The equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
What is vertex form?
A different way to express the equation of a parabola is in its vertex form. A quadratic equation is typically represented as an x 2 + b x + c, and when graphed, it will look like a parabola.
Here, we have
Given
The vertex (1, 2) and the point (-3, 6).
we have to find the equation of the function in vertex form.
We know that
The vertex form of the equation is :
f(x) = a (x-h)² +k
Now, we put the value of x, h, and k and we get
6 = a(-3-1)² + 2
6 = 16a + 2
4 = 16a
a = 1/4
Now, we put the value of a in the vertex form equation and we get
f(x) = 1/4 (x-1)²+2.
Hence, the equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
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What are the 3 ways to write a linear equation?
The 3 ways to write a linear equation is Slope-Intercept Form, Point-Slope Form, Standard Form.
1. Slope-Intercept Form: This form of linear equation is written as y = mx + b, where m is the slope of the line, x is the independent variable, and b is the y-intercept. This form of the equation can be used to graph the line by finding the x-intercept and y-intercept.
2. Point-Slope Form: This form of linear equation is written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. This form of the equation can be used to graph the line by finding a second point on the line and connecting the two points.
3. Standard Form: This form of linear equation is written as ax + by = c, where a and b are not both 0, and c is a constant. This form of the equation can be used to graph the line by finding two points that satisfy the equation.
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pleaseee help :15x+32=200
Answer:
11.2
Step-by-step explanation:
15x + 32 = 200 Subtract 32 from both sides
15x + 32 - 32 = 200 - 32
15x = 168 Divide both sides by 15
[tex]\frac{15x}{15}[/tex] = [tex]\frac{168}{15}[/tex]
x = 11.2
Answer:
i think the answer is x= 11.2
Step-by-step explanation:
15x= 200-32
15x=168
x=168/15
x=11.2
valuate the function for f (−9) if f (x) =3/5x+
The value of the function at x = -9 will be 13/5. Then the correct option is A.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
f(x) = (3/5)x + 8
The degree of the function is one. Then the function is a linear function.
The value of the function at x = -9 will be given as,
f(-9) = (3/5)(-9) + 8
f(-9) = - 27 / 5 + 8
f(-9) = (- 27 + 40) / 5
f(-9) = 13 / 5
The value of the function at x = -9 will be 13/5. Then the correct option is A.
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The complete function is f(x) = (3/5)x + 8.
How do you find a 30 degree angle?
We can construct a 30-degree angle by bisecting a 60-degree constructed angle.
By following the given steps we can create a 30-degree angle,
Use a straightedge to create a segment of a line. Label the ends of it. We will refer to them as points A and B in our design.The drawing compass needle should be positioned on point A and adjusted to meet point B. Draw an arc high above the line segment, starting at point B. Move the needle to point B without changing the compass.Make an arc that crosses the first arc swing upward.Create a line segment from point A all the way up to the junction of the two arcs using the straightedge.Mark the new terminus of that line segment as Point D. The angle ∠ABD constructed is a 60-degree angle.Move the needle arm toward one of the rays' points without altering the compass. On the inside of the angle, swing an arc.The needle arm should be moved to the opposite ray's point without adjusting the compass. Draw an arc inside the angle.Use a straight line to connect the intersection of the two arcs with Point B of the 60° angle. That line segment is an angle bisector of the angle ABD, yielding two 30° angles.Read more questions about Triangles and angles from:
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What theorems apply to equilateral triangles?
Theorems related to equilateral traingle :
Theorem 1: The sum of measures of all 3 interior angles of a triangle is [tex]180^0[/tex].
Theorem 2: The angles opposite to equal sides are also equal in measure.
Theorem 3: The sum of the related internal angles is the measure of the exterior angle of a triangle.
Theorem 4:If a line splits any two triangle sides in the same proportion, it is parallel to the third side of the triangle.
Theorem 5: Each angle of an equilateral traingle have equal measure of [tex]60^0[/tex].
Theorem 6: Any two triangle sides can add up to a length that is longer than the third side.
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When the equation y 4x 10 is written in the standard form the value of C Square will be?
The value of c square when the given equation y = 4x - 10 is written in standard form is equal to 100.
