A ship sails 95 km on a bearing of 140 degrees,than further on 102km on a bearing of 260degrees,and than returns directly to its starting point.Find the length and bearing of the return journey

Answers

Answer 1

Answer:

1. 98.7 km

2. 303.5 degree

Step-by-step explanation:

Using the alternate angle, the angle at B will be 50 + 10 = 60 degree.

To calculate the length AC of the returning journey, use cosine formula to calculate it.

To find the bearing of the returning journey, use sine rule to calculate it.

Please find the attached file for the solution

A Ship Sails 95 Km On A Bearing Of 140 Degrees,than Further On 102km On A Bearing Of 260degrees,and Than

Related Questions

The formula in cell C5 is "=SUMPRODUCT($A$1:$C$1,A2:C2)". If one copies and pastes the formula from the cell C5 into the cell C6, what numerical value will appear in the cell C6?

Answers

Answer:

See Explanation

Step-by-step explanation:

Given

Formula: =SUMPRODUCT($A$1:$C$1,A2:C2)

Required

Determine the numerical value that will appear

The question seem incomplete; however, I'll give a general explanation

FIrst, when the formula is copied from C5 to C6, A2 and C2 changes to A3 and C3 respectively.

This is because they are relative references and they behave on a relative position.

This implies that, when the formula is in cell C5, the formula considers cells A2 and C2 when executing the formula;

However, C6 will consider cells A3 and C3, respectively.

Solve. 2x−y+3z=6 2x+y=3 2y−4z=−4 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=

Answers

Answer:

(3/2, 0, 1)

Step-by-step explanation:

From 2x+y=3 we have => y=3-2x

From 2y-4z=-4 we have -4z=-2y-4 => z=1/2y+1 => z=1/2 (3-2x) +1 => z=5/2-x

Plug in y & z to find x

2x−y+3z=6 => 2x+(3-2x)+3(5/2-x)=6 => 2x+3-2x+15/2-3x=6 => 21/2-3x =6 => x=3/2

plug in x to find y

2x+y=3 => 2(1.5) + y =3 => y=0

plug in y to find z

2y -4z =-4 => 2(0)-4z=-4 => -4z=-4 => z=1

n circle L, arc NOP is 90° and the radius is 5 units. Which statement best describes the length of arc NOP? circle M with radii LM, LN, LO, and LP so that arc MNOP is created

Answers

Answer:

[tex]\frac{1}{4} \times 2\pi r[/tex] i.e circle circumference

Step-by-step explanation:

Data provided as per the question is

Arc NOP = Central angle = [tex]\theta = 90^\circ[/tex]

The Radius of circle = 5 units

The statement is shown below:-

we need to determine the statement which defines the best length of arc NOP

Arc length is

= [tex]\frac{control\ angle}{360} \times circumference\ of\ circle[/tex]

now we will put the values into the above formula

= [tex]\frac{90}{360} \times 2\pi r[/tex]

= [tex]\frac{1}{4} \times 2\pi r[/tex]

Hence, the [tex]\frac{1}{4} \times 2\pi r[/tex] i.e circle circumference is the best statement described.

13. If x + y + z-0 then x+y+z'is equal to:
(a) 3xyz
(b) - 3xyz
(c) xy
(d)-2xy​

Answers

Answer:

a

Step-by-step explanation:

(x³ + y³ +z³) - 3xyz = (x + y + z )(x² +y² +z² - xy -yz - zx)

If x +y + z = 0, then

(x³ + y³ +z³) - 3xyz = 0 *(x² +y² +z² - xy -yz - zx)

(x³ + y³ +z³) - 3xyz = 0

(x³ + y³ +z³)  =  3xyz

Sue likes to run. One day she was running for 3 hours with an average speed of 7 miles per hour. How many miles did she run that day?

Answers

Answer:

21 miles

Step-by-step explanation:

Since every single hour she runs 7miles.

In 3 hours she will run 7*3 miles.

21 miles

Hey there! I'm happy to help!

If Sue ran with an average speed of 7 miles an hour for 1 hour, she would have run 7 miles. So, if she ran at this speed for 3 hours, she would have run 3 times the distance she would if she ran for one hour!

7×3=21

Therefore, Sue ran 21 miles that day.

