The method that he chooses to select his sample is Stratified Sampling.
In Stratified, the population is divided into subpopulations and then the same sampling is applied to each region or subpopulation.
The ability to obtain a sample population that most accurately represents the overall population being investigated while ensuring that each subgroup of interest is represented makes stratified random sampling one popular technique employed by researchers. Researchers use stratified sampling to ensure that specific subgroups are represented in the sample. It also helps in the precise evaluation of each group's characteristics. This technique is often used in surveys to better understand disparities between subpopulations.
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Using the diagram below, a reflection in line r is a transformation for which the following are true.
.
If a point A is on line r, then the image of A
is A itself (that is, A' = A).
Line of reflection.
B'
If a point B is not on line r, then r is the
perpendicular bisector of BB.
Answer:
The diagram shows a line of reflection, labeled as "line r," and a point B on one side of the line. The image of point B, labeled as B', is shown on the other side of the line.
If point A is on line r, then the image of A would be A itself because a reflection in line r means that all points on the line remain unchanged.
If point B is not on line r, then line r would be the perpendicular bisector of line segment BB'. This means that line r would pass through the midpoint of line segment BB' and be perpendicular to it. The image of point B would be on the opposite side of line r from the original point B, but the distance between B and B' would remain the same.
Question 2 of 20
What is another name for this polynomial, based on the number of terms it
contains?
g(x) = 5x + 17x5
Answer:
Based on the given polynomial, g(x) = 5x + 17x5, it is a polynomial of the sixth degree because it contains six terms (one constant term, one linear term, and one quintic term). Thus, another name for this polynomial is a sixth-degree polynomial.
Step-by-step explanation:
glasses of milk and 3 snack bars have a total of 71 carbohydrates (carbs), and 3 glasses of milk and 2 snack bars have a total of 69 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
Answer:So looking at this question, we have two variables (1 - a glass of milk; 2 - a snack bar) and two equations to use to solve for the two variables. Remember that for any number of variables, you need that same number or more equations to solve for the variables.Let's say that a glass of milk is represented by g and a snack bar is represented by s.So we essentially have two equations here:4 glasses of milk + 3 snack bars = 88 carbs, or:4g + 3s = 882 glasses of milk + 4 snack bars = 74 carbs, or:2g + 4s = 74Now that we have this, we can solve for our equations. There are two ways to do this:SUBSTITUTION - solve for one variable, then substitute it inLet's solve for g using the second equation. First, we'll isolate g by subtracting 4s from both sides.2g = 74 - 4sNext, we can divide the whole equation by 2 to solve for g.g = 37 - 2sNow, we can substitute this into the first equation for g and solve for s.4g + 3s = 884(37 - 2s) + 3s = 88148 - 8s + 3s = 88148 - 5s = 88 (now subtract 88 from both sides and add 5s to both sides)60 = 5ss = 12Now we can use this to solve for g in the original equationg = 37 - 2sg = 37 - 2(12) = 37 - 24 = 13ELIMINATION - eliminate one variable to solve for the other, then use that to solve for the firstLet's look at our two equations4g + 3s = 882g + 4s = 74Let's eliminate the variable g first by multiplying the second question by -2.4g + 3s = 88-4g - 8s = -148If we add these two equations together, we get-5s = -60Divide both sides by -5 and we gets = 12Now, we can plug s into either equation to solve for g as we did above.
In terms of relative growth rate, what is the defining property of exponential growth?
In terms of relative growth rate Exponential growth is characterized by a constant relative growth rate.
Exponential growth is the process of increasing quantity over time. Occurs when the instantaneous rate of change of a quantity over time is proportional to the quantity itself. The exponential growth model has the form
y (t) = C eᵏᵗ, where k is the rate constant.
Relative Growth Rate:Relative growth rate (RGR) is the rate of growth relative to size. That is, the rate of growth per unit time relative to the size at that point in time and y'(t)/y(t) is the relative growth rate of a function y at time t.
1/y dy/dt = 1/y d(C eᵏᵗ)/dt
= 1/y(kC eᵏᵗ)
= 1/y ( ky) ( since, y (t) = C eᵏᵗ)
= k
Therefore a constant relative growth rate.
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Complete question:
In terms of relative growth rate, what is the defining property of exponential growth? Choose the correct answer below.
