Answer:
The hypothesis test is a two-tail test
Step-by-step explanation:
The test hypothesis:
Null hypothesis H₀ p = 0,39 or p = p₀
Where p₀ is a nominal proportion (established proportion) and
Alternate hypothesis Hₐ p ≠ 0,39 or p ≠ p₀
Is a two-tail test, (≠) means different, we have to understand that different implies bigger and smaller than something.
For a test to be one tail-test, it is necessary an evaluation only in one sense in relation to the pattern ( in this case the proportion )
Translate the following into an algebraic expression: A number is 30% of 20% of the number x.
Answer: 0.06x
Step-by-step explanation:
An algebraic expression is an expression consist of integer constants, variables, and algebraic operations.The given statement: A number is 30% of 20% of the number x.
The required algebraic expression would be:
30% of 20% of x
[tex]=\dfrac{30}{100}\times \dfrac{20}{100}\times x[/tex] [we divide a percentage by 100 to convert it into decimal]
[tex]=\dfrac{6}{100}\times x\\\\=0.06x[/tex]
Hence, the required algebraic expression would be :
0.06x
Alex has built a garden shed in the shape shown.
(A) Alex plans to paint the outside of the shed, including the roof but not the floor. One can of paint can cover 6m^2 . How many cans of paint will Alex need.
(B)If one can of paint costs $25.50, what will the cost be including 13% tax.
Answer:
A) 22 cans required to paint
B) Including 13% tax, cost of painting = $633.93
Step-by-step explanation:
As we check the figure, we have a composite figure.
Cuboid on the base and a pyramid on the top of it.
To find the area to be painted, we have 4 rectangular faces of cuboid with dimensions 6m [tex]\times[/tex] 3m.
And 4 triangular faces of pyramid with Base = 6m and Height 5m.
So, total area to be painted = 4 rectangular faces + 4 triangular faces
Area of rectangle = Length [tex]\times[/tex] Width = 6 [tex]\times[/tex] 3 = 18 [tex]m^2[/tex]
Area of triangle = [tex]\frac{1}{2}\times Base \times Height =\frac{1}{2}\times 6 \times 5 = 15\ m^{2}[/tex]
Total area to be painted = 4 \times 18 + 4 \times 15 = 72 + 60 = 132 [tex]m^2[/tex]
A) Area painted by 1 can = 6 [tex]m^2[/tex]
Cans required to paint 132 [tex]m^2[/tex] = [tex]\frac{132}{6} = 22\ cans[/tex]
B)
Cost of 1 can = $25.50
Cost of 22 can = $25.50 [tex]\times[/tex] 22 = $561
Including tax of 13% = $561 + $561 [tex]\times \frac{13}{100}[/tex] = $561 + $72.93 = $633.93
So, the answers are:
A) 22 cans required to paint
B) Including 13% tax, cost of painting = $633.93
You work at a coffee house. Roasted coffee beans retain approximately 3/5 of their initial weight. Approximately what percent of their inital weight do they retain?
Answer:
60%
Step-by-step explanation:
We need convert 3/5 into a percent in order to find the answer.
We can convert by first dividing 3 by 5 to find the decimal value.
3/5= .6
Now we need to multiply by 100 to make it a percentage
.6 x 100= 60
60%
Raquel throws darts at a coordinate grid centered at the origin. Her goal is to create a line of darts. Her darts actually hit the coordinate grid at (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6). Which equation best approximates the line of best fit of the darts?
Answer:
The line of best fit
y = 0.633x + 0.561
Step-by-step explanation:
The coordinates that the dart hit include
(–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6)
The x and y coordinates can be written as
x | y
-5|0
1 | -3
4|5
-8|-6
0|2
9|6
So, running the analysis on a spreadsheet application, like excel, the table of parameters is obtained and presented in the first attached image to this solution.
Σxᵢ = sum of all the x variables.
Σyᵢ = sum of all the y variables.
Σxᵢyᵢ = sum of the product of each x variable and its corresponding y variable.
Σxᵢ² = sum of the square of each x variable
Σyᵢ² = sum of the square of each y variable
n = number of variables = 6
The scatter plot and the line of best fit is presented in the second attached image to this solution
Then the regression analysis is then done
Slope; m = [n×Σxᵢyᵢ - (Σxᵢ)×(Σyᵢ)] / [nΣxᵢ² - (∑xi)²]
Intercept b: = [Σyᵢ - m×(Σxᵢ)] / n
Mean of x = (Σxᵢ)/n
Mean of y = (Σyᵢ) / n
Sample correlation coefficient r:
r = [n*Σxᵢyᵢ - (Σxᵢ)(Σyᵢ)] ÷ {√([n*Σxᵢ² - (Σxᵢ)²][n*Σyᵢ² - (Σyᵢ)²])}
And -1 ≤ r ≤ +1
All of these formulas are properly presented in the third attached image to this answer
The table of results; mean of x, mean of y, intercept, slope, regression equation and sample coefficient is presented in the fourth attached image to this answer.
