Step-by-step explanation:
for finding the weight of 12 boxes multiply 12 with the weight of first box and then you will get your answer. Tell me the answer which you found and if it will be correct I will say ok if not I will give you the correct answer
Which are perfect squares? Check all that apply. 9 , 24 , 16 , 200 , 169 , 625
Answer:
A. 9
C. 16
E. 169
F. 625
Step-by-step explanation:
Sarah needs to go to five different stores. How many ways can she go to two of them before lunch?
Answer:
10
Step-by-step explanation:
Solution 1: At first, you might think that because there are 5 ways to choose the first store and 4 ways to choose the second store, the answer is 5 * 4 = 20 but this is over-counting by a factor of 2. Say that two of the stores are A and B. If she went to A then B, that's the same as going to B then A since you still go to the same stores, therefore, the answer is 20 / 2 = 10.
Solution 2: We need to find the number of ways to choose 2 stores from 5, we can do this by calculating ₅C₂ which equals:
5! / 2! * 3!
= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 3 * 2 * 1
= 5 * 4 / 2 * 1
= 10
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
A
Step-by-step explanation:
Which of the following is an example of closure? (1 point)
The equation 5 - 5 = 0 is an example of the natural numbers being closed under subtraction
The equation 1.5 +1.6 = 3.1 is an example of the rational numbers being closed under addition
The equation 4 - 6 = -2 is an example of the whole numbers being closed under subtraction
The equation 1+0= 1 is an example of the natural numbers being closed under addition
Answer:
The equation 1+0=1
Step-by-step explanation:
Other options are not eligible because
1 option -Natural numbers cannot be closed under subtraction
2 option-The equation is not having proper rational numbers, they are decimals
3 option-Whole numbers cannot be closed under subtraction
Thank you!
Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario
Answer:
The test statistic is [tex]t = 2.79[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 59.3[/tex]
The sample size is [tex]n = 79[/tex]
The sample mean is [tex]\= x = 62.4[/tex]
The standard deviation is [tex]\sigma = 9.86[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]
[tex]t = 2.79[/tex]
Please help. I’ll mark you as brainliest if correct!
Answer:
Children = 150
Students = 98
Adults = 75
Step-by-step explanation:
C + S + A = 323
5C + 7S + 12A = 2336
A = 1/2C
C = 150
S = 98
A = 75
The graph represents this system of equations
y=4
y=3 - 1/2x . What is the solution to the system of equations
(-2,4)
(3,4)
(4,-2)
(4,3)
Hey there! I'm happy to help!
When graphing a system of equations, the solution is the point where the two lines meet. We see that they intersect at (-2,4).
Therefore, the solution to the system of equations is (-2,4).
Have a wonderful day! :D
Answer:
A
Step-by-step explanation:
edge 2020 Dec 9
If xy = 1 what is the arithmetic mean of x and y in terms of y? Please show work as detailed as possible
Answer:
(1+y^2) /2y
Step-by-step explanation:
arithmetic mean is the average of x and y
(x+y)/2
Using the equation
xy = 1
and solving for x
x = 1/y
Replacing x in the first equation
(1/y + y) /2
Multiply by y/y
(1/y + y) /2 * y/y
(1/y + y)*y /2y
(1+y^2) /2y
one of these marbles is picked at random. what is the probability that a blue marble is picked?
A.1/3
B.2/5
C.1/2
D.1/4
Answer:
1/3
Step-by-step explanation:
there are twelve marbles total. there are 4 blue marbles.
4/12 = 1/3
Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows:
x 0 1 2 3
p(x) 0.37 0.29 0.22 0.12
Find the mean, of this distribution. Report your answer to two decimal places.
Answer:
1.86
Step-by-step explanation:
Given the following :
X : - - - - 0 - - - - 1 - - - - 2 - - - - - 3 - - - - 4
P(x) - 0.37 - - 0.28 - - 0.22 - - 0.22 - - 0.12
The mean of the distribution can be calculated by evaluated by determining the expected value of the distribution given that the data above is a discrete random variable. The mean value can be deduced multiplying each possible outcome by the probability of it's occurrence.
