The probability that all adjacent points differ in colour is [tex]\frac{1}{5}[/tex].
What is probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given ,
We have first three colour Green that is g1 , g2 and g3
And We have next three colour red that is r1 , r2 and r3
The probability that all adjacent points differ in colour = 3! * [tex]^{4}C_{3}[/tex] 3! / 6!
=> [tex]\frac{ 3! * 4! *3!}{6!}[/tex]
=> [tex]\frac{1}{5}[/tex]
The probability that all adjacent points differ in colour is [tex]\frac{1}{5}[/tex].
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What are the vertical and horizontal asymptotes of F x )= 3x 2 x 2 4?
As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.
What is vertical asymptote?On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).
What is horizontal asymptote?A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.
We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.
Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.
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What is the formula for the volume V of a cylinder with base area B and height H?
The formula for the volume of cylinder with base area B and height H is V = B × H.
What is the volume of the cylinder?A cylinder is a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Area of a circle which is the base of a cylinder = πr²
Given that;
Base area = BHeight = HPlug the given values into the above formula.
V = π × r² × h
V = πr² × h
V = Base area × Height
V = B × H
Therefore, formula for the volume is V = B × H.
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An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 1300 meters, and Plane B was at an altitude of 1092 meters. Plane A is gaining altitude at 17 meters per second, and Plane B is gaining altitude at 21 meters per second. Let x be the number of seconds passed
(A) The expression for each plane are as follows;
Plane A; 1300 + 17x
Plane B; 1092 + 21x
B). The equation to show when the two planes would be at the same altitude is; 1300 + 17x = 1092 + 21x.
Which equation shows when the two planes would be at the same altitude?It follows from the task content that the initial altitudes of plane A and B are 1300 and 1092 respectively.
Since plane A gains altitude at 17 meters per second; The expression for the altitude after x seconds is;
1300 + 17x
Also, since plane B gains altitude at 21 meters per second; The expression for the altitude after x seconds is;
1092 + 21x
Ultimately, at the point when the two planes are at the same altitude; the equation which is true about the situation is;
1300 + 17x = 1092 + 21x.
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How do you find the vertical and horizontal asymptotes of a function using limits?
To find the vertical asymptote, take the limit of the function as x approaches infinity or negative infinity. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain.
To find the vertical asymptote of a function, take the limit of the function as x approaches either infinity or negative infinity. This will give the value at which the output of the function approaches infinity or negative infinity, respectively. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain. If the limit of the function as x approaches the endpoint is finite, then the horizontal asymptote is the value of the limit. If the limit of the function as x approaches the endpoint is infinite, then the horizontal asymptote is undefined. If the limit of the function as x approaches the endpoint is undefined, then the horizontal asymptote is undefined.
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What are three consecutive odd integers of 57?
The required three consecutive odd numbers that sum up 57 are 17, 19 and 21.
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.
Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.
So, we can say that the difference between any two consecutive odd numbers is:
= 2k+3 – (2k+1)
=2k+3-2k-1
=2
So, for every two consecutive odd numbers there is a difference of 2.
Now, let us take ‘n’ to be an odd number.
So, an odd number just before n will be (n-2).
And also an odd number just after n will be (n+2).
Since, it is given that the sum of these three consecutive odd numbers is 57. So, we can write the following equation:
n-2+n+n+2=57
3n=57
So, n = 19
The odd number before n will be = n -2 = 19-2 = 17
And the odd number after n will be = n+2 = 19 + 2 = 21
Therefore, The required three consecutive odd numbers that sum up 57 are 17, 19 and 21.
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Question 67
Use substitution to solve the system of equations.
y=x+8
2x-3y=5
O (19,27)
O (-21, -29)
O (-29, -21)
O (-5,3)
If line a has a slope of -8, what would be the slope of a line perpendicular to line a?
If line a has a slope of 2/5, what would be the slope of a line perpendicular to line a?
The slope of each of the perpendicular lines are:
a. 1/8
b. -5/2.
What is the Slope of Perpendicular Lines?The slope of two lines that are perpendicular to each other have values that are negative reciprocals. That is to say, their product will be equal to -1.
For example, if the slope of two perpendicular lines are -a and 1/a, therefore, their product will be (-a)(1/a) = -1.
a. Line a has a slope that is equal to -8. The negative reciprocal of -8 is 1/8.
