I made a code to solve linear equations using gaussien
eliminations however how can I edit my code such that it prints a 1
if there are infinitely many soloutions and a 0 if there are no
solutions
her
Answers
To modify your code to print a 1 if there are infinitely many solutions and a 0 if there are no solutions, you can add some additional checks after performing Gaussian elimination.
After performing Gaussian elimination, check if there is a row where all the coefficients are zero but the corresponding constant term is non-zero. If such a row exists, it indicates that the system of equations is inconsistent and has no solutions. In this case, you can print 0.
If there is no such row, it means that the system of equations is consistent and can have either a unique solution or infinitely many solutions. To differentiate between these two cases, you can compare the number of variables (unknowns) with the number of non-zero rows in the reduced row echelon form. If the number of variables is greater than the number of non-zero rows, it implies that there are infinitely many solutions. In this case, you can print 1. Otherwise, you can print the unique solution as you would normally do in your code.
By adding these checks, you can determine whether the system of linear equations has infinitely many solutions or no solutions and print the appropriate output accordingly.
To determine whether a system of linear equations has infinitely many solutions or no solutions, we can consider the behavior of the system after performing Gaussian elimination. Gaussian elimination is a technique used to transform a system of linear equations into a simpler form known as the reduced row echelon form.
When applying Gaussian elimination, if at any point we encounter a row where all the coefficients are zero but the corresponding constant term is non-zero, it implies that the system is inconsistent and has no solutions. This is because such a row represents an equation of the form 0x + 0y + ... + 0z = c, where c is a non-zero constant. This equation is contradictory and cannot be satisfied, indicating that there are no solutions to the system.
On the other hand, if there is no such row with all zero coefficients and a non-zero constant term, it means that the system is consistent. In a consistent system, we can have either a unique solution or infinitely many solutions.
To differentiate between these two cases, we can compare the number of variables (unknowns) in the system with the number of non-zero rows in the reduced row echelon form. If the number of variables is greater than the number of non-zero rows, it implies that there are more unknowns than equations, resulting in infinitely many solutions. This occurs because some variables will have free parameters, allowing for an infinite number of combinations that satisfy the equations.
Conversely, if the number of variables is equal to the number of non-zero rows, it indicates that there is a unique solution. In this case, you can proceed with printing the solution as you would normally do in your code.
By incorporating these checks into your code after performing Gaussian elimination, you can determine whether there are infinitely many solutions (print 1) or no solutions (print 0) and handle these cases appropriately.
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Related Questions
write sin x° in terms of the cosine
Answers
Answer:
cos\((x-\frac{\pi}{2})\)
Step-by-step explanation:
If you insists that sine and cosine should be of the same angle use Pythagorean identity. Otherwise you can use identity sin(x) = cos\((x-\frac{\pi}{2})\)
Hope this helps! :)
HELP!!
Who had the highest mean score? Justify your answer using mathematical reasoning.
Answers
Answer:
Katie had the highest mean score.
Step-by-step explanation:
Katie had the highest mean score because her mean score was 81.4, and Annie's highest mean score was 72.4.
Answer: Katie
Step-by-step explanation: In six of out 7 times Katie had higher marks.
Annie mean is 72.42
Katie's mean is 81.42
Multiply and find the value of x
Answers
Answer:
X=15
Step-by-step explanation:
7(3n + 2) - 3n - 5 i need to factor it tysvm!!
Answers
The answer to the Linear expression 7(3n + 2) - 3n - 5 is 18n + 11
What is a linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
From the expression 7(3n + 2) - 3n - 5
By expanding the bracket, we have
21n + 14 - 3n - 5
By collecting like terms, we have
21n - 3n + 14 - 3
18n + 11
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How are geometric sequences similar to arithmetic sequences? How are they different?
Answers
Find the volume of the cylinders. (Use π=3.14)
A. Height= 9ft ; radius= 3ft
B. Radius=13yd; height=8yd
Answers
Question 1
h= 9 ftr= 3 ftQuestion 2
h= 8 ydr= 13 yd Note that:h= heightr= radius To find:The volume of the given cylinders.
