two ships leave a port at the same time. the first ship sails on a bearing of 55° at 12 knots (natural miles per hour) and the second on a bearing of 145° at 22 knots. how far apart are they after 1.5 hours (round to the nearest nautical mile)
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Given that one of the ships travels at 12 nautical miles per hour, then after 1.5 hours, it will travel 12*1.5 = 18 miles
The other ship will travel 22*1.5 = 33 miles
The angle of 145° is measured with respect to the positive x-axis. Then, respect the negative x-axis, its measure is 180° - 145° = 35°
We have to use trigonometric functions to find x1, y1, x2, and y2, as follows:
sin(55°) = y1/18
sin(55°) *18 = y1
14.7 = y1
cos(55°) = x1/18
cos(55°)*18 = x1
10.3 = x1
sin(35°) = y2/33
sin(35°)*33 = y2
18.9 = y2
cos(35°) = x2/33
cos(35°)*33 = x
-27 = x2 (the minus sign comes from the graph)
The distance between two points (x1, y1) and (x2, y2) is computed as follows:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting with the values found,
[tex]\begin{gathered} d=\sqrt[]{(-27-10.3)^2+(18.9-14.7)^2} \\ d=\sqrt[]{(-37.3)^2+4.2^2} \\ d=\sqrt[]{1391.29+17.64} \\ d\approx38\text{ miles} \end{gathered}[/tex]
Related Questions
7. Flora has a square fountain. It is a square fountain and she wants to place a walkway around it. The square fountain measures 4 meters on each side. The walkway will be one meter wide around the fountain.. a. Find the area of the walkway. b. One bag of colored stones covers 1 square meter, how many bags of stones will be needed to cover the entire walkway around the fountain? C. A bag of colored stones cost $24.99. How much will it cost to fill in he walkway with colored stones?
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Answer:
[tex]\begin{gathered} a)20m^2 \\ b)\text{ 20 bags of colored stones} \\ c)\text{ \$499.8} \end{gathered}[/tex]Step-by-step explanation:
Since the square fountain measures 4 meters on each side and the walkway will be one meter wide, let's make a diagram to see the situation:
Then, to calculate the area of the walkway (green shaded region)
[tex]\begin{gathered} A_{total}=b\cdot h \\ A_{total}=6\cdot6=36m^2 \\ A_{founta\in}=4\cdot4=16m^2 \end{gathered}[/tex][tex]\begin{gathered} A_{walkway}=A_{total}-A_{fountain} \\ A_{walkway}=36-16=20m^2 \end{gathered}[/tex]Now, how many colored stones will be needed if one bag covers 1 square meter:
There are 20 square meters on the walkway, then will be needed 20 bags of colored stones.
A bag of colored stones costs $24.99, then multiply 20 by $24.99:
[tex]20\cdot24.99=\text{ \$499.8}[/tex]Help I need a example for graphing two variable inequalities
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Solution:
To graph, a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equals sign. The graph of this equation is a line.
If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ and ≥ ), graph a solid line.
For example,
Consider the linear inequality in two variables below
[tex]y\leq4x-8[/tex]Step 1:
Put x=0 and find y
[tex]\begin{gathered} y=4x-8 \\ y=4(0)-8 \\ y=0-8 \\ y=-8 \\ (0,-8) \end{gathered}[/tex]Step 2:
Put y=0 and find x
[tex]\begin{gathered} y=4x-8 \\ 0=4x-8 \\ 4x=8 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \\ (2,0) \end{gathered}[/tex]Hence,
We are going to use the coordinates below to graph the inequality using a solid line because
The inequality sign used is greater than or equal to
[tex](0,-8),(2,0)[/tex]Hence,
The graph of the inequality will be
simplify the following expression using the distributive property and combining like terms:3(y-4) -5(y+8)
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3(y-4) - 5(y+8)
3y - 12 - 5y - 40
-2y - 52
What is the slope of the line in the graph?A. 1 B. 2C. 0 D. -2
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Always remember that the slope is the number of units on the Y-axis in relation to the X movement.
