The power series representation for function f(x) is; ∑ [tex](-1)^{n}[/tex] × [tex]X^{(6n+9)}[/tex] / (2n+1), and the radius of convergence is infinite, R = ∞.
To find a power series representation for the function f(x) = x⁶×arctan(x³), we can use the power series representation for arctan(x);
arctan(x) = ∑ [tex](-1)^{n}[/tex] × [tex]X^{(2n+1)}[/tex] / (2n+1)
Substituting x³ for x in this series, we have;
arctan(x³) = ∑ [tex](-1)^{n}[/tex] × (x³[tex])^{(2n+1)}[/tex] / (2n+1)
= ∑ [tex](-1)^{n}[/tex] × [tex]X^{(6n+3)}[/tex] / (2n+1)
Multiplying this series by x⁶, we get;
x⁶ × arctan(x³) = ∑ [tex](-1)^{n}[/tex] × [tex]X^{(6n+9)}[/tex] / (2n+1)
So the power series representation for f(x) is;
f(x) = x⁶ × arctan(x³) = ∑ [tex](-1)^{n}[/tex] × [tex]X^{(6n+9)}[/tex] / (2n+1)
To find radius of convergence R, we use the ratio test:
lim |[tex](-1)^{n}[/tex] × [tex]X^{(6(n+1)+9)}[/tex] / (2(n+1)+1) × (2n+1) / [tex](-1)^{n}[/tex] × [tex]X^{(6n+9)}[/tex]|
n->∞
= lim |x⁶ / (2n+3)|
n->∞
As n approaches infinity, the denominator of the fraction approaches infinity, so the limit is zero for all values of x. Therefore, the power series converges for all values of x, and the radius of convergence is infinite, R = ∞.
To know more about radius of convergence here
https://brainly.com/question/31440916
#SPJ1
Express the ratio, 5 1⁄2 : 2 3⁄4 in simplest form
The ratio 5 1⁄2 : 2 3⁄4 can be expressed in simplest form as 11 : 7.
What is ratio?Ratio is a mathematical comparison between two numbers, usually expressed as a fraction. It is used to compare quantities or measurements, and is a useful tool for understanding relationships between different values. Ratios can be used to solve problems and make decisions, as well as to measure and compare proportions in different situations.
This can be derived by multiplying the numerators and denominators of the two ratios by the same number, in this case 2. The resulting fractions are 11⁄2 and 5⁄2, which can then be simplified to 11 : 7.
To know more about ratio click-
http://brainly.com/question/24644930
#SPJ1
Which expression in the result of factoring the expression below by taking out its greatest common factor?
8x^2-24=?
Quadratic Expression: is an expression with the variable with the highest exponent being 2
General form: ax^2 + bx + c
Greatest common factor (GCF): the largest whole number that divides evenly into a set of numbers
When factoring out the GCF of this expression we must look at the "a" term and "c" term
the greatest common factor of the terms a and c is 8we can that factor out the 8 from the original expression, putting it outside the brackets and dividing the original terms by the GCF8/8 =1 and -24/8= -3[tex]8(x^2-3)[/tex] which is the expression factored.
Twenty horses ran in the 2016 Kentucky Derby. The Exacta bet involves picking the first two finishers in order. Determine the number of outcomes for two horses finishing in the first two spots and the probability of winning the Exacta bet if you pick the horses at random.
The probability of winning the Exacta bet if you pick the horses at random is given by P ( A ) = 0.26 %
Given data ,
The Kentucky Derby had 20 horses running in the race in 2016. The number of ways to pick the first horse is 20, as any of the 20 horses could finish in the first spot. Once the first horse is picked, there are 19 remaining horses that could finish in the second spot.
Therefore, the total number of outcomes for two horses finishing in the first two spots (i.e., the Exacta bet) is 20 multiplied by 19, which is 380.
Since there is only one winning Exacta combination out of the 380 possible outcomes, the probability of winning the Exacta bet by randomly picking two horses is 1/380, which is approximately 0.0026, or 0.26%.
