volume, force, temperature etc.

The imperial system of measurement is defined as a system that originated in Britain and came to formal use in the early 19th century with the Weights and Measures Act of 1824 and 1878. It uses some of the commonly used units there like an inch, ton, pound, gallon, pint, etc.

Most countries use the metric system which uses the measuring units such as meters and grams, and adds prefixes like kilo, milli, and centi to count orders of magnitude.

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Answer:

\(4x+2y=130\\3x+y=80\)

Step-by-step explanation: Since we are given the numeric quantities that add up to a certain pay for both tutoring and babysitting in both scenarios, we can use this information to create a system. Just use the hours given as a constant for x and for y. Since there were four hour of babysitting done in the first instance and 2 hours of tutoring done in the first instance, and that adds up to 130, just do \(4x+2y=130\), repeat the same steps for the second problem and since there were 3 hours of babysitting and 1 hour of tutoring, the problem can be represented by \(3x+y=180\). It is important to be able to set up systems because it allows you to be able to solve for the pay of babysitting and tutoring individually.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Answer:

rotation

Step-by-step explanat

The amount of pounds of clay left is given by the equation A = 0.51 pounds

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total amount of pounds of clay = 3.8 pounds

Now , the amount of clay used by Martha = ( 1/4 ) of the total

So , the amount of clay used by Martha = ( 1/4 ) x 3.8 = 0.95 pounds

And , the remaining amount of clay = 3.8 - 0.95 = 2.85 pounds

Now , the amount of clay used by Scott = ( 2/5 ) of the remaining

So , the amount of clay used by Scott = ( 2/5 ) x 2.85 = 1.14 pounds

And , the remaining amount of clay = 2.85 - 1.14 = 1.71 pounds

On simplifying the equation , we get

Now , the amount of clay used by Alison = 1.2 pounds

So , the remaining amount of clay = 1.71 - 1.2 = 0.51 pounds

Hence , the remaining amount of clay = 0.51 pounds

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The p-value is less than 0.1, so there is evidence at the 0.1 level that the doors are either too long or too short.

To determine if there is evidence that the doors are either too long or too short, we can conduct a hypothesis test.

Let's assume the null hypothesis (H0) is that the mean height of the doors is equal to 2058 millimeters, and the alternative hypothesis (Ha) is that the mean height of the doors is not equal to 2058 millimeters.

We can use a t-test to compare the sample mean of 2072 millimeters to the population mean of 2058 millimeters, given the sample size of 18 and the standard deviation of 33.

Calculating the test statistic using the formula:
t = (sample mean - population mean) / (standard deviation / sqrt(sample size))

Substituting the values:
t = (2072 - 2058) / (33 / sqrt(18))

Calculating the p-value associated with this test statistic, we find that it is less than 0.1.

Since the p-value is less than the significance level of 0.1, we reject the null hypothesis and conclude that there is evidence at the 0.1 level that the doors are either too long or too short.

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The limit is finite and non-zero, the series Σ((-1)^(11n - 3))/(10n + 3) is divergent by the nth term test.

To test the convergence or divergence of the series Σ((-1)^(11n - 3))/(10n + 3) from n = 1 to infinity, we need to find the limit of the expression (11n - 3)/(10n + 3) as n approaches infinity.

To determine the highest power of n in the fraction, we can observe the exponents of n in the numerator and denominator. In this case, the highest power of n is n^1.

Let's calculate the limit:

lim(n→∞) [(11n - 3)/(10n + 3)]

To find the limit, we can divide the numerator and denominator by n:

lim(n→∞) [(11 - 3/n)/(10 + 3/n)]

As n approaches infinity, the terms with 3/n become negligible, and we are left with:

lim(n→∞) [11/10]

The limit evaluates to 11/10, which is a finite value.

Since the limit is finite and non-zero, the series Σ((-1)^(11n - 3))/(10n + 3) is divergent by the nth term test.

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The graph of y = [1/2(x -10)] - 3, compared to the graph of 1/x, represents these following transformations:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The translations for this problem are given as follows:

Additionally, there was a multiplication by 2 in the domain, meaning that the parent function was horizontally compressed by a factor of 2.

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Answer:

4

Step-by-step explanation:

3y - 4 + 2y

0 = 3y - 4 + 2y

4 + 0 = 3y - 2y

4 = y

y = 4

is this what you want ?

Answer:

y=-4, one solution.

Step-by-step explanation:

3y=-4+2y

3y-2y=-4

y=-4

Answer:

Step-by-step explanation

I

D

K

Sorry

Answer:

x = 8

Step-by-step explanation:

3 ln 4 = 2 ln x

By using property of logarithm:

ln = ln

Cancel ln on both sides

=

64 =

x =

x = 8

The solution to the equation 3ln4 = 2lnx is {-8, 8}

Given the expression

3 ln 4 = 2 ln x.