A horizontal line always has a slope of 0. (it is not increasing in the Y-axis)
Translate each English phrase in the following problem into an algebraic expression and set up the related equation. Let z be the unknown number. The sum of a number and -41 is equal to the quotient of the number and 11. Step 2 of 3: Translate "the quotient of the number and 11". Answer
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An algebraic expression which represents the translation of "The sum of a number and -41 is equal to the quotient of the number and 11" is z - 1 = z/11.
How to translate an English phrase into an algebraic expression?In order to translate a word problem into an algebraic expression, we would have to assign a variable to the unknown number:
Let z represent the unknown number.
The sum of a number and -41 is given by:
z + (-1) = z - 1 ....equation 1.
The quotient of the number and 11 is given by:
z/11 .....equation 2.
Next, we would equate equation 1 and equation 2 as follows:
Translation; z - 1 = z/11
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is it a function? X (-2, -1, 0, 1, 2 ) Y (-7, -2, 1, -2, -7 )
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To be a function, it is nesessary that the values of x correspond to a unique value of y (a value of x cannot correspond to 2 different values of y). The same value of y can correspond to two or more values of x
As in the given data each value of x has just one value of y. Then, it is a function.
Problem solving.When two expressions are not equivalent, you can use an inequality symbol to show their relationship. Do you ever use an inequality symbol when two expressions are equivalent? Use an example in your explanation.
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Explanation
When two expressions are not equivalent, you can use an inequality symbol
[tex]\begin{gathered} \leq\Rightarrow less\text{ or equal } \\ \ge\Rightarrow greater\text{ or equal } \\ >\Rightarrow greater\text{ than } \\ <\Rightarrow smaller\text{ than} \end{gathered}[/tex]
now, when comparing two expressions that are equivalent , WE CAN NOT USE an inequality simbol, instead of we need to use The equals sign or equal sign formerly known as the equality sign
[tex]=[/tex]for example
[tex]3x+19x=30x-8x[/tex]the = symbold indicates that both sides have the same value ( rigth and left)
I hope this helps you
Question 11 > Alvin can go upstream at a rate of 25 miles per hour and downstream at a rate of 35 miles per hour. One day while Alvin was on the river, he received a call telling him he needs to turn around and come home. So he turned around and went back to his starting point. If his entire trip took 12 hours, how far did he travel on the river? Alvin traveled miles. (Roundtrip) Question Help: Message instructor Submit Question
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Given Data:
The upstream speed is, 25 miles/hr.
The downstream speed is, 35 miles/hr.
The total time is, 12 hr.
Let d be the distance traveled. He can travel 25 miles/ hr in upstream, so the time taken will be,
[tex]t=\frac{d}{25}[/tex]He can travel 35 miles/ hr in upstream, so the time taken will be,
[tex]t^{\prime}=\frac{d}{35}[/tex]Total time is, 12 hr. So we have,
[tex]\begin{gathered} 12=\frac{d}{25}+\frac{d}{35} \\ 12=\frac{d}{5\times5}+\frac{d}{7\times5} \\ 12=\frac{1}{5}(\frac{d}{7}+\frac{d}{5}) \\ 12\times5=\frac{d}{7}+\frac{d}{5} \\ 60\times35=5d+7d \\ 2100=12d \\ d=\frac{2100}{12}=175 \end{gathered}[/tex]Therefore the total distance is, 350 mile
Evaluating functions I don’t understand this one and I can’t find it no where else
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The function given is
[tex]f(x)=4x[/tex]We are to find the inverse of the function
let f(x) =y
[tex]y=4x[/tex]Then, we make x the subject of the formula from here
[tex]\begin{gathered} y=4x \\ x=\frac{y}{4} \\ x=\frac{1}{4}y \end{gathered}[/tex]Then The inverse of the function becomes
[tex]f(x)=\frac{1}{4}x[/tex]Therefore the fourth option is correct
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
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Answer:
Option is the the. correct answer A
Pat bought a washer/dryer for $900 and made 24 payments of $46.23. Howmuch did she pay in interest?a. $1,109.52b. $900c. $92.40d. $209.52
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Given that:
Cost of the washer/dryer = $900
Number of payments made = 24
Amount paid in each payment = $46.23
Total amount she paid
[tex]\begin{gathered} =\text{Amount paid in each payment}\cdot Number\text{ of payments} \\ =46.23\cdot24 \\ =1109.52 \end{gathered}[/tex]Interest paid = Total amount paid - Cost of the washer/dryer
[tex]\begin{gathered} =1109.52-900 \\ =209.52 \end{gathered}[/tex]Option d is correct.