Therefore, the slope of the perpendicular to line a would be 1/8.
b. Line a has a slope that is equal to 2/5. The negative reciprocal of 2/5 is -5/2.
Therefore, the slope of the perpendicular to line a would be -5/2.
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a sailing ship stopped at several islands, releasing one mating pair of goats onto each one. on the smallest island, the limited food supply could only support a total of 1500 goats. if their per capita growth rate is 0.5 per year, how many years will it take before the goat population on the smallest island reaches 1000?
After 6 years the population of goats on the small island reaches 1000.
What is per capita growth rate?It is the rate of increases of population per individual in the population. The term related to time period and entire population.
How to calculate the time to reach the maximum populationgiven, initial population of goat on the smallest island, N° =2,
after t years the population of goats on this island, N= 1000
the maximum goat carrying capacity of this island, K= 1500
per capita growth rate, r = 0.5 per year
now, we use logistic growth equation, dN/dt = r×N[(K-N)/K]
dN/dt = 0.5×1000{1500-1000)/1500}
dN/dt= 166.67
∫dN/166.67 = ∫dt
by integrating both sides
N/166.67 = t+c , where c is the
integration constant
at time t=0, N°=2
c= 0.012
N/166.67 =t+0.12
as N=1000 , t= 5.99 years
hence, after 6 years the population of goat on the island reaches 1000.
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Determine the range of the following graph:
Answer:
-1 ≤ y ≤ 6
Step-by-step explanation:
The range is the values of y.
In this graph lowest point is -1 and the highest is 6.
The points are filled so that means that we include 6 and -1.
So it would be -1 ≤ y ≤ 6.
The width of a rectangle is the length minus 5 units. The area of the rectangle is 14
units. What is the width, in units, of the rectangle?
The width of the rectangle is 2 units.
What is the width of a rectangle?Despite having four sides, a rectangle only has two distinct dimensions since the sides are paired. Though the width is often the shorter of these two dimensions, it is more commonly referred to as the horizontal side when the rectangle is shown lying on its side.
Calculation:Given the width of rectangle is length of rectangle - 5 units.
Let us suppose that length of rectangle is y and width of the rectange is y-5.
The formula of area of rectangle is l×b where l and b are length and breadth respectively.
So substituting in the equation we get
[tex]y* (y-5) = 14.\\y^2- 5y = 14\\y^2 - 5y - 14 = 0[/tex]
Solving the above quadratic equation we get y as 7 and -2.
As length cannot be a negative quantity we take length as 7 and it gives us the result that the width is 2 units.
The width of the rectangle is 2 units.
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A bag contains a (hkv-fhyp-che) red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the
(i) yellow ball?
(ii) red ball?
(iii) blue ball?
Answer -
So since there are 3 balls that are in the bag, it makes the denominator 3 and since they get one- one chance each, so the answer will be-
yellow ball - 1/3
Red ball - 1/3
Blue Ball - 1/3
Finding angle measures of a triangle given two angles of a similar triangle
ok
Answer:
the answer would be this 5,8,3
Determine the domain of the following graph:
Step-by-step explanation:
the domain of a function is the interval or set of all valid x (input) values.
the range of a function is the interval or set of all valid y (function result) values.
the graph shows us that the x values are continuously between -5 and +3.
and the end points are filled, so, they are to be included as valid points (via the <= or >= signs).
so, the domain is
-5 <= x <= 3
Does parallel equal 180?
The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°.
Parallel lines are straight lines that never meet each other no matter how long we extend them
Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).
The fundamental characteristics listed below make it simple to recognise parallel lines.
Parallel lines are defined as straight lines that are always the same distance apart.
No matter how far apart they are from one another, parallel lines can never intersect.
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How will I know if my SSS loan is approved?
You can log into your My.SSS account to see the status of your SSS salary loan.
Your salary loan has been granted if you see the message "SSS Loan Application Has Been Granted." Logging into your My.SSS account will allow you to view the status of your SSS salary loan. Select "Inquiry" first, followed by "Loan Info." Your SSS loan status and other loan information can be found here. If the loan funds have already been credited to your disbursement account, you will also get another SMS message.
The loan must be repaid by the borrower in 24 monthly installments. The second month after the loan's origination date is when the monthly amortization starts.
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What are the properties of the circumcenter of a triangle quizlet?
For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.
What do you mean by a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
What do you mean by circumcenter of triangle?The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.
