A yacht is sailed from A to B on a bearing of 196ºT. To sail from B directly back to A the true bearing would be:
Answers
Let’s express that problem into a diagram for visualisation purposes. In this case, finding the true bearing directly back to point A is denoted by theta.
How can we find theta. Well notice that we can create a right angle triangle. We know that the sum of the angles inside the triangles add up to 180 degrees. Since the triangle we created is a right angled one, we know one of the angles is 90 degrees for sure. So we only need one more angle to go and do some algebra to find theta.
Now we know that the boat sailed on a true bearing of 196 degrees. Let’s split that so that we can create a supplementary angle with x. Since one quarter is 90, that means the other remaining angle will be 106 degrees:
X + 106 = 180 (supplementary)
X = 74
There’s our second angle. Now let’s solve for theta.
180 = 74 + 90 + θ (angle sum in triangle)
180 = 164 + θ
180 - 164 = 180 - 164 + θ (isolate θ by subtracting 164 from both sides; since we do it to both sides, it does not imbalance the equation)
θ = 16
If yacht is sailed from A to B on a bearing of 196ºT, the true bearing to sail directly back to point A from point B is 16° T.
To determine the true bearing from point B back to point A, we need to consider the relationship between true bearings and the reciprocal direction.
Given that the yacht is sailed from point A to point B on a bearing of 196° T (True), the reciprocal direction would be the opposite direction, 180° away on the compass.
Thus, to sail directly back to point A from point B, we would need to subtract 180° from the reciprocal direction.
Reciprocal direction - 180°
Therefore, the true bearing from point B back to point A would be:
196° T - 180° = 16° T
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Related Questions
a radioactive substance decays exponentially. a scientist begins with 180 milligrams of a radioactive substance. after 33 hours, 90 mg of the substance remains. how many milligrams will remain after 43 hours?
Answers
The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Now,
Given that 180 mg is present at t = 0 hours.
After t = 33 hours, substance left = 90mg
By unitary method, after = 1 hour, substance left = [tex]180-\frac{90}{33}=180 -\frac{30}{11}[/tex]mg
The substance left after t = 43 hours = [tex]180 - \frac{30\times43}{11}= 180 - \frac{1290}{11}=180 - 117=62.7273mg[/tex]
Hence, The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.
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each side of the base of a right octagonal prism is 7 in. long. the altitude of the prism measures 12 in. find the lateral area.
Answers
The lateral area of right octagonal prism = 672 in^2.
Which octagonal prism is appropriate?An example of a prismatic uniform polyhedron is the octagonal prism, or op. There are 2 octagons as well as 8 squares in it. Each vertex connects two squares and one octagon. As the name implies, it is an octagonal-based prism.
Describe a 3D figure.Three-dimensional geometry is a solid figure, item, or shape comprising three dimensions—length, breadth, as well as height.. Three-dimensional structures have height, which is equivalent to thickness or depth, unlike two-dimensional shapes.
According to the given data:Solve for lateral surface area:
altitude = 12
base = 7
AL=8ah
Putting the value we get:
AL=8 * 12 * 7
Al = 672 in^2
the lateral area of right octagonal prism = 672 in^2.
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When 1 gallon of gas has been used, the car has traveled miles.
Answers
Answer:
25 miles per gallon
Step-by-step explanation:
Because if 2 gallons is 50 miles then one gallon has to be 25 miles per gallon
Ysau paints the back of an airplane hangar that is in the shape of a semicircle on top of a rectangle. Determine the approximate area that Ysau paints. I 24 ft 12 ft
Answers
Answer:
Step-by-step explanation:
Based on the dimensions of the semicircle and the rectangle, the approximate area that Ysau paints is 514 ft²
What area did Ysau paint?First, find the area of the rectangle:
= 24 x 12
= 288 ft²
The area of the semi-circle is the area of a circle divided by two. The radius is half of the longer side of the rectangle:
= 24 / 2
= 12 ft
Area of the semicircle is:
= (22/7 x 12 x 12) / 2
= 226 ft²
The total approximate area is:
= 226 + 288
= 514 ft²
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Help please I will give brainliest
Answers
Answer:
For sure, A and C. However, I cannot fully read the last one.
