The area of a sector bounded by a 45° arc in a circle with a radius of 2 kilometers is π/² square kilometers.
To calculate the area of a sector bounded by a 45° arc in a circle with a radius of 2 kilometers, we will use the formula for the area of a sector, which is (θ/360) × π × r², where θ is the central angle in degrees and r is the radius of the circle. The central angle for our sector is 45° and the radius r is given as 2 km.
Plugging these values into the formula, we have:
Area of sector = (45/360) × π × (2²) = (1/8) × π × 4 = (1/2) × π = π/2 km².
Therefore, the area of the sector bounded by a 45° arc in a circle with a radius of 2 kilometers is π/²square kilometers.
Find a cartesian equation for the curve. r = 9 sin(θ)
What is the ratio of 5 gallons blue paint to 9 gallons of yellow paint?
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You have been asked to calculate the break-even point for a new line of souvenir t-shirts. the selling price will be $25 per shirt. the labor costs will be $5 per shirt. the administrative costs of operating the company are estimated to be $60,000 annually and the sales and marketing expenses are $20,000 a year. additionally, the cost of materials will be $10 per shirt. what is the break-even quantity?
Which of the following comparisons is False
A..... 5.c is Warner than 5.F
B......15.c is cooler than 60.F
C........30.c is Warner than 90.F
D.......35.c is cooler than 100.F
15 POINTS I REALLY NEED HELP!!!!!!!!!!!!!!!!!!!!!The solution to 16x = 48 is x = ___. (Only input the number.) Numerical Answers Expected! Answer for Blank 1:
A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the orange.
a
By what percentage is the grapefruit heavier than the apple?
PLS answer this soon... before an hour at most.
If prices increase at a monthly rate of 0.5%, by what percentage do they increase in a year?
What is the formula to solve?
We have been given that prices increase at a monthly rate of 0.5%.
Number of months in a year = 12
Let us suppose the item cost $1, then the percentage is given by
[tex]P=P_0(1+r)^n\\ \\ P=1(1+0.005)^{12}\\ \\ P=1.062[/tex]\\
Therefore, increase in a year is
[tex]1.062-1\\ =0.062[/tex]
Therefore, the required percentage in a year is 6.2%
PLEASE PLEASE HELP ASAP
PLZ HELP ASAP INSCRIBED QUADRILATERALS
Evaluate the expression 2x - (4y - 3) + 5xz, when x = -3, y = 2, and z = -1
A teacher took a survey and found that 16 of 25 students liked a certain snack item best. Make a prediction of how many students liked the snack item best if there are 225 students.
In rotation, which point is moved the greatest?
Zachary used the calculations shown to find how much he would spend on 16 ounces of pistachios. 6 ounces of pistachios cost $7.50 mc022-1.jpg Unit price = $0.80 per ounce mc022-2.jpg What was his first error? The price per ounce should have been $45.00 per ounce. The price per ounce should have been $1.25 per ounce. The final cost should have been $20.00. The final cost should have been $16.80.
Find the slope of the line.
Answer:
The slope of the line is [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
To know the slope of a line we can have the equation or to know points of the line. In this case from the graph we can get to points (-4,-1) and (0,-3). Having this and using the equation to calculate the slope, we have:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Defining:
[tex](x1=-4,y1=-1)[/tex] and [tex](x2=0,y2=-3)[/tex]
Replacing this values in the initial equation, this is:
[tex]m=\frac{-3-(-1)}{0-(-4)}[/tex]
[tex]m=\frac{-2}{4} =-\frac{1}{2}[/tex]
The slope of the line is [tex]-\frac{1}{2}[/tex]
Find the amount of annuity.
Amount of each deposit: $295
deposited: quarterly
Rate per year: 10%
Number of years: 6
Type of annuity: due
We need to find the future value of annuity due with the following given values :-
Payment, Pm = 295 dollars.
N=4 (for quarterly)
Rate at 10%, r = 0.10/4 = .025
Time for 6 years, T = 6x4 = 24.
Future Value formula is :-
[tex]FV_{ad}=P_m*(1+r)*[\frac{(1+r)^T-1}{r} ] \\\\ FV_{ad}=295*(1+0.025)*[\frac{(1+0.025)^{24}-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{(1.025)^{24}-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{(1.80872595)-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{0.80872595}{0.025} ] \\\\ FV_{ad}=295*(1.025)*(32.34903798) \\\\ FV_{ad}=9,781.54 \;dollars[/tex]
Hence, the final answer is 9,781.54 dollars.
When flying at an altitude of 5 miles, the lines of sight to the horizon looking north and south make about a 173.7 degree angle. how much of the longitude line directly under the plane is visible from 5 miles high?
Final answer:
The visible portion of the longitude line under the plane from an altitude of 5 miles is approximately 320.38 kilometers, using the formula D = 112.88 km √h where h is the altitude in kilometers.
