The 99 percent confidence interval for the true mean length of the bolt is CI = (2.8712, 3.1288)
How to find the confidence interval?Confidence Interval is used to tell us the degree of certainty or uncertainty that is existent in a sampling method.
The general formula for confidence interval is;
CI = x' ± z(s/√n)
where;
x' is sample mean
z is z-score at confidence level
s is sample standard deviation
n is sample size
We are given;
sample size; n = 36
Sample mean; x' = 3 inches
standard deviation; s = 0.3 inches
confidence level = 99%
z at 99% CL = 2.576
Thus;
CI = 3 ± 2.576(0.3/√36)
CI = 3 ± 0.1288
CI = (2.8712, 3.1288)
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Use power series operations to find the Taylor series at x = 0 for the following function. xsin(Злх/2). The Taylor series for sin x is a commonly known series. What is the Taylor series at x = 0 for sin x? Use power series operations and the Taylor series at x = 0 for sin x to find the Taylor series at x = 0 for the given function.
The taylor series as per the power series operation is sin(x) = 0 + 1x + 0x + −1/3!+3 + 0x
given,
f(x) = sinx
c = 3pi/4
the required series will be .
f(x) = f(c) + f' (c)( x-c ) + f''(c)/2! + .... f x n(c)/n! (x-c)^n
f(c) = sin(c)
= sin(3pi/4)
= 1/2
on solving the equation becomes,
sin(x) = 0 + 1x + 0x + −1/3!+3 + 0x
Assume that f(x) is a real or composite function and that it is a differentiable function of a real or composite neighbourhood number. The following power series is then described by the Taylor series.
The Taylor series can be expressed using sigma notation, where f(n)(a) = nth derivative of f n! = factorial of n.
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A person invested $8, 400 in an account growing at a rate allowing the money to double every 11 years. How much money would be in the account after 12 years, to the nearest dollar?
Answer: $16,800
Step-by-step explanation:
Financial analysts forecast XYZ company's growth for the future to be a constant 8 percent. XYZ's recent dividend was $0.88. What is the value of XYZ stock when the required return is 12 percent?
$23.76 is the value of XYZ stock when the required return is 12 percent.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let the price per share be P
growth rate, g = 8% = 0.08
D = Next years dividend = $0.88 × 1.08 = $0.9504
Required rate of return r = 12% = 0.12
P=D/r-g
P=0.9504/0.12-0.08
P=$23.76
Hence,$23.76 is the value of XYZ stock when the required return is 12 percent.
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omari buys a computer for $1099. He makes a down payment of 20%. His monthly payments for the computer are $144. How many months will it take omari to finish paying off the computer
It will take Omari 7 months to pay off the computer.
What is a percentage?
Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.
To find the amount of the down payment, multiply the price of the computer by the down payment percentage:
down payment = $1,099 * 20% = $219.80
The remaining balance on the computer after the down payment is:
remaining balance = $1,099 - $219.80 = $879.20
To find the total number of months it will take Omari to pay off the computer, divide the remaining balance by the monthly payment:
total months = $879.20 / $144/month = 6.1 months
Since it is not possible to have a fraction of a month.
Hence, it will take Omari 7 months to pay off the computer.
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Rewrite the fraction in the sentence below as a percentage. The 20 overseas investors own 1/10 of the business
The value of the equation A = 1/10 is 10 %
So , the 20 overseas investors owns 10 % of the business
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the percentage of business owned by the overseas investors be = A
Now , the equation will be
The number of overseas investors = 20
The fraction of business the overseas investors own = 1/10
Now , the percentage is always expressed in terms of 100
So ,
The percentage of business owned by the overseas investors = fraction of business the overseas investors own x 100
Substituting the values in the equation , we get
Percentage of business owned by the overseas investors = ( 1/10 ) x 100
Percentage of business owned by the overseas investors = 10 %
Therefore , the value of A is 10 %
Hence , the 20 overseas investors owns 10 % of the business
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which is the correct answers ??????
Given the picture on the right, what could be the possible value of a?
Answer: 20.98
Step-by-step explanation: Pythagorean theorem to find a is the square root of c^2 - b^2 C is 27 and b is 17 so square root of 27^2 17^2 is 20.98
A mountainer climbed 1000' at a rate of X feet per hour. He climbed in additional 5000' at a different rate. This rate was 10' per hour less than twice the 1st rate. Which expression represents the number of hours to mountainer climbed?