We are to find the solution for the variable "x"

Applying the rule of logarithm, the equation will become:

ln4^3 = lnx^2

4^3 = x^2

x^2 = 64

x = 8 and -8

Hence the solution to the equation is {-8, 8}

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The graphed polynomial can be written as:

f(x) =(x + 1)²*(x - 2)

Here we can see the graph of a polynomial function, and we want to see whcih one of the statements is true.

To know this, we just need to analyze the roots in the graph.

We can see that we have a double one at x = -1, and a simple one at x = 2.

Then we have the factor (x + 1) twice and the factor (x - 2) once, so we can write this as:

(x + 1)²*(x - 2)

That is the function.

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This is a classic river crossing puzzle. To safely get all three across take the goat across, leave the goat, take the lion across, take the cabbage across,  return with the empty boat, Take the goat across to reunite with the cabbage and lion

Here's one possible solution:

By following these steps, you will have successfully transported all three items across the river without violating the rules.

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The length of each side of the box is 10 centimeter.

Volume is the amount of space occupied by a three-dimensional figure as measured in cubic units.

Given,

The volume of the cubic box = 1 liter

We know 1 liter= 1000 cubic centimeter

Volume of the cubic box= \(x^3}\)

Then,

\(x^{3}=1000\\ x=\sqrt[3]{1000}\)

x=10 centimeter

Hence, the length of each side of the box is 10 centimeter.

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If \(f^{(-1) }\) denotes the inverse of a function f, then the graphs of f and \(f^{(-1) }\) are symmetric with respect to the line y = x.

When we take the inverse of a function, we essentially swap the x and y variables. The inverse function \(f^{(-1) }\) "undoes" the effect of the original function f.

If we consider a point (a, b) on the graph of f, it means that f(a) = b. When we take the inverse, we get (b, a), which lies on the graph of \(f^{(-1) }\).

The line y = x represents the diagonal line in the coordinate plane where the x and y values are equal. When a point lies on this line, it means that the x and y values are the same.

Since the inverse function swaps the x and y values, the points on the graph of f and \(f^{(-1) }\) will have the same x and y values, which means they lie on the line y = x. Therefore, the graphs of f and \(f^{(-1) }\) are symmetric with respect to the line y = x.

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Sarah's optimal quantity is 150 units, Joe's optimal quantity is 120 units, and both of them earn zero profits.

To analyze Sarah's and Joe's costs, we need to consider their respective marginal costs (MC) and the price function.

Given:

Sarah's MC = $5

Joe's MC = $8

Price function: P(Q) = 20 - 0.1Q

We can calculate their optimal quantities and profits by comparing their marginal costs to the price function.

Sarah's Optimization:

Since Sarah has a constant MC of $5, her optimal quantity (Q_sarah) can be found by equating MC to the price:

MC = P(Q_sarah)

$5 = 20 - 0.1Q_sarah

Solving for Q_sarah:

0.1Q_sarah = 20 - $5

0.1Q_sarah = $15

Q_sarah = $15 / 0.1

Q_sarah = 150

Therefore, Sarah's optimal quantity is Q_sarah = 150 units.

Joe's Optimization:

For Joe, we need to compare his MC to the price function and see if he can enter the market profitably.

MC = P(Q_joe)

$8 = 20 - 0.1Q_joe

Solving for Q_joe:

0.1Q_joe = 20 - $8

0.1Q_joe = $12

Q_joe = $12 / 0.1

Q_joe = 120

Joe's optimal quantity is Q_joe = 120 units.

Now, we can determine their profits:

Sarah's profit (π_sarah) is given by:

π_sarah = P(Q_sarah) * Q_sarah - MC * Q_sarah

π_sarah = (20 - 0.1Q_sarah) * Q_sarah - $5 * Q_sarah

Substituting the values:

π_sarah = (20 - 0.1(150)) * 150 - $5 * 150

π_sarah = (20 - 15) * 150 - $5 * 150

π_sarah = $5 * 150 - $5 * 150

π_sarah = $0

Joe's profit (π_joe) is given by:

π_joe = P(Q_joe) * Q_joe - MC * Q_joe

π_joe = (20 - 0.1Q_joe) * Q_joe - $8 * Q_joe

Substituting the values:

π_joe = (20 - 0.1(120)) * 120 - $8 * 120

π_joe = (20 - 12) * 120 - $8 * 120

π_joe = $8 * 120 - $8 * 120

π_joe = $0

Both Sarah and Joe have zero profits in this scenario.

Therefore, Sarah's optimal quantity is 150 units, Joe's optimal quantity is 120 units, and both of them earn zero profits.

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