Since equations are expressed as "y=," you can solve for X by setting the equations equal to one another. This is effective because, if two equations have the same unknown y value, then they must also have the same unknown y value.
Imagine that you are tasked with resolving the equations y = 2x + 3, and y = 4x + 1. You can write: 2x + 1 = 4x + 3 since y represents the same number in both equations, proving that both equations must be equal. If this is still unclear, consider y to be a number, let's say 5. Since both equal 5, if 2x+3=5 and 4x+1=5, then (2x+3) must equal 4. 5. by changing the value of y in the second equation to that determined in the first. You can find X by setting the two equations equal to one another. Referring to the problem 2x+3=4x+1 from earlier, you would first try to obtain all the X terms on one side of the equation, Therefore, take 2X off of both sides. 3=2x+1 will be all that is left. Now take one away from both sides to get your X term alone, giving you 2=2x. Lastly, multiply both sides of the equation by two to arrive at the solution, X=1. You can enter the value of X that you just discovered (X=1) into either of your original equations to solve for Y. As a result, y=2(1)+3 and y=4(1)+1 will both result in y=5, which is the same.
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A pool has some initial amount of water in it. Then it starts being filled so the water level rises at a rate of .6 cm/min After 20 min, the water level is 220 cm. Graph the relationship between the pool's water level (in cm) and time (in min).
The relationship that represents the given function is y = 0.6x + 208 and the graph is attached below.
The water level rises at the rate of 0.6 cm/min .
After 20 minutes the water level is 220 cm
let the initial water level be a.
∴ 220 = a + 0.6×20
or, 220 = a + 12
or, a = 208 cm
therefore the initial water level is at 208 cm.
Now we will find the relationship.
Let the water level is y and the level rises at the rate of 0.6 cm /min .
The require function will be :
y = 0.6x + 208
The graph of the function is attached .
The set of all pairings (x, f (x)) that singularly represent a function is known as the graph of both the function, which is a common technique for illuminating the function.
When the domain and/or the codomain are sets of real values, each such pair can be thought of as the Cartesian coordinates of a point in the plane.
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Which one of the following statements is true regarding Statistical Plans?
Select one:
A. Transaction-based plans better support the business need for data.
B. Summary-based plans provide the most accurate data for actuarial-related purposes.
C. Transaction-based plans collect loss data only when a claim is closed.
D. Summary-based plans do not provide enough detail for regulatory reporting purposes.
A. Transaction-based plans better support the business need for data.
The true statement regarding statistical plan is Transaction-based plans better support the business need for data
What is statistical plan?The term statistical plan refers to the document that a statistical organization uses to specify the data items that must be provided to the organization as well as the format in which the data must be reported.
The statistical analysis plan SAP includes information on the scope, population definitions, and methodology of planned analyses. The SAP should be built before any such data analysis because it is essential for directing them.
Hence The statement that transaction-based plans better meet the business demand for data is true with relation to statistical plans.
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What foods have the most pesticides?.
Strawberries, apples, cherries, spinach, nectarines, and grape samples were positive for residues of two or more pesticides in more than 90% of the cases. The most pesticides were found in kale, collard, mustard greens, spicy peppers, and bell peppers totaling 103 and 101 pesticides, respectively.
According to the Environmental Working Group's 2022 Shoppers Guide to Pesticides in Vegetables, strawberries and spinach continue to have the highest pesticide levels of any product categories.
According to the EWG, more than 70% of non-organic vegetables contained pesticide residue. Nearly all the produce had pesticide residue levels below limits set by U.S. regulators.
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which types of measurement are used to group respondents or objects into groups or categories and are thus referred to as categorical measures?
The answer to the given question is nominal and ordinal measurements. These two type measurements are used to group respondents or objects into groups or categories and also considered as categorical measures.
What is nominal measurement?Nominal measurement is the least accurate and informative, because it only names the characteristic or identity which we are interested. In nominal variables, the numerical values just "name" the attribute differently. Thus, numerical value is simply a label.
What is ordinal measurement?Ordinal measurement reports the ranking and ordering of the data without chartering the degree of variation. Ordinal measurement includes statistical data type in which variables are in order or rank but without a degree of difference between categories. The ordinal measurement includes qualitative data. This measurement places variables in order or rank, and only allowing to measure the value as higher or lower in measurement.
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when reading a table for bivariate analysis that displays percentages of some attributes, what is the rule of thumb for reading the table?
