Let A be a symmetric matrix that is invertible. This means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. We want to show that B is also symmetric, that is, [tex]B = B^{T}[/tex]
To prove this, we can use the definition of matrix inversion. We know that AB = I, so we can take the transpose of both sides:
[tex]AB^{T} = I^{T}[/tex]
Using the transpose rules, we can rewrite this as:
[tex]B^{T} * A^{T}[/tex] = I
Now, we can multiply both sides of this equation by A:
[tex]B^{T} * A^{T}[/tex]* A = A
Since A is invertible, we can multiply both sides by A⁻¹ to get:
[tex]B^{T}[/tex] = A⁻¹
Therefore, we have shown that the inverse of a symmetric matrix A, which we denote as A⁻¹, is also symmetric, since A⁻¹ = [tex]B^{T}[/tex], which is the transpose of the matrix B.
Hence, we have proved that if a symmetric matrix is invertible, then its inverse is symmetric as well.
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Manny has 1/2 yard of fabric with which he intends to make bookmarks. Each bookmark is made from 1/8 of a yard of fabric. How many bookmarks can manny make
Manny can make 4 bookmarks from 1/2 yard of fabric, each bookmark is made of 1/8 yard of fabric.
Manny has 1/2 yard of fabric, and each bookmark requires 1/8 of a yard of fabric. To find out how many bookmarks Manny can make, we need to divide the total amount of fabric by the amount of fabric used per bookmark:
1/2 ÷ 1/8
To divide by a fraction, we can flip the second fraction (the divisor) and multiply:
1/2 × 8/1
Multiplying the numerators and denominators gives:
(1 × 8) / (2 × 1) = 8/2
Simplifying the fraction by dividing both the numerator and denominator by the greatest common factor of 8 and 2, which is 2:
(8/2) ÷ (2/2) = 4/1
Therefore, Manny can make 4 bookmarks from 1/2 yard of fabric. This problem involves basic arithmetic operations such as division and multiplication of fractions. To solve it, we can flip the second fraction (1/8) and multiply it with the first fraction (1/2). This gives us the total number of bookmarks that can be made with the given amount of fabric. We then simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor.
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Find the missing output value (y)
for the given input value (x).
(3,y)
y=x-5
y = [?]
Enter
The corresponding output value is y = -2 when x = 3 in the equation y = x - 5.
What is the missing output value (y)?Given the equation in the question;
y = x - 5
Input value x = 3
Output value y = ?
The equation given is y = x - 5.
This equation is in the form y = f(x), which means that given an input value x, we can find the corresponding output value y.
In this case, we are given an input value of x = 3 and we need to find the corresponding output value y.
To do this, we simply substitute x = 3 into the equation and solve for y:
y = x - 5
Plug in x = 3
y = 3 - 5
y = -2
Therefore, when x = 3, the corresponding output value is y = -2.
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How many minutes in 420 seconds?
Answer: 7 minutes
Step-by-step explanation:
There is 1 minute every 60 seconds
So if we divide the amount of seconds by 60 we will get the answer.
Therefore our equation is: 420/60
420/60=7
SO the answer is 7 minutes
Hope this helps! :)
VIDEO GAMES A video game developer determines that the profit, in thousands of dollars, from a new video game can be modeled by the
function P(x) = -2x² + 130x - 2000 when x is the price of each game. The game will be profitable if P (x) > 0.
To make the game profitable, the price should be at least $
and no more than $
P(x) = -2x² + 130x - 2000 when x is the price of each game to make the game profitable, the price should be at least $ 25 and no more than $ 40.
Quadratic equations are polynomial equations of degree 2 in one variable of the form f(x) = ax2 + bx + c = 0, where a, b, c, R, and a 0 are all zeros. It is the generic form of a quadratic equation in which 'a' is referred to as the leading coefficient and 'c' is referred to as the absolute term of f. (x). The roots of the quadratic equation (,) are the values of x that fulfil the quadratic equation.
There will always be two roots to the quadratic equation. Roots might be real or fictitious in nature.
p(x) = -2x² + 130x - 2000
The game will be profitable if P (x) > 0.
