While on a one-hour trip, a small boat travels 32 km north and then travels 45 km east. what is the direction of the boat's average velocity for the one-hour trip? 27° north of east 35° north of east due east 54° north of east 45° north of east?
Answers
The boat average velocity for the one hour trip is 54° north of east.
What is Average velocity?
Average velocity is defined as the change in position divided by the time interval in which the displacement occurs.
Given that;
A small boat travel 32 km north and then travels 45 km east.
Now,
Average velocity is calculated as;
By figure,
Average velocity = cotθ = 32/45
θ = cot⁻¹ (32/45)
θ = 54°
Thus, The boat average velocity for the one hour trip is 54° north of east.
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Related Questions
The average full spreading rate over the last 20,000,000 years at placemark a in the red sea is _________. approximately 1 centimeter per year approximately 10 centimeters per year approximately 19 centimeters per year approximately 2 centimeters per year
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A dance studio charges an application fee of $75 and $50 per month for membership. This is represented by the linear equation C = 50x + 75, where C represents the cost and x represents the number of months. They are running a "no application fee" special during the month of January. How should the linear equation be changed to represent the new price?
Answers
C = 50x +75 (-75)
your answer will be C = 50x
hope this helps
To represent the new price during the 'no application fee' special, the dance studio's cost equation would change from C = 50x + 75 to C = 50x by removing the $75 application fee.
Explanation:The dance studio's original cost equation is C = 50x + 75, where C represents the total cost and x represents the number of months of membership. The $75 in the equation represents the application fee. During the "no application fee" special in January, this fee is waived, so the new equation would only include the monthly membership cost, which is $50 per month. The new equation would be C = 50x, removing the application fee entirely from the cost calculation.
A normal distribution has a mean of µ = 100 with σ = 20. if one score is randomly selected from this distribution, what is the probability that the score will have a value between x = 90 and x = 120?
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An airplane allows each passenger 36 kilograms of luggage. Carl has to lower the weight of his suitcase by 25% to stay within the limit. How much did the suitcase originally weight?
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Dividing both sides of this last equation by 0.75, we get x = 48.
Carl's suitcase originally weighed 48 lb. 25% of that is 12. x less 12 is 36 lb, which is acceptable to the airline.
Assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of $32,000 and a standard deviation of $3000. if 100 teachers are randomly selected, find the probability that their mean salary is less than $32,500.
Answers
Answer: 0.9525
Step-by-step explanation:
Given : The salaries of elementary school teachers in the united states are normally distributed with a mean of [tex]\mu=\$32,000[/tex] and a standard deviation of [tex]\sigma=\$3000[/tex].
Sample size : n= 100
Let x be a random variable that denotes the salaries of elementary school teachers in the united states.
Formula : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
Then, the probability that their mean salary is less than $32,500 will be :-
[tex]P(x<32500)=P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{32500-32000}{\dfrac{3000}{\sqrt{81}}})\\\\=P(z<\dfrac{500}{\dfrac{3000}{10}})\approx P(z<1.67)=0.9525\ \ [\text{Using z-value}][/tex]
Hence, the probability that their mean salary is less than $32,500 = 0.9525
what sequence is next 3 9 27 81
Answers
81 x 3 = 243
your answer is 243
hope this helps
If (6 to the power of 2)x = 1, what is the value of x? Explain your answer.
If (6 to the power of 0)x = 1, what are the possible values of x? Explain your answer.
PLEASE HELP AND EXPLAIN I CANT FAIL THIS QUESTION HELPPP!!!
