The fraction of the sector of a circle in radians is (θπ/180). Substituting this fraction into the formula for the area of a circle, and simplifying, results in the formula for the area of the sector being A = (θπ/360) * r^2.
Explanation:In a circle, the angle in degrees is often converted to radians for calculations. A full circle is equivalent to 360 degrees or 2π radians. Therefore, if the sector angle is θ degrees, then in radians, the equivalent is (θ/360) * 2π = θπ/180.
Inserting this into the formula for the area of a circle, which is A = πr2, the area A of the sector becomes a fraction of the full circle's area, which is calculated as follows: (θ/360) * A = (θ/360) * πr2 = (θπ/180) * r2. Simplifying this results in the formula A = (θπ/360) * r2.
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For a sector in a circle, the fraction is θ/2π in radians. After substituting this into the formula for circle's area, we get the area of sector as Area = (θr²)/2.
Explanation:The fraction in radians for a sector in a circle is θ/2π, because there are 2π radians in a whole circle. As the formula for the area of circle A is Area=πr², when we insert this fraction, which represents the proportion of the circle that Sector CAB occupies, we get the formula for the area of a sector: Area= (θ/2π) * πr². This simplifies to Area= (θr²)/2, as the π's cancel out. This formula says that the area of a sector is proportionate to its central angle and the square of the radius of the circle.
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Compute the sales tax on the following transactions. An article retails for $37.50. The city sales tax is 6%, and the federal excise tax is 8%. How much does the article cost altogether?
The article will cost altogether:
$ 42.75
Step-by-step explanation:It is given that:
The retail price of the article is: $ 37.50.
Also, the article will hold a city tax of 6% and a federal excise tax of 8%.
Hence, the total percent tax on article is: 6+8=14%
This means that the cost price of the article is:
Retail Price of article+14% of retail price.
= 37.50+14% of 37.50
= 37.50+0.14×37.50
= 37.50+5.25
= 42.75
Hence, the article will cost: $ 42.75
The measure of arc QS is (4x – 18)°.
What is the value of x?
40.5
49.5
94.5
180
ANSWER IS 49.5
Answer:
Option B. 49.5 degrees
Step-by-step explanation:
Given that arc QS measures 4x-18
Arc QS is a semicircle and hence subtended angle by semicircle at the centre is 180 degrees.
Use this to find the value of x
4x-18 = 180 degrees
Add 18 to both sides
4x=198
Divide by 4
x =198/4 =49.5
So answer is option B
49.5 degrees
Answer:
49.5
Step-by-step explanation:
What is the total amount and the amount of interest earned on $6,500 at 6% for 25 years?
To calculate the total amount and interest earned on $6,500 at 6% simple interest for 25 years, you use the formula I = P × r × t, which gives you interest (I) of $9,750. Adding the interest to the principal, the total amount after 25 years is $16,250.
To calculate the total amount and the interest earned on $6,500 at a simple interest rate of 6% for 25 years, we can use the simple interest formula:
I = P × r × t
Where:
I is the interestP is the principal amount ($6,500)r is the annual interest rate (6%, or 0.06)t is the time in years (25)Using this formula:
I = $6,500 × 0.06 × 25
I = $9,750
The total amount after 25 years will be the principal plus the interest:
Total Amount = P + I
Total Amount = $6,500 + $9,750
Total Amount = $16,250
The interest earned on the investment after 25 years is $9,750.