As given in the question,
Given equation is equal to :
y = 4x - 10
Standard form of the equation in the slope intercept form is written as:
y = mx + c
Here value of m represent slope is equal to 4
And value of c represents the y-intercept form is equal to -10.
Value of c square is given by :
c = -10
Squaring both the sides we get,
⇒c² = ( -10 )²
⇒c² = 100
Therefore, the value of c square in the given equation is equal to 100.
The given question is incomplete , the complete question is :
When the equation y = 4x - 10 is written in the standard form the value of C Square will be?
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You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour. You need to earn at least $450 each week to pay your bills.
Your friend solves the system of inequalities and tells you that a possible solution is
Your question is incomplete but it could be this,
You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour. You need to earn at least $450 each week to pay your bills. Your friend solves the system of inequalities x + y < 60 and 7x + 12y > 450 and tells you that a possible solution is (-3, 50). Is this a possible solution, why or why not?
No, (-3, 50) is not a possible solution to the system of inequalities x + y < 60 and 7x + 12y > 450. The first inequality, x + y < 60, represents the constraint that the total number of hours you work at both jobs must be less than 60. The second inequality, 7x + 12y > 450, represents the constraint that the total amount of money you earn must be at least $450.
The solution (-3, 50) does not satisfy either of these constraints. The value of y, 50, represents the number of hours you work at the sales job, and is greater than the maximum value allowed by the first inequality. Additionally, the value of x, -3, represents the number of hours you work dog walking, which is negative. This is not possible, as you cannot work negative hours. Therefore, (-3, 50) is not a valid solution to the system of inequalities.
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Tim ha 13 pickle to put in 5 lunch bag. He put the ame number of pickle in each bag? how many pickle are left? and he put in a many pickle a he can. How many pickle doe tim put in each bag? How many pickle are left
Tim puts two pickles in each of the five lunch bags, leaving him with three pickles.
If Tim puts the same number of pickles in each of the lunch bags and as many as possible, only a maximum of two can be put in each of the bags:
Dividing 13 pickles by 5 lunch bags, the answer is 2 pickles with a reminder of 3 pickles
13 ÷ 5 = 13/5
Therefore, Tim puts two pickles in each of the five lunch bags and is left with three pickles.
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a researcher is interested comparing quality of sleep between people who work overnight shifts and people who work day shifts. a sample of 50 day shift workers and 50 night shift workers are asked to complete a quality of sleep measure, which the researcher will treat as an interval scale measure. the researcher will compare the mean levels of each group to see if there is a statistically significant difference between the groups. which analysis would be acceptable to use?
The correct analysis would be 3 option
Describe statistics using an example.
A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.
The right response is selection 3. To compare the means of two independent groups, use the independent samples t test. to determine whether there is a substantial difference between the means of the two groups. In this instance, we are comparing two different groups of people: those who work the night shift and those who work the day shift. By definition, these two groups of persons would differ, therefore neither a matched sample test nor a one-sample test would be appropriate. Furthermore, we are not interested in person's r, which is a measure of linear correlation between two variables.
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What are the roots of the quadratic X² 5x =- 6?
The root of the quadratic equation x² + 5x = -6 are -2 and -3.
Given that,
The quadratic equation x² + 5x = -6 with the variable x.
We have to find what are the root of the quadratic equation.
We know that,
Take the quadratic equation x² + 5x = -6
x² + 5x = -6
x² + 5x +6=0
Now find the factors for 6
6=2×3
So,
2+3=5
We get
x² + 2x + 3x+6=0
Taking the common terms
x (x+2) + 3(x+2)=0
(x+2) (x+3)=0
Now
x+2=0
x=-2
And
x+3=0
x=-3
Therefore, The root of the quadratic equation x²+5x = -6 are -2 and -3.
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What will be the mean deviation of the scores 12/15 18?
The mean deviation of the scores is 2 when the mean value is 15.
What is mean deviation?In the statistics, mean deviation indicates the average deviation relative to the mean value of a given statistical data. While calculating mean deviation mean value is subtracted from each data value. After that all these values are added and divided by the total amount of data.
