The probability that a randomly selected bird is a parakeet given that it is green is 54.1%.
What is meant by probability?The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. The likelihood that the coin will land with the heads side up after being tossed into the air is described using the word probability.
Let,
A be the Parakee
B be the Green
To find the probability that a randomly selected bird is a parakeet given that it is green.
That means P(A|B)
The number of birds that are both parakeet and green is n(A∩B)=20
The number of birds that are green is n(B)=37
Hence, using the conditional probability formula P(A∣B) = [tex]\dfrac{n(A\bigcap B}{n(B)}[/tex]
P(A∣B) = [tex]\dfrac{n(A\bigcap B)}{n(B)}[/tex]
P(A∣B) = 20/37
P(A∣B) = 20/37 × 100%
P(A∣B) = 54.1%
Thus, the probability that a randomly selected bird is a parakeet given that it is green is 54.1%.
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help me solve this pls because i need to solev this fast help me
The value of K that will make the expressions equivalent is 10.
How to evaluate the equivalent expression for the value of KConsidering the two expressions:
7 + (1/2)x - 3 + (3/4)x and 1 whole number (1/4)x + k - 6
we shall write the expression 7 + (1/2)x - 3 + (3/4)x in the form of the expression having k and then compare to know the value of k as follows;
(1/2)x + (3/4)x = (2x + 3x)/4
(1/2)x + (3/4)x = 5x/4
7 - 3 = 10 - 3 - 3
7 - 3 = 10 - 6
so;
7 + (1/2)x - 3 + (3/4)x = 5x/4 + 10 - 6
by comparison;
5x/4 is equal to the mixed fraction 1 whole number (1/4)x
k = 10 as obviously -6 is equal to -6.
Therefore, 10 is the value of k that will make expressions equivalent.
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Suppose that a water fountain produces a stream of water that follows the shape of a parabola. assigning the origin of a coordinate system to the point where the water stream emerges from the fountain, a measurement shows that the maximum height of the stream occurs at the point (6, 5). use symmetry to identify a third point and find a quadratic regression equation for the stream of water. a. y = negative 0.139 x squared 1.667 x b. y = negative 0.135 x squared 1.667 x c. y = 0.135 x squared 1.667 x d. y = 0.139 x squared 1.667 x
A quadratic regression equation for the stream of water is,
⇒ y = -0.139x² + 1.667x
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Here, The vertex = (6, 5)
Axis of symmetry is line, x = 6
And, A third point in the parabola is, (12, 0)
Hence, The quadratic regression equation for the stream of water is,
⇒ y = - a(x - 6)² + 5
= -a(x² - 12x + 36) + 5
= -ax² + 12ax - 36a + 5
Since the parabola passes through point (0, 0),
i.e. -36a + 5 = 0
⇒ a = 5/36
⇒ a = 0.139
Therefore, The equation is,
⇒ y = -0.139x² + 12(0.139)x
⇒ y = -0.139x² + 1.667x
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Answer:
Its A
Step-by-step explanation:
In a school election, Jessie received 60 votes, Rachel received 50 votes and Mario received 40 votes. What is the ratio of votes Rachal received to the votes Jessie received?
Therefore , the solution of the given problem of ratio comes out to be Jessie votes to Rachel votes is 6:5.
A ratio is what?A ratio is the simple expression "a / b," where "b" must not be greater than zero, for an ordered pair of numbers "a" and "b." Two ratios are combined to form a ratio. The ratio might be represented as 1:3 if there was just one man and three girls. 3/4 are girls, while 1/4 are boys. A part is a statistic, a percentage of something's size, or a distinction between two or more objects.
Here,
Given: Rachel received 50 votes,
Mario got 40 votes, and Jessie got 60.
To calculate the proportion of Jessie votes to Rachal votes:
Thus,
=> 60 : 50
=>6:5
Therefore , the solution of the given problem of ratio comes out to be Jessie votes to Rachel votes is 6:5.
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Determine the equation of the inverse for f(x)=7x2
The inverse of the equation f(x) = 7x -2 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex].
What is inverse of an equation?A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. The inverse function is denoted by f-1 or F-1 if the function is represented by [tex]f^{-1}(x)[/tex].