-2x² + 130x - 2000 > 0
-x² + 65x - 1000 > 0
x² - 65x + 1000 > 0
x(x-25) - 40(x -25) > 0
x>25 x < 40.
Therefore, price should be at least $ 25 and no more than $ 40.
The values of variables that satisfy the given quadratic equation are referred to as its roots. In other words, if f() = 0, x = is a root of the quadratic equation f(x).
The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.
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what is parameter in statistics
Parameters in statistics is a number that describes a sample, whereas a parameter is a number that describes the entire population (such as the population mean) (e.g., sample mean).
A population in research is the complete group that you are interested in examining. This can refer to a group of individuals (such as all US adults or all employees of a corporation), but it can also refer to a group that includes other kinds of elements, such as things, occasions, organisations, nations, species, and organisms.
A sample is a subset of the entire population. The group of components you actually use to gather data is called a sample.
Each quantifiable attribute of a sample or population can be summarised using statistics and parameters.
The most typical statistic or parameter for categorical variables (such political affiliation) is a proportion.
The mean or standard deviation are frequently reported statistics or parameters for numerical variables (such as height).
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the proportions of families with various numbers of children age 18 or under in a small town are given in the following table. one family is randomly selected from this town. x 0 1 2 3 4 5 p(x) .10 .40 .13 .10 .22 .05 find the probability that the selected family has at least 3 children age 18 or under.
The probability that at least 3 children age 18 or under will be selected is 0.50
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space/total possible outcome
at least 3 children means x≥ 3
therefore ;
probability of atleast 3 children age 18 or under are selected =
.13+ .10 +.22 +.05
= 0.50
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1000 litros de sangre a mililitros.
Answer:
1000 litros x 1000000 ml/litro = 1 000 000 000 mililitros
Given △PQR ~ △STU, find the missing measures in △STU.
The missing measures in △STU could be 28 degree.
WE have been Given △PQR ~ △STU,
WE need to find the missing measures in △STU.
What is law of sines?For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]
[tex]\dfrac{sin\angle Q}{21} = \dfrac{sin\angle T}{6}[/tex]
[tex]\dfrac{sin\angle 64}{21} = \dfrac{sin\angle T}{6} \\\\\dfrac{0.920}{21} = \dfrac{sin\angle T}{6} \\\\{sin\angle T} = \dfrac{0.920 \times 6}{21}[/tex]
Sin angle T = 0.2628
△STU = 28 degree.
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Nancy has 4,111 in an account that pays 1. 07 interest Compounded monthly what is her ending balance after two years
Nancy's ending balance after two years is $31,930.93. Below, you will learn how to solve the problem.
To find Nancy's ending balance after two years, we will use the formula for compound interest:Plugging in the given values:
A = 4,111(1 + 1.07/12)^(12*2)
A = 4,111(1.089166)^(24)
A = 4,111(7.767)
A = $31,930.93
Therefore, Nancy's ending balance after two years is $31,930.93.
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Use the graph above to determine if the questions below are True, False, or Cannot be determined.
A. (True) (False) (Cannot be determined)
B. (True) (False) (Cannot be determined)
C. (True) (False) (Cannot be determined)
D. (True) (False) (Cannot be determined)
E. (True) (False) (Cannot be determined)
F. (True) (False) (Cannot be determined)
The true and false statements are
True, False, False, True, True, True
How to determine the true and false statementsFrom the question, we have the following parameters that can be used in our computation:
The graph
The maximum from the graph is
y = 4
The graph has real zeros because it crosses the x-axis
Also, it is true that the graph increases from negative infinity to x = -1 and it it true that the y-intercept is 3 (because it intersects the y-axis at this pont)
The vertices are (-1, 4)
Lastly, the function is above 0 at the interval (-3, 1)
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In observational studies, the variable of interest ?
a. is not controlled b. is controlled c. cannot be numerical d. must be numerical.
In observational studies, the variable of interest option (a) is not controlled
In observational studies, the variable of interest refers to the data that is being collected and analyzed. It is a specific factor or phenomenon that researchers are looking to gain insight from.