Solution:\(\huge\boxed{Formula: V=\pi{r}^{2}h}\)
\(\huge\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}\)
Let's solve!
Substitute the values according to the formula.
\(V=3.14×{3}^{2}×9\)
\(\large\boxed{V= 254.34 \: {ft}^{3}}\)
Let's work on question 2
Substitute the values according to the formula.
\(V=3.14×{13}^{2}×8\)
\(\large\boxed{V= 4245.28 \: {yd}^{3}}\)
write a polynomial function of least degree with integral coefficients that has the given zeros imaginary
Answers
Polynomial function of least degree with integral coefficients that has the given zeros imaginary \(\\f(x) & =x^4+5 x^2-6\)
As per the given data:
\(\sqrt{6} i$\) is a zero.
Therefore \($-\sqrt{6} i$\) is also a zero.
\($(x+1),(x-1),(x-\sqrt{6} i)$\) and \($(x+\sqrt{6} i)$\) are factors
\($$\begin{aligned}f(x) & =(x+1)(x-1)(x-\sqrt{6} i)(x+\sqrt{6} i) \\& =\left(x^2-1\right)\left(x^2-(\sqrt{6} i)^2\right) \\& =\left(x^2-1\right)\left(x^2-6 i^2\right) \\& =\left(x^2-1\right)\left(x^2+6\right) \\& =x^4+6 x^2-x^2-6 \\f(x) & =x^4+5 x^2-6\end{aligned}$$\)
Therefore the polynomial function is \(\\f(x) & =x^4+5 x^2-6\)
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Write a polynomial function of least degree with integral coefficients that have the given zeros of-1, 1, and i times square root of 6.
Construct a 90% confidence interval for the population mean you. Assume the population has a normal distribution a sample of 15 randomly selected math majors had mean grade point average 2.86 with a standard deviation of 0.78
Answers
The 90% confidence interval is: (2.51, 3.22)
Confidence interval :It is a boundary of values which is eventually to comprise a population value with a certain degree of confidence. It is usually shown as a percentage whereby a population means lies within the upper and lower limit of the provided confidence interval.
We have the following information :
Number of students randomly selected, n = 15.Sample mean, x(bar) = 2.86Sample standard deviation, s = 0.78Degree of confidence, c = 90% or 0.90The level of significance is calculated as:
\(\alpha =1-c\\\\\alpha =1-0.90\\\\\alpha =0.10\)
The degrees of freedom for the case is:
df = n - 1
df = 15 - 1
df = 14
The 90% confidence interval is calculated as:
=x(bar) ±\(t_\frac{\alpha }{2}\), df \(\frac{s}{\sqrt{n} }\)
= 2.86 ±\(t_\frac{0.10 }{2}\), 14 \(\frac{0.78}{\sqrt{15} }\)
= 2.86 ± 1.761 × \(\frac{0.78}{\sqrt{15} }\)
= 2.86 ± 0.3547
= (2.51, 3.22)
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In the expression 2x +5 , 2x and 5 are called
Answers
Answer:
Terms
Step-by-step explanation:
Hello!
The expression 2x +5 has two different terms: 2x and 5
Terms are values in an expression that are different from each other. They are values with different coefficients.
For example:
2x has a coefficient of 2, because 2x = 2(x)5 has a coefficient of 1 because 5 = 1(5)Like Terms:Like terms are values with the same factors or coefficients.
Let's use an example equation: 2x + 5 + 7x - 9
2x and 7x are like terms, because they have a factor of x, which simplifies to 2x + 7x = 9x5 and -9 have the same factor of -1, so if we simplify: 5 + (-9) = 5 - 9 = -4Combining the two terms we have 9x - 4How many digits are in the number 345?
Answers
Answer:
Hi
Step-by-step explanation:
It's 3 digits in this number
2/15 of a class of 30 students are wearing red t-shirts today. How many students is that?
Answers
Answer: 4 students
To find out how many students are wearing red t-shirts, we need to calculate the fraction of the class that is wearing red t-shirts. The fraction is given as 2/15, meaning 2 out of every 15 students are wearing red t-shirts.
