A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?​

Answers

Answer 1

9514 1404 393

Answer:

  36.6 km

Step-by-step explanation:

We assume the initial bearing of the boy is 35°. Then he will make a 90° turn to a heading of 125°. A diagram shows the distance of interest is the hypotenuse of a right triangle in which 35° is the angle opposite the side of length 21 km.

The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(35°) = (21 km)/XZ

  XZ = (21 km)/sin(35°) ≈ 36.61 km

The distance from X to Z is about 36.61 km.

_____

The attached diagram has the angles measured in the usual way for a Cartesian plane: CCW from the +x axis. This will correspond to bearing measures if we relabel the axes so that +x is North, and +y is East.

A Boy Leaves Station X On A Bearing Of 035' To Station Y. Which Is 21km Away. He Then Travels To Another

Related Questions

Consider the following game: You reach into a jar of money, and select a single bill at random to keep. There are 9 five-dollar bills, 5 ten-dollar bills, and 3 twenty-dollar bills in the jar. What should the cost of this game be in order for the game to be fair

Answers

Answer:

[tex]E(x)=\$9.118[/tex]

Step-by-step explanation:

From the question we are told that:

Available bills

 [tex]\$5=N0 9\\\\\$10=N0 5[/tex]

 [tex]\$20=N0 3[/tex]

Therefore

Total Bills

 [tex]n=5+9+3[/tex]

 [tex]n=17[/tex]

Probability of selecting each bill

 [tex]For\$5[/tex]

 [tex]P(\$5)=\frac{9}{17}[/tex]

 [tex]For\$10[/tex]

 [tex]P(\$10)=\frac{5}{17}[/tex]

 [tex]For\$20[/tex]

 [tex]P(\$20)=\frac{3}{17}[/tex]

Generally the equation for Expected winning is mathematically given by

 [tex]E(x)=\sum(X)*P(X)[/tex]

 [tex]E(x)=5*\frac{9}{17}+10*\frac{5}{17}+20*\frac{3}{17}[/tex]

 [tex]E(x)=\$9.118[/tex]

Bob had 10 more cars than Paul. Paul had 15 cars.

Answers

Answer:

Bob had 25 cars

Step-by-step explanation:

10+15=25

Bob at 25 cars
explanation: paul had 15 cars bob had 10 more
15+10=25

For any number n>1, is
|(.5 +.2i)^n|
A. greater than 1?
B. less than 1?
C. equal to 1?
PLZ HELP

Answers

Answer:

B. Less than 1

Step-by-step explanation:

You could plug in values of n greater than 1 and see what happens....

Example n=2 gives |(.5+.2i)^2|

Simplifying inside gives |(.5)^2+2(.5)(.2i)+(.2i)^2|

=|.25+.2i+.04i^2|=|.25+.2i-.04|=|.21+.2i|.

Applying the absolute value part gives sqrt(.21^2+.2^2)=sqrt(.0441+.04)=sqrt(.0841)=.29

This value is less than 1.

We should also be able to do the absolute value first then the power.

|.5+.2i|=sqrt(.25+.04)=sqrt(.29)

So |.5+.2i|^2=.29 which is what we got long way around.

Anyways (sqrt(.29))^n where n is greater than 1 will result in a number greater than 0 but less than 1.

Tim did a survey at a large shopping centre. He asked 400 visitors to the centre to choose the main reason for their visit. The reasons were shops, free parking, food court and location.
From the people taking part in the survey, one person is chosen at random to get a prize. Find the probability a female who chose location gets the prize.

shops free park. food location total
male 88 24 40 21 173
female 110 38 56 23 227
total 198 62 96 44 400​

Answers

Answer:

23 / 400 = 0.0575

Step-by-step explanation:

Given the distribution :

_____shops__ free park. food _: location total

male 88 24 40 21 173

female 110 38 56 23 227

total 198 62 96 44 400​

From the table of the distribution Given, we obtain :

n(Female n location) = 23

n(Total) = 400

Hence, the probability that a female who chose location gets the prize will be ;

n(Female n location) / n(Total) = 23 / 400 = 0.0575

find a number such that when it is multiplied by 7 and 17 is subtracted from the product the result is the same as when it is multiplied by 3 and 19 added to the product .​

Answers

Answer:

9

Step-by-step explanation:

Let the number be X

From the problem we have the following equation:

7x - 17 = 3x + 19

-> 4x = 36

-> x = 9

Answer:

9

Step-by-step explanation:

that is the procedure above

y’all what are the answers

Answers

Answer:

Step-by-step explanation:

100 POINTS!!
Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.


Question: Your friend claims that the only solution to the equation sin(x)=1 is x=90 degrees. Is your friend correct? If there are more solutions, explain how to determine additional solutions.