The country of Scotstats requires the people in their country to have license tags on their car such that the first 3 characters are English letters but no letter may repeat. The last 3 characters must each be a number 0-9 and again no numbers can be repeated. How many license tags are possible?
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Answer
11,232,000 possible license tags.
Explanation
The licenses have space for 6 characters.
We need to note that there are 26 alphabets and 10 numbers to pick from.
So, for the first character, any of the 26 alphabets can take this spot.
For the second character, 25 alphabets are now available for that space. (Since repetition is not allowed)
For the third character, 24 alphabets are available for that.
For the fourth character, any of the 10 numbers can take up that spot.
For the fifth character, only 9 numbers can take this spot now. (No repetition rule too)
For the sixth character, 8 numbers can take that spot.
So, mathematically, the number of license tags possible will be
26 × 25 × 24 × 10 × 9 × 8 = 11,232,000 possible license tags
Hope this Helps!!!
Suppose that the balance of a person’s bank account in US is normally distributed with mean $580 and standard deviation $125. Find the amount of money which would guarantee a person has more money in their account than 80% of US residents.I want an answer and explanation.
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Answer:
[tex]\text{ \$685.25}[/tex]Explanation:
Here, we want to get the amount of money that would guarantee that a person has more money than 80%
That means the probability is greater than 80% or 0.8
Thus, we need to get the z-score that corresponds to this probability
Using a z-score table, we can get this as follows:
[tex]P(x\text{ }>\text{z\rparen= 0.842}[/tex]We will now get the value from the obtained z-score
Mathematically:
[tex]\begin{gathered} z\text{ = }\frac{x-\mu}{\sigma} \\ \\ \text{ x is the value we want to calculate} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]Substituting the values, we have it that:
[tex]\begin{gathered} 0.842\text{ = }\frac{x-580}{125} \\ \\ \text{ x = 580 + 125\lparen0.842\rparen} \\ x\text{ = \$685.25} \end{gathered}[/tex]Simplify -(x+ 5) + 3x completely.A. -4x+ 5OOB. 2x + 5C. 2x - 5D. -4x - 5
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-(x+ 5) + 3x
Distributing the -1:
(-1)*x + (-1)*5 + 3x
-x - 5 + 3x
Combining similar terms:
(-x + 3x) - 5
2x - 5
Question 10 of 12, Step 1 of 29/14CorrectConsider the following quadratic equation:3.x2 - 13x + 2 = -2Step 1 of 2: Using the standard form ax2 + bx + c = 0 of the given quadratic equation, factor theleft hand side of the equation into two linear factors.AnswerKeypadKeyboard Shortcuts= 0
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Solution
- The question would like us to solve the quadratic equation:
[tex]3x^2-13x+2=-2[/tex]- The solution to this equation is given below:
[tex]\begin{gathered} 3x^2-13x+2=-2 \\ \text{Add 2 to both sides} \\ 3x^2-13x+4=0 \\ \\ \text{ We can rewrite the x-term as follows:} \\ -13x=-12x-x \\ \\ 3x^2-12x-x+4=0 \\ Let\text{ us factorize} \\ \\ 3x(x-4)-1(x-4)=0 \\ (x-4)\text{ is common } \\ \\ (x-4)(3x-1)=0 \end{gathered}[/tex]- Thus, the linear factors are
[tex]undefined[/tex]Tori is writing an essay for her English class. She already has 235 words, andon average writes 175 words every hour. The essay needs to be at least 1,600words. How many more hours should she plan to work on it? Write and solvean inequality for the situation.
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Let be "h" the number of hours Tori should plan to work on it.
You know that she writes an average of 175 per hour. This can be represented with this expresion:
[tex]175h[/tex]You also know that there must be at least 1,600 words in the essay for her English class. Since she has 235 words written, you can set up the following inequality:
[tex]235+175h\ge1,600[/tex]The symbol used in the inequality means "Greater than or equal to".