Bivariate table is that which shows the relationship between two variables. The rule of thumb... if the table is scaled down by percentage, read the whole thing. If the table is percentages, read it down.
Bivariate table:
A table that depicts the relationship between two variables by showing the distribution of one variable over the categories of a second variable.
Bivariate Table Primary Purpose:
A bivariate table shows the distribution of one variable over the categories of another variable.
Finally, we mentioned that univariate data can be displayed in many different ways, such as bar charts and box plots. Bivariate data, on the other hand, are usually displayed in scatter plot.
Rule of thumb:
Bivariate analysis results can be represented in form of a two-column data table.
A rule of thumb when reading spreadsheets created by others is then spreadsheet is percentage down, read the whole thing. If the table is percentages, read it down.
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which sampling method is conducted when every 50th person registered to vote in a given state is selected from list of voters
Cluster Sampling method , is the required method .
Because the population is split into two separate groups in two different ways.
In a given problem, a survey says that a sample is selected by dividing the population into the gifts of votes, and we need to figure out how to sample. This is called cluster sampling. Analysts are run using a sample her cluster.
Cluster Sampling Method:
In cluster sampling, researchers divide the population into smaller groups called clusters. Then randomly select from these clusters to form a sample. Cluster sampling is a probabilistic sampling technique commonly used to study large populations, especially those that are geographically dispersed.
How to cluster the samples
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If you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test. True False
If you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test. This statement is True.
What is partial F-test?
A partial F-test is used to determine whether or not there is a statistically significant difference between a regression model and some nested version of the same model.
A nested model is simply one that contains a subset of the predictor variables in the overall regression model.
Partial F-test is a statistical analysis used in multivariate linear regression to determine independent variables are to be considered when fitting a multivariate linear regression mode.
This is necessary because if too many variables are considered, then the model would be too complex. On the other hand, if too few variables are used, then we may get a very weak fit.
Hence if you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test.
The given statement is true.
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ten observations were selected from each of three populations, and an analysis of variance was performed on the data. the following are part of the results. source of variation sum of squares degrees of freedom mean square f between treatments 82.4 within treatments (error) 158.4 total
The MS error in the variance is 5.867 using ANOVA
What is Analysis of Variances(ANOVA )?
ANOVA is a statistical method for determining if the effects of different independent variables on a given dependent variable differ or correlate. ANOVA can be used in finance in a variety of ways, such as to forecast price changes in securities by first identifying the variables that affect stock variations. This study can be a useful tool for understanding how a securities or market index will behave in certain scenarios.
Treatment = k-1=2 The degree of freedom
N-k=30-3=27 for the error degrees of freedom
N-1 = 29 degrees of freedom in total.
MS Therapy = (SS Therapy /df Therapy)
82.4/2 = 41.2
MS error = (SS error/df error)
158.4/27 = 5.867
Hence the MS error in the variance is 5.867
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in short-track speed skating, the track has straight sections and semicircles 16 m in diameter. assume that a 65 kg skater goes around the turn at a constant 12 m/s .
The horizontal force exerted on the skater 1170 N.
The diameter of the semicircular portion of the track is 16 m.
Therefore its radius is
r = 8 m.
The tangential velocity of the skater is 12 m/s.
Therefore the angular speed is
ω = v/r = (12 m/s)/(8 m) = 1.5 rad/s
The horizontal force on the skater is due to centripetal acceleration of
a = r*ω² = (8 m)*(1.5 rad/s)² = 18 m/s².
The force acting on the 65-kg skater is
F = m*a = (65 kg)*(18 m/s²) = 1170 N
Therefore, the horizontal force exerted on the skater 1170 N. The correct answer is 1170 N.
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What are 10 multiples of 3?.
The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 when we can just write the table of 3 all terms.
Given that,
We have to find the 10 multiples of 3.
We know that,
What is multiple?We can find the multiples of a number by counting the digits. A multiple in mathematics refers to the outcome or output of multiplying two numbers together.
The Least Common Multiple is the smallest common multiple of two or more numbers (Least Common Multiple).
The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Therefore, The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 when we can just write the table of 3 all terms.
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the line ___ from the left to ride there for the slope is ____
The line declines from the left to the right, therefore the slope is negative.
Slope = -1.
What is the Slope of a Line?The slope of the line is the rise of a line over its run, which is given as:
Slope (m) = change in y / change in x.
If a line decreases or declines from the left to the right, then the slope is said to be a negative slope.
The line in the graph shows it is a declining from the left to the right, therefore, it is a negative slope.
