Two fire-lookout stations are 14 miles apart, with station B directly east of station A. Both stations spot a fire. The bearing of the fire from station A is Upper N 35 degrees E and the bearing of the fire from station B is N 30 degrees W. How far, to the nearest tenth of a mile, is the fire from each lookout station?
The fire is a distance of 9.33 miles from Station A and 4.67 miles from Station B.
Let's denote the distance of the fire from station A as "x" and the distance of the fire from station B as "y".
From station A, the bearing of the fire is N 35° E. This means that if we draw a line connecting station A and the fire, the angle between this line and the north direction is 35°.
Similarly, from station B, the bearing of the fire is N 30° W. This means that the angle between the line connecting station B and the fire and the north direction is 30°.
Now, let's construct a triangle with vertices at Station A, station B, and the fire. The line connecting station A and station B represents the base of the triangle, and the lines connecting station A and the fire and station B and the fire represent the two sides of the triangle.
Since the triangle is isosceles (both sides are equal), the angles opposite the two sides will also be equal.
Let's denote the angle opposite side x as α and the angle opposite side y as β.
From the given bearings, we can determine the values of α and β:
α = 180° - 35° = 145°
β = 180° - 30° = 150°
Now, using the Law of Sines, we can set up the following ratios:
sin(α) / x = sin(β) / y
Solving for y, we get:
y = (sin(β) / sin(α)) * x
Substituting the known values, we have:
y = (sin(150°) / sin(145°)) * x
Using a calculator, we can evaluate the sin(150°) and sin(145°) to get:
y = (0.5 / 0.996) * x
y = 0.501 * x
Since the two stations are 14 miles apart, we know that x + y = 14.
Substituting the value of y from the previous equation, we have:
x + 0.501 * x = 14
1.501 * x = 14
x = 14 / 1.501
x ≈ 9.33
Now, to find the value of y, we can substitute the value of x into the equation:
y = 0.501 * x
y = 0.501 * 9.33
y ≈ 4.67
Therefore, the fire is 9.33 miles from Station A and 4.67 miles from Station B.
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The fire is approximately 38.7 miles away from station A and 38.4 miles away from station B.
To solve this problem, we can use trigonometry and create a diagram to visualize the situation.
Now, let's label the diagram. We'll use the following labels:
A: Fire-lookout station A
B: Fire-lookout station B
F: Fire's location
Next, we need to determine the angles and distances involved. From the problem statement, we know the bearing of the fire from station A is N 35° E, and the bearing of the fire from station B is N 30° W. Let's mark these angles on the diagram.
To find the distance of the fire from each station, we can consider the angles formed between the stations and the fire. The sum of these angles should be 180° since we have a straight line. Let's find the missing angles by subtracting the given angles from 180°.
For station A:
Angle A = 180° - 35° = 145°
For station B:
Angle B = 180° - 30° = 150°
Now, let's draw lines from each station to the fire, and label the distances as dA and dB.
We can use trigonometry (specifically, the tangent function) to find the distances dA and dB. Tangent of an angle is equal to the opposite side divided by the adjacent side.
For station A:
tan(145°) = opposite side (dA) / adjacent side (14 miles)
dA = 14 * tan(145°)
For station B:
tan(150°) = opposite side (dB) / adjacent side (14 miles)
dB = 14 * tan(150°)
Now, let's calculate these distances using a calculator.
dA = 14 * tan(145°) ≈ 38.7 miles
dB = 14 * tan(150°) ≈ 38.4 miles
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A grain silo has the dimensions shown. (height of 60, diameter of 20). The top of the silo is a hemispherical shape. Find the volume of the grain silo.
Answer:
[tex]20943.96 ft^3[/tex]
Step-by-step explanation:
The silo is shaped as a cylinder with a hemisphere on top of it.