In order to solve it, you can follow these steps:
1. Subtract 235 from both sides of the inequality:
[tex]\begin{gathered} 235+175h-(235)\ge1,600-(235) \\ 175h\ge1,365 \end{gathered}[/tex]2. Divide both sides of the inequality by 175:
[tex]\begin{gathered} \frac{175h}{175}\ge\frac{1,365}{175} \\ \\ h\ge7.8 \end{gathered}[/tex]The answer is:
[tex]7.8\text{ }hours[/tex]HeyI need help with this, having trouble solvingIt is from my ACT prep guide
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We will determine the height of the building as follows:
First, we determine the height above her window, that is:
[tex]\tan (56)=\frac{h_u}{150ft}\Rightarrow h_u=(150ft)\tan (56)[/tex][tex]\Rightarrow h_u=222.3841453\ldots ft[/tex]Now, we calculate the height below her window:
[tex]\tan (32)=\frac{h_l}{150ft}\Rightarrow h_l=(150ft)\tan (32)[/tex][tex]\Rightarrow h_l=93.73040279\ldots ft[/tex]Then, we will have that:
[tex]h_T=h_l+h_l\Rightarrow h_T=150(\tan (56)+\tan (32))[/tex][tex]\Rightarrow h_T=316.1145581\ldots ft\Rightarrow h_T\approx316.1ft[/tex]So, the height of the building is approximately 316.1 ft tall.
I don't understand how to do this (this is a practice assessment)
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Math | English | Art | Total
Boys 13 25 11 49
Girls 7 20 6 33
Total 20 45 17 82
1) Let's set a table, based on the given information:
• Since there are 20 students enrolled in Math let's place it into the Total, 20 -13 = 7
,• 82 students altogether.
,• 11 boys are in Art , 17 altogethe then 17 -11 = 6 girls
,• 20+6+7 = 20+13 = 33 girls altogether.
,• 82 -33 =49 13 +x +11 = 49 x = 49 -24=25
,• And lastly English: 20 +25 = 45
2) That's our table:
Math | English | Art | Total
Boys 13 25 11 49
Girls 7 20 6 33
Total 20 45 17 82
need help with math
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in a class the ratio of the boy to the girls is 7:8 what part of the whole class are girls
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O GRAPHS AND FUNCTIONSFinding inputs and outputs of a two-step function that models a...
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Given the function:
[tex]A(t)=256-16t[/tex]Where A is the amount of money (in dollars) Diane has left in her account after t trips on the toll roads.
(a)
After 8 trips on the toll roads (t = 8):
[tex]\begin{gathered} A(8)=256-16(8)=256-128 \\ \\ \therefore A(8)=\$128 \end{gathered}[/tex](b)
If her account is empty:
[tex]\begin{gathered} A(t)=0 \\ \\ \Rightarrow256-16t=0 \end{gathered}[/tex]Solving the equation for t:
[tex]\begin{gathered} 256=16t \\ \\ \therefore t=16\text{ trips} \end{gathered}[/tex]Solve the system of two linear inequalities graphically.Graph the solution set of the second linear inequality?
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According to the second inequality, y is greater than or equal to -2, which means that the graph will have a solid line, the first step is to pick solid choice.
The boundary line is y=2, we know this by replacing the inequality sign by an equal sign. Two points one this line are (-1,2) and (2,2). We know it because it is an horizontal line that represents a constant function, it means that all the values of y will be 2 (boundary line).
As the equal sign is greater than or equal to, the region that must be shaded is the one above the boundary line.
Tyrone randomly interviewed 55 8th graders at the Westwood Mall Saturday afternoon to determine their reason for going to the mall. Based on the results of his survey, he made the following claim:Two out of four middle school students visit the mall to go shopping.Explain why this claim is misleading.a. Tyrone only interviewed students in the food court.b. Tyrone did not survey enough 8th graders to draw a valid conclusion.c. Tyrone did not use a random sample of 8th graders.d. Since Tyrone surveyed only 8th graders, his sample is not representative of all middle school students.
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Tyrone randomly interviewed 55 8th graders at the Westwood Mall Saturday afternoon to determine their reason for going to the mall.
Based on the results he made the following claim.
"Two out of four middle school students visit the mall to go shopping".