Slope of the line = rise/run = -4/4
= -1.
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What does find the mean of these numbers mean?.
The mean of the numbers means that it is average of the given numbers.
According to the question,
We have the following information:
Mean of the numbers
We know that the mean of a given data set means that we add all the numbers in data set and divide the obtained result by the total numbers.
For example, we have a following data set:
2,5 and 8
Total numbers in the set = 3
Now, the mean of these numbers will be:
Mean = (2+5+8)/3
Mean = 15/3
Mean of the numbers = 5
So, in other words, it can be expressed as the average of the numbers.
Hence, the mean of the numbers means that it is average of the given numbers.
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in 2017, the united states had a population of 320 million people, a crude birth rate (cbr) of 11.8 and a crude death rate (cdr) of 8.5. the net migration rate (the difference between the number of persons entering and leaving a country during the year per 1,000 persons) was 3.9 per 1,000 people. use the formula below to calculate the national population growth rate for the united states in 2017. show your work and clearly label each step.
Therefore, the national population growth rate in the United States in 2017 was 0.72%.
What is growth rate?Growth rate is a metric for determining how quickly a variable has changed over time. It is usually represented as a percentage and is frequently used to calculate the rate of change in economic indicators such as GDP or the rate of inflation. Growth rate may also be used to quantify the rate of change in biological or population processes, such as the growth of an organism's population or the expansion of the size of a tumour. In general, a high growth rate is positive and indicates that a variable is increasing quickly, whereas a low growth rate is considered negative and suggests that a variable is increasing more slowly or may even be decreasing.
How to solve?
Population growth rate = (CBR - CDR + net migration rate) / 10
Population growth rate = (11.8 - 8.5 + 3.9) / 10
Population growth rate = (11.8 - 8.5) + 3.9 / 10
Population growth rate = 3.3 + 3.9 / 10
Population growth rate = 3.3 + 3.9
Population growth rate = 7.2 / 10
Population growth rate = 0.72 %
Therefore, the national population growth rate in the United States in 2017 was 0.72%.
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In the coordinate plane, the point X(0,2) i tranlated to the point X(1,-3). Under the ame tranlation, the point Y(-2,4) and Z(4,5) are tranlated to Y and Z , repectively. What are the coordinate of Y and Z?
The co-ordinates of point Y and Z are (-1,-1) and (5, 0).
What is co-ordinates?
In geometry, a coordinate system could be a system that uses one or additional numbers, or coordinates, to unambiguously confirm the position of the points or alternative geometric components on a manifold like Euclidean space
Main body:
According to given information:
X (0,2) is translated to the point X(1,-3).
so the translation is 1 to right and 5 below
A) y(-2,4)
as the translation is 1 to right and 5 below
hence Y is (-1,-1).
B) Z (4,5)
as the translation is 1 to right and 5 below,
Z = (5,0)
Hence, co-ordinates of point Y and Z are (-1,-1) and (5, 0).
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Which expression is equivalent to log subscript 5 baseline (startfraction x over 4 endfraction) squared? 2 log subscript 5 baseline x + log subscript 5 baseline 4 2 log subscript 5 baseline x + log subscript 5 baseline 16 2 log subscript 5 baseline x + 2 log subscript 5 baseline 4 2 log subscript 5 baseline x + log subscript 5 baseline 4.
The required expression for
[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.
Given,
In the question:
The expression is given as:
Log subscript 5 baseline (startfraction x over 4 endfraction) squared
To find the which expression is equivalent?
Now, According to the question:
The expression is given as:
[tex]log_5(\frac{x}{4} )^2[/tex].
We know that from the properties of logarithm, the following identities
[tex]log m^n = n log m...(1)\\\\log\frac{m}{n} = log m - log n .....(2)[/tex]
Now, [tex]log_5(\frac{x}{4} )^2[/tex] = 2 log [tex]\frac{x}{4}[/tex] (using 1 identity)
Again, Using (2) identity we get,
[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.
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Which congruence theorem can be used to prove that the triangles are congruent two sides and non-included right angle?.
According to the Side-Angle-Side Theorem (SAS), two triangles are congruence if their two sides and the angle between them are equal to those of another triangle's two sides and angle.
What in mathematics is a congruence?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Is congruent the same as equal?If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
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Marty is a competitive eater who can eat approximately one hot dog every 20 seconds. If his next competition gives contestants 15
minutes to eat as many hot dogs as they can, approximately how many hot dogs will Marty
eat?
