In a regatta, a sailboat sailed 66 km east and 43km south from port, and then took the shortest route back. Find the distance and direction (using a bearing) of the return trip. Round your answers to the nearest hundredth

Answers

Answer 1

The distance and direction (using a bearing) of the return trip are approximately 75.90 km and 327.47 degrees (rounded to the nearest hundredth).

To find the distance and direction of the return trip, we can use the Pythagorean theorem and trigonometric functions.

First, we can draw a diagram to visualize the sailboat's path:

```
               North
                 |
                 |
                 |
       43 km     |
       South     |
       ----------O----------------- 66 km East
                 |
                 |
                 |
                Port
```

We can see that the sailboat has formed a right triangle with legs of 43 km and 66 km. To find the distance of the return trip, we can use the Pythagorean theorem:

c^2 = a^2 + b^2
c^2 = 43^2 + 66^2
c^2 = 5765
c = sqrt(5765)
c = 75.90 km

Therefore, the distance of the return trip is approximately 75.90 km (rounded to the nearest hundredth).

To find the direction of the return trip, we can use trigonometric functions. We can see that the angle formed between the sailboat's path and the line connecting the starting point to the ending point is the angle we need to find. To do this, we can use the inverse tangent function:

tan(theta) = opposite/adjacent
tan(theta) = 43/66
theta = atan(43/66)
theta = 32.53 degrees

Since the sailboat traveled south and then east, the return trip is in the northwest direction (315 degrees) from the starting point. To find the bearing, we can subtract the angle we found from 360 degrees:

bearing = 360 - 32.53
bearing = 327.47 degrees

Therefore, the distance and direction (using a bearing) of the return trip are approximately 75.90 km and 327.47 degrees (rounded to the nearest hundredth).

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Related Questions

need help ASAP !!!

\( \sqrt{3652 \times 3652} \)

Answers

Answer:

your answer will be 3652

Step-by-step explanation:

thanks

have a great day

Answer:

√{3652×3652}=√3652²=±3652

Exercise 3: Suppose average pizza delivery times are normally distributed with an unknown population mean and a population standard deviation of six minutes. A random sample of 28 pizza delivery restaurants is taken and has a sample mean delivery time of 36 minutes. Find a 90% confidence interval estimate for the population mean delivery time. Step 5: Interpret the confidence interval.

Answers

The t-score to be used to find the 90% confidence interval for the population mean is; \(t_{(0.05,27)}\) = 1.703

The t-score which is representative of a point with n - k (n, and k represents the sample size and the number of groups in the test respectively) degrees of freedom  from the Student's T-distribution is a standard test statistic obtained by applying a T-test

Therefore, the t-score used for a confidence interval is obtained by by making use of the the following information;

The number of degrees of freedom = n - k

Given,

The number of pizza orders in the sample, n = The sample size = 28

The number of samples used in the estimate, k = 1 group of 28 randomly sampled pizza

The level of confidence (the probability) that the interval contains the population mean = 90%

Therefore, the significance level, α = 1 - 90% = 1 - 90/100 = 0.1

∴ The α-level for the upper and lower limit of the interval are α/2 = 0.1/2 = 0.05 long

The degrees of freedom, df = n - k

∴ For the estimation, DF = 28 - 1 = 27

The t-statistic is therefore the t-value at the intersection of the row for DF = 27 and the 0.05 (one-tail) column (0.05 two-tail column) which gives;

\(t_{(\alpha /2, DF)}\) = \(t_{(0.05, 27)}\) = 1.703

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which is greaterr 0.5 or 0.14

Answers

Answer:

To determine which number is greater, 0.5 or 0.14, you must determine which of the two has a higher ratio with respect to a whole number. Thus, since 0.5 is equal to 1/2 and 0.14 is equal to 7/50, 0.5 is the greater number.

-x+10x=9x+5 i need x please

Answers

Answer:No answer

Step-by-step explanation: Simplify like terms first if possible

on LS=-X+10X=9X

9X=9X+5

We need to get Xs on one side to solve equation

We aim to have the Xs on the left side

we take 9X from both sides

9X-9X=9X-9X+5

0=5

No solution

4(x+6)=3x-7 please could you help me

Answers

Hello!

Let's use the Distiributive property:

4(x+6)

4x+24

4x+24=3x-7

Move all the variables to the left:

4x-3x=-7-24

x=-31

Hope this helps!