The variable of interest is not controlled by the researcher, meaning that the researcher does not influence the data or manipulate the results in any way; rather the researcher simply observes the data and the phenomenon. The variable of interest could be numerical or non-numerical.
If the interest is in the correlation between gender and academic performance, then this is a non-numerical variable, as gender is not a numerical value.
However, if the interest is in the correlation between hours spent studying and grade point average, then this is a numerical variable, as grade point average is a numerical value.
Therefore, option (a) is the right choice.
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what will the median of a sample always equal? (smallest value largest value)/2 50th percentile (q1 q3)/2 square root of the variance
The median of a sample will always equal the 50th percentile.
What is the median of a sample?The median of sample data is the middle value when the data is arranged in order from lowest to highest. In other words, it is the value that separates the lower 50% of the data from the upper 50%.
The median is often used as a measure of central tendency in a dataset because it is not affected by extreme values or outliers in the way that the mean is. If the sample size is odd, the median is simply the middle value, If the sample size is even, the median is the average of the two middle values.
The median is also known as the second quartile and the 50th percentile. As a result, the median of a sample will always equal the 50th percentile.
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A glass case is in the shape of a rectangular prism. The volume of the case is 4/125 cubic foot. How many cubic blocks with a side length of 1/5 foot would be required to find the volume of glass case?
2
3
4
5
A glass case is in the shape of a rectangular prism where the volume of the case is 4/125 cubic foot. The number of cubic blocks with a side length of 1/5 foot required to find the volume of glass case is option C: 4.
What is the rectangular prism?
A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid shape that has six faces, where each face is a rectangle.
The volume of the glass case is 4/125 cubic foot. We can write this as:
V = l × w × h = 4/125
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
To find how many cubic blocks with a side length of 1/5 foot would be required to find the volume of the glass case, we need to find the number of cubic blocks that can fit in the rectangular prism. Since the side length of each block is 1/5 foot, the volume of each block is (1/5)^3 = 1/125 cubic foot.
Therefore, the number of cubic blocks required is:
number of blocks = V / volume of one block
number of blocks = (4/125) / (1/125)
number of blocks = 4
So, we would need 4 cubic blocks with a side length of 1/5 foot to find the volume of the glass case.
Hence, the answer is 4.
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Let A be a matrix with linearly independent columns. Which one of these statements must be true? You have only three attempts at this problem. A. The equation Az b always has a solution for all b B. The equation Ab has a solution for all b precisely when it has more rows than columns. O C. There is no easy way to tell if Ax-b has a solution for all b D. The equation Az -b has a solution for all b precisely when it has more columns than rows. OE. The equation Ax -b never has a solution for all b F. The equation Az-b has a solution for all b precisely when it is a square matrix. G. none of the abovePrevious question
If A be a matrix with linearly independent columns, then the statement that must be true is (A) The equation Az=b always has a solution for all b.
Since the columns of A are linearly independent, the matrix A has full column rank, i.e., its column space is the entire space R^n. Here are the implications of this fact for each statement:
A. The equation Az=b always has a solution for all b.
This is true, because for any b in R^n, we can write it as a linear combination of the columns of A, say b=c_1a_1+c_2a_2+...+c_na_n. Then, the solution to Az=b is simply z=[c_1,c_2,...,c_n]^T.
B. The equation Ab has a solution for all b precisely when it has more rows than columns.
This statement is false. The equation Ab=b is always solvable, regardless of the dimensions of A and b. The solution is simply b expressed in the basis of the column space of A.
C. There is no easy way to tell if Ax-b has a solution for all b.
This statement is also false. Since the columns of A are linearly independent, the equation Ax=b has at most one solution for each b. Therefore, Ax=b has a solution for all b if and only if the columns of A span the entire space R^n. This can be checked by computing the rank of A.
D. The equation Az-b has a solution for all b precisely when it has more columns than rows.
This statement is false. The equation Az=b is always solvable, regardless of the dimensions of A and b, as we have seen in (A).