Have a wonderful day! :D

Monica made a drawing of her patio using the scale 1 inch equals 4 feet. The length of the patio in her drawing was 11 inches. What was the length of the actual patio?​

Answers

1 inch = 4 feet

11 inches = 44 feet (multiply both sides by 11)

Answer: 44 feet

a farmer has 40 4/5 of beans 3/4 of the beans are pinto beans how many pounds of pinto bean are there

Answers

Answer: Amount of pinto beaks [tex]=30\dfrac{3}{5}\text{ pounds}[/tex]

Step-by-step explanation:

Given: Amount of beans a farmer has = [tex]40\dfrac{4}{5}\text{ pounds}=\dfrac{40\times5+4}{5}\text{ pounds}[/tex]

[tex]=\dfrac{204}{5}\text{ pounds}[/tex]

Also, [tex]\dfrac{3}{4}[/tex] of the beans are pinto beans .

Amount of pinto beaks = [tex]\dfrac 34\times[/tex] (Amount of beans a farmer has)

= [tex]\dfrac34\times\dfrac{204}{5}=\dfrac{153}{5}\text{ pounds}[/tex]

[tex]=30\dfrac{3}{5}\text{ pounds}[/tex]

Amount of pinto beaks [tex]=30\dfrac{3}{5}\text{ pounds}[/tex]

Find the length of the missing side. Leave your answer in simplest radical form. A. 296 ft B. 2[tex]\sqrt{74}[/tex] ft C. [tex]\sqrt{206}[/tex] ft D. [tex]\sqrt{26}[/tex] ft

Answers

Answer:

B

Step-by-step explanation:

Since this is a right triangle and we are given the two legs, we can use the Pythagorean Theorem.

The Pythagorean Theorem is:

[tex]c^2=a^2+b^2[/tex]

Where c is the hypotenuse (longest side) and a and b are the two legs.

Plug in 10 and 14 for a and b (it doesn't matter which one) and solve for c.

[tex]c^2=10^+14^2\\c^2=100+196\\c^2=296\\c=\sqrt{296}=\sqrt{4\cdot 74}=\sqrt4\cdot\sqrt{74}=2\sqrt{74}[/tex]

Simplify.
2(x+2) - 4x

Answers

Answer:

-2x+4

Step-by-step explanation:

2(x+2) - 4x

Distribute

2x+4 - 4x

Combine like terms

-2x+4

Answer:

-2x+4

Step-by-step explanation:

2(x+2)-4x

(2x+4)-4x

2x+4-4x

-2x+4

holly drinks 2 2/5 litre of water each day. The water comes in 1 2/5 litre bottles. How many bottles does Holly drink in a week?

Answers

Answer:Holly drank 12 bottles in a week.

Step-by-step explanation:

First change the fraction 1 2/5 litre into a decimal, by doing this, we can know how many litres are there in 2/5.

So= 1 2/5

= 2 ÷5 = 0.4

= 1 + 0.4 = 1.4 liters

1.4 liters is the amount of water in a bottle.

Next, also change the fraction 2 2/5 litres into a decimal.

So=2 2/5

= 2÷5 = 0.4

= 2 + 0.4 = 2.4 liters

She drinks 2.4 liters a day.

To find how many bottles she drank in 1 week, we must multiply the amount of water she drinks in a day to the days in a week.

So= 1 week= 7 days

= 1 day= 2.4 liters

So= 2.4 × 7 = 16.8

She drinks 16.8 in a week.

To find how much bottles she drank in a week, we must divide the amount of liters she drank in one week to the amount of liters are there in a bottle.

So= 16.8 ÷ 1.4= 12 bottles

Holly drinks 12 bottles in a week.

I hope this helps! I'm sorry if it's wrong and complicated.

You have been saving $12 each week for many weeks. One day, you decide to count your savings and find that you have $384. Write and solve a multiplication equation to find how many weeks w you have been saving.

Answers

Answer:

Hope I helped! Brainleist!

Step-by-step explanation:

you get $12/week

and you have $

your equation is

y=12x

now...

y = 384

so

384=12x

x= 32

every rational number is a
a. whole number b. natural number c. integer d. real number

Answers

Greetings from Brasil...

a - whole number

FALSE

3/5, for example isnt a whole number

b. natural number

FALSE

0,457888..., for example isnt a natural number

c. integer

FALSE - like a

d. real number

TRUE

The set of real numbers contains the set of rational numbers

ℝ ⊃ ℚ

Getaway Travel Agency surveyed a random sample of 45 4545 of their clients about their vacation plans. Of the clients surveyed, 21 2121 expected that they would go on 3 33 vacations in the next year. There are 516 516516 Getaway Travel Agency clients. Based on the data, what is the most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 3 33 vacations in the next year?