Let us analyze each of the given options.
a. Tyrone only interviewed students in the food court.
There is no evidence that suggests the interview was conducted at the food court so this is not the correct answer.
b. Tyrone did not survey enough 8th graders to draw a valid conclusion
He interviewed 55 8th graders which are more than enough students so this is not misleading.
c. Tyrone did not use a random sample of 8th graders
It is given in the question that he used a random sample so this is not misleading.
d. Since Tyrone surveyed only 8th graders, his sample is not representative of all middle school students.
If you notice closely, Tyrone interviewed only 8th graders whereas the claim was about all middle school students.
So this is clearly misleading, 8th graders do not represent all middle school students.
Therefore, option d is correct.
if(f) (x)= x/2 - 2 and (g) (x) = 2x^2 + x - 3 find (f+g) (x)|| how do i add functions when the number is a fraction? ||
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Solution
Given
[tex]\begin{gathered} f(x)=\frac{x}{2}-2 \\ \\ g(x)=2x^2+x-3 \\ \\ (f+g)(x)=f(x)+g(x)=\frac{x}{2}-2+2x^2+x-3=2x^2+\frac{3x}{2}-5 \end{gathered}[/tex]Hello,May I please request for help on the word problem number 37, please?
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As the last stand-up comic of the evening is granted. The combination of schedules is made with the other 5 performers.
To find how many ways you can order 5 performers you multiply 5x4x3x2x1 (or factorial 5: 5!)
[tex]5!=5\times4\times3\times2\times1=120[/tex]Then, there are 120 different ways to schedule the appearancesFind the value of 4v-8 given that 11v-8 = 3.Simplify your answer as much as possible.
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Given that 11v - 8 = 3
add 8 to both sides
11v = 3 + 8
11v = 11
Divide both sides by 11
v = 1
to simplify 4v - 8
= 4 (1) - 8
= 4 - 8
= -4
-4
Explanation
Is x = -2 the linear equation that matches this table of ordered pairs?Explain why or why not.Xy-2 7-2 1-2 -5(x, y)(-2,7)(-2, 1)(-2,-5)
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Answer:
All the points given (-2,7) (-2,1) (-2,-5) have the x-coordinate of -2, then those points lie in the x=-2, so it matches the table.
i invest $250 in a simple account that earns 10% annually. After 6 years, how much money have i earned? Hint round to the nearest cent.
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We have to use the simple interest formula
[tex]A=P(1+rt)[/tex]Where P = 250; r = 0.10 (10%); t = 6. Replacing these values, we have
[tex]A=250(1+0.10\cdot6)=250(1+0.6)=250(1.6)=400[/tex]Hence, after 6 years, you have $400.
If we subtract this amount from the investment, we get the profits.
[tex]400-250=150[/tex]Hence, the earnings are $150.On a recent survey, students were asked if they ice skate, snowboard, or ski. The Venn diagram below shows the results of the survey
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The number of students who took the survey was 47 (option B).
How to identify the number of students who took the survey?To identify the number of students who took the survey, we must look at the number of students in each of the Venn diagram spaces. In this case, the number of students who practice each sport are:
Ice Skate: 7 students.Snowboarding: 10 students.Ski: 13 students.Ice Skate and Snowboard: 4 students.Ski and Snowboard: 8 students.Ice Skate and Ski: 2 students.Ice Skate, Snowboard and Ski: 3 students.To know the number of students who took the survey, we must add the number of students in each space as shown below:
7 + 10 + 13 + 4 + 8 + 2 + 3 = 47According to the above, the correct answer is option B, since 47 students took the survey.
Note: This question is incomplete because there is some information missing. Here is the complete information:
Question:
How many students took the survey?
Options
A.32
b.47
c.53
D.56
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The distance to your grandparent's house is 259 miles, and the distance to Atlanta is 555 miles. If it took 7 hours to drive to your grandparent's house, how long would you estimate the drive to Atlanta to take?
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Answer:
15 Hours
Step-by-step explanation:
259miles = 7 hours
555miles = x
Cross Multiply
259x = 555×7
259x = 3885
Divide Both sides by 259
x = 3885 ÷ 259
x = 15 hours
It would take the driver 15 hours to get to Atlanta