Answers

......hope it helps......

Answer:

yes,.to obtain sinx as 1 the angle must be 90degrees

so the answer is correct

but there are more solutions like when the cosine angle is 45 the answer is 1

and when x is 450 still sinx = 1..that is to say sin450= 1

Plz help I’ll mark you

Answers

Answer:

A 1/2

Step-by-step explanation:

Ratio of short length to hypotenuse

= cos60

= 1/2

Lendo 15 páginas por dia, Marcos leu um livro em
9 dias.
Para ler esse mesmo livro em 3 dias, quantas páginas
ele deveria ler por dia?

Answers

Answer:

Olha a foto.

Step-by-step explanation:

Carin opened a money market account with a
deposit of $3,000. This account earns 2% simple
interest annually. How many years will it take for
her $3,000 deposit to earn $420 in interest, assum-
ing she does not withdraw any of the money?

Answers

Answer:

7

Step-by-step explanation:

For simple interest,

I = prt

where I = interest,

p = principal (amount deposited)

r = annual rate of interest

t = time in years

We have r = 2% = 0.02

p = $3,000

I = $420

We need to find t

I = prt

420 = 3000 * 0.02 * t

420 = 60t

t = 420/60

t = 7

Answer: 7 years

Kevin will start with the integers 1, 2, 3 and 4 each used exactly once and written in a row in any order. Then he will find the sum of the adjacent pairs of integers in each row to make a new row, until one integer is left. For example, if he starts with 3, 2, 1, 4, then he takes sums to get 5, 3, 5, followed by 8, 8, and he ends with the final sum 16. Including all of Kevin's possible starting arrangements of the integers 1, 2, 3 and 4, how many possible final sums are there?

Answers

Hello,

there are 5 differents sums:

16,18,20,22,24.

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

Dim i As Integer, j As Integer, k As Integer, l As Integer, u As Integer, v As Integer, nb As Integer

Dim mat(4, 4) As Integer

nb = 0

For i = 1 To 4

   For j = 1 To 4

       If j <> i Then

           For k = 1 To 4

               If k <> j And k <> i Then

                   l = 10 - k - j - i

                   If l > 0 And l < 5 And l <> i And l <> j And l <> k Then

                       mat(1, 1) = i

                       mat(1, 2) = j

                       mat(1, 3) = k

                       mat(1, 4) = l

                       For u = 2 To 4

                           For v = 1 To 4 - u + 1

                               mat(u, v) = mat(u - 1, v) + mat(u - 1, v + 1)

                           Next v

                       Next u

                       'Call visu(mat())

                       nb = nb + 1

                       Print nb,

                       mat(4, 1)

                   End If

               End If

           Next k

       End If

   Next j

Next i

End

Sub visu (m() As Integer)

   Dim i As Integer, j As Integer

   For i = 1 To 4

       For j = 1 To 4 - i + 1

           Print m(i, j);

       Next j

       Print

   Next i

End Sub

Solve for the following equation for x. l x/4 + 3 l < 6

Answers

Answer:

this is the answer I got! i don't know if it helps, but I hope it does

Which table represents a linear function?
Х
1
2
3
4
y
3
6
12
24
х
1
2
3
4
у
2.
5
9
14
х
1
2
3
4
у
-3
-5
-7
-9
х
1
2
3
4
у
-2
-4
-2
0

Answers

Answer:

3

Step-by-step explanation:

x 1,2,3,4

y-3,-5,-7,-9

[tex]y = - 3 - (x - 1) \times 2[/tex]

The linear function is given by y = 7x - 4

A linear function is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept

From the table, using the points (1, 3) and (4, 24):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-3=\frac{24-3}{4-1}(x-1)\\\\ y=7x-4[/tex]

The linear function is given by y = 7x - 4.