~Just a determined gal

#CarryOnLearning

\(MysteriousNature\)

susan is three years older than shirley. their ages total 59 years. how old is shirley

Answers

Answer:

Shirley is 28.

Step-by-step explanation:

Well, to quickly find it:

We'd have to find two numbers that fit this description.

We already know it is going to be within the late 20's and early 30's at the start.

So we start with:

28 + 3 = 31

Then to verify we add these two numbers:

31 + 28 = 59

Now applying to the descriptions,

Shirley would be three years younger Susan.

So Susan would be 31. Shirley is 28.

When Samuel was born, his grandmother opened up a savings account to save money to give to him as a graduation gift. Samuel’s grandmother deposited $1,750 into the account. It earns 4.25% simple interest each year. If his grandmother makes no additional deposits or withdrawals, what will be the total account balance after 18 years?

Answers

Answer:

$3088.75

Step-by-step explanation:

4.25%= .0425
1750 x .0425 = 74.375

74.375 x 18 = 1338.75

1750+1338.75=3088.75

. suppose a population was normally distributed with a mean of 10 and standard deviation of 2. what proportion of the scores are below 12.5? explain your answer with reasoning.

Answers

The proportion of scores that are below 12.5 is 0.8944 or 89.44%.

Given that the population is normally distributed with a mean of 10 and a standard deviation of 2, we can calculate the proportion of scores below 12.5 using the z-score formula.

z = (x - μ) / σwhere x = 12.5, μ = 10, and σ = 2.

Substituting these values into the formula, we get:

z = (12.5 - 10) / 2z = 1.25

We must find the area under the standard normal distribution curve to the left of z = 1.25. This area represents the proportion of scores that are below 12.5.

We can use a standard normal distribution table or calculator to find this area. Using a standard normal distribution table, the area to the left of z = 1.25 is 0.8944.

Therefore, the proportion of scores below 12.5 is 0.8944 or 89.44%.

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how many solutions do 2(x-4)=2x-8 have

Answers

The equation 2(x - 4) = 2x - 8 has infinitely many solutions.

What is an Equation?

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given equation is 2(x - 4) = 2x - 8.

Solving this,

Using the distributive property, a (b + c) = ab + ac, 2(x - 4) = (2 × x) - (2 × 4).

Substituting in the original equation,

(2 × x) - (2 × 4) = 2x - 8

2x - 8 = 2x - 8

2x - 2x = -8 + 8

0 = 0

Right hand side and left hand side are equal if we put any value for x.

So it has infinitely many solutions for x.

Hence the given equation has infinitely many solutions.

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For all x, there exists y such that (y^2 <= x <(y+1)^2) when domain is N(natural number)

this statement is true or false?

Answers

The statement "For all x, there exists y such that \((y^2 < = x < (y+1)^2)\)" is true when the domain is the set of natural numbers (N).

To prove the statement, let's consider any arbitrary natural number x. We need to find a corresponding value of y such that \(y^2 < = x < (y+1)^2\).

First, let's find the lower bound of y. We know that \(y^2 < = x\), so y <= sqrt(x). Since y is a natural number, we can take the floor of the square root of x to get the largest natural number y such that y^2 <= x.

Now, let's find the upper bound of y. We have \((y+1)^2 = y^2 + 2y + 1\). Since we want x to be strictly less than \((y+1)^2\), we need \(x < y^2 + 2y + 1\). Rearranging this inequality, we get \(y^2 + 2y + 1 > x\), which can be written as \((y+1)^2 > x\). So, y+1 is the upper bound of y.

Since we have a lower bound y and an upper bound y+1, we can conclude that there exists a natural number y such that \(y^2 < = x < (y+1)^2\) for any natural number x. Therefore, the statement is true for the domain N (natural numbers).

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Vincent was chagrined when he looked at the clock, for in of an hour
he had only answered 12 homework questions. At that rate, how many
questions would Vincent answer in an hour?

Answers

Answer:

24

Step-by-step explanation:

If Vincent can answer 12 questions in one hour then that means in 2 he can get 24

0.3x-2.4=1.25x
How to solve

Answers

Answer:

hi

Step-by-step explanation:

0

.

3

2

.

4

=

1

.

