A jar of marbles contains the following: two purple marbles, four white marbles, three blue marbles, and two green marbles. What is the probability of selecting a white marble from a jar of marbles?
Answers
Answer:
4/11
Step-by-step explanation:
Total number of marbles = 2(purple) + 4(white) + 3(blue) + 2(green)
= 11
Number of white marbles = 4
Probability of selecting a white marble =
number of white marbles/total number of marbles in the jar
= 4/11
The probability of selecting a white marble from a jar of marbles is 4/11.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Purple Marbles = 2
White Marbles = 4
Blue Marbles = 3
Green Marbles = 2
Total marbles= 2+ 4+ 3+ 2= 11
So, the probability of selecting a white marble from a jar of marbles
= 4/11
Hence, the probability is 4/11.
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Related Questions
According to a survey conducted by the Association for Dressings and Sauces, 80% of American adults eat
salad once a week. A nutritionist suspects that this percentage is not accurate. She conducts a survey of
445 American adults and finds that 374 of them eat salad once a week. Use a 0.005 significance level to
test the claim that the proportion of American adults who eat salad once a week is equal to 80%.
Claim: Select an answer which corresponds to [Select an answer
Opposite: Select an answer which corresponds to [Select an answer
The test is: Select an answers
The test statistic is: z-
(to 2 decimals)
The Critical Value is: z-
Based on this we: [Select an answer
Conclusion: There Select an answer appear to be enough evidence to support the claim that the
proportion of American adults who eat salad once a week is equal to 80%.
Answers
Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.
How to solveTo test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.
Claim: p = 0.80
Opposite: p ≠ 0.80
The test is a two-tailed z-test.
Sample proportion (p) = 374/445 = 0.8404
Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)
z = 2.53 (rounded to 2 decimals)
Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.
Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.
Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.
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Which expression represents 43 minus the sum of 16 and 11?
Answers
A shows 11 plus the sum of 43 minus 16
B shows the sum of 16 plus 11 minus 43
The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 6 credit hours of A, 15 credit hours of B, 31 credit hours of C, and 8 credit hours of D.
a. Compute the student's grade point average. Round your answer to two decimal places.
b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?
Answers
The student's grade point average is 2.32.
The student will not be admitted to the business college.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
(a)
Total grade points earned
= (6 x 4) + (15 x 3) + (31 x 2) + (8 x 1)
= 24 + 45 + 62 + 8
= 139
Total credit hours.
= 6 + 15 + 31 + 8
= 60
Now,
The student's grade point average:
= Total grade points earned / Total credit hours taken
= 139 / 60
= 2.32
(b)
2.32 < 2.5
This means,
The student's grade point average is lower than the required 2.5 GPA for admission to the business college.
Thus,
The student's grade point average is 2.32.
The student will not be admitted to the business college.
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the candle was 1 inches long when new.Each half hour 3/4 inch of the candle burned away.After 4 hours,how long was the candle
Answers
After 2 hours, the candle would have burned away another 1.5 inches (4 half-hour periods * 3/4 inch burned in each period), leaving it with a length of 0 inches. At this point, the candle has completely burned down.
Therefore, after 4 hours, the length of the candle would be 0 inches.
The first 5 terms of a sequence are shown
4,12,36,108,324 ...
what is the common ratio of the function
Answers
Answer:
The common ratio is 3
Step-by-step explanation:
if you divide the first number by the number following it, then the answer is three all the way down the line. So all you need to do to find the following term is to multiply the last number that you know by 3 and you get the number after that
Hope that was helpful :)ratio
Answer:
yes it is 3 I've been solving this for a few days and got 3
The data below consist of 25 samples of 4 observations each on the lengths of particular bolts manufactured for use in a large aircraft. The target length of these bolts is 37 centimeters. Answer the below questions and show all hand written, SPSS (screenshots) or excel work.
a) Is the process in statistical control?
b) If not in statistical control, why? Explain.