We need to find the volume of the shape.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius
h = height
The volume of a hemisphere is given as:
[tex]V = \frac{2}{3} \pi r^3[/tex]
where r = radius
Therefore, the joint volume of both shapes is:
[tex]V = \pi r^2h + \frac{2}{3} \pi r^3[/tex]
The height of the silo is 60 and the diameter is 20.
This means that the radius is 10.
The cylindrical part of the silo and the hemispherical part have the same radius, 10.
The volume of the silo is:
[tex]V = \pi * 10^2 * 60 + \frac{2}{3} * \pi * 10^3\\ \\V = 18849.56 + 2094.40\\\\V = 20943.96 ft^3[/tex]
The volume of the silo is [tex]20943.96 ft^3[/tex]
An art teacher buys 9 bags of cotton balls. There are 68 cotton balls in each bag.
Which expression is best to estimate the number of cotton balls the teacher
buys?
9+70
9*60
9*70
9+60
Answer:
9*70
Step-by-step explanation:
It is not 9+70 or 9+60 because for this problem multiplication is required.
This problem seems to want you to round to the nearest ten's place. Because the one's place in 68 is above 5, the number will round up.
This means that the answer will be 9*70
Answer:
9*70
Step-by-step explanation:
AB
Round your answer to the nearest hundredth.
B
5
?
40°
Answer:
y
Step-by-step explanation:
y\
Answer: 6.53 on khan academy
Step-by-step explanation:
Which equation are correct set ups to solve for the hypotenuse ** 2 answers
(Solve and Round decimal to the nearest hundredths )
Answer:x^2=2^2+4^2. x=4.47
Step-by-step explanation:
Opposite=m=2
Adjacent=n=4
Hypotenuse=x
x^2=m^2+n^2
x^2=2^2+4^2
x^2=4+16
x^2=20
x=√20
x=4.47
There are 197 oak trees in the park. There are 27 more pine trees than oak trees in the park how many trees are there in all
just add.................
197 + 27 = 224
hope this helps
13 POINTS!!!
In ΔJKL, j = 74 inches, k = 14 inches and l=67 inches. Find the measure of ∠L to the nearest degree.
Answer:
55°
Step-by-step explanation:
Using cosine law
67² = 74² + 14² - 2(74)(14)cos(L)
cos(L) = 169/396
L =55.18378419
The measure of angle L to the nearest degree is 55°.
What is Law of Cosines?Law of cosines of triangle states that for three length of sides of the triangle, a, b and c opposite to the angles A, B and C respectively can be related as,
a² = b² + c² - 2bc cos(A)
Given, for a triangle JKL,
j = 74 inches, k = 14 inches and l = 67 inches.
We can use law of cosines to find the measure of angle L.
Using the law of cosines,
l² = j² + k² - 2jk cos(L)
67² = 74² + 14² - (2×74×14) cos(L)
4489 = 5476 + 196 - 2072 cos(L)
4489 = 5672 - 2072 cos(L)
-1183 = - 2072 cos(L)
cos (L) = 0.5709
L = 55.18° ≈ 55°
Hence the measure of angle L is 55°.
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caroline works 8 hours a day 5 days a week she earns £440 each week
how much does she earn per hour ?
Answer:
She earns £11 per hour
Step-by-step explanation:
You divide £440 with 5 days of the week and then you get how much she earns in a day. And then you devide with 8 and u get £11.
Caroline will earn £11 for working per hour.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that caroline works 8 hours a day 5 days a week she earns £440 each week.
The earnings for an hour will be calculated as,
Total hours = 8 x 5 = 40 hours
Earning per hour = £440 / 40
Earning per hour = £11
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A cone is cut by a plane parallel to its base. The small cone on top is similar to the large cone, with a similarity ratio of 1 : 2. The ratio between the volume of the small cone to that of the frustum is _ : _.
Answer:
1:1Step-by-step explanation:
The ratio between the volume of the small cone to that of the frustum is 1:1.
