Q3 The following diagram represents the positions and
bearings of three buoys floating in the ocean.
[a] How far west is Buoy B from Buoy C.
[b] How far east is Buoy A from Buoy B.
[c] How far north is Buoy C from Buoy A.
N
Buoy B
N
077⁰
240m
345m
N
314⁰
Buoy A
Buoy C
Q4 A ship sails on a bearing of 074° for 10 miles followed by a
bearing of 131° for 15 miles. Work out the bearing of the
ship from its starting position to the nearest degree.

Answer:

The equation of the ellipse is:

(x^2)/16 + (y^2)/4 = 1

Step-by-step explanation:

An ellipse is a set of points on a plane, the sum of whose distances from two fixed points (called foci) is constant. The distance between the foci of an ellipse is denoted by 2c, and the distance between the center of the ellipse and one of its vertices is denoted by a.

In this problem, the foci are located at (2,0) and (-2,0), so the distance between the foci is 2c = 4, which means that c = 2. The major vertices of the ellipse are located at (4,0) and (-4,0), so the distance between the center and one of the vertices is a = 4.

The formula for the equation of an ellipse centered at the origin is:

(x^2)/(a^2) + (y^2)/(b^2) = 1

where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex. Since the center of this ellipse is at the origin and the major axis lies on the x-axis, we know that b = a, so we can substitute a for b in the equation:

(x^2)/(a^2) + (y^2)/(a^2) = 1

To find a, we use the fact that c^2 = a^2 - b^2:

a^2 - b^2 = c^2

a^2 - a^2 = 4

b^2 = 4

b = 2

Now we can substitute a = 4 and b = 2 into the equation:

(x^2)/(16) + (y^2)/(4) = 1

This is the equation of the ellipse.

Answer: What is the measure of ∠ D?

By using the angle sum property of quadrilateral, we get the measure of angle ∠D is 76.765°.

Step-by-step explanation:

The mean is the most appropriate measure of center for the given data. While the median and mode were also calculated, the mean provides the best representation of the data's central tendency. The geometric mean was not applicable in this case.

Option A) Mean: To calculate the mean, we add up all the values and divide by the total number of values.

Mean = (20 + 6 + 42 + 13 + 15 + 10 + 9 + 12 + 12) / 9

Mean = 16.222

Option B) Median: To calculate the median, we need to arrange the values in order and find the middle value.

After arranging the values in ascending order: 6, 9, 10, 12, 12, 13, 15, 20, 42

The median is 12.

Option C) Mode: To calculate the mode, we need to find the most frequently occurring value. In this case, there is no value that occurs more than once, so there is no mode.

Option D) Geometric Mean: The geometric mean is used to calculate the average rate of change or growth. It is not suitable for this data set.

Therefore, option A) mean is the most appropriate measure of center for this data.

Learn more about mean here: brainly.com/question/30891252

#SPJ4

Complete question:

The most appropriate measure of center for this data is the.

20, 6, 42, 13, 15, 10, 9, 12, 12

A) mean

B) median

C) mode

D) geometric mean

Answer:

median, A, 65

Step-by-step explanation:

.....

The 99% confidence interval for the population proportion is (0.257, 0.583).

(a) The point estimate of the population proportion of plants alive after the first month in the more humid environment is:

point estimate = x/n = 21/50 = 0.42

So, the point estimate is 0.42.

(b) To find the 95% confidence interval for the population proportion, we can use the formula:

confidence interval = point estimate ± z√(point estimate(1-point estimate)/n)

where z is the z-score corresponding to the desired confidence level, n is the sample size, and √ represents the square root.

For a 95% confidence level, z = 1.96 (from a standard normal distribution table).

Plugging in the values, we get:

confidence interval = 0.42 ± 1.96√(0.42(1-0.42)/50)

= 0.42 ± 0.127

= (0.293, 0.547)

So, the 95% confidence interval for the population proportion is (0.293, 0.547).

(c) To find the 99% confidence interval for the population proportion, we can use the same formula but with a different z-score.

For a 99% confidence level, z = 2.58 (from a standard normal distribution table).

Plugging in the values, we get:

confidence interval = 0.42 ± 2.58√(0.42(1-0.42)/50)

= 0.42 ± 0.163

= (0.257, 0.583)

So, the 99% confidence interval for the population proportion is (0.257, 0.583).

To learn more about population proportion visit:https://brainly.com/question/15087042

#SPJ11

By answering the presented question, we may conclude that If the two graphs are identical, F(x) may polynomials be a valid factorization of G(x), but more study is required to establish this.