How to calculate mean deviation?We are given three score 12, 15 and 18
Number of scores, N = 3
mean of the scores = (12+15+18)/ 3
=15
Let, mean score is denoted by X
List of scores X1 12
X2 15
X3 18
Now, we calculate X1 -X= 12- 15 = -3
X2-X = 15-15 = 0
X3-X = 18- 15 = 3
Absolute value of X1-X = |X1-X| = |-3| = 3
Absolute value of X2-X =|X2-X|= |0| = 0
Absolute value of X3-X = |X3-X| = |3| = 3
Sum of absolute value= ∑|Xi-X| = 6
Hence, mean deviation = ∑|Xi-X|/N = 6/3
mean deviation =2
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What is the median of the following set of scores 19 5 12 13 14?
The median for the given set of scores is 13.
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
Given,
A set of scores 19, 5, 12, 13, 14.
Arranging the set of numbers in ascending order,
=> 5,12,13,14,19
For a total of an odd number of outcomes, the median is defined as the middlemost value after sorting the data in ascending (OR) descending order.
For a total of an even number of outcomes, the median is calculated as the average of the two middlemost values after sorting the data in ascending (OR) descending order.
The total number of terms in the given data is 5, Hence the middlemost value is (5+1)/2 rd value is considered as the median,
Median= 3rd term = 13
Therefore, the median for the given set of scores is 13
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which is true? i. random scatter in the residuals indicates a model with high predictive power. ii. if two variables are very strongly associated, then the correlation between them will be near 1.0 or -1.0. iii. the higher the correlation between two variables the more likely the association is based in cause and effect.
Of the given options the one that is true is if two variables are very strongly associated then the correlation between them will be near 1.0 or -1.0. Hence, option A is correct.
Correlation of 1.0 indicates that the variables are directly related while a correlation of -1.0 indicates that the variables are inversely related.
The degree to which two variables are linearly connected is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It's a typical technique for explaining direct connections without explicitly stating cause and consequence.
However, we utilise correlation to indicate a link between two quantitative variables in statistical terms.
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A number of plums were shared among 3 friends. George received 3/8, Terry received 1/4,Samuel 3/16 And jude received the remaining 36 plums. from the number of plums george received,he gave 22 to jude.how many plums did george remain with?
The plums that remain with George after sharing 22 with Jude will be equal to 50.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data mentioned in the question,
We first need to determine how many plums Jude received. Decide to round everything to the sixteenth.
George is having 3/8 = 6/16
Terry is having 1/4 = 4/16
Samuel is having 3/16
So, remaining will go to Jude = (16 - (6 + 4 + 3))/16 = 3/16
Consequently, if Jude received 3/16 of the plums, and she received 36 plums, 1/16 of the total plums is,
= 36/3 = 12 plums (As a side note, there were 192 plums in total).
George has got 6/16 plums = 6 × 12 = 72
Then, he gave 22 plums to Jude, so he has left with,
72–22 = 50 left.
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How do you prove closed under addition?
A closed under addition can be proved if the sum of any two members of the set also belongs to the set.
We can take any two even integers and add them together. The result is an even integer. A set is closed under scalar multiplication if the product of any member and a scalar is also in the set. In other words, if x is in S and a is any scalar then ax will be in the set if the set is closed under scalar multiplication. For example, the set of 2 x 2 diagonal matrices is closed under scalar multiplication.
For example,
A = {( x, y) , y = 0 }
B= { (x, y) , x+ y = 1 }
Typical elements of A are (1,0), (2,0). The element (1,1) is an element not in A. Typical elements of B are (1,0), (1/2,1/2). The element (1,1) is an element not in B. Now A and B carry an addition that is (x, y)+(x', y')=(x + y, x' + y')). Saying that A is closed under addition just means that whenever you take two elements in A, the sum of those elements is again in A. Let's check if this is the case: two elements in A have the form (x, 0) and (x', 0). The sum of those elements is (x + x', 0), and this is again in A. Thus A is closed under addition.
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What are the dimensions of AB?