Hope this Helps!!!
Answer:
a. y = 0.6x + 0.6
Step-by-step explanation:
What is the rule of 72 used to determine? A. the approximate time it takes an investment to triple in value B. the approximate time it takes an investment to double in value C. the approximate time it takes to earn 10% interest D. the approximate time it takes to earn $72 on any investment amount
Answer:
b. the approx time it takes an investment to double in value
On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?
Answer:
10 miles
Step-by-step explanation:
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
He hiked 10 miles. (
Sanjay makes souvenir pyramids by pouring liquid into a pyramid-shaped mold. The mold he uses has a square base with a side length of 10\text{ cm}10 cm10, start text, space, c, m, end text, and the height of the mold is 10\text{ cm}10 cm10, start text, space, c, m, end text. Sanjay wants to make a smaller pyramid using the same mold, so he plans to fill the mold 2\text{ cm}2 cm2, start text, space, c, m, end text from the top. What is the approximate volume of this smaller pyramid?
Answer:
170.67
Step-by-step explanation:
Answer:
171
Step-by-step explanation:
Modeling the situation
If we fill the pyramid mold 2\text{ cm}2 cm2, start text, space, c, m, end text from the top, we have a smaller pyramid that's similar to the original pyramid.
Since the pyramids are similar, we can set up a proportional equation to find the side lengths and height of the smaller pyramid, and then find its volume.
Hint #22 / 4
Base and height of smaller pyramid
The height of the smaller pyramid is 10-2=8\text{ cm}10−2=8 cm10, minus, 2, equals, 8, start text, space, c, m, end text.
We can solve for the length \blueE{\ell}ℓstart color #0c7f99, ell, end color #0c7f99 in the smaller pyramid using a proportional equation.
\begin{aligned} \dfrac{\blueE{\ell}}{10} &= \dfrac{8}{10} \\\\ \blueE{\ell} &= \blueE{8} \end{aligned}
10
ℓ
ℓ
=
10
8
=8
Hint #33 / 4
Volume of smaller pyramid
\begin{aligned} \text{volume}_{\text{pyramid}} &= \dfrac13(\text{base area})(\text{height}) \\\\ &= \dfrac13 \cdot (\blueE{\ell})^2\cdot (\text{height}) \\\\ &= \dfrac13 \cdot \blueE{8}^2\cdot(8)\\\\ &= \dfrac{512}{3}=170.\overline{6}\\\\ &\approx \purpleD{170.67} \end{aligned}
volume
pyramid
=
3
1
(base area)(height)
=
3
1
⋅(ℓ)
2
⋅(height)
=
3
1
⋅8
2
⋅(8)
=
3
512
=170.
6
≈170.67
Hint #44 / 4
To the nearest cubic centimeter, the volume of the smaller pyramid is about 171\text{ cm}^3171 cm
3
171, start text, space, c, m, end text, cubed.
Hi I need this question please asap.
The sum of Jason’s age and his brother’s age is 55. Jason is 7 years younger than his brother. How old is Jason?
Answer:
Jason is 24 years old
Step-by-step explanation:
Lets say that Jason's age is X, and his brother's age is Y.
We know that X + Y = 55.
We also know that (X + 7) = Y.
This means (X + 7) + Y = 62 (We got the 62 by adding 55 and 7)
Anyway if X+7= Y, and X+7 + Y = 62, then X+7 = 62/2, right?
We divide the 62 by 2 and we get 31.
Alright, so X+7 = 31.
substract both sides by 7.
We get X = 24
Sorry if this seemed longer or more complicated than it should've been, I don't know how to explain it better.
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 4 m from the dock
Answer:
-1.031 m/s or [tex]\frac{-\sqrt{17} }{4}[/tex]
Step-by-step explanation:
We take the length of the rope from the dock to the bow of the boat as y.
We take x be the horizontal distance from the dock to the boat.