A. The relative growth rate at time t is the slope of the exponential function at time t.
B. dy dt If y represents a population, then the relative growth rate can be represented by dy/dt
C. The relative growth rate is proportional to the size of the population
D. The relative growth rate is constant.
S varies directly as t. if s is 20 when t is 4 then t is ____ when s is 30
Answer:
t is 6 when s is 30--------------------------
s varies directly as t:
s = kt, where k- constant of direct variation.If s is 20 when t is 4, find the value of k:
20 = 4k ⇒ k = 20/4 ⇒ k = 5The equation is:
s = 5tWhen s is 30, then t is:
30 = 5t ⇒ t = 30/5 ⇒ t = 6Answer:
Thus, t = 6 if s = 30.
Step-by-step explanation:
Given that,
→ The value of s is 20 when t is 4.
Now value of s when t is 1,
→ s = (20/4)t
→ [ s = 5t ]
Then value of t when s is 30,
→ 5t = 30s
→ t = (30/5)s
→ t = 30/5
→ [ t = 6 ]
Hence, the value of t is 6.
Please answer this question
(x-4/5)-(x+1/6)=1/3
The answer of the algebraic equation is x = 30
How to solve an algebraic expression?
An algebraic equation is when two expressions are set equal to each other, and at least one variable is included
Given: (x-4/5)-(x+1/6)=1/3
(x-4/5)-(x+1/6)= 1/3
The LCM of 5 and 6 is 30
[6(x-4) - 5(x+1)]/30 = 1/3
cross multiply:
[6(x-4) - 5(x+1)] = 30/3
Expand the bracket:
6x -24 -5x -5 = 10
Add/subtract like terms:
x - 29 = 10
x = 10 + 29
x = 30
Thus, the answer is x = 30
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Answer:
39
Step-by-step explanation:
So first up Expand ( - [tex]\frac{4}{5}[/tex]) -(x + [tex]\frac{1}{6}[/tex]): - [tex]\frac{29}{30}[/tex]
so 1 more thing you have to remember their will be no answer so You then have to add this up - [tex]\frac{29}{30} =\frac{1}{3}[/tex]
so last step Multiply by LCM "Least common multiply"
so -29 = 10
and we do not have an answer because The sides are not equal so if you need an answer it will be
39
In the equation P = 7n + 6 , determine the value of P when n = 9. (Just write the numerical answer, no letters )
Answer:
P=69
Step-by-step explanation:
a sociologist wishes to estimate the percentage of the u.s. population living in poverty. what size sample should be obtained if she wishes the estimate to be within 2 percentage points with 99% confidence?
The sample size be obtained if she wishes the estimate to be within 2 percentage points with 99% confidence is 4148 , the correct option is (b) .
In the question ,
it is given that ,
the confidence interval is 99% .
let us consider ,
A sociologist wishes to estimate the percent of the U.S. population living in poverty .
Here , preliminary estimate of population has been ,
p = q = 0.50 .
for given , 99% confidence interval z = 2.756 .
the error percent is 2% , the means E = 0.02 .
So , the required sample size (n) can be calculated using the formula ,
n = (0.50)(0.50)(2.576/0.02)²
n = 0.25 * 16589.44
n = 4147.36
n ≈ 4148 .
Therefore , the sample size is 4148 .
The given question is incomplete the complete question is
A sociologist wishes to estimate the percentage of the U.S. population living in poverty. What size sample should be obtained if she wishes the estimate to be within 2 percentage points with 99% confidence ?
(a) 2401
(b) 4148
(c) 1692
(d) 2.575
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The total cost, C, of renting a van is $65 each day, d, the van is rented plus $.33 for
mile, m, the van is driven. What is the expression for C?
Answer:
.33m+65=C
Step-by-step explanation:
to solve the equation you will need to multipy .33 x the amount of miles drove after you get the answer for that you will need to add 65 then thats your final answer
the mean square for error in the anova provides an estimate of (a) the variance of the random error (b) the variance of an individual treatment average (c) the standard deviation of an individual observation (d) none of the above
The mean square for error in the ANOVA provides an estimate of the variance of an individual treatment average.
What is a variance?
Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance serves as a proxy for dispersion, or the degree to which a set of numbers deviates from their mean.
Here, We have
The mean square for error in the ANOVA provides an estimate
ANOVA = Analysis of VarianceThe correct answer is (B)
The mean square for error (MSE) in the analysis of variance (ANOVA) provides an estimate of the variance of an individual treatment average.
Unlike option C which refers to an individual observation,
option B refers to a group of observations that are classified into a single treatment sample.
The MSE measures (gives an estimate of) the variation within this treatment sample. In this case, the variation is in the average or the mean. This could be average texture, average strength, average penetration, etc.
Hence, the mean square for error in the ANOVA provides an estimate of the variance of an individual treatment average.
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Tomika and Mark had $3,800 in medical expenses and paid an additional $8,009 for medical insurance. The insurance covered 60% of the medical expenses. The IRS allows medical and dental expense deductions for the amount that exceeds 7.5% of a taxpayer's adjusted gross income. If their adjusted gross income is $101,598, how much can they claim as a medical deduction?
Tomika and Mark claim a medical deduction in the amount of $1,839.8.
How to calculate a claim as a medical deduction?To determine how much Tomika and Mark can claim as a medical deduction, you first need to calculate the number of medical expenses that are covered by their insurance.
The first step is to calculate medical insurance :
Medical insurance = 7.5 % of $101,598
Medical insurance = 7.5% x $101,598
Medical insurance = $7,619.88.
Medical deduction claim = $7,619.88 - (100% - 60%)x $3,800
Medical deduction claim = $7,619.88 - 40% x $3,800
Medical deduction claim = $7,619.88 - $1,520
Medical deduction claim = $6,099.88
Therefore, they can claim a medical deduction in the amount of $1,839.8.
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[tex]x^{2} -27=4x[/tex]
The solutions for the given equation are [tex]2+\sqrt{31}[/tex] and [tex]2-\sqrt{31}[/tex]. These are calculated by applying the quadratic formula since the given equation is a quadratic equation.
What is the quadratic formula?The quadratic formula is used for finding the roots of a quadratic equation in the form of ax² + bx + c = 0.
The formula is,
x = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Calculation:The given equation is
x² - 27 = 4x
On rewriting the equation, we get
x² - 4x - 27 = 0
thus, it is in the form of ax² + bx + c = 0. So, this is a quadratic equation.
Then, applying the quadratic formula for finding roots is nothing but its solutions.
Where a = 1; b = -4; c = -27
⇒ x = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
= [tex]\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-27)} }{2(1)}[/tex]
= (4 ± [tex]\sqrt{16+108}[/tex])/2
= (4 ± [tex]\sqrt{124}[/tex])/2
= (4 ± 2[tex]\sqrt{31}[/tex])/2
= 2 ± [tex]\sqrt{31}[/tex]
So, the roots of the given equation are 2 + [tex]\sqrt{31}[/tex] and 2 - [tex]\sqrt{31}[/tex].
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The function f(x) = x² has been transformed to g(x) = (x − h)². If h > 0, then what type of transformation
happened?
O move up
O move down
O move right
O move left
Please answer soon! Thanks in advance
Answer:
Step-by-step explanation:
System A
the two lines have the same slope, so they are parallel and never intercept themselves.
the system has no solution.
System B
By multiplying the first equation by -1
x + 4y = -3
The two equations are equals so the lines are the same.
The system has infinitely many solutions
Dan earns £8.80 per hour. How much will he earn for 6 hours work?
Answer:
£52.8
Step-by-step explanation:
£8.80 per hour
1 hour £8.80
£8.80×6 hours
=£52.8
Answer:
£52.80 after 6 hours
Step-by-step explanation:
8.80*6=52.8 which means £52.80.
Find the dimensions of the box with volume 1000 cm3 that has minimal surface area.
The dimensions of the box with a volume of 1000 cm3 that has a minimal surface area are 10 cm* 10 cm*10 cm.