A polynomial is a mathematical statement composed of variables and coefficients that be combined using only addition, subtraction, multiplication, and non-negative integer exponents. The phrase 2x3 + 5x2 - 3x + 1 is a polynomial, for example, where x is the variable and the coefficients of the various components are 2, 5, -3, and 1. Polynomials may include one or more variables, but each term must have the same variable (s). The degree of a polynomial is the highest exponent of its variable (s). In the above example, the degree of the polynomial is 3. Polynomials are used in many areas of mathematics, including algebra, calculus, and numerical analysis.

If you believe that one polynomial function is not the right factorization of another, you may use your graphing calculator to confirm this by graphing both functions and comparing their graphs.

Then, in your calculator, insert the polynomial function that you believe is the right factorization. Let us refer to this function as G. (x).

Graph the function G(x) on your calculator by hitting the "graph" button or the equivalent button.

Examine the two graphs. If the two graphs disagree, F(x) does not represent the right factorization of G. (x). If the two graphs are identical, F(x) may still be a valid factorization of G(x), but more study is required to establish this.

To know more about polynomials visit:

https://brainly.com/question/11536910

#SPJ1

Answer:

26.4

Step-by-step explanation:

You can add Y together because they have the same variable making it 10y

The equation is now 10y - 84 = 180

Add 84 to 180 since on the left side it was -84 (Imagine it crossed a magic bridge and become the opposite of what it is)

The equation is now 10y = 264

Divide the equation by 10 because 10 crossed a "magic bridge" to the other side and became division instead of multiplication

The equation is now solved = 26.4

We can cross check this by adding it to the first equation

3(26.4) + 7(26.4) - 84

which gives us 180

Hope this helps

Answer: y=26.4

Step-by-step explanation:

First we need to simplify 3y+7y .... that would be 10y.

Now we have 10y-84=180. We can add 84 to both sides of the equation

So now we have 10y= 180+84 = 10y= 264

Divide both sides by 10= y= 26.4

Now we can check this answer by inputting 26.4 to all the y values in the equation.

(3*26.4) +(7*26.4) - 84=180

79.2 + 184.8 -84=180

180=180    so we know 26.4 is the correct answer

Answer:

  k = 2/5

Step-by-step explanation:

Given a diagram with triangles ONM and OAB such that M is the midpoint of OB, A lies on AN with AN = 2·OA, and P is the point of intersection of NM and AB, you want the ratio AP/AB.

Please refer to the attached diagram.

Point C is located at the midpoint of AN, which makes OA≅AC≅CN, or AN is 2/3 of ON. Segments AD and CE are parallel to AN, so divide OM into thirds. The length DM is 2 of those thirds, and the length MB is equal to OM, so is 3 of those thirds. That is, the ratio DM/DB is (2/3)/(2/3+3/3) = 2/5.

Triangle BAD is similar to triangle BPM, so the ratio AP/AB is also 2/5.

The formula for the circumference of a circle is C = 2πr, where "C" is the circumference, "π" is pi (approximately equal to 3.14), and "r" is the radius.

Given that the radius of the circle is 5 inches, we can substitute this value into the formula to find the circumference:

C = 2πr

C = 2π(5)

C = 10π

Therefore, the circumference of the circle is 10π inches.

around 85 degrees. I did it with a protractor.

The amount of plastic wrap used to wrap the container is 3.06π square inches.

What is cylinder ?

A cylinder is a multi object used in geometry that has a round base, a curving surface rising from it, and another circular shape at the top or lid. One way to visualize a cylinder is as a stack of infinitely thin circular discs stacked one on top of the other. The height and radius of a cylinder, which measure the distance from the base to the top and the edge of the circular base, respectively, determine the shape of the object.

The plastic wrap covers the entire surface area of the cylinder. The formula for the surface area of a cylinder is:

Surface area of cylinder = 2πr² + 2πrh

where r is the radius of the circular base of the cylinder, and h is the height of the cylinder.

We can use the given diameter of the circular base, which is 1.8 inches, to find the radius r:

r = d/2 = 1.8/2 = 0.9 inches

We are also given the height of the rectangle, which is 0.8 inches.

Now we can substitute the values of r and h into the formula for the surface area of the cylinder:

Surface area of cylinder = 2π(0.9)² + 2π(0.9)(0.8)

Surface area of cylinder = 2π(0.81) + 2π(0.72)

Surface area of cylinder = 1.62π + 1.44π

Surface area of cylinder = 3.06π square inches

Therefore, the amount of plastic wrap used to wrap the container is 3.06π square inches.