Hence , the probability is 0.26 %
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ1
If x and y vary directly and y is 52 when x is 13 find y when x is 14
Answer:
[tex] \frac{52}{13} = \frac{y}{14} [/tex]
[tex]4 = \frac{y}{14} [/tex]
[tex]y = 56[/tex]
what is the selling price of a shoe when the cost price is K80 and there is a profit of 65% on it
Assuming that the cost price in the question is 80K with a 65% profit percentage on cost price, the selling price of the shoe is 132K.
Given, Cost Price (CP) of the shoe = 80K or 80,000
Profit % = 65%
From the formula, we know,
Profit % = (Profit / Cost Price) * 100
Inserting given values in the formula, we get,
==> 65 = (Profit / 80,000) *100
or, 65 = Profit / 800
Therefore, Profit = 65 * 800
= 52,000
In the case of Profit, Selling Price = Cost Price + Profit
Hence, the Selling Price of the shoe is = 80,000 + 52,000
= 132,000 or 132K (Answer)
For more calculations on Cost Price and Selling Price:
https://brainly.com/question/19104371
helpppppppppppppppppppppppppppp
Carlo works at a factory thaat makes potato chips. He works 6 hours a day loading boxes onto trucks. The factory can produce one box filled with bags of potato chips every 4 minutes. How many boxes filled with chips does the factory make in 20 minutes
Answer:
mark me brilliant
Step-by-step explanation:
The factory produces one box of potato chips every 4 minutes, which means in one minute, it produces 1/4 boxes.
So, in 20 minutes, the factory would produce:
(1/4) x 20 = 5 boxes
Therefore, the factory would make 5 boxes filled with potato chips in 20 minutes.
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of
the money. Assume 365 days in a year.
P = $2000, r = 6%, t = 1 year
120 is the simple interest owed for the use of the money.
What does the phrase "simple interest" mean?
From the time when money was first lent until the time that it should be paid back with interest, this time frame is considered the borrowing period. The term or deadline for this is also an option. A percentage of the principle is how interest is most commonly computed.
P = $2000, r = 6%, t = 1 year
simple interest = P * r * t/100
= 2000 * 6 * 1/100
= 120
Learn more about simple interest
brainly.com/question/25845758
#SPJ1
The simple interest owed for the use of the money is $120.
What is simple interest?Simple interest is the interest charge on a loan calculated using only the original principal amount and a fixed interest rate. It does not use compounding, which causes borrowers to pay interest on principal and interest that accumulates over numerous payment periods.
The simple interest formula is as follows:
SI = P * r * t
where I denotes simple interest, P denotes principal, r denotes interest rate (in decimal), and t denotes time period (in years).
When we substitute the provided values, we get:
SI = $2000 * 0.06 * 1
SI = $120
As a result, the simple interest for the usage of the money is $120.
Learn more about simple interest here;
https://brainly.com/question/25845758
#SPJ1
which of the following shows an equivalent expression to [(5 * 3) * 12] if only the associative property was used to trasnform the expression
The equivalent expression using associative property is; 5×(3×12).
Given expression is; [(5 × 3) × 12]
The associative property is a property of addition and multiplication that allows the grouping of numbers or variables without changing the result.
For addition: (a + b)+c = a+(b + c)
For multiplication: (a × b) ×c = a × (b × c)
In simpler terms, it means that you can add or multiply a set of numbers in any order, and still get the same result.
Therefore, the equivalent expression to [(5 × 3) × 12] using only the associative property would have the same operands but a different grouping. One possibility would be;
[(5 × 3) × 12] = [5 × (3 × 12]
Both expressions simplify to 180.
To know more about associative property here
https://brainly.com/question/28387735
#SPJ1
Select the correct answer. The graph of function f is shown. An exponential function passes through (minus 4, 9), (0, 1), (1, 0), and (5, minus 2). Function g is represented by the table. x -1 0 1 2 3 4 g(x) 24 6 0 -2 Which statement correctly compares the two functions? A. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞. D. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞.