c) Given that the tolerance of these bolts is + .01 centimeters, determine the
i. Cp
ii. CpK values of this process and the
iii. Sigma level Samples
Samples
Sub 1
Sub 2
Sub 3
Sub 4
1
36.99
37.02
37.04
37.01
2
37.01
37.04
37.03
36.98
3
36.98
37.03
37.03
36.99
4
37.00
37.00
37.00
36.98
5
36.98
36.99
36.99
36.96
6
36.99
36.96
36.94
36.97
7
36.98
36.97
37.01
36.96
8
36.93
36.96
36.96
36.93
9
36.91
36.99
36.95
36.92
10
36.97
36.99
36.95
36.94
11
37.05
37.05
37.05
37.05
12
37.00
37.04
37.11
37.05
13
37.05
37.04
37.06
37.04
14
37.08
37.08
37.03
37.08
15
37.08
36.99
37.07
37.06
16
36.93
36.99
37.03
37.03
17
37.06
36.94
37.06
36.98
18
36.94
36.96
36.96
37.01
19
37.01
36.98
37.03
37.00
20
37.03
37.07
36.99
37.03
21
36.99
36.99
37.01
37.00
22
37.01
37.00
37.00
36.99
23
37.02
37.00
37.00
37.00
24
37.01
37.01
37.00
37.03
25
36.99
37.00
37.00
36.99
Answers
Using the properties of confidence interval and probability we can conclude from the observations that the process is not a statistical control process.
(a) The process is not a statistical process .
b) The control & chart is not in control because there some false alarm at 8-15. There are some special causes in the clata (may be in manufacturing) exist.
(c) (i) Given that Target length = 37 USL + LSL = 37 USL+2SL= 74
and Tolerance = 0.01 USL LSL = 0.01
After Solving equation 1 & 2 we get VSL = 37.005, LSL = 36.995
cp =2 × 0.01 6/0.05 × 2.059 = 0.01 ×0.1457 = 0.0686
(ii) Cp = min (Cpu, CP).
Cpu = 37.005-37 0.073 = 0.06849
CPL = 0.06859
Срк = 2 × 0.06849 = 0.024
The application of statistical methods to monitor and regulate the quality of a manufacturing process is known as SPC (statistical process control) or SQC (statistical quality control).
This increases the efficiency of the process, resulting in more specification-conforming goods with less waste (rework or scrap). SPC can be used to any process that can measure the output of a "compliant product" (a product that fulfils standards).
The primary tools of SPC are run charts, control charts, a focus on continuous improvement, and experiment design. Manufacturing lines are one example of a process that employs SPC.
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There were 57 cars in a parking lot at 9:00 AM and 36 different cars at 8:00 PM.
How many cars were there all together?
21 cars
83 cars
93 cars
97 cars
Answers
Answer:
C. 93 cars
Step-by-step explanation:
57 cars + 36 cars = 93 cars
Mav went shopping for a new video game because of a sale. The store was offering a 15% discount. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Answers
Answer:
.85
Step-by-step explanation:
Price she would have to pay =
(Price on Tag (Original Price)) - (Cost Discount) =
(Price on Tag) - (15%)(Price on Tag) =
(100%)(Price on Tag) - (15%)(Price on Tag) =
(100% - 15%)(Price on Tag) =
85% * (Price on Tag) =
.85 * (Price on Tag),
so .85 is the answer.
The total cost of the video game after the discount is given by the equation A = 0.85x , where x is the initial cost of the video game
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 cost of the video game after the discount be represented as A
Now , the equation will be
The cost of the video game be = x
Let the discount percentage be represented as = 15 %
Now , the cost of the video game after discount = cost of the video game - ( cost of the video game x discount percentage )
Substituting the values in the equation , we get
The cost of the video game after discount A = x - ( 15/100 )x
On simplifying the equation , we get
The cost of the video game after discount A = x - 0.15x
The cost of the video game after discount A = 0.85x
Hence , the equation is A = 0.85x
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29 POINTS IF YOU CAN HELP ME!!!!!!!!!!!!!!!!!!!! A Striped bass is swimming at an elevation of −3 feet, while a flounder is swimming at an elevation of −11 feet. Write and interpret a statement of the order showing the elevation of the striped bass compared to the elevation of the flounder. (1 point)
Responses
A, −3 < −11; the flounder is at a higher elevation than the bass.
B, −3 > −11; the bass is at a higher elevation than the flounder.
.
C, −3 > −11; the flounder is at a higher elevation than the bass.
D, −3 < −11; the bass is at a higher elevation than the flounder.
Answers
The correct option is,
⇒ −3 > −11; the bass is at a higher elevation than the flounder.
Option B is true.
What is Elevation?
Elevation is distance above the sea.
Given that;
A stripes bass is swimming at an elevation of −3 feet.
And, A flounder is swimming at an elevation of −11 feet.
Clearly, The bass is at higher elevation than the flounder.
So, -3 > -11
Hence, The correct option is,
⇒ −3 > −11; the bass is at a higher elevation than the flounder.
