Given:
In ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°.
To find:
The length of k, to the nearest inch.
Solution:
According to Law of sine,
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
In ΔKLM, using law of sine, we get
[tex]\dfrac{k}{\sin K}=\dfrac{l}{\sin L}[/tex]
[tex]\dfrac{k}{\sin (55^\circ)}=\dfrac{48}{\sin (46^\circ)}[/tex]
[tex]k=\dfrac{48\times \sin (55^\circ)}{\sin (46^\circ)}[/tex]
On further simplification, we get
[tex]k=\dfrac{48\times 0.819152}{0.7193398}[/tex]
[tex]k=\dfrac{39.319296}{0.7193398}[/tex]
[tex]k=54.66025 [/tex]
Approximate the value to the nearest inch.
[tex]k\approx 55 [/tex]
Therefore, the length of k is 55 inch.
The length of k, to the nearest inch is ∠K=55°.
Calculation of the length of K:
Since
In ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°.
Now here we apply law of sine
[tex]a\div sin\A = b\div sin\ B = c\div sin\c \\\\k\div sin \ k = l\div sin\ L\\\\k\div sin\ 55 = 48\div sin\ 66[/tex]
k = 54.66
k = 55 degrees
hence, The length of k, to the nearest inch is ∠K=55°.
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HELP PLEASE!!! Math question
Answer:
(a). [tex]\frac{3}{7}[/tex]
(b). [tex]\frac{4}{13}[/tex]
Step-by-step explanation:
(a). Odds in favor of winning a new T.V. = [tex]\frac{4}{7}[/tex]
Or probability of not winning a new T.V. = [tex]\frac{4}{7}[/tex]
Since, Probability to win a T.V. + Probability of not winning the new T.V. = 1
Probability of winning a new T.V. = 1 - Probability of not winning a new T.V.
= 1 - [tex]\frac{4}{7}[/tex]
= [tex]\frac{7-4}{7}[/tex]
= [tex]\frac{3}{7}[/tex]
(b). Probability of winning the match + probability of not winning the match = 1
[tex]\frac{9}{13}[/tex] + Probability of not winning the match = 1
Probability of not winning the match = 1 - [tex]\frac{9}{13}[/tex]
= [tex]\frac{13-9}{13}[/tex]
= [tex]\frac{4}{13}[/tex]
A group of students organized a car wash to raise money for a local charity. The students charged $5.00 for each car they washed. In 3 hours, they washed 12 cars. At that rate, how much money could they earn from washing cars for eight hours?A grocery store sells a bag of 5 lemons for $2.00. What is the unit cost of each lemon in the bag?
Answer:
$160 0.4/lemon
Step-by-step explanation:
5 per car wash
12 cars in 3 hours
4 cars per hour times 8= 32 cars in 8 hours
32 times 5= 160
5 lemons for 2.00
Unit cost= 0.4 per lemon
PLEASE HELPP IM BEGGING I REALLY NEED HELP HELP HELP HELP HELP HELP HELL ITS 6TH GRADE MATH CMON PLEAE HELPPPP
Answer:
:)))
Step-by-step explanation:
31/50 - .062 - 62%
17/60 - .17 - 17%
2/5 - 0.4 - 20%
6/5 - 1.2 - 120%
11/25 - .44 - 44%
13/2 - 6.5 - 650%
HELP ASAP what's the reason for statement 3, WILL GIVE BRAINLIEST
Answer:
From prove
Step-by-step explanation:
from prove
Explanation
Two angles are called complementary when their measures add to 90 degrees
James and Eric each mix 6 pitchers of lemonade. James makes 26 fluid Ounces of lemonade per pitcher, and Eric makes 32 fluid Ounces of lemonade per pitcher. They combine their lemonade and pour all of it into glasses. They fill as many glasses as possible with 8 fluid Ounces each. They pour the remaining lemonade into the last glass.
The number of fluid ounces of lemonade made by James and Eric is a
multiple of the number pitchers mixed.
Possible responses are as follows;The number of glasses filled = 43 glassesThe volume of lemonade in the last glass = 8 fluid ouncesReasons for arriving at the above responses:Given and derived parameters;The number of pitchers James and Eric mix = 6 pitchers each
Number of fluid ounces of lemonade James makes per pitcher = 26 fluid Ounces
Volume of lemonade Eric makes per pitcher = 32 fluid ounces
Solution:Volume of lemonade James makes = 26 fluid Ounce × 6 = 156 fluid Ounces
Volume of lemonade Eric makes = 32 fluid ounces × 6 = 192 fluid Ounces
Total volume of lemonade made by James and Eric = (156 + 192) fluid Ounces = 344 fluid ounces
Volume of lemonade per glass = 8 Ounces
Number of glasses filled = 344 fluid Ounces ÷ 8 Ounces/glass = 43 glasses
Therefore, given that the number of glasses of 8 ounces of lemonade that can be filled using the 344 fluid ounces is exactly 43 glasses, we have;
The last glass is the 43rd glassVolume of lemonade in the last glass is 8 fluid ouncesLearn more about division in arithmetic here:
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One evening, a restaurant served a total of 3 1/3 loaves of wheat bread and 1 1/3 loaves of white bread. How many loaves were served in all?