Summation of [P(x) * X] :
(0.37 * 0) + (0.28 * 1) + (0.22 * 2) + (0.22 * 3) + (0.12 * 4)
= 0 + 0.28 + 0.44 + 0.66 + 0.48
= 1.86
What is the solution to the system of equations? -2x-3y+z=-6, z=6, 3x-y+z=13
Answer:
B is the correct answer.
Step-by-step explanation:
-2x+3y+z=-6
z=6
-2x+3y+6=-6
-2x+3y=-12
-2(3)+3(2)
-6+6=0 A is incorrect
-2(3)+3(-2)=-12
-6-6=-12
B is the correct answer.
I am not going to show C or D, because you have the right answer. Hope this helps you. Thank you.
Question 1 (Multiple Choice Worth 4 points)
(08.01) Looking at the spread of your data best fits which step of the statistical process?
Answer:
The answer is "Analysis the information by chart and number processes".
Step-by-step explanation:
They already have articulated a query and also gathered information unless you are searching only at the distribution of your results. Those who are ready to analyze your results for all are there.
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700 t 11,000 The population before construction is 67,000. Determine the projected population 16 yr after construction of the park has begun. people
Complete question :
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700√t + 11,000 The population before construction is 67,000. Determine the projected population 16 yr after the construction of the park has begun. people
Answer:
486,200
Step-by-step explanation:
Given that the rate of change in population is represented by the function:
f(t) = 5,700√t + 11,000
To get the original function, we take the integral of the rate function because the rate of change is obtained by taking the derivate of the original equation
f(t) = 5,700t^1/2 + 11,000
Taking the integral of f with respect to t:
∫(5,700t^1/2 + 11,000)
[5700t^(1/2 + 1)] / (1/2 + 1) + 11000t + C
[(5700t^3/2)/ 3/2] + 11000t + C
Where C = constant
If population before construction = 67000
Then C = 67000
t = time = 16 years
Substitute values into the original change equation:
[(5700(16)^3/2)/ 3/2] + 11000t + 67000
[(5700 * 64) / 1.5] + 11000(16) + 67000
243200 + 176000 + 67000
= 486,200
A population has a standard deviation of 16. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within 2 of the population mean?
a. Since the mean is not given, there is no answer to this question.
b. -0.6826
c. 0.3413
d. 0.6826
e. -0.3413
Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 16[/tex]
The sample size is n = 64
The standard error of mean is mathematically evaluated as
[tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x } = \frac{16 }{\sqrt{64} }[/tex]
[tex]\sigma _{\= x } = 2[/tex]
Generally the probability that the sample mean will be within 2 of the population mean is mathematically represented as
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < \frac{ \= x - \mu }{\sigma_{\= x }} < \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]
Generally [tex]\frac{ \= x - \mu }{\sigma_{\= x }} = Z (The \ standardized \ value \ of \ \= x )[/tex]
So
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < Z< \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( -2 }{\sigma_{\= x }} < Z< \frac{ 2 }{\sigma_{\= x }} )[/tex]
substituting values
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{-2 }{2} < Z< \frac{ 2 }{2} )[/tex]
[tex]P( \mu - 2 < \= x < \mu + 2) = P(-1< Z< 1 )[/tex]
=> [tex]P( \mu - 2 < \= x < \mu + 2) = P(Z < 1) - P(Z < -1)[/tex]
From the normal distribution table [tex]P(Z < 1 ) = 0.84134[/tex]
[tex]P(Z < - 1) = 0.15866[/tex]
=> [tex]P( \mu - 2 < \= x < \mu + 2) = 0.84134 - 0.15866[/tex]
=> [tex]P( \mu - 2 < \= x < \mu + 2) = 0.6826[/tex]
Suppose that you are standing 150 feet from a building and the angle of elevation to the top of the building is 42°. What is the building's height?
Answer:
135.06 feet
Step-by-step explanation:
Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.
opposite side = x
adjacent side = 150 feet
angle = 42°
tan(42°) = x/150 feet
150 feet * tan(42°) = x
x = 135.06 feet
Find the solution of the inequality 5 > r - 3.