Answers

Answer:

241

Step-by-step explanation:

Given the following :

Number of random samples surveyed = 45

Of the random samples surveyed, 21 expected to go on 3 vacations in the next year:

Total number of clients = 516

Percentage of random sample surveyed who intend to go 3 vacations in the next year :

(21 / 45) * 100

0.4666667 * 100 = 46.7%

That is 46.7% of surveyed sample intend to go on 3 vacations in the next year.

Therefore using these to make inference about the number of total client who will go on 3 vacations in the next year:

46.7% of total clients

(46.7 / 100) * 516

= 240.8

= 241 ( to the nearest whole number)

Please answer question

Answers

Answer:

87.6yd²

Step-by-step explanation:

Base: =1/2bh

=1/2(6)(5.2)=15.6

Sides: =1/2bh

=1/2(6)(8)=24 (3 of them)

15.6+24+24+24=87.6yd²

A personal trainer keep track of the number of minutes each of his 20 clients exercise on the treadmill and the number of calories each client burned during that time removing. which TWO of these data points will cause the correlation coefficient to decrease the most?


A). Data point A

B). Data point B

C). Data point C

D). Data point D

Answers

Answer:

Data Point B and Data point E

Step-by-step explanation:

Data point B and data point E are the farthest and are more distant away from the best line of fit compared to other data points. The more clustered data points are, the more the correlation that exists between the variables in question.

Therefore, data point B and data point E, will cause the correlation coefficient to decrease the most.

–20, - 12,5, 22, . . .
An=
A50=

Answers

Answer:

an = 17n - 46

a50 = 804

Step-by-step explanation:

-29, -12, 5, 22, ...

Subtract each number from the next one.

-12 - (-29) = 17

5 - (-12) = 17

22 - 5 = 17

The common difference is 17. This is an arithmetic sequence which starts with -29, and in which each subsequent value is 17 more than the previous value.

a1 = -29

a2 = -29 + 17

a3 = -29 + 2(17)

a4 = -29 + 3(17)

Notice that for each term, you have -29 and something added to it. What you add to -29 is 17 multiplied by 1 less than the number of the term. For term 1, 1 less than 1 is 0. You add 0 * 17 to -29 and get -29. term 1 is -29. For term 2, 1 less than 2 is 1. You add 1 * 17 to -29 and get -12, etc.

For term n, 1 less than n is n - 1. Add (n - 1) * 17 to -29 to get term n.

an = -29 + 17(n - 1)

This formula can be simplified.

an = -29 + 17n - 17

an = -46 + 17n

an = 17n - 46

a50 = 17(50) - 46

a50 = 804

from a group of 25 men,12 were to be given gifts.What is the probability of choosing a man who did not a gift​

Answers

Answer: 13/25

Explanation:

There are 25 men in total
12 were to be given gifts

Find the probability of choosing a man who did not receive a gift:

P = 25/25 - 12/25 = 13/25

Answer:

13/25

Step-by-step explanation:

When you subtract 12 from 25, you get 13. So, 13 men did not get a gift.

Hence,

the probability would be 13/25 of the men who did not get a gift.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

What is the x-value of the solution to the system of equations? 5x + 4y = 8 2x − 3y = 17 −3 −2 4 5

Answers

Answer:

            x = 4

Step-by-step explanation:

5x + 4y = 8   ⇒   4y = 8 - 5x  ⇒  y = (8 - 5x)÷4

2x − 3y = 17

2x - 3(8 - 5x)÷4 = 17    

          ×4            ×4    

8x - 3(8 - 5x) = 68

8x - 24 + 15x = 68

          +24       +24

           23x  =  92  

           ÷23      ÷23

               x = 4

Answer:

it is 4

Step-by-step explanation:

i did it on edge hope it helps.:)

The finite geometric sequence has 10 terms. The sum of all terms with even index is 682 and the sum of all terms with odd index is 1364. Determine the first term. Please also state what does "index" refer to in the question?