E. The equation Ax-b never has a solution for all b.
This statement is false. The equation Ax=b has at most one solution for each b, and it is solvable for all b if and only if the columns of A span the entire space R^n, as we have seen in (C).
F. The equation Az-b has a solution for all b precisely when it is a square matrix.
This statement is false. The equation Az=b is always solvable, regardless of whether A is square or not, as we have seen in (A).
Therefore, the only true statement among the given options is (A) The equation Az=b always has a solution for all b.
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75% of the employees in a specialized department of a large software firm are computer science graduates. a project team is made up of 8 employees. part a) what is the probability to 3 decimal digits that all the project team members are computer science graduates? 0.013 part b) what is the probability to 3 decimal digits that exactly 3 of the project team members are computer science graduates? part c) what is the most likely number of computer science graduates among the 8 project team members? your answer should be an integer. if there are two possible answers, please select the smaller of the two integers. part d) there are 56 such projects running at the same time and each project team consists of 8 employees as described. on how many of the 56 project teams do you expect there to be exactly 3 computer science graduates? give your answer to 1 decimal place. part e) i meet 30 employees at random. what is the probability that the first employee i meet is the first one who is a computer science graduate? give your answer to 3 decimal places. part f) i meet 33 employees at random on a daily basis. what is the mean number of computer science graduates among the 33 that i meet? give your answer to one decimal place.
The probability that all 8 project team members are computer science graduates is approximately 0.100
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Since 75% of the employees in the department are computer science graduates, the probability that a randomly selected employee is a computer science graduate is 0.75. We want to find the probability that all 8 employees on the project team are computer science graduates. Assuming that the employees are chosen randomly, we can model the situation as a binomial distribution with n = 8 and p = 0.75.
Using the binomial probability formula, the probability that all 8 employees on the project team are computer science graduates is:
P(X = 8) = (8C8) * (0.75)⁸ * (1 - 0.75)⁸⁻⁸
= 1 * 0.1001 * 1
= 0.1001
Therefore, the probability that all 8 project team members are computer science graduates is approximately 0.100, to three decimal places.
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What is the conversion of 3/4 to decimal ?
Answer: 0.75
Step-by-step explanation: .
can you help me work out the value
What separate the population into nonoverlapping groups?
Stratified Sampling separates the population into nonoverlapping groups. By using specific criteria to split the population, we may use this strategy to draw a proportional random sample from each division.
The population is divided into non-overlapping groups or strata, and a proportional simple random sample is taken from each stratum to create a stratified sample. Each group's members ought to have some things in common. We must choose the number of people to choose from each stratum after the strata have been established. Here, the proportionality of the chosen number is crucial. In order to make the characteristic of interest more homogeneous inside a stratum than between strata, strata are based on information other than the characteristic being measured that is known to or thought to fluctuate with the characteristic of interest. Hence, strata can be defined based on any property that explains variation in the characteristic of interest.
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1 pts
A box with an open top is formed by cutting squares
out of the corners of a rectangular piece of cardboard
and then folding up the sides. If x represents the
length of the side of the square cut from each corner,
and if the original piece of cardboard is 15 inches by
13 inches, what size square must be cut if the volume
of the box is to be 189 cubic inches?
Use: length: (15-2x)
Width: (132z)
Height: x
The square that must be cut from each corner of the cardboard to form a box with a volume of 189 cubic inches is 3 inches on each.
What is square?Four equal sides and four right angles make up the two-dimensional shape known as the square. It is one of the most prevalent geometric shapes. There are a variety of useful applications for squares, including constructing tiling, patterns, and grids.
Given:
Length = 15 - 2x
Width = 13 - 2x
So, volume = lwh
189 = (15- 2x) (13 -2x) x
189 = (195 - 30x - 26x + 4x²)x
195x -56x² + 4x³ = 189
4x³ - 56x² + 195x - 189 = 0
On solving the cubic equation we get
x= 1.69, 3 and 9.3
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Find an equation of the line L that passes through the point
(−2, 4)
and satisfies the condition. (Let x be the independent variable and y be the dependent variable.)
L is parallel to the line
3x − 2y = 6.