Step-by-step explanation:
Be sure to mark me Brainliest!
Marco earns a commission rate of 6% for
the first $6,500 ins sales and 9% on sales
over $6,500. Find the total graduated
commission on sales of $10,500.
Answers
Total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.
As given in the question,
Macro earns commission rate of 6% for the first $6500
And 9% on sales over $6500
Out of $10,500
For first $6500 Commission =(6500 × 6)/ 100
= $390
For $ (10,500 - 6,500 = 4000) commission = (4000 × 9)/ 100
= $360
Total graduated commission on sales of $10,500 = $( 390 + 360)
= $750
Therefore, total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.
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According to government tests, a late model hybrid car gets 45 miles per gallon of gas. If gasoline sells
at $3.20 per gallon, how many miles will the car travel on $20.00 of gas?
Answers
The car will travel 900 miles on $20.00 of gas.
PLS HELP ASAP!!!! WILL GIVE BRAINIEST!!!!!! 100 POINTS!!!!!
SEE ATTACHED PIC
Answers
Answer:
y-coordinate
Step-by-step explanation:
x-intercepts lie on the x-axis. On the x-axis, y=0 while the x value is changing.
Answer: Set the Y equal to zero and solve for x
Step-by-step explanation:
A jug contains 3/4 pints of orange juice. After you pour 5/8 of a pint into a glass, how much is left in the jug?
Answers
Answer:
1/8
Step-by-step explanation:
7:40pm------What is 89 minutes more? (What time will it be?)
Answers
The current time is 08 : 09 pm
How to determine the current time?The given parameters are
Time = 7 : 40 pm
Minutes added = 89 minutes
The current time is calculated as
Current time = Time + Minutes added
So, we have
Current time = 7 : 40 pm + 89 minutes
Evaluate the sum
Current time = 7 : 129 pm
Rewrite properly as
Current time = 08 : 09 pm
Hence, the current time is 08 : 09 pm
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Ava and Wyatt are reading the same book. At the beginning of the month, Ava was on
page 10 and Wyatt was on page 30. Ava will read 20 pages per day and Wyatt will
read 15 pages per day. Let A represent the page of the book that Ava is on at the end
of t days into the month, and let W represent the page of the book that Wyatt is on at
the end of t days into the month. Graph each function and determine after how many
days, t, Ava and Wyatt will be on the same page of the book.
Answers
Ava and Wyatt will take 4 days to be on the same page of the book.
X-values must be chosen and entered into the equation in order to graph a function. You will obtain a y-value once those values have been entered into the equation. A single point's coordinates are made up of its x and y values.
From the given question we can get:
A = 10 ₊ 20t
W = 30 ₊ 15t
Graph the each function to get the number of days.
A function can only be graphed if X-values are selected and put into the equation. Once those values are introduced into the equation, a y-value will be produced. The values of x and y are the coordinates of a single point.
Hence we get the number of days as 4. and the graph is attached below.
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You play a game on your phone. For every correct move you make, you receive 50 points. For every second that it takes you to complete the game, you lose 3 points. You complete the game in 2 minutes 24 seconds using 35 correct moves. What is your score?
Answers
You get 1750 points from the 35 correct moves (35 x 50) and you get -432 points from time taken (144 x -3) therefore you end the game with 1318 points.
1318 Points.
The vertices of ABCDE are A(-6, 0), B(-3, 0), C(0, -3), D(-3, -6), and E(-6, -3). Find the vertices
of the image after a translation using the rule (x,y) → (x + 9, y - 6) and a dilation with a scale
factor of 1/3 centered at the origin.
Answers
The coordinates of the image of the vertices of the polygon are A''(x, y) = (1, - 2), B''(x, y) = (2, - 2), C''(x, y) = (0, - 1), D''(x, y) = (- 1, - 2) and E''(x, y) = (- 2, - 1).
What are the images of the vertices of a polygon by using rigid transformations?
Rigid transformations are transformations applied on geometric loci such that Euclidean distances in such constructions are conserved. Translations and dilations are common examples of rigid transformations.