The given function is:
f(x) = 7x -2
Write the function in the form of a function:
y = 7x - 2
Interchange the variables in the equations:
x = 7y - 2
Isolate the value of y:
y = x/7 + 2/7
Replace y with [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex]
Hence, the inverse of the equation f(x) = 7x -2 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex].
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The value of which of these expressions is closest to e?
(¹+4)*
B. (1+²
OC. (¹+1)
OD. (1++)"
OA.
Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.
What does expression mean?An algebraic expression must be checked by replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is identical to 6, since 6 + 6 = 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.
Here,
Assumed: expressions
Finding the expression with a value that is closest to e
Solution:
e is worth 2.718, which equals (1 + 1/19).
(1 + 1/19)^19
=> (20/19)^19 = 2.65
=> (1+ 1/22)^22
= >(23/22)^22 = 2.659
=> (1 + 1/20)^20
= >(21/20)^20 = 2.653
=>(1 + 1/21)^21
= > (22/21)^21 = 2.656
As a result, the value of e is closest to the value of 2.659.
Option B is hence the appropriate choice.
Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.
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in a video game players Form teams and work together to earn as many points as possible for their team each team can have between two and four players each player can score up to 20 points in each round of the game Han and three of his friends decided to form a team and play around.
a. the number of players in a game with six different teams of different sizes: two teams have 4 players each and the rest have 3 players each
b. the possible number of players in a game with eight teams
Therefore , the solution to the given problem of expression comes out to be 80.
What does expression mean?Math allows for addition, subtraction, multiplication, and division. Following is the structure of an expression: Calculator, number or variable, and expression The components of a mathematical expression include numbers, variables, and operations (such as subtraction, multiplication , addition, or division etc.) You can contrast phrases and expressions.
Here,
The formula for the number of points Han's team scores in a single round if each player has a perfect score is 20 4.
Each player is limited to a maximum of 20 points.
Han's team has four members.
Thus, assuming each participant receives a perfect score, the expression that will indicate the total points that Han's team receives in one round is:
= 20 × 4
= 80
Therefore , the solution to the given problem of expression comes out to be 80.
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The car travels at a constant speed. After 6 seconds, it travels 180 meters.
Write a proportional equation to find the car's distance, d, at any time,
The equation that can be used to find the car's distance, d, at any time is d = 30 × t.
What is the equation that can be used to find the car's distance, d, at any time?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given that;
Elapsed time t = 6 secondsDistance traveled d = 180Speed s = ?First, we determine the speed of the car.
Speed = Distance ÷ time
Speed = 180 / 6
Speed = 30 m/s
Now, to get the distance traveled at any time, plug the value of the speed of the car into the speed formula and solve for distance d.
Speed = Distance ÷ time
Speed = d / t
d = Speed × t
d = 30 × t
Therefore, the equation is d = 30 × t.
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Which of the following angles are supplementary to ∠1? Select all that apply.
∠6 and ∠7 are the angles which are supplementary to ∠1.
What are Angles?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Supplementary angles are those angles that sum up to 180 degrees.
In the given figure lines l and m are parallel lines.
A transversal passed through parallel lines.
∠1+∠2=180 degrees
∠1+∠3=180 degrees.
∠2 is corresponding angle of ∠6.
∠1+∠6=180 degrees.
∠3 is corresponding angle of ∠7.
∠1+∠7=180 degrees.
Hence, ∠6 and ∠7 are the angles which are supplementary to ∠1.
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Write two equations that represent the graph shown below- one equation using sine, and one equation using cosine.
Two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.
What is sine function?The sine graph or sinusoidal graph is an up-down graph and repeats every 360 degrees i.e. at 2π.
The general form of a cosine function is:
y = a cosb (θ±c) ± d
Here, amplitude, a is = 1
For b, period is = π
2π/b = π
b = 2
c = 0
vertical shift = D = -3
Putting the value into formula
y = 1 cos2 (θ + 0) - 3
y = 1 ×−0.416(θ + 0) - 3
y = −0.416θ−3
y = −0.416x −3 (cosine function)
y = 1 sin2 (θ + 0) - 3
y = 1 ×0.909(θ + 0) - 3
y = 0.909θ−3
y = 0.909x−3 (sine function)
Thus, two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.