They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞.
The correct option is D.
From the given points, we can write an exponential function in the form of f(x) = abˣ, where a and b are constants.
Using the point (-4, 9): 9 = ab⁻⁴
Using the point (0, 1): 1 = ab⁰ = a
Using the point (1, 0): 0 = ab¹
Using the point (5, -2): -2 = ab⁵
Solving these equations, we get a = 1 and b = 1/3. So, the function f(x) = 1(1/3)ˣ = (1/3)ˣ.
For function g(x), we can see that as x approaches -∞, g(x) approaches ∞ , and as x approaches ∞, g(x) approaches 0.
This is because as x gets more negative, 24 times 2⁻ˣ becomes a larger positive number, and as x gets larger, 2ˣ becomes a larger positive number causing the product to approach zero.
Therefore, the two functions have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞, making option D the correct answer.
To learn more about the exponential function;
https://brainly.com/question/14344314
#SPJ1
The trapezoid is composed of a rectangle and two triangles. What is the area of the rectangle? What is the total area of the triangles? What is the area of the trapezoid?
Responses 'ILL GIVE BRAINLY'
Answer:
B) 108 cm²; 27 cm²; 135 cm²--------------------
Area of the rectangle:
A(rectangle) = lw = 12*9 = 108 cm²Area of the two triangles:
A(triangles) = 2*(bh/2) = bh = 3*9 = 27 cm²Area of trapezoid is the sum of the areas we found above:
A(trapezoid) = 108 + 27 = 135 cm²The matching answer choice is B.
A round has a diameter of
115
cm
115 cm115, start text, space, c, m, end text and is
25
cm
25 cm25, start text, space, c, m, end text deep. A hose is filling the pool at a rate of
34
,
000
cm
3
34,000 cm
3
34, comma, 000, start text, space, c, m, end text, cubed per minute.
How long will it take to fill the pool to a depth of
20
cm
20 cm20, start text, space, c, m, end text?
Round to the nearest minute.
It will take approximately 6.1 minutes to fill the pool to a depth of 20 cm at the given fill rate.
How to solve for the time it will take to fill the poolFind the radius of the pool:
Since the diameter is 115 cm, the radius (r) will be half of that:
Radius (r) = Diameter / 2
r = 115 cm / 2
r = 57.5 cm
Calculate the volume of the pool when filled to a depth of 20 cm:
Since the pool is round and assuming it has a cylindrical shape, we can use the formula for the volume of a cylinder:
Volume = π × r² × h
where π (pi) is approximately 3.14159, r is the radius, and h is the height (or depth, in this case).
Volume = 3.14159 × (57.5 cm)² × 20 cm
Evaluate the volume:
Volume ≈ 3.14159 × 3306.25 cm² × 20 cm
Volume ≈ 3.14159 × 66125 cm³
Volume ≈ 207354.2 cm³
Calculate the time it takes to fill the pool to a depth of 20 cm:
We are given that the hose fills the pool at a rate of 34,000 cm³ per minute. To find out how long it will take to fill the pool, we can use the following formula:
Time = Volume / Fill Rate
Time ≈ 207354.2 cm³ / 34,000 cm³/min
Time ≈ 6.1 minutes
It will take approximately 6.1 minutes to fill the pool to a depth of 20 cm at the given fill rate.
Read more on volume here:https://brainly.com/question/1972490
#SPJ1
Find the volume of the composite solid. Round your answer to the nearest hundredth.
T
5 cm
8 cm
t
5 cm
The volume is about
cubic centimeters.
The volume of the composite solid, rounded to the nearest hundredth, is: 213.33 cubic centimeters.
How to Find the Volume of the Composite Solid?The solid given is composed of two square pyramids. Therefore, to find the volume of the composite solid, apply the formula below:
Volume of composite solid = 2(1/3 * length * width * height)
Given the following dimensions:
Length = 8 cm
Width = 8 cm
Height = 5 cm
Plug in the values:
Volume of composite solid = 2(1/3 * 8 * 8 * 5)
≈ 213.33 cubic centimeters (to the nearest hundredth).