We know that the rate of change of the rope length is [tex]\frac{dy}{dt}[/tex] = -1 m/s
We need to find the rate of change of the horizontal distance from the dock to the boat = [tex]\frac{dx}{dt}[/tex] = ?
for x = 4
Applying Pythagorean Theorem we have
[tex]1^{2} +x^{2} =y^{2}[/tex] .... equ 1
solving, where x = 4, we have
[tex]1^{2} +4^{2} =y^{2}[/tex]
[tex]y^{2} = 17[/tex]
[tex]y = \sqrt{17}[/tex]
Differentiating equ 1 implicitly with respect to t, we have
[tex]2x\frac{dx}{dt} = 2y\frac{dy}{dt}[/tex]
substituting values of
x = 4
y = [tex]\sqrt{17}[/tex]
[tex]\frac{dy}{dt}[/tex] = -1
into the equation, we get
[tex]2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)[/tex]
[tex]\frac{dx}{dt} = \frac{-\sqrt{17} }{4}[/tex] = -1.031 m/s
The amount of time to complete a physical activity in a PE class is approximately normally normally distributed with a mean of 32.9 seconds and a standard deviation of 6.4 seconds.
A) What is the probability that a randomly chosen student completes the activity in less than 33.2 seconds?
B) What is the probability that a randomly chosen student completes the activity in more than 46.6 seconds?
C) What proportion of students take between 35.5 and 42.8 seconds to complete the activity?
D) 75% of all students finish the activity in less than____seconds.
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) of 32.9 seconds and a standard deviation (σ) of 6.4 seconds.
The z score is used to measure by how many standard deviation the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}\\[/tex]
a) For x < 33.2 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{33.2-32.9}{6.4} =0.05[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in less than 33.2 seconds = P(x < 33.2) = P(z < 0.05) = 0.5199 = 51.99%
b) For x > 46.6 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{46.6-32.9}{6.4} =2.14[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in more than 46.6 seconds = P(x > 46.6) = P(z > 2.14) = 1 - P(z < 2.14) = 1 - 0.9927 = 0.0073 = 0.73%
c) For x = 35.5 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{35.5-32.9}{6.4} =0.41[/tex]
For x = 42.8 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{42.8-32.9}{6.4} =1.55[/tex]
From the normal distribution table, the proportion of students take between 35.5 and 42.8 seconds to complete the activity = P(35.5 < x < 42.8) = P(0.41< z< 1.55) = P(z < 1.55) - P(z < 0.41) = 0.9332 - 0.6591 = 0.2741 = 27.41%
d) A probability of 75% = 0.75 corresponds to a z score of 0.68
[tex]z=\frac{x-\mu}{\sigma}\\\\0.68=\frac{x-32.9}{6.4} \\\\x-32.9=4.4\\x=4.4+32.9\\x=37.3[/tex]
75% of all students finish the activity in less than 37.3 seconds
2. Compare the function ƒ(x) = –x^2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maximum (vertex)?
Answer:
g(x)
Step-by-step explanation:
The vertex of g(x) as shwon in the graph is located in the point wich coordinates are (3.5,6.25) approximatively
We need to khow the coordinates of f(x) vertex
Here is a way without derivating:f(x) = -x² + 4x -5
let a be the leading factor, b the factor of x and c the constant:
a= -1b= 4c= -5The coordinates of a vertex are: ([tex]\frac{-b}{2a}[/tex] , f([tex]\frac{-b}{2a}[/tex]) )
-b/2a = -4/ (-1*2) = 4/2 = 2
f(2)= -2²+4*2-4 = -4+4-4 = -4
obviosly f(x) has a minimum wich less than g(x)'s maximum
Answer:
Step-by-step explanation:
g(x) i think
a hat contains 2 red apples and 3 green apples. a bucket contains 7 red apples and 3 green apples. a container is selected at random and an apple is drawn out. what is the probability that it will be a red apple
Answer:
15
Step-by-step explanation:
Find C and round to the nearest tenth.
Answer:
29.4 degrees
Step-by-step explanation:
i divided sin by 55 degrees
Four buses carrying 198 students from the same school arrive at a football stadium. The buses carry, respectively 90, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students who were on the bus carrying the randomly selected student. One of the four bus drivers is also randomly selected. Let Y denote the number of students on her bus. a) Which of E[X] or E[Y] do you think is larger
Answer:
E[x] is larger
Step-by-step explanation:
I think E[x] is larger because the expected number of students on the bus of a randomly chosen student is larger.
This is because the higher the number of students present in a bus, the higher the probability that a randomly selected student would have been on that bus.
Whereas, for every driver to be chosen, the probability of any bus being chosen is 1/4 irrespective of the number of students in that particular bus
Simba Travel Agency arranges trips for climbing Mount Kilimanjaro. For each trip, they charge an initial fee of $100 in addition to a constant fee for each vertical meter climbed. For instance, the total fee for climbing to the Shira Volcanic Cone, which is 3000 meters above the base of the mountain, is $400.Let y represent the total fee (in dollars) of a trip where they climbed x vertical meters.Complete the equation for the relationship between the total fee and vertical distance.