Answer:
Para encontrar la ecuación de la línea L que pasa por el punto (-2, 4) y es paralela a la línea 3x - 2y = 6, primero debemos encontrar la pendiente de la línea 3x - 2y = 6.
La forma estándar de la ecuación de una línea es y = mx + b, donde m es la pendiente y b es la intersección en y. Podemos reescribir la ecuación 3x - 2y = 6 en esta forma:
3x - 2y = 6
-2 años
Por lo tanto, la pendiente de la línea 3x - 2y = 6 es 3/2.
Dado que la línea L es paralela a esta línea, también tiene una pendiente de 3/2. Ente
y - y1 = m(x - x1)
donde m es la pendiente y (x1, y1) es un punto en la línea. Nos
y - 4 = (3/2)(x - (-2))
Simplificando esta ecuación, obtenemos:
y - 4 = (3/2)x + 3
y = (3/2)x + 7
Por lo tanto, la ecuación de la línea L que pasa por el punto (-2, 4) y es paralela a la línea 3x - 2y = 6 es y = (3/2)x + 7.
Step-by-step explanation:
espero te sirva, traducelo si no puedes español.
List two ways an individual can improve his or her credit score.
Two ways an individual can improve his or her credit score is,
Pay bills on time and Ask for higher credit limits
What is a credit score?Three-digit credit scores are used to determine how risky it would be for a lender to give credit to a certain individual.
Ask to be added as an authorized user if a family member or acquaintance has a credit card account with a large credit limit and a solid track record of on-time payments.
The credit limit on the account can help your utilization because it is added to your credit reports.
If you make late payments, no credit improvement plan will work.
Even worse, missed payments may appear on your credit records for up to 7 1/2 years.
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The sum of the digits of an odd 2 digit number is 17 what is the number
Answer:
x+y=17
y can be 1,3,5,7 or 9
Let's start at 9
x+9=17
x=8
So the burner is 89
7, 5, 3 and 1 don't work
For example In order x+7=17, x should be 10, which is a contradiction; x is the one-digit number. If 7 doesn't work, lower numbers shouldn't work as well.
Step-by-step explanation:
PLEASE HELP ITS DUE ANY MINUTE
The image is an enlargement of the pre-image |s| > 1. The image is a reduction of the pre-image 0 < |s| < 1. The image is the same as the pre-image rotated 180 s = 1.
What is scale factor?We double the length of each of the original shape's sides by a quantity known as a scale factor to enlarge a given shape. The shape will become smaller or larger depending on the scale factor, which can range from 0 to 1. If the scale factor is greater than 1, the shape will become larger. The image, for instance, displays a dilation with a scale factor of two.
The image is an enlargement of the pre-image |s| > 1.
The image is a reduction of the pre-image 0 < |s| < 1.
The image is the same as the pre-image rotated 180 s = 1.
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Solve for x; Then find the length of PM AND OM
Answer:
[tex]x=12[/tex], PM = 27, OM = 54
Step-by-step explanation:
To find x, we can notice that MP is similar to OP. Therefore, we can create an equation:
[tex]2x+3=4x-21[/tex]
[tex]2x-4x=-21-3[/tex]
[tex]-2x=-24[/tex]
[tex]x=12[/tex]
To solve for PM, we can plug in x from [tex]2x+3[/tex]:
[tex]2(12)+3[/tex]
= 27
To solve for OM, we will need to add OP and PM values and plug in x:
[tex]4x-21+2x+3[/tex]
Plug in x:
[tex]4(12)-21+2(12)+3[/tex]
= 54
What is factors of 47 ?
Factors of 47 are 1 and 47 which implies that it can only be divided by one and itself.
The number 47 is a prime number, which implies that it can only be divided by one and itself. As a result, the components of 47 are 1 and 47.
Generally, a number's factors are the positive integers that divide it evenly with no residual. The factors of 12 are, for example, 1, 2, 3, 4, 6, and 12, since each of these numbers can be divided into 12 without leaving a leftover.
Yet, there are only two elements in the case of prime numbers, such as 47, which are always 1, and the number itself. This is because, by definition, prime numbers have no divisors other than 1 and themselves.