Option B is true.
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1)
Find the value of x in
the triangle below:
17
A) 20.2
B) 18.7
C) 19.5
D) 21.1
E) 22.6
K
84⁰
65°
Mrs. Wilson
Mrs. Crane
Mr. Haynes
Ms. Lindstrom
Mr. Swasey
O Gina Wilson (All Things Algebra), 2014
Answers
The correct option is A) 20.2.
What is triangle sum?
The triangle sum is a property of triangles that states that the sum of the interior angles of a triangle is always equal to 180 degrees. In other words, if you add up the measures of the three angles inside a triangle, the result will always be 180 degrees.
Using the given information and the fact that the angles in a triangle sum to 180 degrees, we can find the value of x as follows:
Start by finding the measure of angle K by subtracting the measures of angles A and B from 180 degrees:
K = 180 - A - B
= 180 - 84 - 65
= 31 degrees
Use the law of sines to set up an equation relating the side lengths and corresponding angle measures:
sin(A)/x = sin(K)/17
Substitute the values we know into the equation and solve for x:
sin(84)/x = sin(31)/17
x = sin(84)*17/sin(31)
Using a calculator, we get:
x ≈ 20.2
Therefore, the value of x in the triangle is approximately 20.2.
So, the correct option is A) 20.2.
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Can someone give me the answer
Answers
Answer:
You earned 260$ before they taxed
What is the y intercept for y=6x+7/2
Answers
y = mx + b
M is 6
B is 7/2
A car travels an average speed of 45km per hour. What distance does it cover in 12 hours?
Answers
Answer:
540 kilometers
Step-by-step explanation:
The car travels 45 kilometers every 1 hour.
In 12 hours, 45 × 12 = 540
The car will have covered a distance of 540 kilometers.
If car travels an average speed of 45km per hour, the car covers a distance of 540 kilometers in 12 hours.
To calculate the distance covered by the car in 12 hours, we can use the formula:
Distance = Speed × Time
Given that the average speed of the car is 45 km per hour and it travels for 12 hours, we can plug these values into the formula:
Distance = 45 km/h × 12 hours
Distance = 540 km
The formula for calculating distance is straightforward: it multiplies the speed (rate of motion) by the time taken. In this case, the car travels at a constant speed of 45 km/h, which means it covers 45 kilometers every hour.
By traveling for 12 hours, it accumulates a total distance of 540 kilometers. This calculation is useful for determining how far an object, in this case, a car, will travel given its speed and the duration of its journey.
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A
X
Find the value of x.
D
X+2
x = [?]
B
3
E
2
C
![AXFind the value of x.DX+2x = [?]B3E2C](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/NizqkSoyno5R9ihZJuX6BBJHmDyqL8LN.png)
Answers
Answer:
x = 4
Step-by-step explanation:
if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.
DE is such a line , then
\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\) ( substitute values )
\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )
3x = 2(x + 2)
3x = 2x + 4 ( subtract 2x from both sides )
x = 4
HELP PLEASE FASTTT !! ANYONE??!
Answers
Answer: The angled line on graphs!
Step-by-step explanation: :)
12 6 12 24
Select one:
A. 240 square units
B. 252 square units
C. 180 square units
D. 216 square units
Answers
Answer:
B
Step-by-step explanation:
divide the given polygon into two (a square and a trapeziumarea of trapezium=1/2(a+b)×b 1/2(12+6)×12 ans 108square unitarea of a square=s×s 12×12 =144square unitadd 108+144=252square unitWhat is this in mixed number
4 1/2 - 2 2/3
Answers
Therefore , the solution of the given problem of fraction comes out to be 1 5/6.
Fraction : What is it ?An whole can be represented by any set of related sums or fractions. In standard English, a percentage is used to represent the quantity of a specific size. 8, 3/4. Also wholes are fractions. Numbers are expressed in mathematics using the ratio of it's own portion to the bottom. These fractions are all made up of basic numbers. Due to variances in actual percentage calculations, numerators, and numerators, a difficult fraction contains a fraction.
Here,
To subtract mixed numbers, we first subtract the whole numbers and then subtract the fractions separately.
4 1/2 - 2 2/3
Subtracting the whole numbers:
4 - 2 = 2
Now, let's subtract the fractions.
1/2 - 2/3
To subtract fractions, we need to have a common denominator. In this case, the least common multiple of 2 and 3 is 6.