The correct option for the equation is C.
What is equation?
An equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main Body:
Using distance=rate multiplied by time as the formula,
mountaineer climbed 1,000 feet at a rate of x feet per hour
1000 = xt₁ <--eq.1
"He climbed an additional 5,000 feet at a different rate."
5000 = x't₂ <--eq.2
"This rate was 10 feet per hour less than twice the first rate."
x' = 2x - 10 <--eq.3
We now have 3 equations/expressions to solve for the number of hours:
From eq. 1 and 2:
Total time = t₁ +t₂ = t
t = 1000/x + 5000/x'
but x' = 2x - 10
t = 1000/x + 5000/(2x-10)
t = 1000/x + 5000/[2(x-5)]
t = 1000/x + 2500/(x-5)
Hence correct option is C.
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State all integer values of a in the interval -2 ≤ x ≤ 4 that satisfy the following
inequality:
-5x+5 ≥7
Explanation
Solve for x:
[tex]-5\text{x}+5 \ge 7\\\\-5\text{x} \ge 7-5\\\\-5\text{x} \ge 2\\\\\text{x} \le 2/(-5)\\\\\text{x} \le -0.4\\\\[/tex]
Note the inequality sign flips when we divide both sides by a negative number.
If x is an integer, then the largest x can be is x = -1, which means x can be any of these values: {..., -4, -3, -2, -1} where the three dots means the pattern continues on to the left forever. If it might help, then you can think of it like this: {-1, -2, -3, -4, ...} but it's of course not the standard way to sort negative numbers.
Now we're told that -2 ≤ x ≤ 4 which when combined with the set above, gets us the answer {-2, -1}
If we replaced x with -2, then,
-5x+5 ≥7
-5(-2)+5 ≥7
10+5 ≥7
15 ≥7
which is true and confirms x = -2 works. I'll let you try out x = -1.
Classify the following triangle. Check all that apply.
A. Equilateral
. B. Obtuse
. C. Scalene
D. Right
N E. Acute
F. Isosceles
The given triangle is Equilateral triangle.
What is triangle ?Triangle is a two dimensional shape having three side and sum of all angles is equals to 360 degree .
A right angled triangle is a triangle having one of its angle with measure of 90° The slant side of that triangle is called Hypotenuse and it is the longest side in that triangle.
We have, triangle with an angle equal to each other and three equal sides.
So, We know that,
When a triangle have angle equals to each other then it is Equilateral triangle.
Now, When a triangle have equal sides then it is Equilateral triangle.
So,
From the above mentioned statements we can say that triangle is Equilateral triangle.
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Select each equation which is equivalent to 60% of 25.
0.6 • 25 = x
x • 1.6 = 25
610=x25
60100=25x
x25=60100
6.0 • 25 = x
The equation which is equivalent to 60% of 25 is x = 0.6 * 25
What is a linear equation with an example?
Ax+By=C represents a two-variable linear equation in its standard form.
A standard form linear equation is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y).
A linear equation with one variable has the conventional form Ax + B = 0. x is a variable, A is a coefficient, and B is constant in this situation.
An equation is used to show the relationship between variables, and numbers.
Let x represent the value of 60% of 25. Hence:
x = 60% of 25
x = 0.6 * 25
Hence, the equation which is equivalent to 60% of 25 is x = 0.6 * 25
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please help due now please very easy
Dontrell bought 5 1/2 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.
____________________
Answer: y= 0.64x
Step-by-step explanation:
Take 3.52 divided by 5.5 = $0.64 per pound of potato
y is the total cost, x is the number of pound
y= 0.64x
Like has blue and red balls.
Every day he win 2 blue balls and lose 3 red.. after 5 days he won the same amount of blue balls as red. After 9 days he had twice as many blue balls as red. How many red balls he have at the beginning
Like has 47 red balls in the beginning.
What is probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The likelihood of choosing a blue and then a red ball at random when two balls are pulled is 5/18.
since, he loses everyday 3 red balls; after 1 day (y-3) red balls
Case1:
x + 10 = y -15
x - y = -25 equation 1
Case2:
(x + 18) = 2(y - 27)
x + 18 = 2y - 54
x - 2y = -54 - 18
x - 2y = -72 equation 2
Now subtract both eq1 and eq2
x - y = -25
x - 2y = -72
y = 47
Like has 47 red balls in the beginning.