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6) A 6-ounce bottle of medicine contains 36 doses. How many doses are in a 15-ounce bottle of the same medicine?
A 15-ounce bottle of the same medicine contains 90 doses.
Unitary method:The unitary method is a method used to solve problems related to proportionality. It involves finding the value of a single unit or the value of a given quantity when the value of one or more units is known.
In the given problem, we will find the number of doses in 1 unit from that will find the number of doses in a 15-ounce bottle.
Here we have
A 6-ounce bottle of medicine contains 36 doses.
Number of doses in a 1-ounce bottle
= 36/6 = 6 doses
Then the number of doses in a 15-ounce bottle of medicine
= 15 × Number of doses in 1 ounce
= 15 × 6
= 90
Therefore,
A 15-ounce bottle of the same medicine contains 90 doses.
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Faith is going to use a computer at an internet cafe. The cafe charges $0. 80 for every minute using a computer on top of an initial charge of $3. Make a table of values and then write an equation for C,C, in terms of t,t, representing the total cost of using a computer for tt minutes at the internet cafe. Number of Minutes Total Cost to Use Computer
00 3\hspace{3px}\color{green}{\checkmark}3✓3
11 3. 80\hspace{3px}\color{green}{\checkmark}3. 80✓3. 80
22 4. 60\hspace{3px}\color{green}{\checkmark}4. 60✓4. 60
33 5. 40\hspace{3px}\color{green}{\checkmark}5. 40✓5. 40
Answer: C=C=
The equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3
The cost of using a computer at the internet cafe can be represented by a linear equation, where C is the total cost and t is the number of minutes used. The equation can be written as C = 0.80t + 3, where 0.80 is the cost per minute and 3 is the initial charge.
To make a table of values, we can plug in different values of t into the equation and solve for C
Number of Minutes (t) Total Cost to Use Computer (C)
0 C = 0.80(0) + 3 = 3
1 C = 0.80(1) + 3 = 3.80
2 C = 0.80(2) + 3 = 4.60
3 C = 0.80(3) + 3 = 5.40
So the equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3.
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Create and solve a proportion to find the value of x. [HINT: What is JK?] triangle JKL = TRiangle GKH
If the base, b, is 6 inches, and the area, A, is 18 square inches, then the height, h, of the triangle is 6 inches.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
The area of a right triangle can be found by using the formula A=1/2bh, where b is the base of the triangle and h is the height. In this example, the base, b, is 6 inches. To find the height, h, we can solve the equation for h: h = 2A/b, where A is the area of the triangle.
Therefore, if we know the area of the triangle, A, we can find the height, h, of the triangle by plugging in the values and solving for h. For example, if the area of the triangle is 18 square inches, then h = 2(18)/6 = 6 inches.
The area of a right triangle can be found by using the formula A=1/2bh and plugging in the known values of b and h. In this example, if the base, b, is 6 inches, and the area, A, is 18 square inches, then the height, h, of the triangle is 6 inches.
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What are the zeros of the polynomial Y=(x+3)(x-2)?
x = -3 and x = 2???
shouldn't it be x = -3 and x = 2?
The price of petrol is increased from R 12.58 per litre to R 13.28per litre Determine the percentage increase in the price
The percentage increase in the price of petrol is approximately 5.56%.
What is percentage?Percentages are used to compare and express parts of a whole, and to express changes or differences in values. For instance, we can use percentages to express:
A discount or a markup in prices
The increase or decrease in a quantity or value
The proportion of a quantity compared to a whole
The probability of an event occurring.
In the given question,
To determine the percentage increase in the price of petrol, we need to calculate the difference between the old price and the new price, divide that by the old price, and then multiply by 100 to convert to a percentage.
The difference between the old price and the new price is:
R 13.28 - R 12.58 = R 0.70
Dividing the difference by the old price:
R 0.70 ÷ R 12.58 ≈ 0.0556
Multiplying by 100 to convert to a percentage:
0.0556 × 100 ≈ 5.56%
Therefore, the percentage increase in the price of petrol is approximately 5.56%.
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