1/2 = 3/6
2/3 = 4/6
Now we can subtract:
3/6 - 4/6 = -1/6
Putting it all together:
4 1/2 - 2 2/3 = 2 - 1/6
The answer in mixed number form is:
1 5/6
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The woods behind Wendy’s house were 8 miles wide and have an area of 24 mi.² what is the length of the woods 
Answers
Answer:
48 miles
Step-by-step explanation:
i think thats it.
Answer: 4.
Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.
Hope this helps!
points that don't belong to any line
Answers
Answer:
Noncollinear points
Step-by-step explanation:
Collinear points lie on the same line. Noncollinear points are the opposite.
You are playing in the NBA Playoffs and attempt a 3-point shot as the buzzer sounds for the end of the
game, if you make the shot your team wins! Your basketball is is traveling on a path described by the
following function: b(x) = -x2 +1.36x + 2. The net is on a level described by the following function:
n(x) = 3 between (8 < x < 8.5). Will you make the shot and win the playoffs?
You may work alone or in a group of up to 3 students total.
BONUS: How high in the air will the basketball be at its highest point?
UNITS: x is in meters, y is in meters
Answers
Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.
Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.
Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.
Assuming that the basketball follows a parabolic path, we can use the formula:
y = ax² + bx + c,
where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.
To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.
Therefore, the points on the trajectory of the basketball are:
(0, 1.5), (8.5/2, h), and (8.5, 0),
where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,
we get:
1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)
Simplifying equations (1) and (2),
we get:
c = 1.5...(4)b = -a(8.5)²/8.5...(5)
Substituting equation (4) in equation (3), we get:
h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5
Substituting the value of a from equation (5) in the above equation,
we get:
h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5
Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,
we can use the formula:
x = ut + 0.5at²,
where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.
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UGENT!!!!!!
Dataset 1: [10 8 22 5 6 1 7]
Dataset 2: [122.5 123.8 121.2 125.8 120.2]
Please calculate the range, variance, and standard deviation for Dataset 1 and
Dataset 2. Please show all math involved.
Answers
Dataset 1:
Range = 21
Variance: = 150.33
Standard deviation: = 12.37
Dataset 2:
Range: = 5.6
Variance: = 1.44
Standard deviation: = 1.2
How to calculate the valueVariance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed.
Dataset 1:
Range: 22-1 = 21
Variance: (sum of squares of deviations from mean) / (number of items - 1) = (902/6) = 150.33
Standard deviation: square root of variance = sqrt(150.33) = 12.37
Dataset 2:
Range: 125.8-120.2 = 5.6
Variance: (sum of squares of deviations from mean) / (number of items - 1) = (7.2) = 1.44
Standard deviation: square root of variance = sqrt(1.44) = 1.2
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In the diagram at right, DE is a midsegment of triangle ABC. If the area of triangle ABC is 96 square units, what is the area of triangle ADE? Explain how you know.
Answers
The area of triangle ADE is,
⇒ A = 48 square units
We have to given that,
In the diagram , DE is a midsegment of triangle ABC.
And, The area of triangle ABC is 96 square units
Now, We know that,
Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.
Hence, the area of triangle ADE is half the area of triangle ABC,
That is,
A = 96 / 2
A = 48 square units
Thus, The area of triangle ADE is,
⇒ A = 48 square units
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find a solution y = 3 x − 4
Answers
Answer: The equation y = 3x - 4 is a linear equation in slope-intercept form, where the slope (3) is the coefficient of x and the y-intercept (-4) is the constant term. To find a solution for this equation, we can substitute a specific value of x and solve for the corresponding value of y.
For example, if we let x = 2, we can substitute it into the equation:
y = 3(2) - 4 = 6
So the solution for x=2 is y=6
We can also graph this equation, it will be a straight line with slope 3 and y-intercept (-4)
Step-by-step explanation:
4x-5 2x+7 Find the value of x
answers should be from
27
37
47
57
Answers
4x - 5 = 2x + 7
First, let's simplify the equation by combining like terms:
4x - 2x = 7 + 5
2x = 12
Next, divide both sides of the equation by 2 to solve for x:
x = 12 / 2
x = 6
Therefore, the value of x that satisfies the equation is 6. None of the provided answer options (27, 37, 47, 57) are equal to 6.
PLEASS HHELPPPP
What is the change in temperature from 15°F to -8°F?
7°F
23°F
-23°F
-7°F
Answers
Hatif has $150 in his account. He saves $80 each month. How long will it take before he has $630 in his account?