Learn more about the volume of composite solid on:
https://brainly.com/question/4031224
#SPJ1
Encuentra la distancia entre los puntos (–
10,–
7) y (–
4,2).
Escribe tu respuesta como un número entero o como una expresión radical totalmente simplificada. No redondees.
The sugar sweet company will choose from two companies to transport as sugar to market. The first company charges 4500 to rent trucks plus an additional fee of 175.25 for each third of sugar per second copy charges 3995 to rent trucks plus an additional fee of 200.50for each total of sugar.
The two companies charge the same when the amount of sugar is 20 thirds per second and the cost when the two companies charge the same is $8,125.
What is amount?
Amount is a term used to describe the quantity or size of something. It can refer to a specific quantity of a substance, such as an amount of money or an amount of a particular material, or it can refer to a more abstract concept, such as an amount of time or effort.
To find the amount of sugar for which the two companies charge the same, we need to set the two costs equal to each other and solve for the amount of sugar.
Let x be the amount of sugar in third per second. Then, the cost C1 charged by the first company is:
C1 = 4500 + 175.25x
And the cost C2 charged by the second company is:
C2 = 3995 + 200.50x
To find the amount of sugar for which the two companies charge the same, we set C1 equal to C2:
4500 + 175.25x = 3995 + 200.50x
Solving for x, we get:
25.25x = 505
x = 20
Therefore, the two companies charge the same when the amount of sugar is 20 thirds per second.
To find the cost when the two companies charge the same, we can substitute x = 20 into either of the cost equations. Let's use C1:
C1 = 4500 + 175.25x
C1 = 4500 + 175.25(20)
C1 = 8125
Therefore, the cost when the two companies charge the same is $8,125.
To learn more about amount visit:
https://brainly.com/question/25720319
#SPJ1
The bar graph shows the number of Asturian households, in thousands, living in poverty from 1999 to 2004. The table holds a quadratic function for the data, where y is the number of households, in thousand living in poverty × years after 1999. 10. 10 1999 2000 2001 2002 2003 2004 QuadReg y = ax2 + bx + c a = 0.2299729818 b = - 0.4599459636 c = 7.5426446323 a. Use the table to express the model in function notation, with numbers rounded to two decimal places #(x) = 0.23x2 + - 0.46x + 7.54 b. According to the function in part (a), in which year was the number of households living in poverty at a minimum? 2000 (Round to the nearest year as needed.) c. Use the model to find the number of households, in thousands, for that year. 7400 (Round to one decimal place as needed.)
Step-by-step explanation:
a. #(x) = 0.23x^2 - 0.46x + 7.54 (numbers rounded to two decimal places)
b. To find the year at which the number of households living in poverty is at a minimum, we need to find the vertex of the quadratic function. The x-value of the vertex is given by -b/2a. Plugging in the values for a and b from the function in part (a), we get:
x = -(-0.46)/(2*0.23) = 1
So the minimum occurs in the year 1999 + 1 = 2000 (rounded to the nearest year).
c. To find the number of households living in poverty in 2000, we need to evaluate the function at x = 1 (since 2000 is 1 year after 1999). Plugging in x = 1 into the function from part (a), we get:
#(1) = 0.23(1)^2 - 0.46(1) + 7.54 = 7.40
So there were approximately 7400 households living in poverty in Asturias in 2000 (rounded to one decimal place).
Use PMT=
to determine the regular payment amount, rounded to the nearest dollar. In terms of paying less in interest, which is more economical for a $210,000
HT
mortgage: a 30-year foxed-rate at 10% or a 20-year fixed-rate at 9.5%? How much is saved in interest?
Select the correct choice below and fill in the answer box within your choice.
(Do not round until the final answer. Then round to the nearest thousand dollars.)
OA. The 30-year 10% loan is more economical. The buyer will save approximately $ in interest
OB. The 20-year 9.5% loan is more economical. The buyer will save approximately Sin interest.