To know more about surface area visit:

brainly.com/question/29101132

#SPJ1

Answer:

the answer is 3,9

Step-by-step explanation:

-3x+2y=9

3(x+y=12)

-3x+2y=9

3x+3y=36

5y=45

_ __

5 5

y=9

x+y=12

x+9=12

-9 -9

_______

x=3

The confidence interval provides an estimate of the population mean of lead content when the traffic flow is 15, which is denoted by the symbol μ.

The confidence interval (461.7, 598.1) estimates the true population parameter of the expected lead content when traffic flow is 15. In this case, the parameter being estimated is the population mean of lead content at a specific level of traffic flow, which is denoted by the symbol μ.

Option (c) "μ lead content, the average lead content" is the correct option, as the confidence interval provides an estimate of the true population mean of lead content when the traffic flow is at a specific level (in this case, 15).

Option (a) "β, the average change in lead content with a change in traffic flow" is not applicable here since the confidence interval is estimating the mean lead content at a specific level of traffic flow, not the change in lead content with a change in traffic flow.

Option (b) "μ lead content traffic flow = 15, the average lead content when traffic flow is 15" is partially correct, but it is important to note that this is a conditional mean, which is the mean of lead content given that the traffic flow is 15. The confidence interval estimates the true population mean of lead content at a specific level of traffic flow, regardless of whether that traffic flow is 15 or any other value.

In summary, the confidence interval provides an estimate of the population mean of lead content when the traffic flow is 15, which is denoted by the symbol μ.

To learn more about confidence interval:

https://brainly.com/question/24131141

#SPJ4

The 99% confidence interval for the true average number of alcoholic drinks all UF female students have in a one week period is option (d)  (3.35, 4.75)

To construct a confidence interval for the true average number of alcoholic drinks all UF female students have in a one week period, we can use the following formula

Confidence interval = sample mean ± (critical value) x (standard error)

Where the standard error is calculated as

Standard error = standard deviation / square root of sample size

We are given

Sample size (n) = 170

Sample mean (X) = 4.05

Standard deviation (s) = 4.66

Confidence level = 99%

To find the critical value, we need to look up the t-value with 169 degrees of freedom (since we are using a t-distribution because the sample size is less than 30) and a 99% confidence level. Using a t-distribution table or a calculator, we find the t-value to be approximately 2.62.

Substituting the values into the formula, we get:

Standard error = 4.66 / √170 ≈ 0.357

Confidence interval = 4.05 ± (2.62) x (0.357) ≈ (3.35, 4.75)

Therefore, the correct option is (d) (3.35, 4.75)

Learn more about Confidence interval here

brainly.com/question/24131141

#SPJ4

Answer:

238.64

Step-by-step explanation:

center to edge is a radius

2pi(radius) = circumference, so 6.28(38) = circumference = 238.64

A function that converts an input of letters and numbers into an encrypted output of a fixed length is called hash. The links in the blockchain that is created using an algorithm.

A hash is a mathematical function that changes an input of any length into an encrypted output of a specific length. Therefore regardless of the quantity of raw data involved or the size of the file, its unique hash is always the same size. Also, a hash cannot be used to "reverse engineer" an input from a hash output, because hash functions are "one-way" (like a meat grinder; you don't can't put ground beef back into a steak). However, if you use such a function on the same data, its hash will be the same, so you can confirm that the data is the same (i.e., unchanged) if you already know its hash.

Hashes are used in various parts of the blockchain system. Each block header contains the hash of the previous block, ensuring nothing has been tampered with as new blocks are added. Cryptocurrency blockchains use hashes to secure information and make the ledger immutable.

It refers to the technique of making an input element of arbitrary length reflect an output element of definite length. For blockchain applications in cryptocurrencies, variable duration transactions are processed by specific hashing algorithms and all produce fixed length outputs. This is true regardless of the duration of the input transaction.

Learn more about function:

brainly.com/question/12431044

#SPJ4

Complete Question:

Fill in the blanks,

A function that converts an input of letters and numbers into an encrypted output of a fixed length is called ________. The links in the blockchain that is created using an algorithm.

Answer:

The exchange rate at the post office is £1= 1.17 euros

How many euros will you get for £280?

Step-by-step explanation:

280 * 1.17 = 327.6

The the speed of a car that travels the given distance in 5 seconds from the information is 65.6 mph.

Speed and time are two fundamental concepts in physics and mathematics that are often used together to describe the motion of objects.

Speed refers to how fast an object is moving, and is typically measured in units of distance per unit of time, such as meters per second (m/s) or miles per hour (mph). Speed can be either constant, meaning the object is moving at the same speed throughout its motion, or variable, meaning the object's speed changes over time.