Properties of circumcenter of triangle are:
In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle. Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle.To learn more about circumcenter visit:
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What is the domain and range of f/x )= x³?
domains = all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value the minimum. The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
domains = all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)
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PLS HELP!
The figure shows a loading dock and a side view of an attached ramp, whose run is 12 feet and whose rise is 39 in. Devyn is wondering whether a long rectangular box can be stored underneath the ramp, as suggested by the dotted lines. The box is 2ft tall and 5ft long. Answer Devyn's question.
With the help of Trigonometry the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.
What is Trigonometry?
Studying the correlations between triangle side lengths and angles is the subject of trigonometry, a branch of mathematics. From the use of geometry in astronomical research, the field first appeared in the Hellenistic world in the third century BC.
Dimensions are the measure of the length, width and height of a given object. Yes, a rectangular box of length 5 feet and height 2 feet can be stored underneath the ramp.
The measure of the sides of a given object is referred to as its dimensions. This can be with respect to its length, width, and height.
It has been given that the height of the ramp is 39 inches. But,
12 inches = 1 feet
So that,
39 inches = x feet
make x the subject of the formula to have;
x = 3.25 feet
Thus the dimensions of the ramp are ;
length = 12 feet
height = 3.25 feet
Therefore, the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.
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When two angles and a non-included side of one triangle are congruent to the corresponding pieces of another triangle?
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
We know that the AAS (angle-angle-side) theorem says that when two angles and any side of a triangle are congruent to two angles and any side of other triangle, then the triangles are said to be congruent.
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Whereas the Angle-Angle-Side Postulate (AAS) tells us that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
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What are the roots of the equation 2x² 3x 2 0?
The solutions or roots of the equation 2x² + 3x - 2 = 0 will be 1 and -2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The quadratic equation is given below.
2x² + 3x - 2 = 0
Factorize the equation, then we have
2x² + 3x - 2 = 0
2x² + 4x - x - 2 = 0
2x(x + 2) - 1(x + 2) = 0
(x - 1)(x + 2)
x = 1, -2
The solutions or roots of the equation 2x² + 3x - 2 = 0 will be 1 and -2.
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The roots of the quadratic equation 2x² + 3x - 2 = 0 are - 2, 1/2.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, A quadratic equation 2x² + 3x - 2 = 0.
Now, Two numbers that multiply to - 4 and add to 3 is 4, - 1.
Therefore,
2x² + 3x - 2 = 0.
2x² + 4x - x - 2 = 0.
2x(x + 2) - 1(x + 2) = 0.
(x + 2)(2x - 1) = 0.
x + 2 = 0 Or 2x - 1 = 0.
x = - 2 Or x = 1/2.
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Which tool would you use to make chart?
The
tools
used to make a
chart
are Info-gram, tableau, Grafan, Chartist
What is a chart?
A
chart
can be defined as a
graphical
representation for
data
visualization, such that the data is represented with symbols as bars lines in line chart, or slices in a pie chart"
It is used to represent tabular numeric data and functions or other kinds of quality structure, providing different information.
The tools used in a chart includes;
Info-gram
tableau
Grafana
Chartist,
FusionCharts,
Datawrapper
ChartBlocks
Hence, a
chart
is a graphic representation of data.
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What are the factors of 6x² 5x 6?
Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .Quadratics can be defined using an equation of a second-degree polynomial.
what is quadratic equation ?The mathematical action known as "squaring," which is typically used to describe a quadratic problem, involves multiplying a variable by itself. This lexicon is based on the idea that the area of a square is equal to the product of the lengths of its sides. The Latin term quadratum, which means square, is where the word "quadratic" comes from.
here
= 6x² - 5x- 6
= 6x² - 9x + 4x - 6
= 2 ( 2x - 3 ) + 3x ( 2x - 3 )
= (3x+2) ( 2x - 3 )
So , Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .
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How do you find the degree and the number of turning points in a polynomial function?
To find the degree of a polynomial function, count the number of terms in the expression. To find the number of turning points, take the degree of the polynomial and subtract 1. The number of turning points will be equal to that number.