Answer:
B
Step-by-step explanation:
the order of a matrix are given as
m × n ( m is the number of rows and n the number of columns
matrix A is of order 2 × 3
matrix B is of order 3 × 2
for the matrices to be conformable for multiplication then
the number of columns in A is equal to the number of rows in B
This is the case here , then the order of the resulting product is
AB : 2 × 3 × 3 × 2 the outer values , that is 2 × 2
does someone mind helping me with this? Thank you!
Try the slop formula. x1 - x2 over y1 - y2. Also, try to cross multiply what you already have.
[tex]\displaystyle\\Answer:\ y=-\frac{3}{2}x+1[/tex]
Step-by-step explanation:
The condition of perpendicularity of the two lines given by the equations:
[tex]\displaystyle\\\left \{ {{y_1=m_1x+b_1} \atop {y_2=m_1x+b_2}} \right.[/tex]
is the relation: m₁ x m₂=-1
[tex]\displaystyle\\Hence,\ m_2=-\frac{1}{m_1}[/tex]
[tex]\displaystyle\\Given: y=\frac{2}{3}x+\frac{2}{3}\ == > \ m_1=\frac{2}{3} \\\\Thus,\ m_2=-\frac{1}{\frac{2}{3} } \\\\m_2=-\frac{3}{2}[/tex]
The equation of the Point-Slope Form is expressed as:
y-y₁=m(x-x₁)
(-2,4) that is x₁=-2 y₁=4
[tex]\displaystyle\\Therefore,\\\ y-4=-\frac{3}{2} (x-(-2))\\\\y-4+4=-\frac{3}{2} (x+2)+4\\\\y=-\frac{3}{2}(x)-\frac{3}{2}(2) +4\\\\y=-\frac{3}{2}x -3+4\\\\y=-\frac{3}{2}x+1[/tex]
How many solutions of the given simultaneous equations 2x 3y 8 4x 6y 7?
The simultaneous equations 2x + 3y = 8 and 4x + 6y = 7 supplied do not have a solution
What do simultaneous equations mean?A collection of two or more equations, each of which contains two or more variables, each of whose values can simultaneously fulfil one or more of the equations in the collection, with the total number of variables in the collection being equal to or fewer than the total number of equations.
Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. The equations are referred to as simultaneous equations since they are solved simultaneously.
Here are a few examples of simultaneous equations:
2x + 4y = 14
4x − 4y = 4.
Given,
2x + 3y = 8 and 4x + 6y = 7
We get,
2x + 3y = 8 ….. (i)
4x + 6y = 7 ….. (ii)
Then we have Multiply (i) by 4
4x + 6y = 16..... (iii)
Therefore, LHS of (ii) and (iii) are same but RHS is different. As a result, the answer is false.
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What is the formula for solving mean deviation?
Formula for solving mean deviation is [tex]\frac{[\sum |X-\mu|]}{N}[/tex].
Mean Deviation Definition:
The mean deviation is defined as a statistical measure that is used to calculate the average deviation from the mean value of the given data set. The mean deviation of the data values can be easily calculated using the below procedure.
Step 1: Find the mean value for the given data values
Step 2: Now, subtract the mean value from each of the data values given (Note: Ignore the minus symbol)
Step 3: Now, find the mean of those values obtained in step 2.
Mean Deviation Formula
The formula to calculate the mean deviation for the given data set is given below.
Mean Deviation = [tex]\frac{[\sum |X-\mu|]}{N}[/tex]
Here,
Σ represents the addition of values
X represents each value in the data set
µ represents the mean of the data set
N represents the number of data values
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what is 5a+6b=c
and what is 5a+8=7b-6
whats the answer for as well for 6a+3=8b+10
The numeric value of the expression c = 5a + 6b is given as follows:
c = 759.5.
How to obtain the numeric value of the expression?The expression in this problem is defined as follows:
c = 5a + 6b.
To obtain the numeric value of the expression, the values of a and b have to be known, and they are discovered solving the system of equations presented as follows:
5a + 8 = 7b - 6.6a + 3 = 8b + 10.In standard format, the system is given as follows:
5a - 7b = -14.6a - 8b = 7.Multiplying the first equation by 6 and the second by -5, we have that:
30a - 42b = -84.-30a + 40b = -35.Adding the two equations, we have that the variable b is given as follows:
-2b = -119
b = 119/2
b = 59.5.