In Data Collection, accuracy may be determined O a. O b. O c. None of the responses are correct By counting the number of values to each other By how close repeated measurements are, to the true value of the attribute being measured O d. By how close repeated measurements of an attribute are, to each other Oe. By how much deviation there is between the measured values and the true value
It is essential to determine accuracy to ensure that the collected data is reliable and can be used to make informed decisions.
How to solve the question?
Data collection is an essential aspect of research and analysis, as it involves gathering information from various sources to make informed decisions. Inaccurate data can lead to incorrect conclusions and flawed decision-making, which can have significant consequences. Therefore, it is crucial to determine the accuracy of the collected data.
Accuracy can be determined in several ways. One way is by how close repeated measurements of an attribute are to each other. This method is known as precision. If repeated measurements are consistent with one another, it indicates that the data is precise. However, precision does not necessarily imply accuracy, as the measured values could be consistently wrong.
Another way to determine accuracy is by how close repeated measurements are to the true value of the attribute being measured. This method is known as validity. Validity ensures that the collected data accurately reflects the attribute being measured. This method is often used in experiments to test the effectiveness of a treatment or intervention. The results of an experiment are valid if they accurately reflect the effects of the treatment or intervention being tested.
Accuracy can also be determined by how much deviation there is between the measured values and the true value. This method is known as error. An error is the difference between the measured value and the true value. The smaller the error, the more accurate the data.
In conclusion, accuracy in data collection is determined by how close the measured values are to the true value, how close repeated measurements are to each other, and how much deviation there is between the measured values and the true value. It is essential to determine accuracy to ensure that the collected data is reliable and can be used to make informed decisions.
To know more about data visit :-
https://brainly.com/question/27358262
#SPJ1
Which diagrams represent the net of a rectangular prism? Select TWO answers choices.
(I know that for sure! <3)
NO LINKS!! URGENT HELP PLEASE!!!
1. Find an exponential function of the form f(x) = ba^-1 + c that has the given horizontal asymptote and y-intercept and passes through P
y = 33; y-intercept 408; P(2, 93)
Answer:
[tex]\bold{f(x) = 375(2.5)^{-x}+ 33}[/tex]
Step-by-step explanation:
An exponential function of form f(x) = ba^(-x) + c has a horizontal asymptote of y = c as x approaches infinity, and a y-intercept of (0, b + c). We can use the given information to set up a system of equations and solve for the unknowns.
The horizontal asymptote is given as y = 33, so we have:
c = 33
The y-intercept is given as (0, 408), so we have:
b + c = 408
Substituting c = 33, we get:
b + 33 = 408
b = 375
So the function we're looking for is of the form:
[tex]\bold{f(x) = 375a^{-x}+ 33}[/tex]
To find a, we use the fact that the function passes through P(2, 93):
93 = 375a^(-2) + 33
60 = 375a^(-2)
a^2 = 375/60
a^2 = 6.25
a = [tex]\sqrt{6.25 } =2.5[/tex]
Therefore, the exponential function that satisfies the given conditions is:
[tex]\bold{f(x) = 375(2.5)^{-x}+ 33}[/tex]
LAB1 Exp 3
Prescription number
Prescription #1
Prescription #2
Prescription #3
mLs needed of soda
mLs needed of solution
1. Difference between ointment and cream -
Generally, Creams tend to have lighter texture and consistency. They are mostly formulated with a blend of two components, that is water and oil.
What is Ointment?
Ointments are essentially greasy and have thicker consistency. They contain more oil content as compared to creams. Creams are absorbed faster via the skin than ointments. While ointments are absorbed slower through the skin than creams.
2. The label may instruct you to shake a liquid medicine before using so that the active ingredients are evenly distributed throughout it. The important thing to remember is that you have to shake a suspension before giving each dose so that the medicine particles are evenly distributed throughout the liquid.