A) r<2
B) r = 2
C) r=8
(D) r < 8
Answer:
[tex]\huge\boxed{r<8}[/tex]
Step-by-step explanation:
[tex]5 > r - 3[/tex]
Adding 3 to both sides
[tex]5 + 3 > r[/tex]
[tex]8 > r\\OR \\r < 8[/tex]
Answer: D. r<8
Step-by-step explanation:
[tex]5>r-3[/tex]
add 3 to both sides
[tex]r-3+3<5+3[/tex]
[tex]5+3=8[/tex]
simplify
[tex]r<8[/tex]
Using the power series methods solve the 1st order Lane-Emden Equation:
xy = 2y + xy = 0
You may only use a power series solution to find both linearly independent functions. This means you may not use Abel’s theorem, variation of parameters or reduction of order.
Answer:
Step-by-step explanation:
xy = 2y + xy = 0
Hence, 2y + xy = 0 ---------(1)
Differentiating equation (1) n times by Leibnitz theorem, gives:
2y(n) + xy(n) + ny(n - 1) = 0
Let x = 0: 2y(n) + ny(n - 1) = 0
2y(n) = -ny(n - 1)
∴ y(n) = -ny(n - 1)/2 for n ≥ 1
For n = 1: y = 0
For n = 2: y(1) = -y
For n = 3: -3y(2)/2
For n = 4: -2y(3)
An ice cream store makes 144 quarts of ice cream in 8 hours. How many quarts could be made in 12 hours?
Hey there! I'm happy to help!
We know that the ice cream store makes 144 quarts in eight hours. What about in one hour? Let's divide this by eight to find out.
144/8=18
So, they make 18 quarts every hour. We want to figure out how many can be made in 12 hours. So, we just multiply 18 by 12!
18(12)=216
Therefore, 216 quarts of ice cream could be made in 12 hours.
Have a wonderful day! :D
The ice cream store will make 216 quarts of ice cream in 12 hours.
What is division?Division is breaking a number up into an equal number of parts.
Given that, An ice cream store makes 144 quarts of ice cream in 8 hours.
Since, they make 144 quarts of ice cream in 8 hours
Therefore, in 1 hour they will make = 144/8 = 18 quarts
So, in 12 hours = 18x12 = 216 quarts.
Hence, The ice cream store will make 216 quarts of ice cream in 12 hours.
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Factor 4(20) + 84. 4(20 + 21) 4(21 + 20) 20(4 + 84) 20(4 + 4)
Answer:
[tex]\huge\boxed{4 ( 20 + 21)}[/tex]
Step-by-step explanation:
4(20) + 84
Resolve Parenthesis
80 + 84
Taking 4 common as both are the multiples of 4
4 ( 20 + 21)
It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive. A random sample 150 of each gender was selected from recent hospital records, and the following results were obtained. Construct 95% confidence interval for the difference of the two proportion. Round your answer to nearest ten-thousandth. Interpret the result.
Complete Question
It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive. A random sample 150 of each gender was selected from recent hospital records, and the following results were obtained.
Men. 43 patients had high blood pressure
Woman. 52 patients had high blood pressure.
Answer:
The 95% confidence interval is
[tex]- 0.1651 < p_m - p_f <0.0451[/tex]
This mean that there is a 95 % confidence that the difference between the true proportions of male and female that are hypertensive is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive
Step-by-step explanation:
From the question we are told that
The sample size for male is [tex]n_1 = 150[/tex]
The number of male that are hypertensive is [tex]m = 42[/tex]
The sample size of female is [tex]n_2 = 150[/tex]
The number of female that are hypertensive is [tex]q = 52[/tex]
The proportion of male that are hypertensive is mathematically represented as
[tex]\r p_m = \frac{43}{150}[/tex]
[tex]\r p_m = 0.287[/tex]
The proportion of female that are hypertensive is mathematically represented as
[tex]p_f = \frac{52}{150}[/tex]
[tex]p_f = 0.347[/tex]
From the question we are told that confidence level is 95%, hence the level of significance is mathematically represented as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha =5\%[/tex]
[tex]\alpha =0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{ \r p_m (1- \r p_m )}{n_1} + \frac{ \r p_f (1- \r p_f )}{n_2} }[/tex]
substituting value
[tex]E = 1.96 * \sqrt{\frac{ 0.287 (1- 0.287 )}{150} + \frac{ 0.347 (1- 0.347 )}{150} }[/tex]
[tex]E = 0.1051[/tex]
The 95% confidence interval is mathematically represented as
[tex](\r p_m - \r p_f ) - E < p_m - p_f < (\r p_m - \r p_f ) + E[/tex]
substituting values
[tex]( 0.287 - 0.347 ) - 0.1051 < p_m - p_f <( 0.287 - 0.347 ) + 0.1051[/tex]
[tex]- 0.1651 < p_m - p_f <0.0451[/tex]
This mean that there is a 95 % confidence that the difference between the true proportion is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive.