Find out more on linear function at: https://brainly.com/question/4025726

the value of (-15/23)+(+30/-46) is ---------.​

Answers

[tex] \frac{ - 15}{23} + \frac{30}{ - 46} \\ = \frac{ - 15}{23} + \frac{(2) \times (15)}{(2) \times ( - 23)} \\ = \frac{ - 15}{23} + \frac{15}{ - 23} \\ = \frac{ - 15}{23} - \frac{15}{23} \\ = \frac{ -3 0}{23} \\ = - 1.3[/tex]

What is the value of h in the figure below? In this diagram, ABAD ~ ACBD.
Д.
С
0
20
А. 80
В. 16
ОО ооо
С. 60
D. 5
Е. 8
о
Е.

Answers

Answer:

[tex]h=\sqrt{16(4)}[/tex]

[tex]h=8[/tex]

[tex]ANSWER:E) 8[/tex]

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

~HOPE IT HELPS

~HAVE A GREAT DAY!!

Find the value of x. What is the value of x?

Answers

Answer:

x = 16

Step-by-step explanation:

The product of the lengths theorem is a property that can be sued to describe the relationships of the sides between the tangents and secants in a circle. One of these products states the following;

The distance between the point of tangency and its intersection point with the exterior secant squared is equal to the product of the exterior secant times the interior secant.

This essentially means the following equation can be formed;

[tex](AB)^2=(DC)(CB)[/tex]

Substitute,

[tex]12^2=x*9[/tex]

Simplify,

[tex]144=9x[/tex]

Inverse operations,

[tex]\frac{144}{9}=x\\\\16=x[/tex]

Answer:

[tex]\boxed{\sf x=7}[/tex]

Step-by-step explanation:

By Targent-secant theorem...

[tex]\sf 9(x + 9) = {12}^{2} [/tex]

Use the distributive property to multiply 9 by x+9.

[tex]\sf 9x+81= {12}^{2} [/tex]

Now, let calculate 12 to the power of 2 and get 144.

[tex]\sf 9x+81=144[/tex]

Subtract 81 from both sides.

[tex]\sf 9x=63[/tex]

Divide both sides by 9.

[tex] \sf \cfrac{ 9x}{9} = \cfrac{63}{9} [/tex]

[tex]\sf x=7[/tex]

Find the product (-3/5) (-2/9)

Answers

I think the answer is 2/15

Answer:

2/15

Step-by-step explanation:

(-3/5) (-2/9)

Rewriting

-3/9 * -2/5

-1/3 * -2/5

A negative times a negative is a positive.

2/15

5/6 ÷ 1/3 - 2/3 (2/5)

Answers

Answer:

[tex] \frac{67}{30} \: \text{or} \:2 \frac{7}{30} [/tex]

Step-by-step explanation:

5/6 ÷ 1/3 - 2/3 (2/5)

= 5/6 ÷ 1/3 - 2/3 × 2/5= 5/2 - 2/3 × 2/5= 5/2 - 4/15= 67/30 or 2 7/30

Hope it helps you! \(^ᴥ^)/

In a mixture of 240 gallons, the ratio of ethanol and gasoline is 3:1. If the ratio is to be 1:3, then find the quantity of gasoline that is to be added.

Answers

Answer:

480 gallons.

Step-by-step explanation:

Given that in a mixture of 240 gallons, the ratio of ethanol and gasoline is 3: 1, if the ratio is to be 1: 3, to find the quantity of gasoline that is to be added the following calculation must be performed:

240/4 x 3 = Ethanol

240/4 = Gasoline

180 = Ethanol

60 = Gasoline

0.25 = 180

1 = X

180 / 0.25 = X

720 = X

720 - 180 - 60 = X

480 = X

Therefore, 480 gallons of gasoline must be added if the ratio is to be 1: 3.

what is 3/2 divided by 1/8

helppp​

Answers

Answer: 12

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

6. Convert 3−i into polar form and hence evaluate
[tex] {(3 - i)}^{7} [/tex]


Answers

9514 1404 393

Answer:

  ≈ 1000√10∠-129.04464° = -1992 -2456i

Step-by-step explanation:

  3 -i = √(3³+(-1)²)∠arctan(-1/3) ≈ √10∠-18.4349°

Then (3-i)^7 = 10^(7/2)∠(7×-18.4349°) = 1000√10∠-129.04464°

  = 1000√10(cos(-129.04464°) +i·sin(-129.04464°))

  = -1992 -2456i

3x+7>10
Solve for x.