If we know that A(x, y) = (- 6, 0), B(x, y) = (- 3, 0), C(x, y) = (0, - 3), D(x, y) = (- 3, - 6) and E(x, y) = (- 6, - 3), then the coordinates of the image are determined below:
Translation
A'(x, y) = (- 6, 0) + (9, - 6)
A'(x, y) = (3, - 6)
B'(x, y) = (- 3, 0) + (9, - 6)
B'(x, y) = (6, - 6)
C'(x, y) = (0, - 3) + (9, - 6)
C'(x, y) = (9, - 9)
D'(x, y) = (- 3, - 6) + (9, - 6)
D'(x, y) = (6, - 12)
Dilation
A''(x, y) = (1 / 3) · (3, - 6)
A''(x, y) = (1, - 2)
B''(x, y) = (1 / 3) · (6, - 6)
B''(x, y) = (2, - 2)
C''(x, y) = (1 / 3) · (0, - 3)
C''(x, y) = (0, - 1)
D''(x, y) = (1 / 3) · (- 3, - 6)
D''(x, y) = (- 1, - 2)
E''(x, y) = (1 / 3) · (- 6, - 3)
E''(x, y) = (- 2, - 1)
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Find the missing terms in the sequence.
4, 6, 10, 16, 24, 34, __, 60, 76, __, 114
Enter the two missing terms with only a comma between them.
Answers
Answer:
46, 94
Step-by-step explanation:
hope this works for you :)
Pls help I’ll give Brainliest
Answers
Answer: I hope this helps.
Step-by-step explanation:
Help I will Mark A Brainlist !!!! Its A Math Question Find the length of a.
Thank you ao much !!! I hope you have a good day!
Answers
Trust
Answer: a=2√5
Step-by-step explanation:
We have a right-angled isosceles triangle
Hence, a=2√5
Mai-Lin measures her heart rate whenever she exercises and tries to make sure that she is staying in her target heart rate zone. The American Heart Association suggests a target heart rate of T=0.75(220-a), where T is a person's target heart rate and a is his or her age.
b. If Mai-Lin's target heart rate is 153, then how old is she? What property justifies your calculation?
Answers
When Mai-Lin's target heart rate is 153, then her age is 16 years.
How to illustrate the function?From the information, the The American Heart Association suggests a target heart rate of T=0.75(220-a),
where T = person's target heart rate
a = his or her age.
Therefore, when the heart rate is 153, the age will be:
T = 0.75(220 - a)
153 = 165 - 0.75a
0.75a = 165 - 153
0.75a = 12
Divide
a = 12/0.75
a = 16
The person's age is 16 years.
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a basket contains 3 types of fruit. The apples weigh 4/9 kilogram, the oranges weigh 1/6 kilogram, and the pears weigh 5/18 kilogram. What is the total weight of the fruit in this basket?
A) 10/33
B)15/18
C)8/9
Answers
Make all of the denominators common
4/9 x 2 = 8/18
1/6 x 3 = 3/18
5/18
8/18 + 3/18 + 5/18 = 16/18
When you simplify you get 8/9
whatsssss those fromm greatesttt to leassttt
Answers
greatest to smallest : [tex]= \sqrt[3]{88} ,\sqrt{19} ,\frac{28}{9}[/tex]
Fraction: A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator
Square root: In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = 16
Use this fraction calculator for adding, subtracting, multiplying, and dividing fractions. Answers are fractions in the lowest terms or mixed numbers in reduced form.
Input proper or improper fractions, select the math sign, and click Calculate. This is a fraction calculator with steps shown in the solution.
If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator.
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
Solution :
[tex]\sqrt[3]{88} \\\sqrt[3]{2.2.2.11} \\2\sqrt[3]{11} \\\sqrt[3]{11} = 2.224\\2.2.224\\4.448 ...(1)\\\\\\\frac{28}{9} = 3.333 ...(2)\\\\ \sqrt{19} = 4.359 ...(3)\\\\Form 1 , 2 & 3 \\\\greatest number to smallest number = 4.448 , 4.359 ,3.333\\= \sqrt[3]{88} ,\sqrt{19} ,\frac{28}{9}[/tex]
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Figure B is a dilated image of figure A. What is the scale factor?