We then need to multiply the fraction 2/15 by the total number of students in the class, which is 30.
2/15 of 30 can be calculated as:
(2/15) x 30 = (2 x 30) / 15 = 60/15 = 4 students
Answer:
\(\huge\boxed{\sf 4\ students}\)
Step-by-step explanation:
Total students = 30
Students wearing red t-shirts:= 2/15 of total
Key: "of" means "to multiply"
= 2/15 × 30
= 2 × 2
= 4 students\(\rule[225]{225}{2}\)
A cylindrical oil tank 8 ft deep holds 620 gallons when filled to capacity. How many gallons remain in the tank when the depth of oil is 3 Tiszt. The number of gallons remain in the tank is (Type a whole number or a decimal)
Answers
Answer:
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. Since the volume of oil in the tank is directly proportional to the depth of the oil, we can calculate the amount of oil left in the tank when it is 3 feet deep using a simple ratio.
First, we need to convert the tank's capacity from gallons to cubic feet because our measurements are in feet. According to the U.S. liquid gallon to cubic foot conversion, 1 gallon is approximately 0.133681 cubic feet. So, the tank's total volume in cubic feet is 620 gallons * 0.133681 cubic feet/gallon.
Let's denote the total volume of the tank as V_total and the remaining volume when the tank is 3 feet deep as V_remaining.
V_total = 620 * 0.133681 cubic feet.
Given that the total height (h_total) of the tank is 8 feet and the remaining height (h_remaining) is 3 feet, we can set up the following proportion:
h_remaining / h_total = V_remaining / V_total.
By cross-multiplying and solving for V_remaining, we can find the remaining volume in the tank when it's 3 feet deep. Then, we convert this volume back to gallons by dividing by 0.133681.
Let's calculate that.
Apologies for the confusion; I made a mistake. I can't execute calculations directly in this manner. I'll carry out the calculations below instead:
The total volume of the tank in cubic feet is:
V_total = 620 gallons * 0.133681 cubic feet/gallon = 82.9022 cubic feet.
The remaining volume when the tank is 3 feet deep can be calculated with the proportion:
h_remaining / h_total = V_remaining / V_total.
After cross-multiplying and solving for V_remaining, we have:
V_remaining = (h_remaining / h_total) * V_total = (3 ft / 8 ft) * 82.9022 cubic feet = 31.0941 cubic feet.
Then, we convert this volume back to gallons by dividing by 0.133681:
V_remaining_gal = 31.0941 cubic feet / 0.133681 = 232.63 gallons.
Rounding to the nearest whole number, approximately 233 gallons remain in the tank when the depth of the oil is 3 feet.
There is space in a multi-storey car park for 5 rows of 20 cars on each of the 8 floors. How many spaces are left if 2124 cars have already parked?
Answers
Answer: -1324 spaces left in the car park.
Step-by-step explanation: There are 8 floors in the multi-storey car park and each floor has 5 rows of 20 cars, so there are 8 * 5 = <<85=40>>40 rows in the car park in total.
If each row has space for 20 cars, then the total number of parking spaces in the car park is 40 * 20 = <<4020=800>>800.
If 2124 cars have already parked, then there are 800 - 2124 = <<800-2124=-1324>>-1324 spaces left in the car park.
It is not possible for the car park to have negative spaces, so the answer must be 0. Therefore, if 2124 cars have already parked, there are 0 spaces left in the car park.
Adding a derivational suffix to a word often changes the part of speech. true or false
Answers
Adding a derivational suffix to a word often changes the part of speech is true.
What is derivational suffix ?
A derivational suffix is a type of affix that is added to the end of a base word to create a new word with a different meaning, often a different part of speech.
For example, adding the derivational suffix "-ness" to the base word "kind" creates the new word "kindness," which is a noun that refers to the quality or state of being kind. Similarly, adding the derivational suffix "-able" to the base word "value" creates the new word "valuable," which is an adjective that describes something that is worth a lot.
