The gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1)
This gradient is a vector that points in the direction of the greatest rate of increase of the function f(x, y, z) = log(x2 + y2 + z2). To evaluate this gradient, the partial derivatives of the function with respect to x, y, and z must be calculated.
The partial derivative of the function with respect to x is (2x / (x2 + y2 + z2)). When x is 1, this simplifies to 2/1. Similarly, the partial derivative with respect to y is 0, and the partial derivative with respect to z is (2z / (x2 + y2 + z2)), which simplifies to 2/1 when z is 1. Therefore, the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1).
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What is the value of 5 + 5.3^4?
810
410
O65
120
Therefore , the solution of the given problem of expression comes out to be 794.0481.
Describe expression.combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.
• 3 x/2 variable is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.
Here,
Given : 5 + [tex](5.3)^{4}[/tex]
=> 5 + (5.3)*(5.3)*(5.3)*(5.3)
=> 789.0481 + 5
=> 794.0481
Therefore , the solution of the given problem of expression comes out to be 794.0481.
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what can you say about the series ∑an in each of the following cases
a) lim |(an+1)/(an)∑|=1
n→[infinity] b) lim nth root(|(an)|=2/3
n→[infinity]
c) lim |(an+1)/(an)|=0.8
n→[infinity]
d) lim |(an+1)/(an)|=3/2
n→[infinity]
e) lim |(an+1)/(an)|=3
n→[infinity]
f) lim nth root(|(an)|=1/2
n→[infinity]
In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.
In case a, since the limit of the ratio of consecutive terms is 1, the series is convergent and its sum is equal to the limit of the sequence of partial sums of the series.In case b, since the limit of the nth root of the absolute value of the terms is 2/3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case c, since the limit of the ratio of consecutive terms is 0.8, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case d, since the limit of the ratio of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case e, since the limit of the ratio of consecutive terms is 3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case f, since the limit of the nth root of the absolute value of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit.Learn more about Convergent here:
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What is the domain of the following function?
Therefore , the solution of the given problem of equation comes out to be each diagonal measures 8.4 units in length..
Define equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.
Here,
Given: 16x + 2 = 36x - 6
8 = 20x
x = 8/20,
simplifying to 2/5, or 0.4
You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.
Re-enter the value of x into a single of the equations.
=>16(0.4) + 2
=>6.4 + 2
=>8.4
To make sure, confirm with the other diagonal.
=>36(0.4) - 6
=>14.4 - 6
=>8.4
Each diagonal measures 8.4 units in length..
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The complete question is "To find the diagonal x value by the given equation 16x + 2 = 36x - 6 "
Deshad runs a river tubing company that serves 300 customers a day during sunny, summer days. He knows that 45% of the customers rent life jackets. Suppose that Deshad calculates the daily proportion p ^ on top of customers who rent life jackets from his sample of 300. We can assume the customers each day represent a random sample
Here acccording to the question,We are examining the conditions under which the sampling distributions of the sample proportions given.
What is sampling distribution?
Sampling distribution is a statistic that determines the probability of an event based on data from a small group within a large population. Its primary purpose is to establish representative results of small samples of a comparatively larger population. Since the population is too large to analyze, you can select a smaller group and repeatedly sample or analyze them. The gathered data, or statistic, is used to calculate the likely occurrence, or probability, of an event.
Sampling distribution According to the given ScenarioWe are examining the conditions under which the sampling distributions of the sample proportions appear uniform, roughly normal, skewed to the left or skewed to the right.
When np10 and n(1p)10, where n is the sample size and p is the sample of proportions, are true, we know that the sampling proportions of the sample distributions will have a normal shape.
Aforementioned that our sample size is 300 people and that p = 0.45, we can use the given data to calculate
Successes anticipated: np= 300(0.45) = 135 10
Failures predicted: n(1p)=300 (10.45)=165 10
Since both of these statements are accurate, sample distribution sampling proportions will have a normal shape.
Because we anticipate each sample to have at least 10 successes and 10 failures, we have a normal sampling distribution.