Answers
Explanation:
the function g is defined as followed
g(x)=2x^2-7
if the graph of g is translated vertically downward by 3 units, it becomes the graph of a
function h
FIND THE EXPRESSION FOR h(x)
(If you know how to answer these questions please help with the next 2 or three I will post afterwards)
Answers
Since the graph of g is translated vertically downward by 3 units, the graph of function h is equal to h(x) = 2x² - 10.
The types of transformation.In Mathematics, there are different types of transformation and these include the following:
ReflectionRotationTranslationDilationWhat is a translation?A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.
Since the graph of g is translated vertically downward by 3 units, the graph of function h would be represented by the following expression:
Note: g(x) = 2x² - 7
h(x) = g(x) - 3.
h(x) = 2x² - 7 - 3.
h(x) = 2x² - 10.
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AB=2x+7,AC=7x-3,BC=4x-2
Answers
The value of x on the line segment is 8
How to determine the value of x?The given parameters are:
AB = 2x + 7
AC = 7x - 3
BC = 4x - 2
The above means that the point B is on the line segment AC
So, we have:
AC = AB + BC
This gives
2x + 7 + 4x - 2 = 7x - 3
Evaluate the like terms
-x = -8
Divide both sides by -1
x = 8
Hence, the value of x on the line segment is 8
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
(14+3)(2
x 6)
Answers
Answer: 204
Step-by-step explanation:
(14+3)(2 x 6)=
(17)(2 x 6)=
(17)(12)=
17*12=
17*(10+2)=
17*10+17*2=
170+34=204
Answer:204
Step-by-step explanation:
Members of a sports club are junior, adult
or senior.
80 of these members were asked whether
they prefer tea, coffee or hot chocolate.
25 members are senior, of which 13
prefer coffee.
10 juniors prefer tea.
There are no adult members who prefer
hot chocolate.
2 out of the 18 juniors prefer coffee.
4 out of the 28 members who prefer tea
are seniors.
What fraction of members in the club
prefer hot chocolate?
Give your answer as a fraction in its
simplest form.
Answers
Fraction of members in the club that prefer hot chocolate = [tex]\frac{7}{40}[/tex]
It's Given that :
A sports club has 80 participants.
Senior Members = 25
Junior Members = 18
Adult Members = 80 - (25 + 18) = 80 - 43 = 37
JUNIOR MEMBERS :
Prefers tea = 10
Prefers Coffee = 2
Prefers hot chocolate = 18 - (10 + 2) = 18 - 12 = 6
SENIOR MEMBERS :
Prefers tea = 4
Prefers coffee = 13
Prefers hot chocolate = 25 - (4 + 13) = 25 - 17 = 8
ADULT MEMBERS :
Prefers tea = 28 - (10 + 4) = 28 - 14 = 14
Prefers coffee = 37 - 14 = 23
Prefers hot chocolate = 0 (none)
Calculation of Fraction of members in the club that prefer hot chocolate = 8 + 6 = 14 members out of 80 members
= [tex]\frac{14}{80} = \frac{7}{40}[/tex]
Therefore 7 / 40 of members prefer hot chocolate.
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Harry tosses a nickel 4 times. The probability that he gets at least as many heads as tails is.
Answers
HHHH, 0 tails and 4 heads
HHHT, 1 tails and 3 heads
HHTH, 1 tails and 3 heads
HHTT, 2 tails and 2 heads
HTHH, 1 tails and 3 heads
HTHT, 2 tails and 2 heads
HTTH, 2 tails and 2 heads
HTTT, 3 tails and 1 heads
THHH, 1 tails and 3 heads
THHT, 2 tails and 2 heads
THTH, 2 tails and 2 heads
THTT, 3 tails and 1 heads
TTHH, 2 tails and 2 heads
TTHT, 3 tails and 1 heads
TTTH, 3 tails and 1 heads
TTTT, 4 tails and 0 heads
Eleven of these outcomes have a head-to-tail ratio of at least one head for every two tails. Therefore, there is an 11/16 chance of getting at least as many heads as tails.