Let's define the dimensions of the box as x, y and z. The surface area of the box is given by: 2(xy + xz + yz). We want to minimize the surface area. Since the volume is 1000 cm3, we know xyz = 1000. Therefore, the surface area of the box is given by:
2(xy + xz + yz) = 2(1000/x + 1000/y + 1000/z), We need to minimize 2(1000/x + 1000/y + 1000/z) subject to xyz = 1000. This is a constrained optimization problem. We can solve this problem using Lagrange multipliers. Let L(x, y, z, λ) be the Lagrangian given by:
L(x, y, z, λ) = 2(1000/x + 1000/y + 1000/z) + λ(xyz - 1000), To find the minimum, we need to find the critical points of the Lagrangian. Taking the partial derivatives of L with respect to x, y, z, and λ, we get:
∂L/∂x = -2000/x² + λyz = 0
∂L/∂y = -2000/y² + λxz = 0
∂L/∂z = -2000/z² + λxy = 0
∂L/∂λ = xyz - 1000 = 0
From the last equation, we get xyz = 1000. Substituting this value in the first three equations, we get:
∂L/∂x = -2000/x² + 2000/x = 0
∂L/∂y = -2000/y² + 2000/y = 0
∂L/∂z = -2000/z² + 2000/z = 0
Solving these equations, we get x = y = z = 10. Therefore, the dimensions of the box with minimal surface area and volume of 1000 cm3 are x = y = z = 10 cm.
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5.most people in developed countries would prefer to die at home; however, according to the textbook, only about what percentage die at home? a.10% b.20% c.30% d.40%
Percentage Of people Prefers to die at home in developed countries is 30%
Lets have Brief explanation
What is scientific research?
Scientific research is research carried out using organised, constructed scientific techniques for data collection, analysis, and interpretation.
There is growing scientific research regarding the choices people would prefer to make regarding their care as they approach death.
According to a number of studies, between 50% and 70% of patients undergoing treatment for a serious illness also state that they would prefer to die at home.
Even though many people would prefer to get care and pass away at home, hospital death is nonetheless common in many nations.
According to the research, between 25% and 30% of people want to die at home, and the classic scenario involves 30% of people.
Percentage Prefer to die at home = 30%
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if g is a simple undirected graph with 12 vertices and 3 connected components, what is the largest number of edges it might have?
If a graph have 12 vertices and 3 connected components, then the largest number of edges it might have is 45.
What is vertex?
One of the items joined together in a graph is referred to as a vertex (or node). Edges or links are the connections between the vertices in any graph.
As given in the question,
The vertices (n) = 12,
Connected components (k) = 3
let m be the number of edges it the graph might have,
The number of edges in the graph can be calculated by the following formula:
[tex]m \le \frac{(n-k+1) \times (n-k)}{2}[/tex]
putting the values from the question,
[tex]m \le \frac{(12-3+1) \times (12-3)}{2}[/tex]
[tex]m \le \frac{(10) \times (9)}{2}[/tex]
[tex]m \le 45[/tex]
By the above equation, we can say that maximum number edges of is 45.
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a bag contains 40 pieces of candy, of which 36 are mint and 4 strawberry flavor. if the pieces of candy are distributed in a random manner to four children so that each child receives 10 pieces, what is the probability that all four strawberry pieces will be received by the same child?
The probability that all four strawberry pieces will be received by the same child 9/10 outcome.
Total piece of candy = 40
Mint flavor = 36
Strawberry = 04
There are 36 + 04 = 40 total outcomes for the chocolate pick.
There are 36 outcomes resulting in you picking a mint candy.
Probability is the number of outcomes you’re testing for divided by the number of total outcomes. So in this case that’s 36/40 or 4/5 . And also,
04 /40 = 1/10
Therefore, adding both, we get,
4/5 + 1/10 = 9/10
The probability that all four strawberry pieces will be received by the same child is 9/10.
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Find x . 6x+2x-17+6x-1+-3x+20
In the preceding equation, x has the value -2/11.
How do equations work?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality. Usually, it only has one variable and an equal sign. as in 2x - 4 Equals 2.
Equations can be categorized as identities or conditional equations.
6x+2x-17+6x-1-3x+20=0
14x-3x=18-20
11x=-2
x= -2/11
Therefore, in the preceding equation, x has the value -2/11.
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What is the slope of all lines parallel to the line 3x 7y =- 7?
The slope of all lines parallel to the line 3x + 7y = -7 is 3/7.
To find the slope of the line 3x + 7y = -7, we can use the slope-intercept formula y = mx + b, where m is the slope.