Notice that the bigger cone is double than the smaller cone, which means the smaller cone is half of the volume of the bigger cone, if you wipe the small one, you would have the frustum with the same volume as the wiped part, because if you delete the smaller cone, you would be deleting half volume of the bigger cone, giving at the end a relation 1 : 1 between the frustum and the smaller cone.
Please hurry!
Which of the following is true of the values of x and y in the diagram below?
A. y < x
B. y > x
C. y + x = 1
D. y/x = 1
Answer:
y/x = 1
Step-by-step explanation:
sin 45 = cos 45 = y /1 = x/1
so y = x
or y/x =1
What is it that when you take away the whole, you still have some left over?
Answer:
wholesome!!! brainliest pls :)
Answer:
wholesome
Step-by-step explanation:
you take away the first word which is whole
and u still have the word some left over
hope this helped if this isnt what ur looking for plz tell me
why is tesla stock increasing/decreasing in value
Answer:
elon musk
Step-by-step explanation:
elon sends out random, uncalled for tweets, which mess with the stock value.
For example, when the stock was very high, he tweeted,"Tesla stock too high"
At a camp, kids can choose swimming, art, or music.
40 kids choose swimming, 16 choose art, and 24 choose music.
What is the ratio of kids who choose art to kids who choose swimming?
Answer:
3:5
Step-by-step explanation:
all figures can be divided by 8, so
swimming- 40/8= 5
arts 16/8= 2
music 24/8= 3
therefore, the ratio would be 3:5
Answer:
3/5
Step-by-step explanation:
I took it but got it wrong so i did the math problem and got this 3/5
Please Help it’s urgent
Answer:
<LKH and <JKM
Step-by-step explanation:
<LKH and <JKM are vertical angles because they are vertically opposite.
Ming would like to buy a plane ticket so she can visit her family this Thanksgiving, which is November 26. She has found that tickets for flights on days closer to Thanksgiving are more expensive than flights on days further away from Thanksgiving. A calendar from an airline company showing ticket prices by day is below.
Answer:
$165
Step-by-step explanation:
Answer:
156$
Step-by-step explanation:
Grace hit 12 balls in the batting cage out of 20 pitches. Tomorrow she is going to go to the same batting cage and get 30 pitches.
Use experimental probability to predict how many of the 30 pitches she will hit.
Answer:
she is expected to hit 18 out of the 30 pitches
Step-by-step explanation:
In this question, we are required to use experimental probability to make a prediction.
From the hits she has today, we can estimate the number of hits she might be getting tomorrow.
Since she made 12 hits out of 20 today, the probability that she has a hit will be 12/20 = 3/5
Now if she is having 30 pitches tomorrow, the expected number of hits would be the probability of getting a hit multiplied by the total number of pitches.
That would be 3/5 * 30 = 18 pitches
Find the area of the triangle. Pls help!
Answer:
84 mm^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 b *h
The base is 14 and the height is 12
A = 1/2 (14*12)
A = 84 mm ^2
Area of a triangle formula: A = 1/2bh
Solve using the values given in the picture.
A = 1/2(14)(12)
A = 1/2(168)
A = 84
Therefore, the volume of the triangle is 84mm²
Best of Luck!
Question 11 point(s) Jared made Ask Your Teacher cups of snack mix for a party. His guests ate Ask Your Teacher of the mix. How much snack mix did his guests eat?
Answer:
[tex]8\frac{1}{2}[/tex] cups
Step-by-step explanation:
To determine the quantity of snack mix Jared guest ate, we multiply the quantity of snack mix the guest ate by the quantity of snack mix Jared made. i.e we determine [tex]\frac{2}{3}of12\frac{3}{4}[/tex] by multiplying both fractions together
quantity of snack mix Jared guest ate = [tex]\frac{2}{3}of12\frac{3}{4}=\frac{2}{3}*12\frac{3}{4}=\frac{2}{3}*\frac{51}{4}=\frac{17}{2} =8\frac{1}{2}[/tex]
Rebecca earns $6.25 per hour working after school. She needs at least $125.00 if she wants to buy a new bicycle. Which inequality shows the solution to how many hours Rebecca must work to earn the money for the bicycle? Let h equal the number of hours Rebecca must work.