As a result, the sample distribution has a roughly normal shape.
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BUILD PERSEVERANCE Part A Simplify the expression. (8x + 6) + (5 − x) − 2 (3x+1)
The expression is x + 9.Generally speaking, an expression is at its simplest form when it is most usable.
What is its most basic form?Generally speaking, an expression is at its simplest form when it is most usable. as in this: 5x + x 3.To simplify an expression, create a similar expression devoid of any identical terms. Therefore, we shall rephrase the expression using the fewest number of terms possible.Determine the domain before you can simplify a rational expression.The collection of all possible inputs to a function, including all potential values for the variables, that enable the function to function.Explanation:
8x + 6+5 - x - 6x - 2
= x + 9.
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STEM Osmium is the densest chemical element. A cubic centimeter of osmium has a mass of about 23 grams. If a chemist has 2,530 grams of osmium, about how many cubic centimeters does the chemist have?
Answer: To solve this problem, we can use the fact that a cubic centimeter of osmium has a mass of about 23 grams and the information provided about the chemist's amount of osmium.
First, we can divide the total mass of osmium by the mass of a cubic centimeter of osmium to find out how many cubic centimeters of osmium the chemist has. The equation would look like this:
2,530 grams / 23 grams/cubic centimeter = 110 cubic centimeters
So, the chemist has approximately 110 cubic centimeters of osmium.
It's worth mentioning that an exact value would require additional information as 23 grams per cc is an approximate value and also any impurities or loss of material in the sample also effect the total mass.
Step-by-step explanation:
Define an exponential function, f(x), which passes through the points (0,125) and (3,8). Enter your answer in the form a*b^x
Answer:
Step-by-step explanation:
put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8
b^3=8/125
b=2/5
then the answer is 125*(2/5)^x
Wyatt is paying back a loan with a nominal interest rate of 13.62%. if the interest is compounded quarterly, how much greater is wyatt’s effective interest rate than his nominal interest rate?
a. 0.96 percentage points
b. 0.40 percentage points
c. 0.25 percentage points
d. 0.71 percentage points
please select the best answer from the choices provided a b c d
0.71 percentage points greater is wyatt’s effective interest rate than his nominal interest rate.
What is intrest?Interest is a fee paid by a borrower to a lender for the use of borrowed money. It is calculated as a percentage of the amount borrowed, and is usually paid periodically at intervals. Interest is generally considered to be a form of compensation for the time and risk taken by the lender in providing a loan or other form of credit.
The effective interest rate is calculated by taking the (1 + nominal interest rate/number of compounding periods per year) to the number of compounding periods per year power minus 1. In this case, the effective interest rate would be 0.1362 x (1 + 0.1362/4)^4 - 1, which is 0.1439 or 14.39%. The difference between the nominal interest rate of 13.62% and the effective interest rate of 14.39% is 0.71 percentage points.
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Please help me with my HW
Answer: 4k^7
Step-by-step explanation:
11,778 divide 26
Show work pls
Answer:
453
Step-by-step explanation:
To perform long division of 11,778 by 26, we follow these steps:
452
_____
26 ) 11,778
-104
------
157
156
----
21
Therefore, 11,778 divided by 26 is equal to 452 with a remainder of 21.
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HELPPP 1. Write an equation of the ellipse with foci (0,14) and co-vertices at (±4,0).
The equation of the ellipse with foci (0,14) and co-vertices at (±4,0) is [tex]x^2/16+y^2/36[/tex].
Define ellipse.An ellipse is a geometric shape that is defined as the set of points such that the sum of the distances between the points and two fixed points (foci) is constant. It is a type of conic section and is defined by the equation:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
Where a and b are the semi-major and semi-minor axes, respectively. An ellipse can also be defined as the shape that results from the intersection of a plane and a cone at an angle that is not perpendicular to the base of the cone.
[tex]c=14, b=4, a²=b²+c²== > a=2√9\\x^2/b^2 + y^2/a^2\\x^2/16+y^2/36[/tex]
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Reduce 22/154
to its lowest form.