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Maricopa's Success scholarship fund receives a gift of $ 200000. The money is invested in stocks, bonds, and CDs. CDs pay 3 % interest, bonds pay 5.5 % interest, and stocks pay 11.9 % interest. Maricopa Success invests $ 50000 more in bonds than in CDs. If the annual income from the investments is $ 14480 , how much was invested in each account?
On solving the question, we got that - Maricopa Success invested $45000 in stocks, Maricopa Success invested $75000 in bonds and Maricopa Success invested $50000 in CD's.
What is equation?A theorem of equality between two expressions consisting of equations, variables and/or numbers. Essentially, equations are problems, and the development of mathematics has been driven by attempts to find answers to these problems in a systematic way. The equations vary in complexity from simple algebraic equations (containing only addition or multiplication) to differential, exponential equations (containing exponential terms), and integral equations. They are used to express many of the laws of physics. See also system of equations.
Equations -
s + b + C = 170000
11.4s + 4.4b + 3.25C = 1005500
b = C + 25000
And,
Rearrange::
s + b + C = 170000
1140s + 440b + 325C = 100550000
0 + b - C = 25000
Now,
Use any method you know to solve the system to get:
stocks = 45000
bonds = 75000
CD's = 50000
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Solve x 2 =-6x-5 by completing the square
[tex]\fbox{x=$\dfrac{-7}{6}$ }[/tex]
Flip the equation:
[tex]-6x-5=2[/tex]
Add 5 to both sides:
[tex]-6x-5+5=2+5[/tex]
[tex]-6x=7[/tex]
Divide both sides by -6:
[tex]\dfrac{-6x}{-6} =\dfrac{7}{-6}[/tex]
[tex]x=\dfrac{7}{-6}[/tex]
COLLEGE PREP Which point lies on the perpendicular bisector of the segment with endpoints M(7,5) and N(-1,5) ?
(2,0)
(3,9)
(4,1)
(1,3)
The point on the perpendicular bisector of the segment MN, M(7, 5), N(-1, 5), is (3, 9)
What is the perpendicular bisector of a line?The perpendicular bisector of a segment, divides the segment into two segments that have the same length, and which forms an angle of 90° with the line.
The specified endpoints on the segment MN = M(7, 5), and N(-1, 5)
The y-coordinates of the points M and N are the same, therefore, the segment is an horizontal segment.
The midpoint of the line is therefore;
(7 + (-1 - 7)/2, 5 + (5 - 5)/2) = (3, 5)
The slope of the segment, MN, m = (5 - 5)/(-1 - 7) = 0
The slope of the perpendicular line is therefore;
-1/0 = ∞
The segment MN is parallel to the x-axis, therefore, the perpendicular bisector is parallel to the y-axis, and the x-values of points on the perpendicular bisector have the save value s the x-value of the midpoint of the segment MN, (3, 5), which is x = 3
The point that lies on the perpendicular bisector of the segment MN from the options is therefore; (3, 9)
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Write the inequality represented by the graph in standard form, y = ax2 + bx + c.
y =
a =
b =
c =
The value of the coefficients a, b, and c will be 2, 2, and negative 24. And the sign will be (<).
How to get polynomials with zeroes?Let a, b, c, and d are the zeroes of the polynomial.
Then the polynomial is given as,
⇒ (x - a)(x - b)(x - c)(x - d)
The degree of the polynomial will be greater than or equal to the number of zeroes.
From the graph, the zeroes are -4 and 3. Then the factor of will be (x + 4) and (x - 3). Then the polynomial 'y' is given as,
y = a(x - 3)(x + 4)
At (1, -20), we have
- 20 = a(1 - 3)(1 + 4)
- 20 = a (-2)(5)
a = 2
Then the inequality is given as,
y < 2(x - 3)(x + 4)
y < 2(x² + x - 12)
y < 2x² + 2x - 24
The value of the coefficients a, b, and c will be 2, 2, and negative 24. And the sign will be (<).
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(8-12) x (8 x 4) +7²
Step-by-step explanation:
[tex](8 - 12) \times (8 \times 4) + {7}^{2} \\ [/tex]
[tex]( - 4) \times (32) + 49[/tex]
[tex] -12 8 + 49 =79 [/tex]
Jordan got a loan from her mom for school at $11,000 at 4% interest, compounded monthly. If she pays off $200 per month, how long will it take to pay off the loan? ________ months, or about _______ years. ?