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Which example illustrates the commutative property of addition for polynomials?
(2x^2 + 5x) = –(–2x2 – 5x)
(2x^2 + 5x) + 0 = (2x^2 + 5x)
(2x^2 + 5x) + (4x^2 – 4x) = 2x^2 + 5x + 4x^2 – 4x
(2x^2 + 5x) + (4x^2 – 4x) = (4x^2 – 4x) + (2x^2 + 5x)
D) The example (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials.
The commutative property of addition for polynomials states that the order in which polynomials are added does not affect the result of the sum. In other words, it states that if we have two polynomials A and B, the result of adding A and B (A+B) will be the same as adding B and A (B+A).
For example, consider the polynomials (2x^2 + 5x) and (4x^2 - 4x). If we add these two polynomials in the order given, (2x^2 + 5x) + (4x^2 - 4x) = 6x^2 + x. Now, if we add these two polynomials in the reverse order, (4x^2 - 4x) + (2x^2 + 5x) = 6x^2 + x. We can see that the order of the polynomials does not affect the result of the sum, and thus it holds the commutative property of addition.
Option (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials, because it shows that the order of the polynomials does not matter and it gives the same answer.
It is important to note that the other options does not illustrate the commutative property.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
In what quadrant does coordinate 2 3 lie?
The coordinate (2, 3) lies in the first quadrant of a Cartesian plane, which is the upper-right quadrant when the origin (0, 0) is the center.
The coordinate (2, 3) lies in a Cartesian plane, which is a two-dimensional plane with an origin (0, 0) at the center. There are four quadrants on the Cartesian plane. To find which quadrant the coordinate (2, 3) lies in, we must look at the signs of the x- and y-coordinates. The x-coordinate is 2, which is a positive number, and the y-coordinate is 3, which is also a positive number. This means that the coordinate (2, 3) lies in the first quadrant, which is the upper-right quadrant when the origin is the center. The other quadrants are numbered in a clockwise direction, starting with the first quadrant, which is the upper right. The second quadrant is the upper left, the third quadrant is the lower left, and the fourth quadrant is the lower right.
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(05.06 LC) DO CORRECTLY
Which graph best represents a constant function? (5 points)
Constant functions have graph that are horizontal lines in the plane and are linear functions. Graph 3 is the correct answer.
What is a constant function?One of the simplest forms of real-valued functions is a constant function, which is used to express a quantity that remains constant across time. Constant functions have graphs that are horizontal lines in the plane and are linear functions. The x-value serves as the function's domain, which is depicted on the x-axis, and the y-axis serves as its range, which is indicated by the symbol f(x).
We know that the constant functions remain constant, that is they do not change their value. Constant functions have graphs that are horizontal lines in the plane and are linear functions.
Hence, graph 3 is the correct answer.
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What are the 2 parts of exponential notation?
The two parts of the exponential notation can be named as the "Base" and the second part is number raised to base called as Exponent .
Consider the Exponential Expression : aⁿ ;
The above exponent notation is read as the number "a" to the power of "n" ,
it means that the number "a" is multiplied "n" number of times .
The two parts of this Exponential Notations are :
the number "a" is called the base and "n" is called as the power or exponent .
Therefore , the two parts of the exponential notation are the base and the power/exponent .
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I=$180
P=___
r=4.5%
t=3 years
what’s p?
Using the formula of Simple Interest, the value for the principal amount is obtained to be P = $1333.33.
What is Simple Interest?
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
The value for Simple Interest is given as = $180
The value for rate is given as = 4.5%
The value for time is given as = 3 years
To find the value for Principal amount, follow the formula for Simple Interest -
SI = P R T/100
Where P is the principal amount, R is the rate and T is the time.
Substitute the values in the equation -
180 = (P × 4.5 × 3)/100
180 = 13.5P / 100
P = (180 × 100) / 13.5
P = 18000 / 13.5
P = 1333.33
Therefore, the value for principal amount is $1333.33.