Given that the speed R varies inversely with the time T

R = 41 mph T =  8 seconds

The distance can be calculated as( speed * time)

Distance = ( speed * time)

= 41 * 8 = 328miles

The total distance travel  can now bw seen as 328miles, the speed  of a car that travels the given distance in 5 seconds can now be calculated as

Speed =Distance / time.

= 328miles/ 5 seconds

= 65.6 mph.

Learn more about speed at:

https://brainly.com/question/4931057

#SPJ1

In the percentage , the total number of students in sixth grade is 250.

What is percentage?

Percentage is Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.

Here we know that total number of students is 100%.

Students purchased their  lunch = 24%

Students brought their lunch from home = 190

Then percentage of students brought their lunch from home is

=> (100%-24%) = 190

=> 76% = 190

Then Total number of students in sixth grade is,

76%   = 190

100% = x

=> x = [tex]\frac{190\times100\%}{76\%}[/tex] =  250.

Hence the total number of students in sixth grade is 250.

To learn more about percentage refer the below link

https://brainly.com/question/24877689

#SPJ1

The standard deviation of demand over the lead time is 23.72.

The demand over lead time is normally distributed with a mean of 80. The reorder point for a 95% service level is 119. To calculate the standard deviation of demand over the lead time, we need to use the following formula:

z = (x - μ) / σ, where z is the number of standard deviations from the mean, x is the reorder point for a 95% service level, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

To solve for σ, we need to first find the z-score for a 95% service level, which can be obtained from the standard normal distribution table.

The z-score for a 95% service level is 1.645.

Substituting the given values in the formula, we get:

1.645 = (119 - 80) / σ

Solving for σ, we get:σ = (119 - 80) / 1.645

σ = 23.72

Therefore, the standard deviation of demand over the lead time is 23.72.

To learn more about standard deviation visit : https://brainly.com/question/475676

#SPJ11

A.

by simply putting the suggested solution into the equation and see if it stays true. if yes, it is a solution.

(5 + 2i)² - 10(5 + 2i) = -29

25 + 20i - 4 - 50 - 20i = -29

21 - 50 = -29

-29 = -29 true

yes, it is a solution.

B. for a parabola the 2 solutions are usually symmetrical around the center line.

so, I suspect 5 - 2i to be a solution too.

(5 - 2i)² - 10(5 - 2i) = -29

25 - 20i - 4 - 50 + 20i = -29

21 - 50 = -29

-29 = -29 true

yes, it is a solution too.

C.

nowhere.

with 2 complex solutions there are no real number solutions left. and that means there is no intersection with the x-axis.

every quadratic equation must have 2 and only 2 solutions. a solution is normally an intersection with the x-axis (the x- value when y = 0).

1) The time it will take for both to have cleaned the same number of rows is: 1 minute

2) The number of rows cleaned by then is: 16 rows

We are told that Volunteers from the Band Booster Club have already cleaned 5 rows of bleachers and will continue to clean at a rate of 3 rows per minute. If the number of minutes is x, then the equation here is:

3x + 5

Similarly, the leadership class has completed 6 rows and will continue working at 2 rows per minute. If the number of minutes is x, then the equation here is:

2x + 6

The point at which they have cleaned the same number of rows will be:

3x + 5 = 2x + 6

3x - 2x = 6 - 5

x = 1 minute

Thus, after 1 minute they would have cleaned 8 + 8 = 16 rows of bleachers

Read more about Algebra Word problems at: https://brainly.com/question/4344214

#SPJ1

The study has a measurement bias due to the small sample size and the likely difference between the population of city x and the sample used in the study, resulting in a Type I Error (false positive) of 1.67, meaning an overestimation of the true relative risk of the association by 67%.

In this case, the study has a measurement bias due to the small sample size and the likely difference between the population of city x and the sample used in the study. As a result, we can expect the relative risk to be overestimated. This is known as a Type I Error (false positive) and can be calculated using the formula:

Type I Error = (4.0 – 1.5) / 1.5 = 1.67

In other words, the study overestimated the true relative risk by 67%. This is an example of an inflated relative risk due to a lack of representativeness of the sample population.