We can rearrange the equation 3x + 7y = -7 to the slope-intercept form 7y = -3x -7.
We can then divide both sides of the equation by 7 to get the slope, m = -3/7.
Therefore, the slope of all lines parallel to the line 3x + 7y = -7 is 3/7.
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Jamal owns a parking garage and is trying to find the relationship between hour of the day and number of cars in the garage. He finds that between 4 am and 10 am he can model this with a linear relationship. The equation for this model is y = 3. 56x + 2. How many cars were in the garage at 4 am?.
The slope of the equation, given, is the pace at which a car enters a garage. Hence, it is 3.56, or around 4 automobiles per hour. Option D is the correct answer.
In statistics, a straight line of correlation between two variables is referred to as a linear relationship (or linear association). The mathematical equation y = mx + b can be used to represent linear relationships graphically.
Jamal is the owner of a parking garage and is attempting to determine the correlation between the number of automobiles in the garage and the hour of the day. He discovers that he can represent this using a linear relationship between 4 am and 10 am. y = 3.56x + 2 is the model's equation.
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The complete question of the above answer is
Jamal owns a parking garage and is trying to find the relationship between the hour of the day and the number of cars in the garage. He finds that between 4 am and 10 am he can model this with a linear relationship. The equation for this model is y = 3.96x + 2. About how many cars are entering the garage every hour?
A) 1
B) 2
C) 3
D) 4
i need help please thanks
Step-by-step explanation:
"to solve for h" just means to transform the equation, so that instead of V we get h alone on one side of the equation.
V = pi×r²×h
h = V / (pi×r²)
that's it.
for the slope question :
the slope is the factor of x (2/3 and 3/2) and indicates how steep the line is. and it is expressed as y/x ratio defining how many units y changes, when x changes a certain amount of units.
the bigger the number, the steeper the line.
so, the 4th answer option is correct. g(x) is steeper than f(x).
the lines are not parallel, because they do not have the same slope.
they are not perpendicular, because perpendicular slopes turn the y/x ratio upside down AND flip the sign.
e.g. the perpendicular slope of 2/3 would be -3/2.
pls help!! answer quickly please!
The answer for the equation should be 46
Answer:
the answer is 25
hope it is right
please mark as brainliest
What is the equation in standard form of the line that passes through the point (6, negative1) and is parallel to the line represented by 8x + 3y= 15?.
The line that connects the coordinates (6, -1) and is parallel to the line denoted by the equation 8x + 3y = 15 has the standard form equation 8x + 3y = 45.
What is an equation of a line?A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
Standard version of the equation is Ax + Bx = C.
A, B, and C are constants where
In light of this, the slope intercept form y = mx + b
m = slope, and b = y-intercept
8x+ y = 15
3y= -8x+15
y= -8/3x + 5
slope = -8/3
The line passes through (6, -1)
-1 = -8/3 (6)+b
-1 = -48/3+ b
-1 = -16 +b
b = -1+16
b = 15
Therefore,
y =-8/3x + 15
8/3 x+ y = 15
8x + 3y = 45
Hence, The equation in standard form of the line that passes through the point (6, -1) and is parallel to the line represented by 8x + 3y= 15 is
8x + 3y = 45.
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What is the slope of the line passing through (- 1/3 and 4 7?
The slope of the line passing through the two points [tex](-1,3)[/tex] and [tex](4,7)[/tex] is [tex]\frac{4}{5}[/tex]
The formula for finding the slope when two points are given
[tex]y=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\y=\frac{7-3}{4-(-1)} \\y=\frac{4}{4+1} \\y=\frac{4}{5}[/tex]
The slope of the line is [tex]\frac{4}{5}[/tex]
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Please help meeee !!!!!
Answer:
The only answer that does not have a 2 digit quotient would be 6,701÷36.
The GPA's at RHS are Normally distributed with a mean of 2.8 and a standard deviation of 0.7. Let G = a random student's GPA.
Find P(G<2.5)
The value of P(G<2.5) is 14.23%.
What is observation?
The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. Using scientific tools to perceive and record data is another way that observation may be used in science.