Answer:
[tex]y(x)=100+0.1x[/tex]
Step-by-step explanation:
Let y represent the total fee (in dollars) of a trip where they climbed x vertical meters.
We know that there is an initial fee of $100, so we know that if we climb x=0 meters, we have a fee of y(0)=100.
[tex]y(0)=100[/tex]
As there is a constant fee (lets called it m) for each vertical meter climbed, we have a linear relationship as:
[tex]y(x)-y(0)=m(x-0)\\\\\\y(x)-100=mx\\\\\\y(x)=100+mx[/tex]
We know that for x=3000, we have a fee of $400, so if we replace this in the linear equation, we have:
[tex]y(3000)=100+m(3000)=400\\\\\\100+3000m=400\\\\3000m=400-100=300\\\\m=300/3000=0.1[/tex]
Then, we have the equation for the total fee in function of the vertical distance:
[tex]y(x)=100+0.1x[/tex]
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 249 cubic units.
What is the height of the cylinder?
O2 units
4 units
O 6 units
O 8 units
Answer:
h = 6 unitsStep-by-step explanation:
Volume of a cylinder = πr²h
where r is the radius
h is the height
The height of a right cylinder is 3 times the radius of the base is written as
h = 3r
Volume = 249cubic units
So we have
249 = π r²(3r)
249 = π3r³
Divide both sides by 3π
r³ = 249/3π
r = 2
h = 3(2)
h = 6 units
Hope this helps you
For the functions f(x)=x4−x3−7x2+9x−2 and g(x)=x−1, find (f/g)(x) and (f/g)(2).
Answer:
[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]
[tex](f/g)(2)=-4[/tex]
Step-by-step explanation:
[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex] and undefined for x = 1.
Notice that (x-1) is in fact a factor of f(x), so the quotient of the two functions introduces a "hole" for the new function at x = 1.
f(2) can be found by simply evaluating the expression for x = 2:
[tex](f/g)(2)=2^3-7(2)+2=-4[/tex]
what is 20% of 50naira?
Answer:
10
Step-by-step explanation:
To find 20% of 50 you need to times 20 with 50 and divide by 100.
20×50÷100
=10
Question 3 (5 points)
POINT
-POINT A
POINT B
What are the coordinates of the point labeled B in the graph shown above?
A) (3, 2)
B) (-3,2)
OC) (-2,3)
D) (-2, -3)
Question 4 (5 points)
Answer:
(D) -2,-3
Step-by-step explanation:
From the origin, we can find the current position of point B by counting.
B is 2 to the left of the y-axis, meaning that it's x value is -2.
B is 3 down of the x-axis, making it's y value -3.
Therefore, the coordinates of point B are -2,-3.
Hope this helped!
Answer: (D) -2,-3
Step-by-step explanation:
Write the equation of the line in slope intercept form that passes through the points (4,-2) and (2,-1)
Answer:
y + 2 = (-1/2)(x - 4)
Step-by-step explanation:
Let's move from (2, -1) to (4, -2) and measure the changes in x and y. x increases by 2 units from 2 to 4, and y decreases by 1 unit from -1 to -2. Thus, the slope of the line connecting the two points is m = rise / run =
-1
--- = (-1/2).
2
Using the point-slope formula, we get:
y + 2 = (-1/2)(x - 4)
Ash Lee bought a new Brunswick boat for $17,000. He made a $2,500 down payment on it. The bank's loan was for 60 months. Finance charges totaled $4,900. His monthly payment is:
Answer: $323.33
Step-by-step explanation:
($17,000 + $4,900 - $2,500) ÷ 60 months = $323.33 per month
↓ ↓ ↓
price finance down payment
If two points are given, then exactly one line can be drawn through those two points. Which geometry term does the statement represent?
Answer:
its a postulate
Step-by-step explanation:
The statement represents a geometric postulate.
A postulate is one of the basic concepts of geography, and indicates an assumption that is accepted as true in the given theory.
In this way, the main characteristic of the postulate is its general acceptance by the spectrum that studies it, that is, by the totality or vast majority of the scientists who are dedicated to its analysis.
Learn more in https://brainly.com/question/17252827
A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
(a) Using Bayes’ Theorem, when a person tests positive, determine the probability that the person is infected.
(b) Using Bayes’ Theorem, when a person tests negative, determine the probability that the person is not infected.
Answer:
A) P(A|B) = 0.01966
B) P(A'|B') = 0.99944
Step-by-step explanation:
A) We are told that A is the event "the person is infected" and B is the event "the person tests positive".