Learn more about measurement here:

https://brainly.com/question/18827844

#SPJ1

If f ( x ) = f ( g ( x ) ) , where f ( 5 ) = 7 , f ' ( 5 ) = 5 , f ' ( 0 ) = 3 , g ( 0 ) = 5 , and g ' ( 0 ) = 3 ,f'(0) = 15

We start by using the chain rule to find the derivative of f(x) with respect to x:

f'(x) = f'(g(x)) * g'(x)

Next, we evaluate this equation at x = 0, and use the given values to solve for f'(0):

f'(0) = f'(g(0)) * g'(0)

f'(0) = f'(5) * 3 (since g(0) = 5 and g'(0) = 3)

Now, we need to find f'(5) using the given information. We can start by using the definition of the derivative:

f'(5) = lim h->0 [f(5+h) - f(5)] / h

We know that f(5) = 7, so we can simplify this expression:

f'(5) = lim h->0 [f(5+h) - 7] / h

Using the fact that f(x) = f(g(x)), we can substitute g(x) for x:

f'(5) = lim h->0 [f(g(5+h)) - 7] / h

Now, we can use the mean value theorem to approximate f(g(5+h)):

f'(5) = lim h->0 [f'(g(c)) * g'(5+h)] / 1

where 5 < c < 5 + h. Since f'(5) = 5 and g'(5) = 3, we can simplify this expression:

f'(5) = lim h->0 [5 * 3] / 1 = 15

Therefore, we have found that f'(0) = f'(5) * 3 = 5 * 3 = 15.

For more questions like Equation click the link below:

https://brainly.com/question/29657983

#SPJ11

Answer:

because he is wittery hitting da gwity

Answer:

Step-by-step explanation:

The mean is found by adding the numbers and dividing by how many numbers there are.

              [tex]Mean=\frac{-2+3+0-15+5-20-4}{7} =\frac{-33}{7} =-4\frac{5}{7}[/tex]

Answer:

  x = 10

Step-by-step explanation:

You want to find the value of x, where a chord of segment lengths 9 and x crosses a chord of segment lengths 6 and 15.

The product of the segment lengths is the same for intersecting chords:

  9x = 6·15

  x = 90/9 . . . . divide by 9

  x = 10

The inequality in the expression [tex]41-x < 17[/tex] is the less than inequality

The solution to the inequality is [tex]x > 24[/tex]

The inequality is given as:

[tex]41-x < 17[/tex]

Subtract 41 from both sides of the inequality

[tex]41 - 41 -x < 17 - 41[/tex]

Evaluate the difference

[tex]-x < -24[/tex]

Multiply both sides by -1

[tex]-1 \times -x < -24 \times -1[/tex]

Evaluate the product

[tex]x > 24[/tex]

We don't have enough information to determine the exact side length of either square A or square C, so we cannot directly calculate their areas. However, we can use the relationship between the areas of the squares to make some conclusions.

Since the area of square B is 64 square units, we know that its side length is √64 = 8 units.

Similarly, since the area of square C is 100 square units, we know that its side length is √100 = 10 units.

Square A is composed of square B and four identical triangles. We know the area of square B is 64 square units, so we need to determine the area of the four triangles to find the area of square A.

Each triangle has a base of 8 units (which is also the length of one side of square B) and a height of half the length of one side of square A. Let's call this length x.

The area of one triangle is (1/2) * 8 * x = 4x square units.

The total area of the four triangles is 4 times the area of one triangle, which is 16x square units.

Therefore, the area of square A is 64 + 16x square units.

We still don't know the exact value of x, but we can make some observations. Since square A is larger than square B, we know that x > 4. And since the triangles make up exactly half of square A (the other half being square B), we know that the area of square A is twice the area of the four triangles. Therefore:

64 + 16x = 2(16x)

64 + 16x = 32x

64 = 16x

x = 4

So the length of each side of square A is 8 + 2x = 16 units, and its area is 64 + 16x = 128 square units.

The length of CA is just the length of one side of square C, which is 10 units.

Number of people = number of cups of coffee + 1 = 5 + 1 = 6

Therefore, there were 5 friends with Dylan at the cafe.

Let's start by subtracting the change Dylan received from the amount he paid to find out the total cost of everything he bought:

Total cost =

We know that Dylan bought himself a cup of tea, which costs less than a cup of coffee. So, the £5.39 must have been spent on buying coffee for his friends.

Let's assume that each cup of coffee costs £1. We can use this assumption to find out how many cups of coffee Dylan bought for his friends:

Number of cups of coffee = total cost ÷ cost per cup of coffee = £5.39 ÷ £1 = 5.39

Since we can't buy a fraction of a cup of coffee, we can round this number down to the nearest whole number. Therefore, Dylan bought 5 cups of coffee for his friends.

However, we need to remember that Dylan himself also bought a drink, which wasn't a cup of coffee. So, the total number of people at the cafe was:

Number of people =[tex]number of cups of coffee + 1 = 5 + 1 = 6[/tex]

Therefore, there were 5 friends with Dylan at the cafe.

To know more about the order of subtraction visit:

https://brainly.com/question/30143384

#SPJ1