Answers
(6²)x = 1
if yes then x =1/(6²) = 6-² or 1/36
also (6^0)x= 1
recall 6^0 = 1
so you have 1x=1
x=1
For each sequence, find a formula for the general term, a_n. for example, answer n ^2 if given the sequence: \lbrace 1, 4, 9, 16, 25, 36, . . . \rbrace
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The general term is an = n^2.
solve the equation 0.35(x+4)=0.25(x-6)
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Answer:
x=-29
Step-by-step explanation:
First multiply 0.35 by x+4 and 0.25 by x-6 after you do that you will get
0.35x+1.4=0.25x-1.5
now add 1.5 from -1.5 and 1.4 now your equation on will look like this
0.35x+2.9=0.25x
Now subtract 0.35x from both sides of the equation and your equation will look like this
2.9=0.1x
at this point you divide to get your answer, divide 2.9 and 0.1x by -0.1 and you will end up with 2.9 over -0.1 once you divide you will get -29=x
The value of x is -29.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
0.35(x+4)=0.25(x-6)
Now, solving for x
0.35 x + 1.4 = 0.25x - 1.5
0.10x = -2.9
x= -29
Hence, the value of x is -29.
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Serena has 6 photo albums with 15 photos in each. Her friend Maya has 8 albums with 13 photos in each. If Serena adds another 12 photos to her albums how many photos will Serena and Maya have in all?
Answers
so serena has (6 * 15) = 90 photos.
maya has 8 albums with 13 photos in each.
so maya has (8 * 13) = 104 photos
if serena add another 12 photos to her album....(90 + 12) = 102 photos
so in total, serena and maya have 102 + 104 = 206 photos <=
maya=8x13=104
serene=90+12=102
so add maya and serene;
102+104=206 answer
What symbols relate to the numbers 25 ? 35
Answers
find all sets of three consecutive even integers whose sum is greater than 102 and less than 116
Answers
there sum will be
2k+2(k+1)+2(k+2)
2k+2k+2+2k+4
6k+6
so setting the inequality
102<6k+6<116
subtracting 6 from all sides
96<6k<110
16<k<18.3333
since k is an integer
the only integers between 16 and 18.3
are 17 and 18
so
when k=17
2(17),2(17+1),2(17+2)
34,36,38
when k=18
2(18),2(18+1),2(18+2)
36,38,40
so to check are soultion we substitute
34+36+38=108 which is between 102 and 116
36+38+40=114 which is between 102 and 116
so our soultion is correct
the final answer will be
{{36,38,40},{38,40,42}}
Tyler is playing a game in which he needs to guess an integer. Which of the following is a number that tyler can gues
Answers
Crystal is having a painting party with her friends. Each friend will need two canvases. The equation to find the total number of canvases Crystal needs is c=2f , where c is the number of canvases and f is the number of friends. Which variable is the independent variable? A. c B. f C. There is no relationship between the variables.
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Suppose you are a small business owner. How would a market demand schedule or a market demand curve be useful?
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5/2(6x-7)+ 4/3(2+9x)
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6
=15x - 35/2 + 8/3 + 12x
= 27x - 105/6 + 16/6
= 27x - 89/6
If there is a positive correlation between salary and education, then based on the table shown, which of the following careers requires the most education? a. accountant b. paralegal c. photographer d. surveyor
Answers
Answer:
Option a. accountant.
Step-by-step explanation:
We have been given the positive correlation graph between salary and education
Positive correlation means a linear relationship between two that means if education increases salary increases.
We need to tell which among the given options requires most education the one which will have highest salary.
That means the Accountant among the given option requires most education.
Because he has highest salary among given four options.
What is the simplified form of the left side of the following equation?
2x-4+5x=8
Select the correct answer below.
A.2x+1
B.3x-4
C.5x-2
D.7x-4
Answers
The term 2x and the term 5x are like terms and can be combined into 7x.
The answer is 7x - 4
Find the distance between 0,3 and -2-5 round nearest hundreth
Answers
The formula for distance will be the √ (x2-x1)²+(y2-y1)². (as you can see)
Don't be intimidated!
Step one:
Take the two cordinates (0,3) and (-2,-5)
Step two: It doesn't matter which one you choose, but choose one to be your x1,y1 and another to be your x2,y2
In this situation I choose (0,3) to represent (x1,y1) and (-2,-5) to represent (x2,y2). DO NOT over think this, you got it!