In the diagram, ∆ABC and ∆DBE are similar. What is the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE? A. 1.33 B. 0.75 C. 0.66 D. 0.55
Answer:
B
Step-by-step explanation:
Calculate the ratio of corresponding sides, image to preimage, that is
scale factor = [tex]\frac{DE}{AC}[/tex] = [tex]\frac{12.09}{16.12}[/tex] = 0.75 → B
The scale factor of the dilation will be 1.33. Then the correct option is A.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
In the diagram, ∆ABC and ∆DBE are similar.
Then the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE will be
⇒ 16.12 / 12.09
⇒ 1.33
Then the correct option is A.
More about the dilation link is given below.
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Is math a feature of the universe or a feature of human creation?
Answer:
a feature of the universe
Step-by-step explanation:
Math is a feature of the universe because what we call math is just a way of explaining how things work.
You are certain to get a red card when selecting 27 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusiv
Answer:
If something is guaranteed, it has a probability of 100%, or 1.
Step-by-step explanation:
A standard deck has 52 cards. Of these, half are red cards (diamonds and hearts) and half are black cards (clovers and spades)
Half of the deck is 26 cards (52 ÷ 2 = 26), so you have 26 red and 26 black cards.
What this means in our context is, if we draw 27 cards, even if we drew all 26 black cards, we would still have 1 red card.
So the probability is 100%, or 1, of drawing a red card when we pick 27 cards from a deck, no matter how it's shuffled
The probability of getting a red card is 1.
No matter how you shuffle the cards, the no of cards will remain the same.
Therefore, it will not affect the probability.
What is probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
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A number is chosen at random from 1 to 50. Find
the probability of selecting multiples of 10.
Step by step.
Answer:
1/10
Step-by-step explanation:
There are 5 numbers in the range that are multiples of 10: 10, 20, 30, 40, 50. The probability of choosing one of those at random from the set of 50 numbers is ...
5/50 = 1/10
10 - 2x, when x = 3
Answer:
4
Step-by-step explanation:
Plug in 3 as x in the expression:
10 - 2x
10 - 2(3)
10 - 6
= 4
Answer:
4
Step-by-step explanation:
10 - 2x
Let x =3
10 -2(3)
10 -6
4
Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register. The store is required to reveal (in the fine print) the distribution of discounts available. Determine whether the following probability assignment is legitimate?
10% off 20% off 30% off 50% off
a. 0.2 0.2 0.2 0.2
b. 0.5 0.3 0.2 0.1
c. 0.8 0.1 0.05 0.05
d. 0.75 0.25 0.25 -0.25
e. 1 0 0 0
Answer:
b
Step-by-step explanation:
it makes the most senses the lower the discount the higher the chance
An inequality is shown: −np − 4 ≤ 2(c − 3) Which of the following solves for n?
Answer:
[tex]\huge\boxed{n\leq\dfrac{2-2c}{p}\ \text{for}\ p<0}\\\boxed{n\geq\dfrac{2-2c}{p}\ \text{for}\ p>0}[/tex]
Step-by-step explanation:
[tex]-np-4\leq2(c-3)\qquad\text{use the distributive property}\\\\-np-4\leq2c-6\qquad\text{add 4 to both sides}\\\\-np\leq2c-2\qquad\text{change the signs}\\\\np\geq2-2c\qquad\text{divide both sides by}\ p\neq0\\\\\text{If}\ p<0,\ \text{then flip the sign of inequality}\\\boxed{n\leq\dfrac{2-2c}{p}}\\\text{If}\ p>0 ,\ \text{then}\\\boxed{n\geq\dfrac{2-2c}{p}}[/tex]
A website developer wished to analyze the clicks per day on their newly updated website. Let the mean number of clicks per day be μ. If the website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average, what are the null and alternative hypotheses?