22/154=11/77=1/7
1/7 is the lowest form
What does ∈ mean in math?
This is a symbol in mathematics that represents "to the power of" or "exponent".
It is used to indicate that a number or expression is being multiplied by itself a certain number of times. For example, if the expression 2aˆ3 is written, it means that 2 is being multiplied by itself 3 times, or 2x2x2. In other words, 2aˆ3 = 2x2x2 = 8.
The number to the right of the aˆ symbol is called the "exponent". The number or expression to the left of the aˆ symbol is called the "base". When a number is raised to the power of one, it is equal to itself. Any number to the power of zero is equal to one. The exponent can be a positive, negative, or fractional number.
Exponents are used to simplifying calculations and can be used to represent large numbers in a more concise form.
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The diagram shows a cuboid with a volume of 42 cm³. K ? cm Work out the missing length of the cuboid. 2 cm 3 cm
Using the formula for the volume of cuboid that is the product of length, breadth and height, The answer is 7cm.
What is a cuboid?A cuboid is a three-dimensional shape with six rectangular faces, three of which are pairs of congruent squares and the other three are rectangles. It is also known as a rectangular prism. The opposite sides of a cuboid are parallel and equal in area. The length, width, and height of a cuboid are three of its measures of size.
What do you mean by volume and formula for volume of cuboid?The volume of a three-dimensional object is a measure of the amount of space it occupies. It is typically measured in units of cubic units, such as cubic centimeters (cm^3) or cubic meters (m^3). The formula for the volume of a cuboid is length x width x height. For example, if a cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm, its volume would be 5 x 3 x 2 = 30 cubic centimeters. In general, the volume of a three-dimensional object can be found by multiplying the area of its base by its height.
length = 2cm
breadth =3cm
volume = 42 cm³
volume = l*b*h
42 = 2*3*h
h= 42/6 =7cm
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3. 2 Roulette wheel: The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2
green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance
of capturing the ball.
a) You watch a roulette wheel spin 9 consecutive times and the ball lands on a red slot each time. What is
the probability that the ball will land on a red slot on the next spin?
(please round to four decimal places)
b) You watch a roulette wheel spin 320 consecutive times and the ball lands on a red slot each time. What
is the probability that the ball will land on a red slot on the next spin?
x (please
round to four decimal places)
The probabilities for the game of roulette that involves spinning a wheel with 38 slots, for a and b, are 0.4737, or 18/38, or 47.37%.
The following are the rationales:
(a) The probability of the ball landing on a red slot on any given spin is 18/38, or 0.4737, or 47.37%. This probability does not change based on the outcome of previous spins, as each spin is independent of the others and the probability of landing on a red slot is always the same. So, the probability of the ball landing on a red slot on the next spin is also 18/38, or 0.4737, or 47.37%.(b) The probability of the ball landing on a red slot on any given spin is 18/38, or 0.4737, or 47.37%. This probability does not change based on the outcome of previous spins, as each spin is independent of the others and the probability of landing on a red slot is always the same. So, even though the ball has landed on a red slot 300 consecutive times, the probability of the ball landing on a red slot on the next spin is still 18/38, or 0.4737, or 47.37%Learn more about probability here: brainly.com/question/25839839
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What is 0.632 as a fraction? Move numbers to the blanks to complete the fraction.
8
79
125
313
457
495
632
999
Answer:
Step-by-step explanation:
Converting 0.632 to a fraction, Step-by-Step
Step 1:
The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:
\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}
1×1000
0.632×1000
=
1000
632
Step 3:
Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:
\frac{632}{1000} = \frac{79}{125}
1000
632
=
125
79
can somebody please help me solve this question:
you are going to climb the roof of your two-story house using a 15-foot ladder. If the safety directions say that you can put the ladder only 2 feet from the house, how far up will you be able to reach on your house?
thanks
Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet
What is Pythagoras TheoremPythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:
x² = y² + z²
where x is the hypothenuse and y, z are the legs of the right angle triangle.