Derivational suffixes can change the meaning and function of a word, and they are often used to create new words in English. Some common derivational suffixes include "-er," "-able," "-ness," "-ful," "-ish," and "-ize."
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Complete question is: Adding a derivational suffix to a word often changes the part of speech is true.
Table 3. Ages of Building Residents
Ages of Building Residents Frequency
18 to 20 years old 19
21 to 24 years old 37
25 to 34 years old 43
35 to 44 years old 27
45 to 64 years old 39
65 years old and over 35
19. Use the pie chart in Figure 3 to find the probability that a student attained a B or a C on the quiz? (Round results to 3 decimal places.)
Figure 3. The grades attained by students on a recent quiz.
Section 3.2
20. Classifying Events. A uniquely numbered ball is randomly selected from a bin. Then another ball is selected from the bin. Are the events for selecting the balls independent or dependent?
Answers
19). The probability that a student attained a B or a C on the quiz is 0.42, or 42%. 20). The events for selecting the balls are dependent. This is because the probability of selecting the second ball is affected by the selection of the first ball.
The probability that a student attained a B or a C on the quiz can be found by adding the probabilities of the two events together. First, find the probability of attaining a B by dividing the number of students who attained a B by the total number of students. Do the same for the probability of attaining a C. Then add the two probabilities together to find the total probability.
Probability of attaining a B = (Number of students who attained a B) / (Total number of students) = 17 / 100 = 0.17
Probability of attaining a C = (Number of students who attained a C) / (Total number of students) = 25 / 100 = 0.25
Total probability = 0.17 + 0.25 = 0.42
Therefore, the probability that a student attained a B or a C on the quiz is 0.42, or 42%.
After the first ball is selected, there is one less ball in the bin, which changes the probability of selecting the second ball. Therefore, the events are dependent.
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Which graph shows the line y - 2 = 2(x + 2)?
Answers
Answer:
Graph B
Step-by-step explanation:
I think it os Graph B but I'm not sure because when I put it in Desmos to graph it, the line interests 6 on the Y axis.
I included a picture of what Desmos gives me
In seven years, huang will be two times as old as he was last year. how old is he now? 5 years old 8 years old 9 years old 14 years old
Answers
The present age of huang is \(9\) years. or now he is \(9\) years old.
Age is the length of time that a person has lived.
Present age is the real age, it tells how old the person is now.
In seven years mean after seven years.
Last year is the previous year of present age.
In seven years, huang will be two times as old as he was last year.
Let the present age of huang be \(x\)
After seven year huang age will be \(x+7------1\)
It is given that, two times as old as he was last year \(2(x-1)------2\)
These both quantity are given to be equal.
So equating both equation,
\(x+7=2(x-1)\\x+7=2x-2\\2x-x=7+2\\x=9\)
Hence, the present age of huang is \(9\) years. or now he is \(9\) years old
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4 pythagorean theorem
Answers
Answer:
look at the photo..................
Answer:
u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye
Step-by-step explanation:
Please no links . What’s the answer ?
Answers
Answer:
600 square feet
Step-by-step explanation:
I notice it says "Estimate" in bold. Therefore, you would round all of the measurements. They're all pretty simple to round (to the nearest tens place). From here, you subtract the length of the large room from the length of both rooms. So, 50 - 30 = 20. This is the length of the small room. We now multiply this by the width of the small room (since area of a rectangle is length * width) and we get:
20 * 30 = 600, our final answer
Hope it made sense. I would appreciate Brainliest, but no worries.
Researchers want to determine if people who smoke cigarettes also drink alcohol. They surveyed a group of individuals and the data are shown in the contingency table below. What is the odds ratio for smokers who drink alcohol against non- smokers who drink alcohol? Round your answer to two decimal places. Drink Alcohol Do Not Drink Alcohol Total Smokers 108 11 130 Non-smokers 317 114 420 Total 425 125 550 A Provide your answer below. e here to search 11
Answers
The odds ratio for smokers who drink alcohol against non-smokers who drink alcohol ≈ 3.89.