Answers

Answer: x>1

Step-by-step explanation:

To solve for x, we want to isolate x.

3x+7>10       [subtract both sides by 7]

3x>3             [divide both sides by 3]

x>1

Therefore, we know that x>1.

Answer:

Step-by-step explanation:

3x + 7 > 10

3x > 10 - 7

3x > 3

x > 1

x ∈ ( 1, ∞ )

An electronic system contains three cooling components that operate independently. The probability of each component's failure is 0.05. The system will overheat if and only if at least two components fail. Calculate the probability that the system will overheat.

Answers

Answer:

[tex]Pr= 0.00725[/tex]

Step-by-step explanation:

Given

[tex]p = 0.05[/tex] ---- probability that each component fails

[tex]n = 3[/tex]

Required

[tex]P(System\ Overheats)[/tex]

We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z

The events that the system will overheat are: xyz', xy'z, x'yz and xyz

Where ' means that the component did not fail, and the probability is 1 - p (i.e. complement rule)

So, we have:

[tex]xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375[/tex]

[tex]xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375[/tex]

[tex]x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375[/tex]

[tex]xyz \to 0.05 * 0.05 * 0.05 =0.000125[/tex]

So, the required probability is:

[tex]Pr= 0.002375 +0.002375 +0.002375 + 0.000125[/tex]

[tex]Pr= 0.00725[/tex]

.4.1 Here are the data from Exercise 2.3.10 on the num-ber of virus-resistant bacteria in each of 10 aliquots: 14 14 15 26 13 16 21 20 15 13 (a) Determine the median and the quartiles. (b) Determine the interquartile range. (c) How large would an observati

Answers

Answer:

(a)

[tex]Q_1 = 14[/tex]

[tex]Median = 15[/tex]

[tex]Q_3 = 20[/tex]

(b) [tex]IQR = 6[/tex]

Step-by-step explanation:

Given

[tex]14\ 14\ 15\ 26\ 13\ 16\ 21\ 20\ 15\ 13[/tex]

[tex]n = 10[/tex]

Solving (a): Median and the quartiles

Start by sorting the data

[tex]Sorted: 13\ 13\ 14\ 14\ 15\ 15\ 16\ 20\ 21\ 26[/tex]

The median position is:

[tex]Median = \frac{n + 1}{2}[/tex]

[tex]Median = \frac{10 + 1}{2} = \frac{11}{2} = 5.5th[/tex]

This implies that the median is the average of the 5th and the 6th data;

So;

[tex]Median = \frac{15+15}{2} = \frac{30}{2} = 15[/tex]

Split the dataset into two halves to get the quartiles

[tex]Lower: 13\ 13\ 14\ 14\ 15\[/tex]

[tex]Upper: 15\ 16\ 20\ 21\ 26[/tex]

The quartiles are the middle items of each half.

So:

[tex]Lower: 13\ 13\ 14\ 14\ 15\[/tex]

[tex]Q_1 = 14[/tex] ---- 14 is the middle item

[tex]Upper: 15\ 16\ 20\ 21\ 26[/tex]

[tex]Q_3 = 20[/tex] ---- 20 is the middle item

Solving (b): The interquartile range (IQR)

This is calculated as:

[tex]IQR = Q_3 - Q_1[/tex]

[tex]IQR = 20 - 14[/tex]

[tex]IQR = 6[/tex]

Solving (c): Incomplete details

A Sociology instructor gives students points for each​ discussion-board post and points for each reply to a post. Ana wrote 6 posts and 8 replies and received 114 points. Jae wrote 5 posts and 4 replies and received 79 points. Determine how many points a discussion post is worth and how many points a reply is worth?

Answers

Answer:

5 points per post and 2 points per replies

It says I need too put 20 characters in too ask the question so ignore this part

Answers

I believe it’s b your welcome

Wires manufactured for a certain computer system are specified to have a resistance of
between 0.11 and 0.16 ohm. The actual measured resistances of the wires produced by
Company A have a normal probability distribution, with a mean of 0.14 ohms, and a
standard deviation of 0.003 ohms. What is the probability that a randomly selected wire
from Company A’s production lot will meet the specifications?