Answers

Answer:

First term=1024

Common ratio = ½

Step-by-step explanation:

Index means its position

Even index means the 2nd, 4th, 6th ....terms

Graph the function f(x)=6x^5+8x^4-7x^3-5x^2+10 by making a table of values.

Answers

Answer:

Step-by-step explanation:

A fifth-grade polynomial requires a minimum of 6 different points to create an adequate graph. Let is [tex]X[/tex] the dominion of the polynomial, such that [tex]0[/tex], [tex]1[/tex], [tex]2[/tex], [tex]3[/tex], [tex]4[/tex], [tex]5[/tex] [tex]\in X[/tex]. The values of the function for each value are calculated herein:

x = 0

[tex]f(0) = 6\cdot 0^{5}+8\cdot 0^{4}-7\cdot 0^{3}-5\cdot 0^{2}+10[/tex]

[tex]f(0) = 10[/tex]

x = 1

[tex]f(1) = 6\cdot 1^{5}+8\cdot 1^{4}-7\cdot 1^{3}-5\cdot 1^{2}+10[/tex]

[tex]f(1) = 12[/tex]

x = 2

[tex]f(2) = 6\cdot 2^{5}+8\cdot 2^{4}-7\cdot 2^{3}-5\cdot 2^{2}+10[/tex]

[tex]f(2) = 254[/tex]

x = 3

[tex]f(3) = 6\cdot 3^{5}+8\cdot 3^{4}-7\cdot 3^{3}-5\cdot 3^{2}+10[/tex]

[tex]f(3) = 1882[/tex]

x = 4

[tex]f(4) = 6\cdot 4^{5}+8\cdot 4^{4}-7\cdot 4^{3}-5\cdot 4^{2}+10[/tex]

[tex]f(4) = 7674[/tex]

x = 5

[tex]f(5) = 6\cdot 5^{5}+8\cdot 5^{4}-7\cdot 5^{3}-5\cdot 5^{2}+10[/tex]

[tex]f(5) = 22760[/tex]

The table is now presented:

 x                 y

 0                10

 1                 12

 2               254

 3               1882

 4               7674

 5              22760

Finally, the graphic is now constructed by using an online tool (i.e. Desmos). The image is included below as attachment.

Can someone help me with this page I don’t know how to do this type of math

Answers

2a+4=10
subtract 4 from 10 and you get 6, then you divide by 2 and a=3

4b-3=17 same here
you do the opposite sign so you add 3 to 17 and you get 20 then you divide by 4 and b=5

3c+5=11
subtract 5 from 11 you get 6 then you divide by 3 and c=2

Which of these expressions is equivalent to 3x(x-1)-5(x-1)? Select all that apply.
3x^2-8x+5
x-1(3x-5)
(3x-5)(x-1)
(x-1)(3x+5)

Answers

Answer:

3x(x-1)-5(x-1)

=3x²-3x-5x+5 (we can count it one by one)

=3x²-8x+5 (we can calculate the same variable)

#i'm from indonesia

hope it helps.

Answer:

[tex]\boxed{3x^2 -8x+5}[/tex]

[tex]\boxed{(3x-5)(x-1)}[/tex]

Step-by-step explanation:

[tex]3x(x-1)-5(x-1)[/tex]

Expand brackets.

[tex]3x(x)+3x(-1)-5(x)-5(-1)[/tex]

[tex]3x^2 -3x-5x+5[/tex]

Combine like terms.

[tex]3x^2 -8x+5[/tex]

[tex]3x(x-1)-5(x-1)[/tex]

Take x-1 as a common factor.

[tex](3x-5)(x-1)[/tex]

The straight line PQ with a gradient -2 passing through point (-3, 10). Find the y-intercept of the straight line PQ . Please help me and explain it . Thank you so much ​

Answers

Answer:

y- intercept = 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope( gradient ) and c the y- intercept )

Here m = - 2 , thus

y = - 2x + c ← is the partial equation

To find c substitute (- 3, 10) into the partial equation

10 = 6 + c ⇒ c = 10 - 6 = 4

Thus y- intercept c = 4

The circumference of a circle is 6π in. What is the area, in square inches? Express your answer in terms of \piπ.

Answers

Step-by-step explanation:

Hey, there!!

According to the question,

There is given circumference = 6pi in.

or, 2.pi.r = 6pi.in

or, r = 6 pi.in/ 2

Therefore, the radius (r)= 3in.

now,

area = pi.r^2

a= pi× (3in)^2

Therefore, the area is 9.pi.in^2.