The given contingency table below can be used to determine the odds ratio for smokers who drink alcohol against non-smokers who drink alcohol:
Drink Alcohol Do Not Drink Alcohol Total Smokers
108 11 130
Non-smokers 317, 114, 420
Total 425, 125, 550
The probability that an event will occur is the fraction of times you expect to see that event in many trials.
Probabilities always range between 0 and 1. The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.
We are given two categories (smokers and non-smokers) and within these categories, we have to calculate the odds ratio of the event "drinking alcohol".
Therefore, we can calculate the odds ratio for smokers who drink alcohol against non-smokers who drink alcohol by using the formula below:
odds ratio = (ad/bc) = (108/11)/(317/114)
= (108/11)*(114/317) ≈ 3.89
As a result, the odds ratio between alcohol consumption by smokers and non-smokers is 3.89.
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What is the equation of this line?
A: y=2x-3
B: y=1/3x-2
C: y=3x-2
D: y=1/2x-3
Answers
step by step : rise over run
hope this helps
what is the point-slope form of a line with slope -4 that contains the point (-2, 3)
Answers
Answer:
\(y - 3 = - 4(x + 2)\)
The larger of two numbers is eight more than the smaller. If the sum of the two numbers is 32, what are the two numbers
Answers
The two numbers are 12 and 20
How to determine the numbers
Let the small number be x
Let the large number be y
We have that;
y = 8 + x (1)
But;
x + y = 32 (2)
Now, substitute the value of y as 8 + x in equation (2)
x + 8 + x = 32
collect like terms
2x + 8 = 32
2x = 32 - 8
2x = 24
Make 'x' the subject
x = 24/ 2
x = 12
But;
y = 8 + x
y = 8 + 12
y = 20
Thus, the two numbers are 12 and 20
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Find the x- and y-intercepts of the graph of -2x + 3y = 34. State each answer as an integer or an improper fraction in simplest form.
Answers
The x and y-intercept are the point at which graph cuts the respective axis thus the x-intercept of -2x + 3y = 34 is (-17,0) while y-intercept is (0,34/3).
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand the behavior of the graph.
As per the given graph,
-2x + 3y = 34
The x-intercept is the point on the x-axis where the function cuts and since at the x-axis the value of y is 0 thus its coordinate will be (x,0).
Substitute y = 0 into -2x + 3y = 34
-2x + 0 = 34 ⇒ x = -17 so coordinate (-17,0)
Similarly y-intercept (0,y)
0 + 3y = 34 ⇒ y = 34/3 so coordinate (0,34/3)
Hence "The x and y-intercept are the point at which graph cuts the respective axis thus the x-intercept of -2x + 3y = 34 is (-17,0) while y-intercept is (0,34/3)".
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solve for m
m-2.02= -0.58
Answers
m = 1.44
a nationally advertised brand of hand soap is sold as a single bar, a package of 2 bars, a bundle of 8 bars, or as a liquid in a pump bottle. the person in charge of marketing this brand of soap wanted to see which packaging configuration sold best at different locations. the marketing person took a random sample from each of three locations and recorded the number sold at each location. is there sufficient evidence to conclude that there is a relationship between location and type of package? use a 0.01 alpha level. a. Type the null and alternative hypotheses for this problem. b. Type the name of the appropriate test to use. c. Choose the appropriate output (Output 1 or Output 2). d. Type the appropriate p-value. e. Type the conclusion (Step 7) based on the hypotheses, output, and p-value.
Answers
A chi-square test of independence is used to analyze the relationship between location and type of package for soap.
What is chi-square test?
A chi-square test is a statistical test used to determine if there is a significant association or relationship between categorical variables.
To analyze whether there is a relationship between location and type of package for the soap brand, a statistical test needs to be performed. Here are the steps to answer the given questions:
a. Null and alternative hypotheses:
- Null hypothesis (H0): There is no relationship between location and type of package for the soap brand.