To find the degree of a polynomial function, the first step is to count the number of terms in the expression. For example, if the expression is 3x^2 + 4x + 2, then the degree is 2 because there are three terms.The second step is to subtract 1 from the degree of the polynomial. In the example, subtracting 1 from 2 gives us 1. Therefore, the polynomial has 1 turning point.A turning point is a point on the graph of the polynomial where the slope of the tangent line is 0. This means the graph changes direction at the turning point. In the example, the graph changes direction at the point (1, 5).In summary, to find the degree and the number of turning points in a polynomial function, count the number of terms in the expression to find the degree, then subtract 1 from the degree to find the number of turning points.
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What is the additive inverse of
Answer:
Subtraction
Step-by-step explanation:
The additive inverse of something will use subtraction, basically the opposite
The cost of a phone is reduced by 20%. The new cost is $70.40. What was the original price?
The original price 1. $ 88.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means)
Given;
The cost of the product was reduced by 20%, leaving $ 70.4 as the final price.
Cost of phone after 80% off= $70.40
So, now we will do a cross-multiplication;
If the percent is 80% =70.40
Let, the original price 100% = x
80x = 70.40. 100
80x = 7040
X = 7040: 80
X = 88
Therefore, the 100 percent value of phone will be $88
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The sum of 3 33 consecutive odd numbers is 69 6969. What is the third number in this sequence?.
The third number in this sequence is 23.
The sum of three consecutive odd numbers can be written as (2n-1) + (2n+1) + (2n+3) = 69, where n is a positive integer. Expanding the left side gives us 6n+1 = 69, which means n = 11. The third number in the sequence is (2n+1) = (2 × 11+1) = 23. Therefore, the third number in the sequence is 23.
In the given sequence, 1, –3, 9, –27, 81,..., each number is multiplied by -3 to get the next one in the sequence. Since the absolute values of the numbers in the sequence are increasing, the sequence is diverging to an infinite value, either positive or negative. Therefore, it can be concluded that the given sequence is a divergent sequence.
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let h of x equals the integral from negative 5 to x of negative 4 times quantity t minus 2 close quantity squared plus 8 dt. where does h(x) have a relative minimum?
The relative minimum of h(x) occurs at x = 2. Integrals can be used to solve a wide range of problems in mathematics and physics, such as finding the area under a curve
An integral is a mathematical concept that involves the concept of integration, which is a way to find the area under a curve or the volume of a solid of revolution. Integrals can be classified into two types: indefinite integrals and definite integrals.
To find the relative minimum of the function h(x), we need to find the value of x that minimizes the value of h(x).
First, let's find the derivative of h(x). We can do this by applying the chain rule to the function inside the integral:
[tex]h'(x) = (-4 * (t - 2)^2 + 8)' = (-4 * (t - 2)^2 + 8)' = -8 * (t - 2)[/tex]
Next, we need to find the points where h'(x) = 0 or is undefined. Setting h'(x) = 0 and solving for t, we find that t = 2. Substituting this value back into the original expression for h(x), we get:
[tex]h(x) = -4 * (2 - 2)^2 + 8 = 8[/tex]
Since h'(x) is undefined at t = 2, we need to check whether the function is increasing or decreasing at that point. To do this, we can take the second derivative of h(x):
[tex]h''(x) = (-8 * (t - 2))' = -8[/tex]
Since the second derivative is negative at t = 2, this means that the function is decreasing at that point.
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What is the remainder when x³ 3x² 4x 6 x 3?
The expression x³ 3x² 4x 6 can be expanded to x³ + 3x² - 4x - 6. When this expression is evaluated for x = 3, the result is 24, so the remainder is 0.
The expression x³ 3x² 4x 6 can be expanded to x³ + 3x² - 4x - 6. To find the remainder when this expression is evaluated, we must first substitute in a value for x. For this example, let x = 3. When we substitute 3 for x, the expression becomes 3³ + 3x² - 4(3) - 6. We can simplify this expression by performing the operations in order of operations. First, we can calculate 3³, which is equal to 27. Next, we can calculate 3x², which is equal to 27. Subtracting 4(3) from 27 gives us 15. Finally, subtracting 6 from 15 gives us 9.
The remainder of evaluating
x³ 3x² 4x 6 for x = 3 is 9.
x³ 3x² 4x 6 = 3³ + 3x² - 4(3) - 6 = 27 + 27 - 12 - 6 = 24
Remainder = 24 - 3 = 0
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How do you find the slope of a perpendicular line with an equation and point?
First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.
By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
What is the formula for finding the area of an isosceles triangle?
Answer:
base x height also A=1/2bh
Step-by-step explanation:
that’s the formula