Answer:
61 months, about 5.07 years
Step-by-step explanation:
You want the time it takes to pay off a loan of $11,000 at 4% compounded monthly when the payment is $200 per month.
Number of paymentsThe number of payments required can be found by solving the amortization formula, or using any spreadsheet, financial calculator, or suitable app.
The attachment shows the number of months required is about 60.9.
It will take 61 months, or about 5.07 years to pay off the loan.
__
Additional comment
The formula for the number of monthly payments on a loan amount of P at interest rate r with monthly payments of A is ...
[tex]N = -\dfrac{\log{\left(1-\dfrac{Pr}{12A}\right)}}{\log{\left(1+\dfrac{\vphantom{R}r}{12}\right)}}[/tex]
You wish to test the following claim H^Ц at a significance level of а=0.10. For the context of this problem. Ц₄=Ц₂-Ц₁ where the first data set represents a pre-test and the second data set represents a post-test.
Hₐ² Ц =0
Ha² Ц ≠0
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-4est simples for n=25 subjects. The average difference (post - pre) is d=-34.3 with a standard deviation of the differences of sd=42.9.
What is the critical value for this test? (Report answer accurate to three decimal places.) critical value . ± ____
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
fest statistic = ____
We have a two-tailed test, as we are testing if the mean is different of a value.
The t-distribution is used, as we have the standard deviation for the sample, and the parameters are given as follows:
25 - 1 = 24 degrees of freedom.Significance level of 0.10.Using a t-distribution calculator, the critical value is of:
t = ± 1.7109.
How to obtain the test statistic?The equation for the test statistic is defined as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In the context of this problem, the values of these parameters are of:
[tex]\overline{x} = -34.3, \mu = 0, s = 42.9, n = 25[/tex]
Hence the value of the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{-34.3 - 0}{\frac{42.9}{\sqrt{25}}}[/tex]
t = -4.
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A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 3(1.09)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 5.98 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 2 to m = 8, and what does it represent?
f(m) = 3 * 1.09 * m = 3.27 * m
A:
solve f(m) = 5.98 to find how long it takes for fish to reach that length
5.98 = 3.27 * m
m = 5.98/3.27 = 1.83 months
A reasonable domain would technically depend on other factors like standard deviation, however, a domain of [0,3] could be reasonable without further information.
B:
The y intercept (0 because f(0)=0 ) represents the length of fish at the beginning of the marine biologists study, or when the number of months is zero
C:
Rate of change equals the change in y over the change in x.
[tex]\frac{f(8)-f(2)}{8-2}=\frac{26.16-6.54}{6}=\frac{19.62}{6}=3.27\frac{cm}{month}\\[/tex]
This represents the average number of cm the length of the fish change per month in the interval [2, 8]
Your final grade in a class is based on your score on two tests and the final exam . You scored a 74 % and 82 % on the tests and an 80 % on the final exam . Find your final grade when the final exam is twice the weight of each test .
Using the Final Exam Grade formula above, I want a 90 in the class and I currently have an 85 . The final is worth [tex]$40 \%$[/tex] of the term grade.
First, convert the weight of the final exam from percent to decimal: [tex]$40 \div 100=0.40$[/tex]
[tex]$$\begin{gathered}F=\frac{90-((1-0.4) \times 85)}{0.4} \\F=\frac{90-((0.6) \times 85)}{0.4} \\F=\frac{90-51}{0.4} \\F=\frac{39}{0.4} \\F=97.5\end{gathered}$$[/tex]
So if I have an 85 in the class, I want a 90, and the final exam is worth 40%, I need a 97.5 to get a 90 in the class.
Using the Final Class Grade formula above, [tex]$F=88.6, w=15$, and $C=91$.[/tex]
First, convert the weight of the final exam from percent to decimal: 15 div 100=0.15
So I went into the final with a class grade of 91 . I got 88.6 on the final which was worth $15 \%$ of the course grade. My final grade in the class was 90.64.
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T/F?
Arrays can be passed as parameters to a function by value, but it is faster to pass them by reference.
Arrays can be passed as parameters to a function by value, but it is faster to pass them by reference. The given statement is False.
An array is a collection of items of same data type stored at contiguous memory locations. This makes it easier to calculate the position of each element by simply adding an offset to a base value, i.e., the memory location of the first element of the array.
In Pass by value, function is called by directly passing the value of the variable as an argument. So any changes made inside the function does not affect the original value.