- Alternative hypothesis (Ha): There is a relationship between location and type of package for the soap brand.
b. The appropriate test to use:
To determine the relationship between two categorical variables (location and type of package), a chi-square test of independence is commonly used.
c. The appropriate output:
To conduct a chi-square test of independence, Output 2, which includes the observed counts and expected counts for each cell in a contingency table, is typically used.
d. The appropriate p-value:
After performing the chi-square test, the output will provide a p-value. The p-value represents the probability of observing the data under the null hypothesis. We will compare this p-value to the significance level (alpha) of 0.01 to determine if there is sufficient evidence to reject the null hypothesis.
e. The conclusion:
Based on the obtained p-value, we can make a conclusion. If the p-value is less than the significance level (0.01), we reject the null hypothesis and conclude that there is a relationship between location and type of package. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis and do not conclude a significant relationship between location and type of package.
To provide a more specific conclusion, the actual data from the three locations and the corresponding output of the chi-square test are needed.
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Do Exercise 8.89 on page 350 in the textbook. 7. 8.89 Political Prisoners. In Exercise 8.73, you found a 95% con Tidence interval of 18.8 months to 48.0 months for the mean dura tion of imprisonment, , of all East German political prisoners with chronic PTSD a. Determine the margin of enor, E b. Explain the meaning of E in this context in terms of the accuracy of the estimate. c. Find the sample size required to have a margin of error of 12 months and a 99% confidence level. (Recall that o 42 months.) d. Find a 99% confidence interval for the mean duration of imprison ment, , if a sample of the size determined in part (e) has a mean of 36.2 months.
Answers
The margin of errors figures that E ≈ 1.66 months when Tidence interval of 18.8 months to 48.0 months for the mean dura tion of imprisonment, , of all East German political prisoners with chronic PTSD.
What would be the margin of error?a) The formula for the margin of error (E) is
E = z* (σ/√n)
where n is the sample size, is the population standard deviation, and z* is the critical value for the specified confidence level. The sample standard deviation (s) from Exercise 8.73 can be used to estimate, even if we don't know what it is.
s equals 7.45 months
The crucial value for a two-tailed test with a 95% confidence level is:
z* = 1.96
When these values are added to the formula, we obtain:
E = 1.96 * (7.45 / √85)
E ≈ 1.66 months
What is the meaning of E in this context in terms of the accuracy of the estimate?The amount of uncertainty or imprecision in the estimate of the population mean based on the sample mean is shown by the margin of error (E). With a specified level of confidence, it is a measurement of how different the sample mean is expected to be from the actual population mean. When it comes to East German political prisoners with severe PTSD, a margin of error of 1.66 months indicates that we may be 95% certain that the genuine population mean sentence will fall between 18.8 - 1.66 = 17.14 months and 48.0 + 1.66 = 49.66 months.
What is the sample size required to have a margin of error of 12 months and a 99% confidence level?We can apply the same formula as previously and solve for n to determine the sample size needed to achieve a 99% confidence level and a 12-month margin of error:
n = (z* σ / E)^2
Inputting the values provided yields:
n = (2.576 * 7.45 / 12)^2 \sn ≈ 25
Hence, in order to attain the specified margin of error and confidence level, a sample size of 25 would be needed.
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write and solve the equation to find the number:
1: the sum of 4 and three times a number is 19
2: ten less the quotient of a number and 3 is 6
Answers
Answer:
whats the whole question
Step-by-step explanation:
Solve the equation - 5x – 3 = 3x + 13
Answers
\(-5x-3=3x+13\)
\(8x=-16\)
\(x=-2\)
Hope this helps.
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In a math question, Magda correctly answered a question that asked for a typical measure of orange juice in a full family-size jug. Which was her answer
Answers
Magda said the typical measure of orange juice in a full family-size jug is 1 gal in value.
What is meant by mathematical expression?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.
The collection of mathematical symbols that emerges from the right arrangement of numbers is known as a mathematical expression and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
The three different types of algebraic expressions are monomial, binomial, and polynomial.
The complete question is : In a math question, Magda correctly answered a question that asked for a typical measure of orange juice in a full family-size jug. Which was her answer?
a. 2 cups
b. 1 gal
c. 10 gal
d. 10 fl oz
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