Thus, using bayes theorem, the probability that the person is infected is; P(A|B)
From bayes theorem,
P(A|B) = [P(A) × P(B|A)]/[(P(A) x P(B|A)) + (P(A') x P(B|A'))]
Now, from the question,
P(A) = 1/400
P(A') = 399/400
P(B|A) = 0.8
P(B|A') = 0.1
Thus;
P(A|B) = [(1/400) × 0.8)]/[((1/400) x 0.8) + ((399/400) x (0.1))]
P(A|B) = 0.01966
B) we want to find the probability that when a person tests negative, the person is not infected. This is;
P(A'|B') = P(Not infected|negative) = P(not infected and negative) / P(negative) = [(399/400) × 0.9)]/[((399/400) x 0.9) + ((1/400) x (0.2))] = 0.99944
A train travels 45 feet in 1/10 if a second. How far will it travel in 3.5 seconds
Answer:
1575 ft
Step-by-step explanation:
Convert 1/10 to decimal to make the math simpler.
1/10 = 0.1
Divide 3.5 by 0.1.
3.5/0.1 = 35
Multiply 35 by 45.
35 × 45 = 1575
The train will travel 1575 feet in 3.5 seconds.
The distance covered by the train in 3.5 seconds will be 1575 feet.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
A train travels 45 feet in 1/10 in a second.
Then the speed will be
Speed = 45 / (1/10)
Speed = 45 x 10
Speed = 450 feet per second
The distance covered by the train in 3.5 seconds will be
Distance = 450 x 3.5
Distance = 1575 feet
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ2
please factor!
7x^2+27xy-4y^2
Complete the table
Distance(ft)
Height(ft)
Answer:
a = 6, b = 7, c = 8, d = 7 and e = 6
Step-by-step explanation:
Let's remember that the complete revolution of the wheel is 360 degrees, and the distance traveled by a complete revolution is the length of the circumference: 2*pi*radius.
The inicial height of the point is 6 ft, and the radius of the wheel is 1 ft.
When the distance traveled is 0, the wheel turned 0 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.
So the height will be a = 6 + 0 = 6 ft
When the distance traveled is pi/2, the wheel turned 90 degrees, and the point will be half the complete height of the wheel, which is 2 feet.
So the height will be b = 6 + 1 = 7 ft
When the distance traveled is pi, the wheel turned 180 degrees, and the point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel.
So the height will be c = 6 + 2= 8 ft
When the distance traveled is 3pi/2, the wheel turned 270 degrees, and the point will be half the complete height of the wheel, which is 2 feet.
So the height will be d = 6 + 1 = 7 ft
When the distance traveled is 2pi, the wheel turned 360 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.
So the height will be e = 6 + 0 = 6 ft
So the answers are:
a = 6, b = 7, c = 8, d = 7 and e = 6
Answer:
6, 7, 8, 7, 6
Step-by-step explanation:
what is this? 15.8 = d/25
Answer:
395
Step-by-step explanation:
15.8=d/25
multiply both sides by 25 to remove the denominator
25×15.8=d
d=395
21. In the figure given below, AC is parallel to DE. Find the valuesof xy and z and hence find the 2DBE.
21-70X
509
Answer:
X= 50°
Y= 70°
Z= 30°
BDE= 30°
2BDE= 60°
Step-by-step explanation:
(2x -70 )+z+(2x+20)=180...(sum of angle on a straight line)
2x -70 = BDE... alternate angles
Y + (2x-70)+(50+x-20) = 180...(sum of angles in a triangle)
X-20 = z ... alternate and opposite angles
(2x -70 )+z+(2x-+20)=180
2x-70 + x-20 +2x +20= 180
5x -70= 180
5x = 250
X= 50°
X-20 = z
50-20= z
30° = z
2x -70 = BDE
2(50) -70 = BDE
100-70 = BDE
30°= BDE
Y + (2x-70)+(50+x-20)
Y + 100-70 +50 +50 -20 = 180
Y + 200-90=180
Y= 70°
2BDE = 2*30
2BDE= 60°
A system of equations is shown below: Equation A: 3c = d − 8 Equation B: c = 4d + 8 Which of the following steps should be performed to eliminate variable d first?
Answer:
multiplying the equation A
Step-by-step explanation:
3c=d-8 ####### *4
+ c=4d + 8
After that you will get the value of c and d.
Answer:
Multiply equation A by -4
Step-by-step explanation:
3c = d - 8
c = 4d + 8
Multiply equation A by -4.
-12c = -4d + 32
c = 4d + 8
Add the equations.
-11c = 40
Variable d is eliminated.