Answer:
45 hotdogs
Step-by-step explanation:
if he eats 1 hot dog every 20 seconds he will eat 3 hotdogs in a minute (20x3=60seconds aka a minute) so you multiply that by 15 and you get 45
What two numbers add up to 72?.
Answer:
-1 + 73 =72
-2 + 74 = 72
-3 + 75 = 72
FILL IN THE BLANK. to test if there is a difference in two population means, a ___should be used. anova one sample t test two sample t test none of the above
To test if there is a difference in two population means, a difference in sample mean should be used , the correct option is (b) .
In the question ,
we have to find the what is used to test whether their is a difference in two population means or not .
For each hypothesis problem, there is test statistic .
This test statistic is compared to the critical value to make the decision about the hypothesis.
Hence choosing the appropriate test statistics matters a lot.
Here two samples are there. It is clearly given for which we have to test the hypothesis that is sample means .
Hence, we can say that the test statistic is, the difference in sample mean .
Therefore , the difference in sample mean is used to test if there is a difference in two population means .
The given question is incomplete , the complete question is
To test if there is a difference in two population means, a ___ should be used.
(a) alpha
(b) the difference in sample means
(c) the degrees of freedom
(d) the difference in the population means
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Two owner of a cattle ranch, Robert and Val, want to find the average weight for the ranch’ 200 cow. Intead of weighing all of the cow:
Robert weigh 25 cow and get an average weight of 1,550 pound (tdev = 50)
Val weigh 100 cow and get an average weight of 1,380 pound (tdev = 50)
What i Val’ margin of error, rounded to the nearet whole number? (The formula i 1. 96 (td dev) / quare root of N
Using its formula, it is found that Val's margin of error is 9.8 pounds.
What is the margin of error?
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.
The margin of error formula:
The margin of error is given by the following equation:
M = 1.96(s/√n)
Where,
s is the standard deviation.
n is the sample size.
Here, we have
Given
The standard deviation is 50, hence s = 50
Val weighed 100 cows, hence n = 100
By applying the margin of error formula and we get
M = 1.96(50/√100)
M = 1.96(50/10)
M = 9.8
Hence, Using its formula, it is found that Val's margin of error is 9.8 pounds.
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Solve the system by elimination. Check your solution x+2y=7 / 13-5y=x
Answer:
x = 3
y = 2
Step-by-step explanation:
x + 2y = 7 and
13 - 5y = x
transfer x to the left side and 13 to the right side of the equation for the second equation:
-x - 5y = -13 now find the sum of both equations:
x + 2y - x - 5y = 7 - 13 add/subtract like terms
-3y = -6 divide both sides by -3
y = 2
To find the value of x replace y with 2:
x + 2*2 = 7
x + 4 = 7 subtract 4 from both sides
x = 3
How do you solve an equation in slope intercept form without graphing?.
To solve a system of linear equations without graphing, you can use the substitution method.
How do you solve a system of equations without graphing?
To solve a system of linear equations without graphing, you can use the substitution method. This method works by solving one of the linear equations for one of the variables, then substituting this value for the same variable in the other linear equation and solving for the other variable.
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Which is a way to solve the equation 4x = 128 if you do not know a power of 4 that equals 128?.
When you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is; Find intersections on the graph of y = 4ˣ and y = 128.
Define the term mathematical equation?The explanation of an equation in arithmetic is a mathematics statement that indicates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 is composed of the two equations 3x + 5 and 14, whose are separated by the 'equal' sign.Consider the given equations;
y = 4ˣ and y = 128
Since, the power of 4 equals 128 is unknown.
Thus, draw the graph of equation y = 128. and y = 4ˣ .
Consider the intersected point from the graph.
Thus, when you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is;
Find intersections on the graph of y = 4ˣ and y = 128.
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a company has given you the task to research the salary of thirty-five-year-olds in new york city. would you be more interested in looking at the mean, median, or mode?
The correct answer is median.
The salary of 35 year olds would vary greatly, with significant variations. Undoubtedly, this type of data contains outliers. Because median is unaffected by outliers in the data set, it would be appropriate for the data that included outliers.
The observations are divided into two equal portions by the median. When observations are organised in order of magnitude, it reflects the middle value for the group of observations.
When data are input in ascending order, the median value is the middle value. In other words, the observation is in the middle.
If there are an even number of observations overall, the median is calculated as the average of the middle two observations.
The median is the middle observation in the arranged data if the total number of observations is an odd number.
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what would you expect to see if there was a large variance for a sample of difference scores in a repeated-measures t-test?