In Pass by Reference, Function is called by directly passing the reference/address of the variable as an argument. So changing the value inside the function also change the original value. In JavaScript array and Object follows pass by reference property. Parameters passed as an arguments does not create its own copy, it refers to the original value so changes made inside function affect the original value.
Thus, the statement that Arrays can be passed as parameters to a function by value, but it is faster to pass them by reference is False.
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Suppose that the efficacy of a certain drug is 0.35. Consider the sampling distribution (sample size n = 156)
for the proportion of patients cured by this drug.
What is the mean of this distribution?
What is the standard error of this distribution?
(Round answer to four decimal places.)
a) The mean of this distribution is of: 0.35.
b) The standard error of this distribution is of: 0.0382.
How to define the sampling distribution of p?The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has mean and standard deviation defined as follows:
Mean: equals to proportion p.Standard deviation: [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex](the standard deviation can also be called standard error).
The sample size and the proportion for this problem are given as follows:
n = 156, p = 0.35.
Then the standard error for this distribution is calculated as follows:
s = square root(0.35 x 0.65/156) = 0.0382.
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What are the coordinates of the image of vertex R after
a reflection across the y-axis?
(-4, 3)
(4, -3)
(-3, -4)
(3, 4)
Answer:
(3, 4 )
Step-by-step explanation:
under a reflection in the y-axis
a point (x, y ) → (- x, y ) , then
R (- 3, 4 ) → R' (3, 4 )
The diagram below shows a sketch of the graph of y=f(x). The graph crosses the y-axis at the point (0,-2), and the x-axis at the point (8,0).
On a piece of paper sketch the graph of y= -4 f(x+3).
Record below the coordinates of the point where the graph crosses the x-axis and the coordinate of the point where x= -3.
x = ______
y = ______
and
x = ______
y = ______
The coordinates of the intersection with the x-axis are
(8,0), and the coordinates of the point where x = -3, (-3 0).
What are the coordinates of the axis?
A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.
We have,
The graph shows the sketch of y = f(x).
The graph crosses the y-axis at the point (0,-2), and the x-axis at the point (8,0).
The coordinates of the intersection with the x-axis are:
x = 8
y = 0
The coordinates of the point where x = -3,
y = 0.
Hence, the coordinates of the intersection with the x-axis are
(8,0), and the coordinates of the point where x = -3, (-3 0).
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Is 3/8 the same as 1 1/2 of a 4th
(Please give an explanation)
Answer: Yes.
Step-by-step explanation: 3/8 and 1 1/2 of a fourth are equivalent amounts. To see why, you can use a common denominator to compare the two fractions. If we convert both fractions to eighths, then 3/8 becomes 3/8 and 1 1/2 of a fourth becomes 6/8. Since 3/8 and 6/8 are both equal to 3/4, it follows that 3/8 and 1 1/2 of a fourth are also equal.
7x - y = 6
-7x + y = -6
Answer:
X= 6+y/7
Step-by-step explanation:
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 50 miles far the eye.
What is Barometric Air Pressure?The measurement of air pressure in a certain location is called barometric pressure, which is the force of air pressing down on the surface of the globe, the oceans, and the land. .
p(x) =0.48ln (x + 1) + 27
Lets take P(50)
P(50)= barometric pressure at 50 miles from the eye of the hurricane P(50) as x
P(50) = 0.48 ln (50 + 1) + 27
P(50) = 0.48 ln (51) + 27
P(50) = 0.48 x 3.9318 + 27
where,
ln(51) = 3.9318
P(50) = 28.89
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which of the following linear systems has the ordered pair (1, 1)as a solution?
The linear systems has the ordered pair (1, 1)as a solution will be x + y = 2 and x - y = 0. Then the correct option is A.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let's check all the options, then we have
A) x + y = 2 and x - y = 0
Add both equations, then we have
x + y + x - y = 2 + 0
2x = 2
x = 2 / 2
x = 1
Then the value of the variable 'y' is calculated as,
1 - y = 0
y = 1
Then the solution of the equations is (1, 1).
The linear systems has the ordered pair (1, 1)as a solution will be x + y = 2 and x - y = 0. Then the correct option is A.
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The missing option is given below.
A) x + y = 2 and x - y = 0
B) x + y = 2 and x + 2y = 0
C) x + y = 0 and x - y = 2
D) None of the above