Then the variable a is obtained as follows:
5a + 8 = 7(59.5) - 6
a = (7(59.5) - 6 - 8)/5
a = 80.5.
Thus the numeric value of the expression is given as follows:
c = 5(80.5) + 6(59.5)
c = 759.5.
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What is the median of the following data 1 4 7 3 9 5 3 2 7 5?
The median of the given data is 4.5.
The middle value in a sorted, ascending, or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.
For finding the median, the data should be arranged in ascending or descending order first.
Arranging the data in ascending order, we get 1, 2, 3, 3, 4, 5, 5, 7, 7, 9.
There is an even number of observations.
Hence the median is the mean value of (n/2)th and [(n/2)+1]th term.
Here, the 10/2th term = 5th term which is 4
[(n/2)+1]th term= 6th term which is 5
thus, 4+5/2 = 4.5
Hence, the median of the given data is 4.5.
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Quadrilateral ABCD with vertices A(-4, 1), B(-2, 3), C(0, -2) and D(-5, -2): k=3
The vertices of the image of quadrilateral ABCD, after a dilation with a scale factor of 3, are given as follows:
A'(-12,3).B'(-6,9).C'(0,-6).D'(-15,-6).What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure, thus a dilation is classified as a non-rigid transformation.
The vertices of the quadrilateral ABCD in this problem are given as follows:
A(-4, 1), B(-2, 3), C(0, -2) and D(-5, -2).
The scale factor of the dilation is given as follows:
k = 3.
Then the coordinates of the image, given by the answer at the beginning of the answer, were obtained multiplying the coordinates of each of the vertices by 3.
Missing InformationThe problem asks for the coordinates of the image of quadrilateral ABCD after the dilation with the given scale factor.
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What is the formula for pyramids?
Formula for pyramids:
Volume V = /3 B*h
Surface area S = B + 1/2 p*s
Explain the formula for pyramids?A three-dimensional object's volume, which is expressed in cubic units, is a measure of the amount it can hold.A three-dimensional figure's surface area, which is expressed in square units, is a measurement of the entire area that the figure's surface encloses.The difference between both the height as well as slant height must be understood before we can determine the surface area and volume of a pyramid.A pyramid's height is measured perpendicularly from its apex to its base, while its slant height is measured angularly from of the apex to the midway of one of its triangular faces.
Here are the calculations for any pyramid's volume and surface area.
Volume V = /3 B*h
Surface area S = B + 1/2 p*s
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What 2 digit number added to 27 is reversed?
We can claim that when two-digit numbers (14, 25, 36, 47, 58, and 69) are added to 27, the results are reversed.
What are 2-digit numbers?A number is referred to be a 2-digit number when it has two digits.
The range of 2-digit numbers, which have two digits, is 10 to 99.
They can't start with zero since it will be interpreted as a single-digit number.
The digit in the tens slot might be any value between 1 and 9.
The numbers 45, 78, and 12 all have two digits, for example.
So, we know:
14 + 27 = 41
25 + 27 = 52
36 + 27 = 63
47 + 27 = 74
58 + 27 = 85
69 + 27 = 96
Therefore, we can claim that when two-digit numbers (14, 25, 36, 47, 58, and 69) are added to 27, the results are reversed.
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Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 1 − √6, 1+ √6, and 5-i
(Simplify your answer)
What is polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Since we know that complex solutions ALWAYS come in pairs, the minimal polynomial must include the root of 4-i as an acceptable root..
This leads to a polynomial of ...
p(x) = (x - 5)(x - (4+i))(x - (4-i))
Now we can simplify...
(x - (4+i))(x - (4-i)) --> x2 + [(4+i)+(4-i)]x + (4+i)(4-i) --> x2 + 8x + [ 16 -4i + 4i -i2 ] = x2 + 8x +17
Take this quadratic and multiply by (x-5) to get the final, minimal polynomial...
p(x) = (x-5)(x2 + 8x +17) = x3 + 8x2 + 17x -5x2 + 40x - 85 = x3 + 3x2 + 57x - 85
So p(x) = x3 + 3x2 + 57x - 85
p(x) has only real coefficients, the leading coefficient of 1, and is the smallest to allow for the two solutions requested
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1) {(9,-8), (8,-9), (-9, 5), (3, 8), (7, 8) }
Domain:
Range:
Function?: function or not?