Explanation:
The question asks how much of the longitude line directly under the plane is visible from an altitude of 5 miles high. To find this distance, we can use the formula given for horizon distance: D = 112.88 km √h, where h is the altitude in kilometers. Since 5 miles is approximately 8.05 kilometers, we can calculate the distance to the horizon by taking the square root of the altitude and multiplying by 112.88 kilometers.
First, calculate the square root of the altitude:
√8.05 ≈ 2.838.
Then, we multiply by the constant:
D ≈ 112.88 km × 2.838 ≈ 320.38 km.
Therefore, from an altitude of 5 miles, the visible portion of the longitude line directly under the plane is approximately 320.38 kilometers long.
Which algebraic expression represents “the bagels were divided equally into fifteen bags”?
15 + b
157b
Which algebraic expression represents “the bagels were divided equally into fifteen bags”?
a. 15 + b
b. 157b
c. 15/b
d. b/15
Answer:
Option D [tex]\frac{b}{15}[/tex]
Step-by-step explanation:
Let
b-----> the number of bagels
we know that
To find the algebraic expression of "the bagels were divided equally into fifteen bags" , divided the number of bagels by fifteen
so
[tex]\frac{b}{15}[/tex]
Solve the equation by completing the square x^2-18x+58=0. is it
A. x= -9+-√23
B. x= -9+-√139
C. x= 9+-√139
D. x= 9+-√23
Answer:
x = 9 ±√23
Step-by-step explanation:
How many ways can you choose 3 of of 7
describe how you shaded bars to show data
a weightlifter uses 45 pound plates and 10 pound plates to lift 260 pounds .let x represent the number of 45 pounf weights and y represents the number of 10 pound weights .
part 1 Rights an equation is standard form that represents the situation.
part 2. if the weightlifter uses eight 10 pound weights, how many 45 pound weights did he use???????
A standard form equation representing the weightlifting situation is 45x + 10y = 260. If eight 10-pound plates are used, the number of 45-pound plates used is 4.
Explanation:The situation given can be translated mathematically to an equation in standard form as follows: 45x + 10y = 260. This equation signifies that the total weight lifted (260 pounds) is equal to the sum of the weight of the 45
pound plates
(which each weighs 45 pounds multiplied by the number of plates, represented by x) and the 10 pound plates (which each weighs 10 pounds multiplied by the number of plates, represented by y). In the second part of the question, we're told that the weightlifter uses eight 10-pound weights, so y=8. Substituting y=8 into the equation from above, it simplifies to 45x + 80 = 260, which solves to x = 4. So, if the weightlifter uses eight 10 pound plates, then he uses four 45 pound plates.
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The sum of three numbers is 12. The sum of twice the first number, 5 times the second number, and 6 times the third number is 59. The difference between 8 times the first number and the second number is 23. Find the three numbers.
The question requires solving a system of linear equations which results from given conditions on three unknown numbers. The unknowns can be represented by the letters x, y, and z which need to be solved for by leveraging the knowledge of algebra.
Explanation:The question given is a classic example of a system of linear equations. Let's represent the first number as x, the second number as y, and the third number as z. From the question, we have the following equations:
[tex]x + y + z = 12 \\2x + 5y + 6z = 59 \\8x - y = 23[/tex]
Solving this system, we can find the values for x, y, and z which represent the three numbers. One of the methods for solving such a system is substitution or elimination method. Nevertheless, the solving such system requires a strong understanding of basic algebra including addition, subtraction, multiplication, and division of numbers and algebraic expressions.
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he table below shows 10 data values: What values of minimum, Q1, median, Q3, and maximum should be used to make a box plot for this data? (1 point) 301 345 305 394 328 317 361 325 310 362 Minimum = 300, Q1 = 345, median = 330, Q3 = 317, maximum = 362 Minimum = 300, Q1 = 317, median = 330, Q3 = 345, maximum = 362 Minimum = 301, Q1 = 310, median = 326.5, Q3 = 361, maximum = 394 Minimum = 301, Q1 =361, median = 326.5, Q3 = 310, maximum = 394
Answer:
the third one its 100% verified
Step-by-step explanation:
please answer the question in the picture above
Kim is a single woman in her mid-20s working while taking college credits to earn a bachelors degree. She is financing her education herself through both her income and taking out student loans. Her earnings in 2010 were $30,000 before taxes. She paid $5000 intuition and paid $350 interest on her student loan. In filing her state tax return form Kim takes a deduction for tuition paid and the interest paid on the loan. In taking these two deductions by how much did she lower taxable income? What is her taxable income now? What is her marginal tax rate? What will she owe in taxes for 2010?
What is 40,630 written in scientific notation?
Answer:
4.063 x 10*4
Step-by-step explanation:
take the big number and move it from the exponent then bwa
What is the area of a parallelogram that has a base of 6 cm and a height of 4 mm
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Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6).