The [tex]$z$[/tex]-score for this observation of 2.30 is:
Z= (2.3-2.8)/0.7=-1.71
The table shows a value of 0.8577 , and because this z-score is negative, this is the proportion greater than a GPA of 2.30. So the proportion less than 2.30 is 1-0.8577 =0.1423 . Expressing it mathematically we have:
[tex]$$\begin{aligned}P(X \leq 2.7) & =P(Z \leq-1.07) \\& =1-P(Z \geq-1.07) \\& =1-P(Z \leq 1.07) \\& =1-0.8577 \\& =0.1423=14.23 \%\end{aligned}$$[/tex]
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Sam and taylor own and operate a car wash service. Sam cleans the interior of each car and taylor cleans the exterior. The time it takes sam to finish the interior has a mean of 202020 minutes with a standard deviation of 6. 46. 46, point, 4 minutes. The time it takes taylor to finish the exterior has a mean of 181818 minutes with a standard deviation of 4. 84. 84, point, 8 minutes. Both of their finishing times are approximately normally distributed.
The probability that they finish within 10 minutes of each other here their times are independent
i.e P( -10 < X₂ - X₁ < 10) where X₂ - X₁ = D Normally distributed, is 0.78 ..
Let X₁ be a random variable as taylor cleans the exterior of each car.
mean , μ₁ = 20 ,
standard deviations, σ₁ = 4.8
let X₂ be a random variable as sam cleans the interior of each car.
mean, μ₂ = 18
standard deviations, σ₂ = 6.4
If the two random variables are normal, then their difference , X₂ - X₁ also be normal.
As two normal variables here are normally distributed, therefore the distribution of the difference between the two variables here is given as: X₂ - X₁ = X
with mean, μ = μ₂ - μ₁ = 2
standard deviations, σ = σ₁² + σ₂²
= 6.4² + 4.8² = 64
To any bivariate Normal distribution of (X₁,X₂) Thus the variable
Z = (X−μ)/σ = (X₂−X₁ −(μ₂ - μ₁))/(√σ₁² + σ₂²)
= X - 2 /√64 = (X - 2 )/8
The probability here is computed as:
P( -10 < X₂ - X₁ < 10) = approx P(∣D∣<10)
where D is difference between their finishing times. Converting it to a standard normal variable, we have here:
= P( (-10 - 2) / 8 < Z < (10 - 2) / 8)
= P( -1.5 < Z < 1)
= P(Z < 1 ) - P(Z < -1.5)
Getting it from standard normal tables,
= 0.8431 - 0.0668
= 0.7763
Therefore 0.7763 is the required probability here.
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Complete question:
Sam and Taylor own and operate a car wash service. Sam cleans the interior of each car and Taylor cleans the exterior. The time it takes Sam to finish the interior has a mean of 20 minutes with a standard deviation of 6.4 minutes. The time it takes Taylor to finish the exterior has a mean of 18 minutes with a standard deviation of 4.8 minutes. Both of their finishing times are approximately normally distributed.
Suppose we select a car at random, and define the random variable D as the difference between their finishing times. We can assume that their times are independent.
Find the probability that they finish within 10minutes of each other.
You may round your answer to two decimal places.
P\left(|D|<10\right)\approxP(∣D∣<10)≈P
Look at the simultaneous equations below.
x - 4y = 12
x - 2 = 6y
(1)
(2)
a) Rearrange equation (2) to make the subject.
b) Using your answer to part a), solve the simultaneous
equations using substitution.
(a) The equation of subject x are,
x = 4y + 12
x = 6y + 2
(b) The values of x and y are x = 32, y = 5.
What is simultaneous equations?
A system of equations, also referred to as an equation system or a set of simultaneous equations, is a finite set of equations for which common solutions are sought.
Consider, the given equations
x - 4y = 12 ..(1)
x - 2 = 6y ..(2)
(a) We have to rearrange equations to make x the subject.
So, the equation of subject x are
x = 4y + 12
x = 6y + 2
(b) Now to solve the system of equations.
Let
x = 4y + 12 ..(3)
x = 6y + 2 ..(4)
Plug value of equation (4) in equation (3),
6y + 2 = 4y + 12
2y = 10
y = 5
Plug y = 5 in equation (3)
x = 4(5) + 12
x = 20 + 12
x = 32
Hence, the values of x and y are x = 32, y = 5.
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