The two lines, P and Q, are graphed below: Line P is drawn by joining ordered pairs negative 8,15 and 6, negative 12. Line Q is drawn by joining ordered pairs 4,16 and negative 9,10 Determine the solution and the reasoning that justifies the solution to the systems of equations
Answer:
[tex]\text{Solution: }\left(-\dfrac{2654}{435},\dfrac{1644}{145}\right)[/tex]
Step-by-step explanation:
Line P is drawn by joining ordered pairs (-8,15) and (6,-12)
Using two point formula of line. Find equation of line P
[tex]\dfrac{y-15}{x-(-8)}=\dfrac{-12-15}{6-(-8)}[/tex]
[tex]\dfrac{y-15}{x+8}=\dfrac{-27}{6+8)}[/tex]
[tex]\dfrac{y-15}{x+8}=\dfrac{-27}{14}[/tex]
[tex]y=\dfrac{-27}{14}(x+8)+15[/tex]
[tex]y=\dfrac{-27}{14}x+\dfrac{-27}{14}\times 8 + 15[/tex]
[tex]y=\dfrac{-27}{14}x-\dfrac{3}{7}[/tex]
[tex]\text{Equation of line P:}y=\dfrac{-27}{14}x-\dfrac{3}{7}[/tex]
Line Q is drawn by joining ordered pairs (4,16) and (-9,10)
Using two point formula of line. Find equation of line Q
[tex]\dfrac{y-16}{x-4}=\dfrac{10-16}{-9-4}[/tex]
[tex]\dfrac{y-16}{x-4}=\dfrac{-6}{-13}[/tex]
[tex]\dfrac{y-16}{x-4}=\dfrac{6}{13}[/tex]
[tex]y=\dfrac{6}{13}(x-4)+16[/tex]
[tex]y=\dfrac{6}{13}x-\dfrac{6}{13}\times 4 + 16[/tex]
[tex]y=\dfrac{6}{13}x+\dfrac{184}{13}[/tex]
[tex]\text{Equation of line Q:}y=\dfrac{6}{13}x+\dfrac{184}{13}[/tex]
Using graphing find solution of system of equation.
We draw the line on graph and see the intersection point.
Please see the attachment of the line.
Answer:
(−2, 4), because it is the point of intersection of the two graphs
Step-by-step explanation:
BECAUSE
1. In the figure, m DE = 106 degrees and m BC = 62 degrees. The diagram is not to scale.
What is m< A?
A) 44 degrees
B) 22 degrees
C) 75 degrees
D) 85 degrees
2. In the figure, m AB = 45 degrees and m CD = 23 degrees. The diagram is not drawn to scale.
What is the value of x?
A) 34 degrees
B) 56.5 degrees
C) 22 degrees
D)68 degrees
Can someone please check my work and tell me if I'm correct or not and explain.
The measure of the missing angles in both instances is; m∠A = 22 degrees and x = 34 degrees
How to find the angles in the triangle?
1) For question 1, the formula for the missing angle from triangle is;
m∠A = ¹/₂(∠DE - ∠BC).
Thus;
m∠A = ¹/₂(106 - 62).
m∠A = 44/2
m∠A = 22 degrees
2) To get the missing angle, we will use the formula;
x = ¹/₂(AB + CD)
This is because the measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
x = ¹/₂(45 + 23)
x = 34 degrees
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Trip bought an ice cream cone that is 4 inches tall with a radius of 2 inches the cone has a mass of about 3 ounces when empty after it is filled with ice cream and topped with a Hemisphere of ice cream with a radius of 2 inches it has a mass of 35 ounces what is the density of the ice cream use 3.14 for pie round your answer to the nearest thousand your answer will be in ounces per cubic inches
I am struggling with Parts B and D of this calculus question. I think that Parts A and C are OK. I wonder if Parts B and D require the graph that I drew for Part A?
Assume that the starting point of a path in such a grid is labeled the origin ≡ (0,0). the destination is the point (m,n). in other words, there are (n+1) streets in the x direction and and (m+1) streets in the y direction; and any portion of of any of these streets can be used to reach the destination. find the total number of distinct paths; assuming that all streets are available.
the distance between bay town and oak glen is 175 miles. if the equation y=-x+175 represents the distance left to travel to oak glen, what does the domain represent? what is the domain?
a) time left to reach oak glen; x>0
b) distance left to reach oak glen; x>0
c) time it takes to travel oak glen; x>0
d) distance traveled since leaving bay town; x>0
The correct option is D, distance traveled since leaving bay town; x>0.
What is the domain and range of a function?The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.
Given that the distance between bay town and oak glen is 175 miles. If the equation y=-x+175 represents the distance left to travel to oak glen.
Since the distance left to travel to oak glen can be 0 this will be when you reach Oak glen, while the minimum will be when the journey is just started and you haven't travelled even a single mile.
Therefore, the domain of the function is from 0 to 175, and the domain represents the distance traveled since leaving the bay town.
Hence, the correct option is D, distance traveled since leaving bay town; x>0.
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Write an equation of the graph:
y = |x| translated two units downward
y = |x| - 1 is the answer
ur mom
what is the measure of AB
Graph BCD with vertices.