Answers

Answer:

8d68d68fu9d6rf0d

c9yd7xpjd

puf68d6rif7

What is the average (with 0 decimal places) across all schools for the total score? Group of answer choices 1287 1215 1221 1229

Answers

Answer:

See explanation

Step-by-step explanation:

Required

The average

The data whose average is to be calculated are not given.

However, the formula to calculate the average is:

[tex]\bar x = \frac{\sum x}{n}[/tex]

Assume the data is:

[tex]1287\ 1215\ 1221\ 1229[/tex]

This means that the number of schools is 4

So:

[tex]\bar x = \frac{1287+ 1215+ 1221+ 1229}{4}[/tex]

[tex]\bar x = \frac{4952}{4}[/tex]

[tex]\bar x = 1238[/tex]

The average of the assumed data is 1238

Find the missing term in the following pattern.

320, 160, 80 blank space then, 20, 10

Answers

40

Step-by-step explanation:

Each number is followed by a number that is half its value, so the sequence goes like

320, 160, 80, 40, 20, 10.

320, 160, 80, 40, 20, 10

During a recent election, 54 of every 100 registered voters in a certain city voted. If there were 157,400 registered voters in that city, how many people voted?

Answers

84,996 of the registered voters voted. If 157,400 is 100 percent of the registered voters then you can take 54 percent of 157,400 (157,400 * 54) which equals 84,996
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A sample of 10.6 g of KNO3 was dissolved in 251.0 g of water at 25 oC in a calorimeter. The final temperature of the solution was 21.5 oC. What is the molar heat of solution of KNO3 whats is love......... If 8x7y=8 is a true equation, what would be the value of -8+8x7y? Look at the pictures and write sentences use the verb present continuos tense. there are these Karens at my house putting their trash in front of MY HOUSE and what can i do? Lionel sells to two groups of customers 50% of its sales are to wholesalers and 50% to retailers. All sales to retailers are cash sales. Collections from wholesalers are follows: 75% in the month of sale and 25% in the month following sale. ii) 60% of direct material purchases are paid in cash in the month of purchase, and the balance is paid in the month following the purchase. iii) All other expenses are paid in the month incurred. iv) Manufacturing overhead includes monthly depreciation of $15,000. v) Sales: March, $320,000. vi) Purchases of direct materials: March, $175,000. vii) Other receipts: April Donation received, $2,000 May Sale of used office furniture, $4,000. viii) Other disbursements: May Purchase of Ice Cream Mixer, $10,000. ix) Repays loan: April, $30,000. x) Cash balance on April 1, is expected to be $50,000. in what way do you think overseas commitment " influence the rise and fall of nations in Europe MCQ ................ URGENTLook at picture to see question The American colonists viewed the deaths of native Americans due to disease as:unfortunate divinely sanctioned opportunities preventable realities none of these responses are correct Which of the following are rational numbers? DeAndre Hopkins caught a 66 yard pass during the game. How many feet was the football thrown? In decline in ownership of all four types of gadgets reflects problems in the economy, which statement can best be inferred from the chart above? What did the Compromise of 1877 accomplish for both political parties? Explain. Be sure to include a topic sentence,historical evidence that supports what the compromise provided for both major political parties at this time in history,and a concluding sentence. Two students with masses of 40kg and 32 kg are sitting 22 m apart. What is the gravitational force of attraction between them? Which of the following were NOT uses of the stars to ancient humans? a) calendars b) hunting guides c) clocks 39/50 as a percentage? This is mandated by Homeland Security Presidential Directive (HSPD) 5 and provides a consistent nationwide approach for governments, the private sector, and nongovernmental organizations to work effectively and efficiently together to prepare for, respond to, and recover from domestic incidents, regardless of cause, size, or complexity? simplify 3xy 2y step by step On December 31, there were 53 units remaining in ending inventory. These 53 units consisted of 9 from January, 10 from February, 14 from May, 8 from September, and 12 from November. Using the specific identification method, what is the cost of the ending inventory