The domain is {9, 8, -9, 3, 7}, the range is {-8,-9, 5, 8} and the relation is a function
How to determine the domain and the range?From the question, we have the following parameters that can be used in our computation:
{(9,-8), (8,-9), (-9, 5), (3, 8), (7, 8) }
The domain is the set of the x values
So, we have the following representation
x = {9, 8, -9, 3, 7}
Remove repeated entries
x = {9, 8, -9, 3, 7}
So, the domain is {9, 8, -9, 3, 7}
Similarly, we have
Range = {-8,-9, 5, 8}
Also, the relation is a function
This is because the no x value has several y values
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In AOPQ, m/O = (2x − 5)°, mZP = (3x − 8)°, and mZQ = (10x – 17)º.
-
What is the value of x?
Answer:
x = 14
Step-by-step explanation:
You want the value of x in ∆OPQ, where ∠O = (2x − 5)°, ∠P = (3x − 8)°, and ∠Q = (10x – 17)º.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°. This means ...
∠O +∠P +∠Q = 180°
(2x -5)° +(3x -8)° +(10x -17)° = 180° . . . . . use the given expressions
15x -30 = 180 . . . . . . divide by °, collect terms
x -2 = 12 . . . . . . . . . divide by 15
x = 14 . . . . . . . . . . add 2
The value of x is 14.
__
Additional comment
The measures of the angles are ...
O = 23°, P = 34°, Q = 123°
In what ratio is the line segment joining (- 1/3 and 4 7 divided at the point?
The ratio in which line segment joining (-1, 3) and (4, -7) is is 3: 2 and at a point (2,-3).
What is line segment?A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
What is segment?a piece of a geometric figure that has been removed by one or more points, lines, or planes is known as segment.
The formula that we used is:
[tex]P(x,y)=\frac{mx2+nx1}{m+n},\frac{my2+ny1}{m+n}[/tex]
x = m(x₂) + n(x₁)/(m + n)
⇒ 2 = m(-1) + n(3)/(m + n)
⇒ 2(m + n) = 3n - m
⇒ 2m + 2n = 3n - m
⇒ m/n = 3/2
Therefore, The ratio in which line segment joining (-1, 3) and (4, -7) is is 3: 2 and at a point (2,-3).
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672,342 = 6.72342 × 10n
what is the value of n?
5
3
4
6
Answer: 5
Step-by-step explanation: If n is the exponent and the base is 10, 6.72342 is to be multiplied by 10 power 5 to give the answer as 672342.
6.72342 * 10^5 = 6.72342 * 100000
= 672342
a north carolina licence plate consists of a sequence of seven symbols: number, letter, letter, letter, number, number, number, where a letter is any one of 26 letters and a number is one among 0, 1, . . . , 9. assume that all license plates are equally liely. (a) what is the probability that all symbols are different? (b) what is the probability that all symbols are different and the first number is the largest among the numbers?
The answers to both the subparts using probability are shown:
(A) The probability that every sign is unique is 378/845.
(B) The probability that each sign is unique and that the first number is the biggest one among the others is 189/1690.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.
The probability is calculated by dividing the total number of outcomes by the total number of potential events.
Odds and probability are two different concepts.
Calculating odds involves dividing the probability of an event by the probability that it won't happen.
(A) Since there are three positions for letters and four places for numbers.
Consequently, the final result will be 10⁴×26³.
Since each letter and number should be distinct, the necessary probability is:
= 10 * 9 * 8 * 7 * 26 * 25 * 24 / 10⁴ * 26³
= 378/845
(B) In this instance, the likelihood that the first number will be the greatest among the four numbers is 1/4 because it should be.
In order to obtain the result, multiply the result in (a) by 1/4 as follows:
= 378/845 * 1/4
= 189/1690
Therefore, the answers to both the subparts using probability are shown:
(A) The probability that every sign is unique is 378/845.
(B) The probability that each sign is unique and that the first number is the biggest one among the others is 189/1690.
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