Answer: the answer is in the steps.
Step-by-step explanation:
6.25h ≤ 125.00
Train A has a speed 20 miles per hour greater than that of train B. If train A travels 270 miles in the same times train B travels 210 miles, what are the speeds of the two trains?
Answer:
speed of train A = 70 + 20 = 90 miles per hour
speed of train B = 70 miles per hour
Step-by-step explanation:
Let
speed of train B = a
speed of train A = a + 20
Recall
speed = distance/time
The travel time is same for both train. Therefore, let us make time subject of the formula in the speed equation.
Time = distance/speed
270/a + 20 = 210/a
cross multiply
270a = 210(a + 20)
270a = 210a + 4200
270a - 210a = 4200
60a = 4200
divide both sides by 60
a = 4200/60
a = 70
speed of train A = 70 + 20 = 90 miles per hour
speed of train B = 70 miles per hour
A submarine travels 19 miles in 1/2 hour. Write an equation to find out how long it would take the submarine to travel 57 miles at the same rate. Then find the time.
Answer:
1.5 hours
Step-by-step explanation:
We can write a ratio to solve
19 miles 57 miles
-------------- = --------------
.5 hours x hours
Using cross products
19x = 57*.5
19x =28.5
Divide each side by 19
19x/19 = 28.5/19
x =1.5
1.5 hours
I put the wrong answer don’t mind me
A pond is initially stocked with 1000 catfish, and the fish population is then sampled each month to estimate its size. It is determined to be increasing at a rate of 1.5% each month. What is the projected population after one year?Which function represents exponential decay?
Answer:
A year is 12 months long. 1.5 percent each month would total 18 percent in a year. 18 percent of 1000 is 180. The final number of fish is 1180
Step-by-step explanation:
The inside of a refrigerator in a medical laboratory measures 17 inches long by 18 inches wide by 42 inches high. How many cubic inches can it hold?
Answer:
12,852
Step-by-step explanation:
V= l*w*h
V=17*18*42
V= 12,852
Which of the figures is not a net for a cube? Explain.
Find the quotient.
3 divided by 3636
A. 1,212
B. 1,202
C. 122
D. 112
E. 102
help asap!!
You roll two six-sided dice. What is the probability that the sum is odd or a multiple of 5? Round your answer to the nearest tenth of a percent.
Answer:
The probability that the sum is odd or a multiple of 5
P(E₁∪E₂) = 0.58 = 58%
Step-by-step explanation:
Step ( i ) :-
Given the two dice are thrown ,The total number of exhaustive cases
n(S) = 6² = 36
Let 'E₁' be the event of getting the sum is odd on two dice
E₁ = { (1,2)(1,4),(1,6),(2,1),(2,3),(2,5),(3,2)(3,4),(3,6),(4,1)(4,3),(4,5),(5,2),(5,4),(5,6),(6,1),(6,3),(6,5)}
n(E₁) = 18
Let 'E₂' be the event of getting the sum is multiple of 5 on two dice
E₂ = { (1,4),(2,3), (3,2),(4,1),(4,6),(5,5),(6,4)}
n(E₂) = 7
n(E₁∩E₂) = {(1,4),(2,3),(3,2),(4,1)} = 4
Step(ii):-
The probability that the event of getting the sum is odd on two dice
[tex]P(E_{1}) = \frac{n(E)}{n(S)} = \frac{18}{36}[/tex]
The probability that the event of getting the sum is multiple of '5' on two dice
[tex]P(E_{2}) = \frac{n(E_{2} )}{n(S)} = \frac{7}{36}[/tex]
The probability that the event of getting the sum is odd and multiple of '5' on two dice
[tex]P(E_{1} n E_{2}) = \frac{n(E_{1} n E_{2} )}{n(S)} = \frac{4}{36}[/tex]
The probability that the sum is odd or a multiple of 5
P(E₁∪E₂) = P(E₁) + p(E₂) - P(E₁ ∩ E₂)
= [tex]\frac{18}{36} + \frac{7}{36} - \frac{4}{36}[/tex]
[tex]\frac{18+7}{36} - \frac{4}{36} = \frac{25-4}{36} = \frac{21}{36}[/tex]
P(E₁∪E₂) = 0.58 = 58%
Final answer:-
The probability that the sum is odd or a multiple of 5
P(E₁∪E₂) = 0.58 = 58%
The probability that the sum is odd or a multiple of 5 is 56 %.