3. Emulsions are stabilized by adding an emulsifier or emulsifying agents. These agents have both a hydrophilic and a lipophilic part in their chemical structure. In addition to this protective barrier, emulsifiers stabilize the emulsion by reducing the interfacial tension of the system.
Read more about emulsions here:
https://brainly.com/question/6711819
#SPJ1
What is the area of ΔABC given m∠B = 83°, a = 25 feet, and c = 40 feet?
561.46 feet2
496.27 feet2
186.23 feet2
128.51 feet2
The area of a triangle ABC is 496.25 square feet. Therefore, option B is the correct answer.
Given that, in the triangle ABC, m∠B = 83°, a = 25 feet, and c = 40 feet.
The area of a triangle can be expressed using the lengths of two sides and the sine of the included angle. Area of a triangle = ½ ab sin C.
Here, area of a triangle = 1/2 ×25×40 sin83°
= 25×20×0.9925
= 496.25 square feet
Therefore, option B is the correct answer.
To learn more about the area of a triangle visit:
brainly.com/question/27701864.
#SPJ1
What is the equation of a line that goes through the point (0,−4) and has a slope of 2 ?
Hint: Use the formula sheet to determine the formula(s) needed to solve the problem.
The equation of the line that goes through the point (0, -4) and has a slope of 2 is y = 2x - 4.
What is equation of line?The relationship between the coordinates of each point (x, y) on a line is represented by the equation of a line, which is linear in the variables x and y. All of the points on the line satisfy the equation, in other words.
We can use the point-slope form of the equation of a line to find the equation of the line that goes through the point (0, -4) and has a slope of 2.
The point-slope form of the equation of a line is:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line and m is the slope of the line.
Plugging in the values, we get:
y - (-4) = 2(x - 0)
Simplifying, we get:
y + 4 = 2x
Subtracting 4 from both sides, we get:
y = 2x - 4
Therefore, the equation of the line that goes through the point (0, -4) and has a slope of 2 is y = 2x - 4.
Learn more about equation of line on:
https://brainly.com/question/28278374
#SPJ1
Part A: Create your own experiment with 5 or more possible outcomes.
Part B: Create the sample space for your experiment in Part A. Explain how you determined the sample space.
HELP ME IM SO CUNFUSED!!!
Answer:
Part A: Experiment: Rolling a fair six-sided die.
Part B: Sample space: {1, 2, 3, 4, 5, 6}. This sample space was determined by listing all possible outcomes of rolling a fair six-sided die.
I hope that's what you are looking for.
PLEASE HELP!!!! PLEASE HELP...I NEED THE AREA!
The area of the composite figure that is composed of triangles and a rectangle is: 154 mm².
How to Find the Area of a Composite Figure?The composite figure given comprises two different triangles and one rectangle. Therefore, to find the area of the composite figure, we need to calculate the area of each shape in the figure.
Area of rectangle = length * width = (7 + 7) * 4
= 14 * 4
Area of rectangle = 56 mm²
Area of the larger triangle = 1/2 * base * height
= 1/2 * 14 * 11
= 77 mm²
Area of the smaller triangle = 1/2 * 14 * 3
= 21 mm²
Therefore, area of the composite figure = 56 + 77 + 21
= 154 mm²
Learn more about the area of composite figure on:
https://brainly.com/question/16293887
#SPJ1
PLEASE HELP!
The profit P (in dollars) made by a cinema from selling x bags of popcorn can be molded by P=2.36x-(x^2/25000)-3500, 0<=x<=50,000.
a) On what intervals is P increasing and decreasing?
b) How many bags of popcorn must the cinema sell in order to maximize profit and what is the maximum profit per bag?
The maximum profit is given as $31,310
How to solvea. In order to determine the intervals in which profitability P increases and decreases, we need to analyze the first derivative of its respective function, P(x).