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day
Step-by-step explanation:
We are given that a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
Let [tex]\mu[/tex] = mean number of clicks per day.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day
Here, the null hypothesis states that the mean number of clicks per day is 200 clicks a day.
On the other hand, the alternate hypothesis states that the mean number of clicks per day is different than 200 clicks a day.
Hence, this is the correct null and alternative hypotheses.
Answer: Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
Step-by-step explanation:
Let [tex]\mu[/tex] be the mean number of clicks per day.
Given, a website developer wished to analyze the clicks per day on their newly updated website.
The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.
i.e. he wants to check either [tex]\mu=200\text{ or }\mu\neq 200[/tex]
Since a null hypothesis is a hypothesis believes that there is no difference between the two variables whereas an alternative hypothesis believes that there is a statistically significant difference between two variables.
So, Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
Hence, the required null and alternative hypotheses.
Null Hypothesis [tex]H_0:\mu=200[/tex]
Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]
Rosa is trying to copy an angle. She reads and understands all of the steps, but insists on drawing circles instead of arcs. Which of the following is the best response to tell Rosa?
A. It is acceptable to draw circles instead of arcs, but because they are bigger and take up more space, your drawing may become messy, increasing the chance for errors. <-- MY ANSWER
B. You have to use arcs because a compass cannot make a full circle.
C. You have to draw arcs because arcs and circles are not interchangeable.
D. She is right because it is better to draw circles than arcs. Circles are clearer and easier to draw than arcs so you are less likely to make a mistake.
Thanks!
You have the correct answer. It is choice A. Nice work.
I prefer using full circles because sometimes the arcs could be too small in measure to not go where you want them to. If you're worried about things getting too cluttered (a legitimate concern), then I recommend drawing everything in pencil and only doing the circles as faint lines you can erase later. Once the construction is complete, you would go over the stuff you want to keep with a darker pencil, pen or marker. You can also use the circle as a way to trace over an arc if needed.
Choice B is false as a full circle can be constructed with a compass. Simply rotate the compass a full 360 degrees. Any arc is a fractional portion of a circle.
Choice C is false for similar reasoning as choice B, and what I mentioned in the paragraph above.
Choice D contradicts choice A, so we can rule it out. Arcs are easier to draw since it takes less time/energy to rotate only a portion of 360 degrees. Also, as mentioned earlier, having many full circles tend to clutter things up.
Please solve this question by using the strategy Elimination Method or Solve By Substitution. This is the math equation: 1/2x+y=15 and -x-1/3y=-6
2nd Question: 5/6x+1/3y=0 and 1/2x-2/3y=3
First pair of equations :
[tex]\dfrac{1}{2}x+y=15\ ..(i)\\\\-x-\dfrac{1}{3}y=-6\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]x+2y=30\ ..(iii)[/tex]
By Elimination Method, Add (i) and (ii) (term with x eliminate), we get
[tex]2y-\dfrac{1}{3}y=30-6\\\\\Rightarrow\ \dfrac{5}{3}y=24\\\\\Rightarrow\ y=\dfrac{24\times3}{5}=14.4[/tex]
put y= 14.4 in (iii), we get
[tex]x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2[/tex]
hence, x=1.2 and y =14.4
Second pair of equations :
[tex]\dfrac{5}{6}x+\dfrac13y=0\ ..(i)\\\\ \dfrac12x-\dfrac{2}{3}y=3\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]\dfrac{5}{3}x+\dfrac{2}{3}y=0\ ..(iii)[/tex]
Elimination Method, Add (i) and (ii) (term with y eliminate) , we get
[tex]\dfrac53x+\dfrac12x=3\Rightarrow\ \dfrac{10+3}{6}x=3\\\\\Rightarrow\ \dfrac{13}{6}x=3\\\\\Rightarrow\ x=\dfrac{18}{13}[/tex]
put [tex]x=\dfrac{18}{13}[/tex] in (i), we get
[tex]\dfrac{5}{6}(\dfrac{18}{13})+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{15}{13}+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{1}{3}y=-\dfrac{15}{13}\\\\\Rightarrow\ y=-\dfrac{45}{13}[/tex]
hence, [tex]x=\dfrac{18}{13}[/tex] and [tex]y=\dfrac{-45}{13}[/tex] .