2

5

0.3x-2.4=1.25x

0.3x−2.4=1.25x

3

1

0

2

.

4

=

1

.

2

5

Answer:

x = -2.52631578

Step-by-step explanation:

Combine multiplied terms into a single fraction.

0.3x - 2.4 = 12.5x

3x/10 - 2.4= 1.25x

Again, combine multiplied terms into a single fraction.

3x/10 - 2.4= 1.25x

3x/10 - 2.4 = 5x/4

Add 2.4  to both sides of the equation

3x/10 - 2.4 = 5x/4

3x/10 - 2.4 + 2.4 = 5x/4 + 2.4

Simplify (Add the numbers)

3x/10 = 5x/4  + 2.4

Multiply all terms by the same value to eliminate fraction denominators.

3x/10 = 5x/4  + 2.4

2  x 2 x 5 x 3x/10 = 2 x 2 x 5(5x/4 +2.4)

Therefor, x = 2.52631578

Hope this helps, have a great day! :)

ASAP PLEASE
One day Danny is walking on the street, and he saw that someone left their phone open, so he picked it up, and it shows that he earned ten bobux from that action, and when he made 1000 bobux, he can get a brand new phone, so how many more times he has to pick up a phone.

Answers

Answer:

he has to pick the phone up 100 more times

Answer:

He gotta do it 100 times

Step-by-step explanation:

Take 1000 divide it by 10 you get 100.

bobux big brain

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

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

Answers

Answer:

m ∠ E = 29°

Step-by-step explanation:

34 + 117 + m = 180

151 + m = 180

-151         -151

m ∠ E = 29°

I hope this helps!

2. There were 198 men and 256 women at a party of the men and
One-fourth of women left early.how many people remained at the party?

Answers

Answer:1/4 ×256/1= 64 women that left party

256-64= 192 women who remained

192+198=390 men and women at the party

Step-by-step explanation:

download the document below and complete the proof of the triangle sum theorem. once completed, save the file for upload at the bottom of this page.

Answers

The request is to download a document and complete the proof of the Triangle Sum Theorem. After finishing the proof, the completed file should be saved for upload on a webpage.

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees. To complete the proof, it is necessary to provide a logical and coherent argument that supports this theorem. The document provided likely contains a partially completed proof, and the task is to finish it.

The proof of the Triangle Sum Theorem typically involves using the properties of parallel lines and alternate interior angles. By extending one side of the triangle, parallel lines can be created that intersect with the other sides. This forms interior and exterior angles that can be related to the interior angles of the triangle. Through geometric reasoning and the use of angle relationships, the proof should demonstrate that the sum of the interior angles of a triangle equals 180 degrees.

Once the proof is completed, the document should be saved for upload on the webpage specified, most likely for evaluation or further review. It is important to follow any instructions provided regarding the file format or naming conventions for the upload.

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A sketch of y = x² + 6x + 15 has been drawn.
Complete the sketch by entering the
corresponding values on the axes.

Answers

Answer:

Vertex=(-3,6) and Y intercept is 15/(0,15)

e^2x+2x-1=0
Solve the equation ​

Answers

Answer

x=0

Step-by-step explanation:

Rewrite the question -2x+1=u and x= -u-1/2

Simplify

Rewrite 1=e^(u-1)u in Lambert Form e^(u)u

Solve u=1

Substitute back u= -2x+1, solve for x

x=0

:)I Hope you enjoy this:)

Ryan is riding on a bike course that is 80 miles long. So far, he has ridden 56 miles of the course. What percentage of the course has Ryan ridden so far?

Answers

Hi :)

To find percentage, divide 56 by 80 and multiply by 100

To remember this, know that since 56 is of 80, of/number x 100  56/80 x 100

You should get something like 70, which happens to be your answer, 70%

Hope this helps,

Jeron

P.S (brainliest? only if i helped)

the sum of two numbers is 10, and twice their diffrence is 4. find the two numbers by graphing

Answers

Answer:

One number is 6 and the other number is 4

Step-by-step explanation:

Helping in the name of Jesus.

the sum of two numbers is 10, and twice their diffrence is 4. find the two numbers by graphing

2 of 6
Given that a = 12 cm and b = 17 cm, work out the area of the triangle.
Give your answer rounded to 1 DP.