Given the profit equation: P(x) = 2.36x - (x^2 / 25000) - 3500, the process begins by articulating its derivative, P'(x):
P'(x) = d(2.36x) - d(x^2 / 25000) - d(3500)
P'(x) = 2.36 - (2x / 25000)
P'(x) = 2.36 - x / 12500
Seeing that P'(x) > 0 implies a rising P while P'(x) < 0 portrays a decreasing P, those values must be determined. Subsequently, the critical points may be found by setting P'(x) = 0:
2.36 - x / 12500 = 0
x / 12500 = 2.36
x = 2.36 * 12500
x = 29500
To adequately evaluate the intervals (0, 29500) and (29500, 50000), we must gauge whether P'(x) is positive or negative:
For x greater than zero & less than 29500:
P'(x) = 2.36 - x / 12500 > 0
For x higher than 29500 but falling beneath 50000:
P'(x) = 2.36 - x / 12500 < 0
Hence, P is augmented on the interval from 0 until 29500, whereas it diminishes from 29500 to 50000.
b. Differentiate again the profit function we get
P'(x)= -1/12,500 <0
Therefore the profit will be maximum.
Hence 29500 bags of popcorn must cinema sell in order to maximize profit.
The maximum profit = $31,310
Read more about maximum profit here:
https://brainly.com/question/29257255
#SPJ1
d = 8.3 mm
Calculate the radius of the circle.
D = 8.3 mm
The radius of the circle is 4.15 mm.
The radius and diameter are both important properties of a circle, and they are related to each other. The diameter is the distance across the circle through its center, while the radius is the distance from the center to any point on the circle. The radius and diameter are related by the formula
D = 2r
Where "D" is the diameter and "r" is the radius.
To calculate the radius of a circle given its diameter, we use the formula
r = D/2
Where "r" is the radius and "D" is the diameter. The formula tells us that the radius is equal to half of the diameter.
In this case, we are given that the diameter is 8.3 mm. To find the radius, we simply substitute this value into the formula and solve for "r"
r = D/2
r = 8.3 mm/2
r = 4.15 mm
Therefore, the radius of the circle is 4.15 mm.
To know more radius here
https://brainly.com/question/11137975
#SPJ1
please provide the answer along with proof.
Note that where the above conditions are given, the probability of A ∩ B is 1/20 and the probability of the union of A and B P( A∪B) = 2/5. See the explanation below.
How were the above probabilities derived?We are given that A and B are events that are independent, P(A∩B), we can rightly state that:
P(A∩B ) = P(A) x P (B)
(1/5) x (1/4)
= 1/20
For P(A∪B)
⇒ P( A ∪B) = P (A ) + P(B) - P(A ∩B)
We can substitute the probabilities to derive:
P(A∪B) = (1/5) + (1/4) - (120)
We can write the above as:
⇒ 4/20 + 5/20 - 1/20
= 8/20
Simplifying , we get:
P(A∪B) = 2/5
Hence it is correct to state that the P(A ∩ B) = 1/20, while P(A∪B) = 2/5.
Learn more about probability:
https://brainly.com/question/30034780
#SPJ1
Which fraction is closer to 1 ?
Group of answer choices
They are the same distance from 1
4/7
5/9
5/9 is closer to 1 than 4/7.
To find out, we can subtract each fraction from 1 and take the absolute value of the result. The fraction with the smaller absolute value is closer to 1.
For 4/7:
1 - 4/7 = 3/7
For 5/9:
1 - 5/9 = 4/9
Since 4/9 is smaller than 3/7, 5/9 is closer to 1.
~~~Harsha~~~
Which of the following is a point-slope equation of a line that passes through
the points (5, 2) and (-1,-6)?
A. y-2-(x-5)
B. y-2--(x-5)
C. y-2-(x-5)
D. y-2--(x-5)
The point-slope equation of a line that passes through the points (5, 2) and (-1,-6) include the following: B. y - 2 = 4/3(x - 5).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-6 - 2)/(-1 - 5)
Slope (m) = -8/-6
Slope (m) = 4/3.
At data point (5, 2) and a slope of 4/3, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 4/3(x - 5)
Read more on point-slope here: brainly.com/question/24907633
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