When there was a large variance for a sample of difference scores in a repeated-measures t-test, then there is probably not a significant difference between treatment groups and the participant's scores would be predictable.
In a repeated measures t-test, the test statistic is given by
[tex]t = \frac{d}{s_{d} / \sqrt{n} }[/tex]
Since [tex]s_{d}[/tex] = the standard deviation of difference scores is large occurs in the denominator of the test statistic.
Thus, there probably is not a significant difference between treatment groups and the participant's scores would be predictable.
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your online reviews have averaged 4.2 over 120 reviews. how many 5 ratings do you need to get to a 4.5 average
You already got 4.2 averaged from 120 reviews. To get a 4.5 average, you need more 72 reviews with 5 ratings.
This problem can solved using average value approach.
Average value can be calculated using:
Average = sum of data value / number of data
Let p = number of required 5 ratings to get a 4.5 average.
Then,
sum of data value = 120 x 4.2 + p x 5
number of data = 120 + p
Hence,
Average = (120 x 4.2 + p x 5) / (120 + p)
4.5 = (504 + 5p) / (120 + p)
540 + 4.5p = 504 + 5p
0.5 p = 36
p = 72
Hence, you need 72 reviews with 5 ratings.
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A rectangular playground i to be fenced in uing a wall on one ide and 210 meter of fencing for the other three ide. The area A(x) in quare meter of the playground i a function of the length x in meter of the ide parallel to the wall. A. Write an expreion for A(x)
The function of the length 'x' in meters of the side parallel to the wall is A(x) = x/2(210 - x)
What are perimeter and area?
While area describes the space it occupies, perimeter describes how far the shape's edge extends. A shape's perimeter is its entire circumference. The region that an object's shape defines as its area.
Given, perimeter (P) = 210 meters ........... (i)
Let the length parallel to the wall be 'x' and the width be 'y'
So, the perimeter of the fence is
P = 2y + x ............... (ii)
From eq. (i) & (ii), we get
210 = 2y + x
or, y = 1/2(210 - x)
The area of the wall is calculated as:
A = xy
or, A = x * 1/2(210 - x)
or, A = x/2(210 - x)
Rewrite as
A(x) = x/2(210 - x)
Hence, the function of the length 'x' in meters of the side parallel to the wall is A(x) = x/2(210 - x)
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Mrs. Stevens bought 5 identical gifts for her children. Each gift was valued at $80. She paid 1/2 of the total cost and financed the remaining balance through her credit union for 18 months at 9 % interest. What was the total amount of money she borrowed?
The total amount of money that she borrowed would be= $227.
What is a credit union?A credit union could be defined as the union that identifies am individual as their members and there offer financial assistance to such an individual.
The number of gifts bought by Mr Steven = 5 identical gifts.
The price for each gift = $80
The total money that Mr Steven spent on gift = 5×80 = $400.
The amount paid was 1/2 of total cost = 1/2×400 = $200
The amount of money she borrowed for her credit union is calculated using simple interest formula;
si = P*T*R/100
si = 200×1.5 × 9/100
si = 2700/100
si = $27
The amount borrowed= 200+27 = $227.
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What is the solution to the system of equations y 1. 5x 4 y =- X?.
The solution of the given equations y=1.5x-4 and y=-4 is given by the coordinates (x,y) as (0, -4)
Illustrate System Of Equations.
A system of equations is two or more equations that contain the same variables. A solutions to a system of equations are the point where the lines intersect. There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.
[tex]y=1.5x-4 , y=-4[/tex]
Substitute the value of y as - 4
-4=1.5x-4
Solving for x, by transposing the terms we get
1.5x = - 4 + 4
1.5x = 0
x = 0
Therefore, the solution is (0, -4).
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add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
The correct response is 110.
Consider two numbers that are inside 1000.
324 and 434 are these two numbers.
As a result, for any number abc, the terms a, b, and c each have a place value of 100, 10, and 1.
We will therefore add the corresponding digits and multiply them by their place value when adding the two numbers abc and def.
In order to add 324 and 434, we will
(3+4)×100 + (2+3)×10 + (4+4)×1
The solution is 700+50+8=758.
This is equivalent to (324 + 434 = 758)
Similar steps apply for subtraction; simply choose the larger number and continue the same procedures, changing the + sign in the inner bracket to a -.
(4-3)×100 + (3-2) (3-2)×10 + (4-4)×1
Therefore, the correct response is 110.
This equals (434-324) = 110.
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