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contents of 2x + 3y answer
The Slope Intercept Form Of 2x + 3y = 8 Is y = -2x/3 + 8/3
How to determine the slope intercept formFrom the question, we have the following parameters that can be used in our computation:
2x + 3y = 8
Make 3y the subject of the formula
So, we have the following representation
3y = -2x + 8
Divide through by 3
This gives
y = -2x/3 + 8/3
Hence, the equation is y = -2x/3 + 8/3
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Complete question
contents
The Slope Intercept Form Of 2x + 3y = 8 Is
Interpret the number line diagram shown below, and write a statement about the temperature for Tuesday compared to Monday at 11:00 p.m.
Help
Statement about the temperature for Tuesday compared to Monday at 11:00 p.m is temperature on Monday is 50⁰ F lesser than Tuesday
What is Number system?A number system is defined as a system of writing to express numbers.
In the given number line each unit is 10⁰ F
On Monday at 11:00 p.m. the temperature is 40⁰ F
Tuesday at 11:00 p.m. the temperature is -10⁰ F
The difference between two temperatures is 40⁰ F-( -10⁰)
40⁰ F+10⁰F
50⁰ F
The temperature on Monday is 50⁰ F lesser than Tuesday
Hence, statement about the temperature for Tuesday compared to Monday at 11:00 p.m is temperature on Monday is 50⁰ F lesser than Tuesday
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In △OAB , points C and E lie on OA¯¯¯¯¯¯¯¯ , points D and F lie on OB¯¯¯¯¯¯¯¯ , and CD¯¯¯¯¯¯¯¯∥EF¯¯¯¯¯¯¯¯∥AB¯¯¯¯¯¯¯¯ . If OC=3 , EA=5 , OD=6 , and DB=14 , what is CE ?
Answer:
2
Step-by-step explanation:
Xavier's mother has a large collection of shoes. the table shows flip flop 8, boots 4, and clogs 6. if xavier mother chose a pair of shoes at random, what is the probability that the shoes would be a flip flop, write your answer is a fraction.p(flip flop)
The probability of having a flip flop is 4/9.
What is the probability of flip flops?In the question, we can see from the data that we have that Xavier's mother has a large collection of shoes. the table shows flip flop 8, boots 4, and clogs 6.
Recall that probability deals with the possibility that an event may occur or not occur under a given circumstance. We know that;
Total number of the shoes = 4 + 6 + 8 = 18
Probability of a flip flop = 8/18 = 4/9
This is the possibility that what would be picked is a flip flop.
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M=-3(-1,2) Write in slope intercept form, solve, graph
3x+y=-1 is the equation for slope as -3 and point as (-1,2).
What is equation?Algebraic expressions are used to express mathematical expressions, and algebraic expressions are used to express mathematical expressions. For example, 3x + 5 = 14 is an equation containing two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
Here,
slope=-3
point=(-1,2)
(y-y1)=m(x-x1)
y-2=-3(x+1)
y-2=-3x-3
3x+y=-1
The equation for slope as -3 and point as (-1,2) is 3x+y=-1.
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Which statements about the line that passes through (−2, 0) and (2, −4) aretrue? Select all correct statements. The slope of the line is 1. The line intersects the y-axis at (0, −2). The equation of the line is y = −x − 2 The line intersects the x-axis at (−2,
The correct options for the line are-
B. The line intersects the y-axis at (0, −2).C. The equation of the line is y = −x − 2.D. The line intersects the x-axis at (−2, 0).Define the equation of the line?The formula for a straight line reads y=mx+c where c is the height from which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.Coordinate are: (−2, 0) and (2, −4)
Slope m = y2 - y1 / x2 - x1
m = (-4 + 0)/(2 + 2)
m = -4/4 = -1
Slope is -1 , option A incorrect.
For the y-intercept
Use point (-2, 0) and slope m = -1
0 = -1(-2) + b
b = -2
As, y-intercept is -2.
Option B correct.
Find equation of the line.
y = mx+ b
y = -x + (-2)
y = -x - 2
Thus, equation of the line is y = −x − 2.
Option C is also correct.
Find the x-intercept.
if y = 0
0 = -x - 2
x = -2
Thus, line intersects the x-axis at (−2, 0).
The option D is also correct.
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The complete question is-
Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.
A. The slope of the line is 1.
B. The line intersects the y-axis at (0, −2).
C. The equation of the line is y = −x − 2.
D. The line intersects the x-axis at (−2, 0).
A cylinder with a height of 9cm. And a width of 10cm. Find the exact volume.