Final Step:
Simply plug those numbers into the represented formula it should end up like
√(-2-0)²+(-5-3)²
Simply solve it yourself or use a calculator such as Desmos to find you answer
Hope this helps!
a²+b²=c², where a and b are the length of the legs of the triangle, and c is the length of its hypotenuse.
What does that have to do with finding the distance between two points? For that, I want you to take a look at the two images I've attached to this post. If we just plot the two points on the x-y plane and draw a line between them, the connection to Pythagoras isn't too obvious, but when we connect the x and y components of the points, it should become immediately clear. The vertical and horizontal components of the points combine with the diagonal to form a right triangle, and the distance is the length of its hypotenuse!
We can't apply the theorem yet, though; we'll first need to find the lengths of the legs before we can determine the length of the hypotenuse. For that, we'll need to find the distance between each of the points' corresponding coordinates. To find those, we just need to subtract those coordinates from one another. We find the distance between the x coordinates to be 0 - (-2) = 2 and the distance between the y coordinates to be 3 - (-5) = 8.
(Note that we could've chosen to do the subtraction the other way around, too, obtaining negative differences. Usually, we'd deal with these by taking the absolute value of the result, but in this case, our answers will get squared away - literally - by the Pythagorean Theorem.)
Now that we have the legs of the triangle, we're ready to find the hypotenuse. We enter our values in:
2²+8² = d²
4 + 64 = d²
68 = d²
√68 = d
(we've chosen d here to represent "distance," though it plays the same role c did in the other statement of the theorem)
And from there, you can use the calculator of your choosing to get a good approximation.
One last note: here's a generalization of everything we did here, now that you have some background for why it is the way it is, and where exactly it comes from:
For any two points [tex](x_1,y_1), (x_2,y_2)[/tex]:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
What is the value of the expression 54.36 divided by 0.1
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what is the expressions equivalent to 50+30
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The cartesian coordinates of a point in the xy-plane are (x, y) = (-3.84, -2.87) m. find the polar coordinates of this point.
Answers
First, use the Pyth. Thm. to determine the length of the ray from the origin to this point: (-3.84)^2 + (-2.87)^2 = L^2; L = sqrt (22.98), or approx. 4.79. The angle is 0.64 radian + pi radians, or 3.78 radians (which, as you can verify, is in QIII.
Thus, the point (-3.84, -2.87) becomes (4.79, 3.78 rad) in polar coordinates.
Let me know if you need help with the trigonometry involved here.
Which mathematical expression is equivalent to the expression "nine less than six times the number t"?
Question 5 options:
A. 6 - 9t
B. 6t - 9
C. 9 - 6t
D. 9t - 6
Answers
The Expression is 6t - 9.
What is Equations?An equation is a mathematical statement that connects two expressions of equal value by using the "equal to" symbol.
A mathematical statement with two algebraic expressions on either side of an "equal to (=)" sign is called an equation. It demonstrates the equality of the relationship between the expression written on the left and right sides.
Given Expression "nine less than six times the number t"
which means number 9 should less than product of 6 and t
six times the number t implies the product of t and 6 which is equal to
6t,
and subtract 9 from 6t we get
6t - 9
Hence the expression "nine less than six times the number t" is 6t - 9.
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Marcos is organizing a fundraiser for his youth group. He spent $38.00 on paper products, $187.00 on food, and $40.00 on decorations. If his budget was $280.00, how much money does Marcos have left?
$15.00
$25.00
$115.00
$125.00
Answers
Answer:
15$
These are simple algerbra problems.
Suppose that you invest $5873 in an account that earns interest at an APR of 4.4%, compounded monthly. Determine the accumulated balance after 7 years.
Answers
P = $5873, the principal
r = 4.4% = 0.044, the interest rate
n = 12, twelve monthly compoundings in a year
t = 7 years
Note that
n*t = 12*7 = 84
r/n = 0.044/12 = 0.003667
The accumulated balance after 7 years is
A = 5873*(1 + 0.003667)⁸⁴ = $7,986.90
Answer: $7,986.90
which has the greater volume: a 4 meter cube or a rectangular solid that that is 8 meters long, 2 meters wide and 2 meters high
Answers
Answer:
The cube has the greater volume.