I WILL CHOOSE THE BRAINLIEST!!!!
Answers
the probability that a random selected student walks to the school is 19.5%, the correct option is D.
How to find the probability?We want to find the probability that a random selected student walks to the school.
To find it, we just need to take the quotient between the number of students that walk to the school and the total number of students.
The number of students that walk to the school is:
42 + 36 = 78
The total number of students is:
85 + 77 + 30 + 47 + 42 + 36 + 44 + 39 = 400
Then the probability is:
P = 78/400 = 0.195
To get this in percentage form, we just multiply by 100%.
0.195*100% = 19.5%
The correct option is D.
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proof let a be a square matrix of order n. (a)show that is symmetric. (b)show that is skew-symmetric. (c)prove that a can be written as the sum of a symmetric matrix b and a skew-symmetric matrix c, a
Answers
(a)Symmetric matrix -
Let matrix A be of order 3×3 =
[tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]
So, the transpose of A will be -
A' =
[tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]
So, we can say that A=A'. So, it is symmetric.
(b) Skew - symmetric matrix -
Let us consider a matrix B =
[tex]\left[\begin{array}{ccc}0&-6&4\\-6&0&7\\4&7&0\end{array}\right][/tex]
matrix B is said to be skew-symmetric if aij =−aji.
(B' =−B)
B' =
[tex]\left[\begin{array}{ccc}0&6&-4\\6&0&-7\\-4&-7&0\end{array}\right][/tex]
(c) A + A′ is a symmetric matrix for any square matrix A with real number entries, whereas A - A′ is a skew-symmetric matrix.
Proof: If B = A + A', then B ′ = (A + A ) ′
(A + B)′ = A′ + B′, thus = A′ + (A′)′
(as (A′)′ =A) = A′ + A
= B (because B + A = B + A′)
B = A+A′ is a symmetric matrix as a result.
Let C now equal A-A′.
Why does C' equal (A-A′)′=(A′)′?
= A′ - A (Why?)
=- (A - A′) = - C
A - A′ is a skew-symmetric matrix as a result.
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You took a test last week and the average grade was a 73. The standard deviation was
4.9 points. List the values at one, two, and three standard deviations from the mean
and-one, -two, -3 deviations from the mean.
Edit View Insert Format Tools Table
12pt Paragraph
BIUA
2VT² V
⠀
Answers
Values at one, two and three standard deviations are 77.9, 82.8 and 87.7 respectively. Values at -1, -2 and -3 standard deviations are 68.1, 63.2 and 58.3 respectively.
The average grade given = 73
So, the mean, μ = 73
The standard deviation, σ = 4.9
We need to find the 1,2 and 3 standard deviations and -1, -2 and -3 deviations from the mean.
We use the formula z = μ + nσ to find the values at nth deviations.
When n = 1
z = 73 + 1 x 4.9 = 77.9
When n = 2
z = 73 + 2 x 4.9 = 82.8
When n = 3
z = 73 + 3 x 4.9 = 87.7
When n = -1
z = 73 -1 x 4.9 = 68.1
When n = -2
z = 73 - 2 x 4.9 = 63.2
When n = -3
z = 73 - 3 x 4.9 = 58.3
Hence, these are the required values.
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Which expressions are equal to 8 × 10 5 squared? Select all that apply.
Answers
The expression equal to 8 × 10 5 squared is 64 × 10^10
What is scientific notation?
Scientific notation is a mathematical way of expressing numbers that are too large or small to be written in decimal form.
Given the expression;
(8 × 10^ 5)²
expand the bracket
(8)² × (10)^ 5× 2
Find the squares
64 × 10^10
This is expressed as;
64 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
Thus, the expression equal to 8 × 10 5 squared is 64 × 10^10
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The temperature in California was 105 on Thursday. The temperature in the North Pole was -20. What is the difference between the two temperatures.
Answers
Answer:
125
Step-by-step explanation:
105 - (-20) = 105 + 20 = 125