A. 90pi cm^3
B. 45pi cm^3
C. 900pi cm^3
D. 225pi cm^3
Answer:
The correct answer is D. 225pi cm^3.
To find the volume of a cylinder, you use the formula:
V = πr^2h
Where V is the volume, π is pi, r is the radius of the base, and h is the height of the cylinder.
In this case, the height is 9cm, and the width is 10cm. To find the radius, we divide the width by 2:
r = 10cm / 2 = 5cm
Now we can plug in the values into the formula:
V = πr^2h
V = π(5cm)^2(9cm)
V = π(25cm^2)(9cm)
V = 225π cm^3
So the volume of the cylinder is 225π cm^3
Step-by-step explanation:
Answer: D) 225pi cm^3.
Step-by-step explanation:
Can anybody help me solve this
Answer: (5x^2-7)(x-4)
Step-by-step explanation:
5x^2(x-4)-7(x-4)
= (5x^2-7)(x-4)
How do polynomial identities apply to complex numbers?
Polynomial identities can be applied to complex numbers in the same way they are applied to real numbers, by replacing the real numbers in the polynomial with complex numbers and following the same algebraic rules and procedures.
What is a complex number?
A complex number is a number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
Polynomial identities are equations that are always true for any values of the variables, regardless of whether the variables represent real numbers or complex numbers. Complex numbers can be represented in the form of a + bi, where a and b are real numbers and i is the imaginary unit.
For example, the identity[tex](x + y)^2 = x^2 + 2xy + y^2[/tex] is true for any real numbers x and y, and it also applies to complex numbers a + bi and c + di. The identity becomes [tex](a + bi + c + di)^2 = (a + c)^2 + 2(a + c)(bi + di) + (bi + di)^2[/tex]
Another example is the identity [tex](a+bi)^2 = a^2 + 2abi - b^2[/tex] which is always true for any complex number a+bi. This identity applies to any complex number and can be used to simplify polynomials involving complex numbers.
Hence, polynomial identities can be applied to complex numbers in the same way they are applied to real numbers, by replacing the real numbers in the polynomial with complex numbers and following the same algebraic rules and procedures.
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The Davenports just got plans approved to install a Rectangular patio in their backyard a scale drawing of the paddle using a scale of 3in.: 10ft on the scale drawing, the patio measures 6 in. by 12 in. How many square feet will their patio cover?
The total area of the patio will be 20 * 40 = 800 square feet.
What is area of the scale model?The proportionate relationship between a linear dimension of a feature on a model, map, or drawing of an object and the same feature on the genuine thing. A scale model is a physical representation of an object that is geometrically equivalent (known as the prototype).
Since the scale drawing is 3 inches : 10 feet, this means that every 3 inches on the drawing represents 10 feet in real life. Hence, 1 inch on the drawing represents 10/3 = 3.33 feet in real life.
So the patio measures 6 inches by 12 inches on the drawing, which corresponds to 6 * 3.33 feet by 12 * 3.33 feet in real life, or 20 feet by 40 feet.
Therefore, the total area of the patio will be 20 * 40 = 800 square feet.
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What type of triangle has side lengths 5'7 and 11?
As the triangle cannot be equilateral since the sides are not equal. So the obtuse triangle has side lengths 5, 7 and 11.
Assume that a triangle has sides that measure 5, 7, and 11.
Finding the sum of the squares on the triangle's two shorter sides and comparing it to the square on the longest side will reveal the type of triangle.
A triangle must be sharp in order to:
Let a = 5, b = 7 and c = 11
a^2 + b^2 = (5)^2 + (7)^2 = 25 + 49 = 74
c^2 = (11)^2 = 121
(1) If the triangle is
a^2 + b^2 > c^2
Therefore, the triangle is not acute.
(2) Eqviangular means that each internal angle must be 60 degrees in length.
As a result, the triangle is not eqviangular.
(3) The triangle cannot be equilateral since the sides are not equal.
(4) We note that a^2 + b^2 = c^2.
The triangle is hence obtuse.
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What is a dilation of a line?
A dilation of a line is a transformation that changes the size of the line but preserves its shape.
It is a type of similarity transformation. A dilation can either be a reduction, in which the line is made smaller, or an enlargement, in which the line is made larger. In both cases, the line's shape is preserved, but the size is changed.
The center of dilation, also known as the scale factor, is a fixed point around which a dilation takes place. The scale factor is a value that represents the amount of change in size, it can be greater than 1 for an enlargement or less than 1 for a reduction.
In geometry, a dilation is represented by a multiplication of the coordinates of a point by a scale factor. For example, a dilation of a line with a scale factor of 2 will result in the line being twice as long as the original line.
In conclusion, a dilation of a line is a transformation that changes the size of the line but preserves its shape. The center of dilation or scale factor is a fixed point around which a dilation takes place and is represented by a multiplication of the coordinates of a point by a scale factor.
It can be either an enlargement or a reduction depending on the scale factor value.
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The egg displayed is composed of 4 arcs from 4 sectors.
• The arc AC has centre B.
• The arc BD has centre A.
• The arc AB has centre O.
• The arc CD has centre E.
• The radius of the central circle is 1cm.
• OE and OB form a right angle.
Calculate the perimeter of the egg.
The perimeter of the egg comprising of arcs AB, AC, BD, and CD is π·(6-√2)/2 centimeters
What is the perimeter of a plane figure?The perimeter of a figure is the length of the boundary line of a plane occupied by the figure.
The perimeter of the egg can be found by finding the sum of the lengths of the arcs that together form a composite figure of the perimeter of the egg
The length of arc AC centered at point B is found as follows;
The angle at the center B is the base angle of the isosceles right triangle
The acute angle of an isosceles right triangle is 45°, therefore, the angle at B = 45°
The radius of the arc AC, AB = AO + OB = BC
AO and OB are the radii of the circle with center O
AO = OB = 1 cm
AB = 1 + 1 = 2 = BC
The length of AC = (45/360)× 2×π×2 = π/2
AC = π/2
The radii and angle at the center of arc BD are also 2 cm and 45°
The length of arc BD is therefore, (45/360) × 2 × π × 2 = π/2
BD = π/2
The angle at the center of arc CD = ∠CED
∠CED ≅ ∠AEB (Vertical angle postulate)
∠AEB = ∠AEO + ∠BEO = 45° + 45° = 90°
∠CED = ∠AEB (Definition of congruency)
∠CED = ∠AEB = 90°
The radius of the arc CD, CE = ED = BC - EB
EB = √(1² + 1²) = √2
CE = 2 - √2
Length of arc CD = (90°/360°) × 2 × π × (2 - √2)) = π × (2 - √2))/2
CD = π·(2 - √2)/2
The radius of the arc AB = 1 cm
Angle at the center of arc AB = 180°
Length of arc AB = π × 1 = π
AB = π
The perimeter of the egg = AC + CD + BC + AB
Therefore;
The perimeter of the egg = π/2 + π × (2 - √2))/2 + π/2 + π = π·(6 - √2)/2
The perimeter of the egg is π·(6 - √2)/2 cm
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Is x 8 a factor of the function f x 2x3 17x2 64?
A factor of a polynomial function is a polynomial that divides the function evenly when using polynomial division.
To check if x - 8 is a factor of the function f(x) =[tex]2x^3 - 17x^2 + 64[/tex] , we can use polynomial division.
When dividing f(x) by x - 8, the remainder should be zero.
x - 8 is a factor of the function when the remainder is zero.
In this case, the quotient is [tex]2x^2 + x + 8[/tex] , and the remainder is zero, so x - 8 is a factor of the function f(x) = [tex]2x^3 - 17x^2 + 64.[/tex].
So we can say [tex]f(x) = (x-8)(2x^2 + x + 8)[/tex]
Alternatively, we can also use synthetic division to check if x - 8 is a factor of the function.
Synthetic division is a shorthand method of dividing a polynomial by a linear factor such as x - 8.
If the remainder is zero, then x - 8 is a factor of the function.
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A flower bed is in the shape of a rectangular prism. Its dimensions are 3 feet wide by 16 feet long by 6 inches deep.
a. How many cubic feet of topsoil do you need to fill the flower bed?
b. You can spread topsoil at a rate of 4 cubic feet per minute. How long will it take you
to spread all the topsoil?