Answer:
4 2/3
Step-by-step explanation:
Chan Hee bought 9.8 pounds of coffee that cost $7.45 per pound. How much did he spend on coffee?
(GIVING BRAINLIEST!!)
Ingrid dug a trench eighteen twentieths of a meter long. The next day she dug nine twentieths of a meter more of the trench. What is a reasonable estimate of the total length of the trench?
A) one half meter
B) 1 meter
C) one and one half meters
Answer:
Solution :-
On first day, Ingrid dug eighteen twentieth of a meter = (18/20) of 1 meter = (18/20) * 1 = (9/10) meters .
Now,
→ Next day, Ingrid dug nine twentieth of a mater = (9/20) of 1 meter = (9/20) * 1 = (9/20) meters .
So,
→ Total length of the trench = Ingrid dug in first day + Ingrid dug next day = (9/10) + (9/20) = (9*2 + 9)/20 = (18 + 9)/20 = (27/20) = 1.35 meters.
Therefore,
→ Total length of the trench = 1.35m ≈ 1.00 meter .
Hence, a reasonable estimate of the total length of the trench is 1.00 meter.
so, b
Step-by-step explanation:
Answer:
2 meters
Step-by-step explanation:
I need help ASAP I’ll mark you brainliest if you help pls
Answer:
1 hour sorry if wrong
Step-by-step explanation:
Help me please *an image is attached*
1. Nancy is walking around a circular track with a radius of 45 feet. If she walks the equivalent of 210 degrees, find the total distance she has walked around the track to the nearest foot.
2. A windshield wiper blade is 18 inches long. Calculate the area covered by the blade as it rotates through an angle of 122 degrees. Round your answer ti the nearest square inch.
3. A spray irrigation system waters a section of a farmer's field. If the water shoots a distance of 75 feet, what is the area that is watered as the sprinkler rotates through an angle of 80 degrees? Round your answer to the nearest square foot.
Answer:
see explanation
Step-by-step explanation:
(1)
The distance walked ( arc length ) is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{210}{360}[/tex]
= 2π × 45 × [tex]\frac{21}{36}[/tex]
= 90π × [tex]\frac{7}{12}[/tex]
≈ 165 ft ( to the nearest foot )
(2)
The area (A) covered is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{122}{360}[/tex]
= π × 18² × [tex]\frac{61}{180}[/tex]
= 324π × [tex]\frac{61}{180}[/tex]
≈ 345 in² ( to the nearest square inch )
(3)
The area (A) is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{80}{360}[/tex] ( r is the distance shot by sprinkler )
= π × 75² × [tex]\frac{8}{36}[/tex]
= 5625π × [tex]\frac{2}{9}[/tex]
≈ 3927 ft² ( to the nearest square foot )
Answer:
9514 1404 393
Answer:
top down: 1, 5, 6, 4, 8, 2, 3, 7
Step-by-step explanation:
It appears the expected order may be ...
__
Write the formula for the arc length of a circle with central angle, θ, in degrees.
\textit{Arc Length}=\dfrac{\theta}{360^{\circ}}\cdot 2\pi rArc Length=
360
∘
θ
⋅2πr
Replace 360° with 2π radians.
\dfrac{\theta}{360^{\circ}}=\dfrac{\theta}{2\pi}
360
∘
θ
=
2π
θ
Replace the angle ratio in degrees with the angle ratio in radians.
\textit{Arc Length}=\dfrac{\theta}{2\pi}\cdot 2\pi rArc Length=
2π
θ
⋅2πr
Simplify by cancelling
\textit{Arc Length}=\theta rArc Length=θr
A can of beans has a diameter of 8 inches and a height of 5 inches. What is the volume of the can? Use 3.14 for Pi. Round to the nearest tenth.
Recall the formulas V = pi r squared h and V = B h.
cubic inches
Answer:
251.2 in³
Step-by-step explanation:
The volume is the area of the groundplane times the height.
The area is πr², and r is half the diameter = 4.
So area = 3.14*4*4 = 50.24 and volume = 5*50.24=251.2
Answer:
251.2
Step-by-step explanation:
Over the summer, Jasper exercised 40 minutes a day.
After school began, Jasper figures he is exercising for
90 minutes a day. What is the percent increase?
Answer:
44%
Step-by-step explanation:
40/90 when put into a decimal is 0.4 repeating. Rounding that, it is 0.44, or 44%
How do you write 410,000 in scientific notation?