Step-by-step explanation:
The volume of a cube is given as:
[tex]V=x^3[/tex]
Where [tex]x[/tex] is the measure of 1 side (all sides of a cube are same)
The volume of a rectangular solid is given as:
[tex]V=l*w*h[/tex]
Where [tex]l[/tex] is the length, [tex]w[/tex] is the width, and [tex]h[/tex] is the height.
From the problem,
Volume of cube = [tex](4)^{3}=64[/tex] [since each side is given as 4]Volume of rectangular solid = [tex]8*2*2=32[/tex] [the length is given as 8, width is 2, and height is 2]The cube has the greater volume.
Marcus rented a movie for $4 and some video games for $6 each. He paid $22. How many games did he rent?Choose two answers: one for the equation that models this situation and one for the correct answer.
A.Equation: 6 + 4x = 22
B.Answer: 3 video games
C.Answer: 4 video games
D.Equation: 4 + 6x = 22
Answers
4 + 6x = 22
This is so because he only bought one movie, but he bought "some" video games. The variable x represents some in the problem.
Solve the equation.
4 + 6x = 22
Subtract 4 from both sides of the equation.
6x = 18
Divide both sides by 6.
x = 3
Marcus rented 3 video games.
Solution :
D. 4 + 6x = 22
B. 3 video games
Answer:
4 + 6x = 22 and 3 video games
Step-by-step explanation:
ape-x
How do I write 18,801,310 in expanded form using exponents
Answers
the answer is
18,801,310 = (1 x 10^9) + (8 x 10^8) + (0 x 10^7) + (8 x 10^6) + (0 x 10^5) + (1 x 10^4) + (0 x 10^3) + (3 x 10^2) + (1 x 10^1) + (0 x 10^0)
Expanded form of a certain number involves writing out the place Number value of each digit in the number. The expanded Form of 18,801,310 is [tex] (1 \times {10}^{7} ) + (8 \times {10}^{6} ) + (8 \times {10}^{5} ) + (0 \times {10}^{4} ) + (1 \times {10}^{3} ) + (3 \times {10}^{2} ) + (1 \times {10}^{1} ) + (0 \times {10}^{0} ) [/tex]
[tex]1 = 10 \: million \: place \: = 1 \times 10000000 = 1 \times {10}^{7} [/tex][tex]8 \: = 1 \: million \: place \: = 8 \times 1000000 = 8 \times {10}^{6} [/tex][tex]8 = 100 \: thousand \: place \: = 8 \times 100000 = 8 \times {10}^{5} [/tex][tex]0 = 10 \: thousand \: place \: = 0 \times 10000 = 1 \times {10}^{4} [/tex][tex]1 = 1 \: thousand \: place \: = 1 \times 1000 = 1 \times {10}^{3} [/tex][tex]3 = 1 \: hundred \: place \: = 1 \times 100 = 1 \times {10}^{2} [/tex][tex]1 = 10s \: place \: = 1 \times 10 \: = 1 \times {10}^{1} [/tex][tex]0 = 0 \times {10}^{0} [/tex]Hence,
[tex]18,801,310 = (1 \times {10}^{7} ) + (8 \times {10}^{6} ) + (8 \times {10}^{5} ) + (0 \times {10}^{4} ) + (1 \times {10}^{3} ) + (3 \times {10}^{2} ) + (1 \times {10}^{1} ) + (0 \times {10}^{0} )[/tex]
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A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"
Let c represent the number of children.
Which expression represents the number of parents?
c−9
9−c
c⋅9
c + 9
Answers
Answer: c-9
Step-by-step explanation: i did the quiz
courtlynn combines 7/8 cup sour cream with 1/2 cup cream cheese. she then divides the mixture between two bowls. how much mixture does courtlynn put in each bowl?