A test consists of 10
a. True
b. False questions. to pass the test a student must answer at least 9 questions correctly. if a student guesses on each question, what is the probability that the student will pass the test?
How to find an area of a circumbscribed hexagon using the diameter?
You play darts with a friend. The board is a circle with a 6-inch radius. The “Bull’s Eye” is a smaller circle in the center of the board with an 0.25-inch radius. You throw darts (small metal arrows) at the board. At the end of six weeks, she has thrown 500 darts. She hit the board every time and hit the Bull’s Eye 1 time If you throw 500 darts, how many times should you expect to hit the Bull’s Eye by random chance? Compare this result to your friend’s result. Is she a skilled player for hitting the bull’s eye or is the result of hers expected?
The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2-foot border of the floor visible on all sides. What should the length (the longer side) of the rug be?
Frank owns 300 acres of land. If he divides the land into 1/2 acre plots, how many plots will he have?
Elijah is going to spin a spinner 180 times. mc008-1.jpg He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah’s prediction?
Answer:
its C on Edge
Answer:c
Step-by-step explanation:
Claire says the area of a square with a side length of 100 centimeters is greater than the area of a square with a side length of 1 meter. Is she correct? Explain
Is Part A correct? And can someone please help me with part B? (Highlighted)
A tree's root is 9 feet below ground and spans a radius of 6 feet. If the total length of the tree from root tip to top is 23 feet, what is the tree's elevation above ground?
a. 14 feet
b. 17 feet
c. 26 feet
d. 32 feet
Please help me with this
which statement most accurately explains why x^5/x^2 is equal to x^3?
Bryant collects a set of 20 data representing the lengths of worms he found in the garden. The variance of the set of measurements is 36. What is the standard deviation from the mean? _____ millimeters
A ________ sample is a sample in which each member of the population has a known, nonzero, chance of being selected for the sample.
A random sample is a subset of a population where every individual has an equal and known chance of being selected, providing a representative segment for study.
A random sample is a sample in which each member of the population has a known, nonzero, chance of being selected for the sample. This means that in a random sample, every individual in the larger population has an equal opportunity to be included. There are various methods to achieve a random sample, such as simple random sampling, stratified sampling, or using random digit dialing. Random samples are crucial because they tend to be representative of the population, thereby allowing the results of studies to be generalizable.
a man made lake is stocked with 10,000 fish. This population is expected to decline by an annual rate of 15%. Predict the fish population 5 years after the lake is stocked
The population will be approximately 4,437 fish after 5 years.
To predict the fish population 5 years after the lake is stocked,
We can use the formula for exponential decay:
[tex]\[ P = P_0 \times (1 - r)^t \][/tex]
Where:
P is the final population[tex]\( P_0 \)[/tex] is the initial populationr is the annual rate of decline (expressed as a decimal)t is the number of yearsGiven:
[tex]\( P_0[/tex] = 10,000 (initial population)r = 0.15 (annual rate of decline, expressed as 15% or 0.15)t = 5 (number of years)Substituting the values into the formula:
[tex]\[ P = 10,000 \times (1 - 0.15)^5 \][/tex]
[tex]\[ P = 10,000 \times (0.85)^5 \][/tex]
Calculating:
P ≈ 10,000 × 0.443705
P ≈ 4437.05
So, the fish population 5 years after the lake is stocked is approximately 4437 fish.
The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)
The greatest common factor of 24and 36 is the least common multiple of a pair of numbers.which two number could they be ? Pls make sure to explain this specifically!!
A.3 and 6
B.4 and 6
C.8 and 9
D.8 and 12
Factor x2 – 8x + 15.
Which pair of numbers has a product of ac and a sum of b?
Two rafts are traveling In opposite directions on a straight river. The raft going with the current is traveling at a speed of 12 mph. The raft going against the current is traveling at a speed of 70 miles per hour. Both rafts travel the river for two hours. Which equation represents the situation? Assume the raft traveling with the current travels X miles in the raft traveling against the current travels y miles.
A. 12/x - 7/y = 1/2
B. 12x + 7y = 2
C. x/12 - y/7 = 2
D. x/12 + y/7 = 4
E. 12x + 7y = 4