Answer:
4.1x10^5
Step-by-step explanation:
An employer's accountant has announced that
the budget for the next year must be cut by
33. How much must be cut from the
budget if last year's budget was
$166,245?
A. $11,830
B. $55,415
C. $166,245
D. $498,735
The amount of budget cut from last year's budget which was $166,245 will be $54860.85 which is nearly $55,415 from the given option. Hence the correct option is (B).
What is the percentage?The percentage is the 1 of the hundred or simply the amount or value of any number or data in the range of 100 called percentage.
For example, if Ramesh got 87 marks out of 150 then it required a lot of attention to drawing a conclusion about Ramesh's marks but if I say Ramesh got 58% then it will be easier to think and draw any conclusion.
Given that last year budget was $166,245 and the cut was 33% so it means it will be 0.33 of the $166,245 so
$166,245 × .33 = $54860.85 but in option, it is not mentioned so the nearest answer among the option will be (B).
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PLS HELP DUE TODAYY
Luis wants to buy a skateboard that usually sells for $79.79. All merchandise is discounted by 12%. What is
the total cost of the skateboard if Luis has to pay a state sales tax of 6.25%. Round your intermediate
calculations and answer to the nearest cent.
Step-
Identify the domain of the function shown in the graph.
Answer: C!
Step-by-step explanation: The domain is the x-axis, which goes from -5 to 5, so this makes the answer C.
Hope this helps :)
Solve each proportion.
2/8=5/r+8
Answer:
r=-20/31
Step-by-step explanation:
1)divide the numbers
2) subtract 8 from both sides of the equation
If the #2 pencil is the most popular, why’s it still #2?
Let f(x) = 4|x|
If g(x) is the graph of f(x) shifted right 5 units, write a formula for g(x)
g(x)=
Answer:
g(x)=4|x-5|
Step-by-step explanation:
Since the question wants you to shift 5 units to the right, all you need to do is add that - 5 inside the absolute value with the x, and it will shift the function 5 units to the right. I even attached a picture to prove that when adding - 5 inside the absolute value with the x, it shifts the function g(x) 5 units to the right.
Hope this helps! :)
Find the missing lengths of the sides
Answer:
I believe the answer is the second one, please let me know if I am wrong.
Help please simplify
Answer:
2
Step-by-step explanation:
1.) Simplify the numerator
2√2a/√2a
2.) Cancel the common factor of √2a
3.) The answer is 2
Hope this helps!!!!!
Please someone help I will give lots of points for the brilliantest answer.
Answer:
5 + 3 = 8
10 + 6 = 16
15 + 9 = 24
No she will need a total of 48
Step-by-step explanation:
24 + 16 + 8 = 48
Answer:
25 liters blue for a total of 40.
The rest of the table is:
Blue: White: Total:
15 9 24
20 12 32
25 15 40
Step-by-step explanation:
I multiplied 8 times 5 to get 40 (the total amount of liters)
Then I also had to multiply 5 by 5 to balance out the equation, and got 25.
What is the y-intercept for the given graph?
A track team ran 8 and 3/4 miles (mi) in 5 days. If they ran the same distance each day, how far did they run in one day?
Answer:
1.75
Step-by-step explanation:
First I converted
8 3/4 to 8.75
then I divided
8.75 / 5
= 1.75
The team ran 1.75 miles each day if they ran the same distance each day.
What is the division operation?
In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.
For example 4/2 = 2
A track team ran 8 and 3/4 miles (mi) in 5 days.
To find out how far the track team ran in one day, you need to divide the total distance run by the number of days.
8 and 3/4 miles = 8.75 miles (by converting mixed numbers to decimal)
total distance = 8.75 miles / 5 days
Apply the division operation, and we get
total distance = 1.75 miles/day
Therefore, the team ran 1.75 miles each day.
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Identify each pair of angles as corresponding, alternate interior, or alternate exterior.
9)
A alternate exterior
B corresponding
C alternate interior
10)
A) Corresponding
B) Alternate exterior
C) Alternate interior
Answer:
9) Corresponding
(The agles correcpond off of reflection)
10) Alternate interior
(The interior brings the negative side and flips it to the possative on the x axis)
Step-by-step explanation:
Hopefully this helped, if not HMU and I will try my best to get you a better answer!
Have a wonderful day! :)
.helppppppppppppppp!!!!!
answer: B
Step-by-step explanation: Its the only one that makes sense because as you see there are only four numbers to go off of, and b is the only one tht makes sense tbh
What is the 21st term of the sequence with a1 = -6 and d = 4?
Answer:
answer is 74
Step-by-step explanation:
-6+4 x 20
- 6+80=74
-3/4x+9 xccccccccccccccccccccccccccccccccccccccccc
The ratio of blue task to red task on the bullentin board is 3 to 5. There are 50 red tracks. How many blue tracks are on the board?