To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.
x² = y² + z²
15² = 2² + z²
z² = 15² - 2²
z² = 221
z = √221
z = 14.87 feet
The height is 14.87 feet
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What is the answer of 2x^2 4x 6 0?
The answer of the equation "2x^2 - 4x - 6 = 0" is -1 and 3.
The equation is solved using factorization:
2x^2 - 4x - 6 = 0 , given equation
2x^2 - 6x + 2x - 6 = 0 , factorizing
2x(x - 3) + 2 ( x - 3 ) = 0 , taking 2x common from the first two terms and 2 common from the last two terms
(2x + 2) (x - 3) = 0
now solving further
( 2x + 2 ) = 0 & ( x - 3 ) =0
2x = (0 - 2) , x = (0 + 3)
2x = (-2) , x = 3
x = (-2/2)
x = -1
Thus, the equation gives the solution as x = -1 and x = 3.
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You are given that $x$ is directly proportional to $y^3$, and $y$ is inversely proportional to $\sqrt{z}$. If the value of $x$ is 3 when $z$ is $12$, what is the value of $x$ when $z$ is equal to $75$
The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]
To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.
When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:
[tex]$x = ky^3$[/tex]
where k is the constant of proportionality.
Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:
[tex]$y = \frac{m}{\sqrt{z}}$[/tex]
where m is the constant of proportionality.
Substituting the second equation into the first equation gives:
[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Since the value of x is 3 when z is 12, the equation can be written as:
[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]
Rearranging gives:
[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]
Substituting this value of k into the original equation gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Substituting z as 75 gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]
Simplifying gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]
Therefore, the value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].
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5. Suppose you went on vacation but forgot your smart phone
charging cable. Your phone battery died after two full days
(48 hours) of use. This situation is modeled by the equation
f(h) = 48, where h is the hours of cell phone use and
f(h)is the percentage of battery life left.
What is the upper bound of the parameter h?
hrs
What is the lower bound of the parameter h? •
hrs
The upper and lower bounds of the parameter h is found to be 0 and 1 respectively.
What is upper and lower bound of a function?
A number U serves as an upper bound for a function f, meaning that for any x, f(x) ≤ U. A number L serves as a function's lower bound, ensuring that for all x, f(x) ≥ L.
Given,
[tex]f(h) = \frac{48-h}{48}[/tex]
where f(h) = Percentage of battery left
h = Hours of cell phone use
Lower Bound of parameter h,
h = 0 ( When percentage is 100%)
f(h) = [tex]\frac{48 - 0}{48}[/tex] = 1
Upper bound of parameter h,
h = 48 (When percentage is 0%)
f(h) = [tex]\frac{48-48}{48}[/tex] = 0
Therefore the upper bound of h is 0 and lower bound of h is 1.
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What is the value of 8 power 8?
Answer:16,777,216
Step-by-step explanation:
Put one pair of bracket into this calculation to make it correct.
7 x 5 - 2 + 3 = 42
The equation becomes true if we put brackets in the following way:
7x(5 - 2 + 3) = 42
Where do we need to put the bracket?Here we have the expression:
7x5 - 2 + 3 = 42
And we want to find where we need to put brackets in such a way that the equation becomes true.
If we solve the equation as it is, we will get:
7x5 - 2 + 3 = 42
35 - 2 + 3 = 42
36 = 42
Now, let's return to the equation:
7x5 - 2 + 3 = 42
If we put one pair of brackets that includes from the 5 to the 3, we will get:
7x(5 - 2 + 3) = 42
7x(4) = 42
42 = 42
So the equation becomes true.
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When can parallelism make your algorithms run faster when could it make your algorithms run slower?
When an algorithm necessitates extensive sharing of instantaneous results, parallelism slows it down. Because there are multiple independent parallel processes and the right number of threads, parallelism will speed up an algorithm.
What algorithm is parallelizable?The ones with data dependencies are the most challenging. It will be exceedingly challenging, for instance, if you are dealing with a vector and the input for the computation at point n depends on the output at position n-1.