Probability :When two dice are rolled, then
Total number of outcomes is [tex]=6^{2}=36[/tex]
Outcomes for the sum is odd or a multiple of 5 ,
[tex](1,2),(2,1),(2,3),(3,2),(1,4),(4,1),(1,6),(6,1),(2,5),(5,2),(3,4)\\\\(4,3),(3,6),(6,3),(4,5),(5,4),(6,5),(5,6),(4,6),(6,4)[/tex]
Number of favourable outcomes are [tex]=20[/tex]
the probability that the sum is odd or a multiple of 5 is,
[tex]P(E)=\frac{20}{36} =0.56[/tex]
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The Duquesne Incline in Pittsburgh, Pennsylvania, has an angle of elevation of 30º. The track has a length of about 800 feet. Find the height of the incline.
The height of the Duquesne Incline in Pittsburgh, Pennsylvania, is approximately 400 feet.
To find the height of the incline, we can use trigonometry, specifically the sine function.
Let's consider the triangle formed by the incline track, where:
The angle of elevation (angle between the incline track and the ground) is 30 degrees.
The length of the incline track (base of the triangle) is about 800 feet.
We want to find the height of the incline (the side of the triangle opposite the 30-degree angle).
Using the sine function, we have:
[tex]sin(angle) = opposite\ side / hypotenuse[/tex]
In this case, the angle is 30 degrees, the opposite side is the height (h) of the incline, and the hypotenuse is the length of the incline track (800 feet).
So, the equation becomes:
[tex]sin(30^o) = h / 800[/tex]
h = 800 * 0.5
h = 400 feet
Therefore, the height of the incline is approximately 400 feet.
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The perimeter of quadrilateral ABCD is 640. The perimeter of quadrilateral LMNO is 144. What is LM
Answer:
LM = 36
Step-by-step explanation:
A quadrilateral is a shape with 4sides. There are different type of quadrilateral such as square, rectangle, trapezium, parallelogram, kite and rhombus.
Perimeter of a quadrilateral is the addition of all 4 sides.
Since the shape is not specified neither is there a diagram, let's assume the quadrilateral is a square.
See attachment for diagram used in solving the question.
Perimeter of square = length+ length+ length+ length
= 4× length
Perimeter of quadrilateral ABCD:
640 = 4×length
Length = 640/4
Length = 160
Perimeter of quadrilateral LMNO:
144 = addition of all 4 lengths
144 = LM + MN + NO +OL
Since we are considering a square all the sides are equal.
LM = MN = NO = OL
144 = 4×LM
LM = 144/4
LM = 36
okay who can tell me pi divided by 5.6 squared times 2
Answer:
0.20035667433
Step-by-step explanation:
Answer:
0.20035667433 , is the answer.
Step-by-step explanation:
Honestly whenever it comes to pi in maths , you can usually always use a calculator so on a calculator write in 'pi (5.6) *squared* x 2'
What is the slope of the line shown below?
Answer:
2
Step-by-step explanation:
Slope is often called rise/run.
This is the amount the line goes upwards, rise, compared to the amount it goes sideways, run.
Compare the two shown points. From the left point the the right, the rise is 6, while the run is 3, creating the rise/run of 6/3. This is simplified to 2.
Answer:
C
Step-by-step explanation:
