The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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2x + 3 5x – 42 x = [ ? ]
3
Craig stops at a gas station to fill his tank. He must choose between full-service and self-service and between regular,
midgrade and premium gasoline. How many possible combinations are there?
A2.
B6
C4
D8
Answer:
B, 6
Step-by-step explanation:
As there are 2 service options and 3 regular options All you do is multiply them:
2×3=6
Heres a different way to show it:
FS = Full service
SS = self service
R = regular
M = Midgrade
P = Premium
FS,R FS,M FS,P
SS,R SS,M SS,P
So it's 6
Answer:
B. 6
Step-by-step explanation:
Full/self service = 2 options
regular/mid/premium = 3 options
2 x 3 = 6
What is the degree of polynomial 5x³ 4x² 7x?
The degree of the polynomial [tex]5x^{3} + 4x^{2} + 7x[/tex] is 3 , that means it is a third degree polynomial called as cubic polynomial .
What is Degree Of Polynomial ?
The degree of the polynomial is defined as the highest power of the polynomial expression. But, if the polynomial has multiple variables, the degree of polynomial can be found by adding the powers of the different variables in the polynomial expression.
For Example : the degree of polynomial ⇒ [tex]9x^{2} + 7x + 2[/tex] is 2 .
The polynomial is given as : [tex]5x^{3} + 4x^{2} + 7x[/tex] , we have to find the degree ,
So , we can see that the the term having the highest power of the given polynomial is [tex]5x^{3}[/tex] , and the degree is 3 .
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write 300/1,100 as a percent
Answer:
27.3%
Step-by-step explanation:
300/1100 = 0.2727
to get percentage we multiply ^^ by 100
so = 27.27% or rounded to nearest tenth = 27.3
Jordan missed 7 out of 13 test questions. How is this written as a ratio
Answer:
7:13
Step-by-step explanation:
Answer:
if im thinking correctly ratios can be written in 3 ways
Step-by-step explanation:
so it could be 7/13, 7 to 13, or 7:13
Using the Pythagorean Theorem PLEEEEEEEEEEEEEAAAAAASE!
A car traveled 48 miles west and then 14 miles south. How far is the
car from its starting point?
Answer:
50 miles.
Step-by-step explanation:
You can visualize this as a triangle. the west route is one leg and the south route is the other. The distance from the starting point is the hypotenuse. 48^2+14^2=c^2, c=50.
Answer:
50
Step-by-step explanation:
[tex]48^{2} + 12^{2} = x^{2} \\X= 50[/tex]
ITS DUE TODAY PLS HELP MEEE
Answer:
x=12
Step-by-step explanation:
10x-18+6x+6=180
16x-12=180
16x=180+12
16x=192
x=192/16
x=12
plz mark as brainliest
extra points!!no links tho
given the function f(x)=x^2+10x+20
a.state whether the vertex represents a maximum or a minimum point for your function. explain your answer
b.rewrite f(x) in vertex form by completing the square
Answer:
a. the vertex represents a minimum point b. f(x) = (x + 5)² - 5Step-by-step explanation:
a.
a = 1 > 0 ← that means the parabola opens up, so the vertex is minimum of the function
b.
[tex]f(x)=x^2+10x+20\\\\f(x)=\underline{x^2+10x+25} - 25+20\\\\f(x)=(x+5)^2-5[/tex]
Change to vertex form
2x²16x+33
[tex]y=2x^2+16x+33\\\\y=2x^2+16x+32+1\\\\y=2(x^2+8x+16)+1\\\\y=2(x+4)^2+1\\\\or\\\\y=2x^2-16x+33\\\\y=2x^2-16x+32+1\\\\y=2(x^2-8x+16)+1\\\\y=2(x-4)^2+1[/tex]
What is the coefficient of x² in the polynomial x³ 4x² 7x 2?
The provided phrase, x3+4x2+ 7x+ â' 2 has four terms. and coefficient are 1 , 4 ,7 for the expression
What does the phrase mean?
Expressions are made up of terms. A term might be either a constant, a variable, or a combination of both.
What kind of phrase would that be?
A single letter, a single positive or negative integer, or a number of variables multiplied but never added or subtracted might be the only variable. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient. single-word illustrations: Three times in one phrase.
The mathematical operator + separates the four components in the equation x3+4x2+ 7x+â' 2.
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Give three solutions of the inequality
6 - 11x < 61
Answer:
x > -5
( -5, ∞)
Step-by-step explanation:
6 - 11x < 61
Subtract 6 from both sides
-11x < 55
Divided both side by -11. When divided by a negative number the < switch to >
So, the answer is
x > -5
Or
(-5, ∞)
The amount of eroded rock is measured in cubic kilometers (km3). A cubic kilometer is a cube that measures 1 km on each side. How many km3 of rock were eroded
The amount of eroded rock in cubic kilometres is 1 km3.
To calculate the amount of eroded rock in cubic kilometres, we need to find the volume of the area that has been eroded. The volume of a rectangular shape is found by multiplying the length, width, and height (or depth) together.
In this case, the area that has been eroded is 10 km long, 5 km wide, and 20 m deep. However, we need to convert the depth from meters to kilometres to match the units of the other measurements. Since 1 km = 1000 m, we can convert the depth by dividing by 1000:
20 m / 1000 = 0.02 km
Now that all of the measurements are in kilometres, we can find the volume by multiplying them together:
10 km * 5 km * 0.02 km = 1 km3
So the amount of eroded rock in cubic kilometres is 1 km3.
Complete Question:
The amount of eroded rock is measured in cubic kilometres (km3). A cubic kilometre is a cube that measures 1 km on each side. How many km3 of rock were eroded in an area that is 10 km long, 5 km wide, and 20 m deep?
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What is the product of - 2 1/2 and - 3 1/3
A fish tank contains 24 L of water. Water is added to increase the volume by 12.5%. What is the new volume of water in the tank?
Answer:
27 L
Step-by-step explanation:
To find 12.5% of 24, move the decimal all the way to the left and multiply 24 by 0.125. You get 3, which is how much was added to the original volume.
24 + 3 = 27, which is the new volume.
Help please due in 10 minutes
Answer:
C)
hope this helped
Step-by-step explanation:
help please
For each comparison below, select the correct symbol (<,>, or =) that indicates the relationship between the first and second quantity.
Answer:
See belowStep-by-step explanation:
f(x) is quadratic function and g(x) is linear (since AP in the right column).
Find the equation of the function f(x), use the points on the graph:
f(x) = ax² + bx + c c = 5 as the y-intercept is (0, 5)a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = ba(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4The function is:
f(x) = -x² + 4x + 5Find the equation of g(x)
Find the slope of g(x):
m = (1 - 7)/(-1 + 4) = -2Use (-4, 7) to find its equation:
y - 7 = -2(x + 4)y = -2x + 7 - 8y = -2x - 1See the required comparison belowThe y-intercepts:
f(x) ⇒ 5, g(x) ⇒ -1-5 < - 1Values at x = 3:
f(3) = -3² + 4(3) + 5 = 8g(3) = -2(3) - 1 = - 78 > 7Average rate of change in the interval [2,5]:
f(x) ⇒ (0 - 9)/(5 - 2) = -3g(x) ⇒ (-11 + 5)/ (5 - 2) = -2-3 < -2Max of function in the interval [-5, 5];
f(x) ⇒ 9, vertex of the functiong(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function9 = 9Answer:
Step-by-step explanation:
What grade are you in bc I did this
Identify the similar triangles in the figure then find the value of X.
A. Write the similarity statement in the form of triangle~triangle.
B. What is the value of X.
Answer:
x = 8
Step-by-step explanation:
∠ B ≅ ∠ D
∠ A ≅ ∠ C
Then
Δ BAD ≅ Δ DCE ( AA postulate )
Then the ratios of corresponding sides are equal, that is
[tex]\frac{BA}{DC}[/tex] = [tex]\frac{BD}{DE}[/tex] , substitute values
[tex]\frac{x}{4}[/tex] = [tex]\frac{12}{6}[/tex] = 2 ( multiply both sides by 4 to clear the fraction )
x = 8
The ranges of values = 40 and the number of sets = 10 , then the length of set is
For example, if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 6}, then x=6>5=y, but if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 7}, then x=6=y. not sufficient.
What is values?Values are ideals or beliefs that a group or an individual hold and are essential for determining what is desirable or undesirable to them. Values can also be seen as overall conceptions people hold toward the world and aligns their behavior, motivation, perceptions, and personality. Values establish a framework through which people can compare what is most important and, in most cases, forms the basis for making choices. People interact with the world based on their values, which vary from person to person.An individual can value integrity, while another will value loyalty, and these values are shaped by a person's past experiences or cultural background. Notably, an individual can have several sets of values, but the degree to which the person can value these things can vary. A good example is someone who values family and wealth. There could be situations whereby such an individual can be faced with choosing between family and wealth, and it is very normal to sacrifice one over the other.To learn more about values refer to:
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Complete question is: If the ranges of values = 40 and the number of sets = 10 , then what will be the length of set ?
What is 2 polynomials called?
Binomial is the referred to the polynomial algebraic expression that has two terms.
What is Binomial?An expression with two dissimilar terms joined by an addition or subtraction operator is called a binomial in algebra. Since there are two terms, for instance, 2xy + 7y is a binomial. According to the quantity of terms present, algebraic expressions can be divided into different types, such as monomial, binomial, trinomial, etc.
An expression in algebra with two terms is called a binomial. Alternatively stated, a binomial expression is an algebraic expression made up of two terms that are dissimilar and have constants and variables. Using mathematical operators like + (plus) and - (minus), these terms are joined. Depending on how many terms it contains, an algebraic expression is classified as a binomial, monomial, trinomial, quadrinomial, etc.
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Consider r (x) = StartFraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline EndFraction, where a, b, c, and d are positive integers and b < d. What value does r(x) approach as x approachesInfinity? 0 StartFraction a Over c EndFraction StartFraction b Over d EndFraction Infinity
Answer:
The correct answer is 0 or choice A on edge
Step-by-step explanation:
right on edge
Therefore, value of r(x) as x approaches Infinity : zero
[tex]\bold{\lim_{x \to \infty} r(x)=0}[/tex]
What is function?"A function is a special relationship where for each input and their is single outputs."
What is limit?"Limit is defined as the value that a function approaches for the given input value."
For given situation,
We have been given a function,
r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction
We can rewrite it as,
[tex]r(x)= \frac{ax^b+8}{cx^d}[/tex] , where a, b, c, and d are positive integers and b < d.
We need to find the value of r(x) approach as x approaches Infinity.
This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]
Now, we find the value of limit for given function.
[tex]\lim_{x \to \infty} r(x)[/tex]
= [tex]\lim_{x \to \infty} \frac{ax^b+8}{cx^d}[/tex]
= [tex]\lim_{x \to \infty} (\frac{ax^b}{cx^d} + \frac{8}{cx^d})[/tex]
= [tex]\lim_{x \to \infty} \frac{a}{cx^(d-b)} + \lim_{x \to \infty} \frac{8}{cx^d}[/tex] ...............(since d > b)
= [tex]0 + 0[/tex]
= [tex]0[/tex]
Therefore, [tex]\bold{\lim_{x \to \infty} r(x)=0}[/tex]
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Subtract -2a+7b=-5 from the other equation so the b-terms become opposites
When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.
What is equation?In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.
To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b
This is only possible when the other term has 14,
Lets solve
2a + 7b = - 5
- 4a + 14b = -10
-2a -7b = 5
Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.
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Flow chart to find the biggest of 3 numbers
The flowchart to find the biggest of 3 numbers is mentioned below:
Define Flowchart.A flowchart is a type of diagram that represents an algorithm, process, or workflow. It is a visual representation of the steps and decisions involved in a problem-solving or decision-making process. Flowcharts use a variety of symbols and shapes to represent different types of steps and decisions, such as inputs, outputs, process steps, and decision points. They are used to communicate the logic of a program or process to different stakeholders, such as developers, managers, and users.
Define Algorithm.An algorithm is a set of instructions or a step-by-step procedure for solving a problem or completing a task. It is a well-defined sequence of operations or actions that are taken in order to achieve a specific goal or outcome. Algorithms can be expressed using natural language, pseudocode, or programming languages. The steps in an algorithm must be unambiguous and have a clear stopping point.
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What is the slope of a logarithmic graph?
The slope of a logarithmic graph depends on the type of logarithm used.
For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.
For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.
For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.
It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.
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Please I need help with this question
ind the general solution of the given differential equation. dr / d theta + r sec theta = cos theta
r = ___
r = (sin theta + C)^(-1) where C is an arbitrary constant of integration.
Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y.
r = (cos(theta) - d/d(theta) of sec(theta)) / sec(theta)
The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. Be a function with the form: y=f(x), where x is an independent variable, f is an unknown function.
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Please help with all
What are the solutions of the equation 9x4 minus 2x2 7 0?
The solution of the equations are x = √1 = ± 1
Now, According to the question:
The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]
Using the substitution rule we put [tex]x^{2}[/tex] = u .
The given equation now changes to
[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)
Equation(1) is a simple quadratic equation which can be solved by factorization as follows:
[tex]9u^2 - 2u - 7 = 0[/tex]
(9u + 7)(u - 1) = 0
Therefore
9u + 7 = 0 → u = -7/9
u -1 = 0→ u = 1
Since u = [tex]x^{2}[/tex] implies
x = √-7/9 = ± i√7/9
x = √1 = ± 1
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The complete question is this:
What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.
The mean length of 10 childrens' index finger is 6.8cm.
The mean length of 7 adults' index finger is 12.8cm.
What is the mean length (rounded to 2 DP) of these 17 people's index finger?
Answer:
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
please help tysm! ;))))))))))
Answer:
7 : 1 or 7/1
.........................
Pythagorean Theorem & Irrational Numbers:Question 2
What is the length, in units, of the line segment with
endpoints at (1, 4) and (3, 7)?
Select one: answer is to the power of
13
15
137
5
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
d = √(7-4)²+(3-1)²
= √3²+2²
= √9+4
= √13