When this occurs, you must comprehend what the original algorithm is doing and take an alternative approach. For the aforementioned case, it might be a difficulty with digital signal processing including a feedback-containing digital filter. These are challenging to parallelize, but that is not the sole solution. Instead, you might use the filter and signal's fast Fourier transforms, multiply them, and then perform the inverse transform. All of these operations can be partially parallelized.
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Solve the proportion below. 7/x = 19/114 x=____
A. 8
B. 4
C. 28
D. 24
What additional information would be necessary to determine sin A?
We can determine sin an in the above triangle using the available information without applying the Pythagorean theorem since the length of BC is required because it is the side opposite A.
We are told that we must calculate sin(a) without utilizing the Pythagorean theorem.
Now, we can see from the abbreviation SOHCAHTOA that if we wish to determine Sin a, it will be; sin a = opposite/adjacent
We must now locate a side opposing the angle A or the hypotenuse.
As a result, since the triangle is ABC, the required side is BC because it is the side opposite to A.
Finally, the length of BC is required because it is the side opposite A.
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The complete question should be like:
What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.
Given the table of values, determine the the constant of proportionality, then write the equation of the proportion.
The constant of proportionality is 9 and equation of the proportion.
is y= 10x.
What is Constant of Proportionality?If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality.
Given:
As, we know using the Constant of Proportionality
y = kx
or, k = y/x where k is Constant of Proportionality.
Then, from the table we have
k = 90/9
k= 10
Thus, y = kx
or, y= 10x
Hence, the equation of the proportion is y= 10x.
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Fill in the blank question.
Miss Wade's science class of 20 students is going on a field trip to the zoo. Each student will also take a train ride around the zoo. Mr. Sexton's class of 25 students is going on a field trip to the state park and will take a canoe trip. Admission to the zoo is twice that of the state park's entry fee as shown in the table. Each group will spend the same total amount of money.
Answer:
The total cost of the science class trip to the zoo is $1200
Step-by-step explanation:
The cost of the science class trip to the zoo is $1200, and the cost of Mr. Sexton's class trip to the state park is $1000.
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently.
Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300.
PLS HELP ME IM ABT TO CRY!!!! 100 PTS
Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn.
Salesman C does not earn any commission. His weekly salary is $900.
If Salesman A has exactly ____ sales, he will reach his maximum weekly commission.
Answer:
Sales = 20
Step-by-step explanation:
Simply make the equation "1300 = 65s" to solve the problem
1300 = 65s
Divide both sides by 65.
1300/65 = 65s/65
Divide 1300 by 65 to get 20.
20=s
Swap sides so that all variable terms are on the left-hand side.
s=20
How do you plot a graph step by step?
Plotting a graph step by step is mentioned below.
Define Graph.In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
What is Bar graph?Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.
There are a few steps to follow when plotting a graph:
Identify the variables in the problem and choose which one to plot on the x-axis and which one to plot on the y-axis.Determine the range of values for each variable. This will help you decide how big to make the scales on the x and y-axis.Choose a scale for each axis. The scale should be such that all the points in the problem can be plotted on the graph. A typical scale is to have equal intervals between each tick mark on the axis.Plot the points on the graph by locating their x-coordinate and y-coordinate on the x-axis and y-axis, respectively, and connecting them with a dot.Draw the x- and y-axes and label them with the appropriate units and ranges. Be sure to include a label on the graph itself so that it's clear what the graph represents.Plot any lines or curves that are also a part of the problem. This could be a line of best fit, a linear regression line, a polynomial function or any other lines or curves that the problem calls for.Once you finished with the line/curve, it is a good practice to give the graph a title and to label the axis with the units used.Lastly, review the graph and ensure that it is accurate and clearly presents the information from the problem.To know more about graph visit:
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Pepito bought 2 t-shirt at 149.95 each and a pair of pants for php 30.75, if her money was a 200 pesos bill. How much was her change?
If pesos had it would be so pesos have 169.25 dollars left 200-30.75=169.25