Hope it helps....

Answer:

A ≈ 2.86

Step-by-step explanation:

Using the formulas

A = πr²

C = 2πr

Solving for A

A = C²/ 4π = 6²/ 4·π ≈ 2.86479

Is there an association between favorite core subject and favorite elective? If so, describe it.

Answers

Answer:

Yes

Step-by-step explanation:

Take note that a favorite core subject represents subjects that are widely recognized as important to the student's line of study, they include subjects like Maths, English, Science, and Engineering.

While Elective subjects are optional subjects that are deemed less important than the core, but by choosing one's favorite elective subject shows that individual places a certain level of importance that is almost that of the core subject.

Which data set has an outlier?

Answers

Answer:

Option B

Step-by-step explanation:

You can tell this because it has the largest difference from the second highest listed value.

Answer:

Answer Is D

Step-by-step explanation:

Find the missing probability. P(A)=15,P(A∪B)=1225,P(A∩B)=7100 ,P(B)=?

Answers

Answer:

p(B) = 8310

Step-by-step explanation:

We will use the addition rule of probability of two events to solve the question. According to the rule given two events A and B;

p(A∪B) = p(A)+p(B) - p(A∩B) where;

A∪B is the union of the two sets A and B

A∩B is the intersection between two sets A and B

Given parameters

P(A)=15

P(A∪B)=1225

P(A∩B)=7100

Required

Probability of event B i.e P(B)

Using the expression above to calculate p(B), we will have;

p(A∪B) = p(A)+p(B) - p(A∩B)

1225 = 15+p(B)-7100

p(B) = 1225-15+7100

p(B) = 8310

Hence the missing probability p(B) is 8310.

hey can you help me w/ some math ?? i make $8.50 an hour. monday through sunday only wednesday’s off. how much will i have in 2 years from today ? monday, tuesday & sunday is from 4-9pm .... then friday,saturday & sunday is from 4-10pm.

Answers

Answer:

$29252.1669

Approximately $29252.1

Step-by-step explanation:

For Monday,  Tuesday and Sunday:

=> 8.50 x 5 x 3

=> 8.5 x 15

=> 127.5

I multiplied 8.5 and 5 because you work for 5 hours. Then multiplied them with 3 it is for 3 days.

For Friday, Saturday, Thursday:

=> 8.5 x 6 x 3

=> 8.5 x 18

=> 153

I multiplied 8.5 and 6 because you work for 6 hours. Then multiplied them with 3 because it is for 3 days.

In 1 week you get:

=> 153 + 127.5

=> 280.5

In 1 year there are 52.1429 weeks.

So, you get:

=> 52.1429 x 280.5

=> 14626.08345

For 2 years, you get:

=> 14626.08345x 2

=>  29252.1669

=> Approximately $29252.1

10. RP3-M

Jeanette purchased a concert ticket on a web site. The original price of the ticket was $75.

She used a coupon code to receive a 20% discount. The website applied a 10% service fee

to the discounted price. Jeannette's ticket was less than the original price by what percent?

Answers

Answer:

Jeannette's ticket was less than the original pice by 30%

Step-by-step explanation:

original price = $75

percentage discount = 20% of original price = 20% of $75

discounted price = [tex]\frac{20}{100} \times\ 75\ =\ 15[/tex]

discounted price = $15

website service fee = 10% of original price

website service fee = [tex]\frac{10}{100}\times 75 = \$7.5[/tex]

New discounted price = discount price + website service fee

= 15 + 7.5 = $22.5

Next, let us calculate what percentage of the original price that will give the new discount price.

Let the percentage of the original price = x%

x% of 75 = $22.5

[tex]\frac{x}{100} \times\ 75\ = 22.5\\\\\frac{75x}{100} = 22.5\\\\75x = 2250\\\\x = \frac{2250}{75} \\\\x = 30[/tex]

Therefore, Jeannette's ticket was less than the original pice by 30%

A line that contains the points (5, −3) and (7, 3) has a slope, m, that equals

Answers

Answer:

m = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, - 3) and (x₂, y₂ ) = (7, 3)

m = [tex]\frac{3+3}{7-5}[/tex] = [tex]\frac{6}{2}[/tex] = 3

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