Answers

Answer:

102 cm²

Step-by-step explanation:

area of a triangle = 1/2 * base * height

                             = 1/2 * 12 * 17

                             = 102 cm²

Write an algebraic equation that relates the Profit to the Number of T-Shirts Sold. Use n to represent T-Shirts and p to represent the Profit.

Write an algebraic equation that relates the Profit to the Number of T-Shirts Sold. Use n to represent

Answers

Answer:

y= 3x -5

Step-by-step explanation:

since when x is 0, and y is -5, you know that the y intercept is -5.

look at the table

1x -5 = -2

x= 3

Boom.

LONG LIVE KOREA!

2,6,18,54,162,486,1458.. find the term in position 12 (include all the steps, using the formula)​

Answers

Answer:

Gl=2 r=3 so you can simply answer it gl r^11

2× 3^11

The gas tank of Tyrell's truck holds 19.8. Gallons. When the tank is empty, Tyrell fills it with gas that costs $3.65 per gallon. About how much will it cost to fill the tank?

Answers

it would cost about $72.27 to fill the tank, but if it’s asking for estimate then you might have to round it to $70

I gave a store keeper 10 ghana cedis note for some goods bought.he ask fo another 5gp for ease change if he then give me 50gp.how much did i pay for the goods?

Answers

You paid a total of 9.55 Ghana cedis for the goods.

Initially, you gave the storekeeper a 10 Ghana cedis note. The storekeeper requested an additional 5 Ghana pesewas (gp) for ease of change. Therefore, the total amount given to the storekeeper was 10.05 Ghana cedis.

Later, the storekeeper gave you 50 Ghana pesewas (gp) in change.

To calculate the total amount paid for the goods, we need to subtract the change received from the total amount given.

Total amount given - Change received = Amount paid for goods

10.05 Ghana cedis - 0.50 Ghana cedis (50 Ghana pesewas) = 9.55 Ghana cedis.

Therefore, you paid a total of 9.55 Ghana cedis for the goods.

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Originally Kim's house was 1.750 f12. After a remodel, her house was 2,275 ft? What percent of the original area is Kim's house after the

Answers

After the remodel, Kim's house occupies 130% of the original area, indicating an increase in size compared to the initial measurement.

To calculate the percentage of the original area that Kim's house occupies after the remodel, we can use the formula:

Percentage = (New Area / Original Area) * 100

Given:

Original area = 1,750 ft^2

New area = 2,275 ft^2

Substituting the values into the formula:

Percentage = (2,275 / 1,750) * 100

Percentage = 1.3 * 100

Percentage = 130%

Therefore, Kim's house after the remodel occupies 130% of the original area.

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On a test that has a normal distribution, a score of 48 falls two standard deviations
above the mean, and a score of 28 falls two standard deviations below the mean.
Determine the mean of this test.

Answers

To determine the mean of the test, we can use the information given about the scores falling two standard deviations above and below the mean.

Let's denote the mean of the test as μ and the standard deviation as σ.

We are given:
48 falls two standard deviations above the mean, so 48 = μ + 2σ.
28 falls two standard deviations below the mean, so 28 = μ - 2σ.

To solve for the mean μ, we can set up a system of equations with these two equations:

48 = μ + 2σ
28 = μ - 2σ

Adding the two equations together eliminates the σ term:
48 + 28 = μ + 2σ + μ - 2σ
76 = 2μ

Dividing both sides by 2 gives us the value of the mean μ:
76/2 = 2μ/2
38 = μ

Therefore, the mean of the test is 38.

I hope this helps! :)

The ratio of the length of a rectangle to
the width of the rectangle is 5:7.
Which of the following could be the
length and width of the rectangle?
A.) length: 15 units width: 20 units
B.) length: 10 units width: 15 units
C.) length: 20 units width: 24 units
D.) length: 22.5 units width: 31.5
Units

Answers

Answer:

Step-by-step explanation:

B. why? i dont know

Multiply. Write each product in simplest form.
9. 3×11
10. //
13. 021-
12.
20
=
=
=
11. 2×4=
8 9
X
18 20
14.
=

Answers

Answer:

Te conozco y sé qué

Como Nuevo de fabrica el otro

Can someone help me ?? I’ll give brainliest!

Can someone help me ?? Ill give brainliest!

Answers

The answer is 72 is you need me to explain I’d be glad to help.
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