Answers
Answer:
6 months
Step-by-step explanation:
We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.
Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.
The equation representing the situation is:
$150 + $80n = $630
Now, let's solve for "n":
$80n = $630 - $150
$80n = $480
n = $480 / $80
n = 6
Therefore, it will take Hatif 6 months to reach $630 in his account.
34. A motorist started a journey at 10.25a.m. and ended at 6.15 p.m. Calculate the time
used for the journey.
Answers
Write the times for each hour from start time:
10:25 am
11:25 am
12:25 pm
1:25 pm
2:25 pm
3:25 pm
4:25 pm
5:25 pm
6:25 pm
There are 8 hours between 10:25 am and 6:25 pm.
they finished at 6:15 which is 10 minutes before 6:25 ( 25-15 = 10)
10 minutes less than a full hour is 50 minutes ( 60 - 10 = 50)
8 hours - 1 hour = 7 hours
7 hours + 50 minutes = 7 hours 50 minutes total time.
Answer:
seven hours and 50 minutes
Step-by-step explanation:
Please help me find the answer to this question
Answers
-------------------------------------------------------------------------------------------------------------
Answer: The top right table
-------------------------------------------------------------------------------------------------------------
Given: \(\textsf{y = 30 - 3x}\)
Find: \(\textsf{Match the table of values with the equation}\)
Solution: First we must understand what form our equation is in and what each of the numbers represent. This form is known as the slope intercept form which is formatted as y = mx + b. Our equation is slightly re-ordered but we can change that by converting it to y = -3x + 30 where m is equal to -3 and b is equal to 30. Let us know talk about what m and b are. M is the slope of the equation or also known as the rise/run or the change in y over the change in x. B is the y-intercept which is basically the value of y when x is equal to 0. In this case, our b is equal to 30.
Looking at the tables we can see what the value of y when x is equal to 0 for each table. The only table that matches up stating that y is equal to 30 when x is 0 is the top right table.
You do not have to go any further but if you want to confirm that the slope is as expected we can do the following: \(\frac{y_2\ -\ y_1}{x_2\ -\ x_1}\).
Plug in the values and simplify
\(\frac{48\ -\ 30}{-6\ -\ 0}\)\(\frac{18}{-6}\)\(-3\)Therefore, we can confirm that the slope matches up with the given equation as well. So, the final answer would be that the top right table would correspond to the equation y = 30 - 3x.
What is the maximum amount of good Y that can be purchased if X and Y are the only two goods available for purchase and Px = $5, Py = $10, X = 20, and M = 500?
Answers
The maximum amount of good Y that can be purchased is 25 units, given that the price of Y is twice as much as the price of X and the total budget is $500.
This means that the consumer can afford to purchase 20 units of good X at a price of $5 per unit, which would cost $100 in total, leaving $400 to spend on good Y. With a price of $10 per unit, the consumer can purchase 25 units of good Y at a cost of $250, which is the maximum amount of Y that can be purchased with the remaining budget. Therefore, the consumer can purchase a total of 20 units of X and 25 units of Y with the given prices and budget, maximizing their utility subject to their constraints.
In microeconomics, this type of analysis is known as utility maximization. The consumer's goal is to maximize their satisfaction or utility subject to their budget constraint. In this case, the consumer's budget constraint is the amount of money they have to spend on goods X and Y, and the prices of the two goods determine the slope of the budget constraint. The consumer maximizes their utility by choosing the combination of X and Y that gives them the most satisfaction given their budget constraint. The optimal choice is the combination of X and Y where the marginal utility per dollar spent on each good is equal.
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Which equation represents a line which is parallel to the line y = 3/8x + 7?
Answers
The given equation of line is : y = 3/8x + 7
If two lines are parallel then the slopes of thier lines are equal.
The general equation of line is : y = mx + b, with slope is m :
Option : A)
\(\begin{gathered} 8x+3y=-12 \\ 3y=-8x-12 \\ y=\frac{-8x}{3}-\frac{12}{3} \\ y=\frac{-8x}{3}-4 \\ \text{Here, slope is }\frac{-8}{3} \\ \frac{-8}{3}\ne\frac{3}{8} \\ Thus,\text{ the given equation of line is not parallel.} \end{gathered}\)Option : B)
\(\begin{gathered} 8x-3y=18 \\ 3y=8x-18 \\ y=\frac{8}{3}x-\frac{18}{3} \\ y=\frac{8}{3}x-6 \\ \text{Slope is }\frac{8}{3} \\ \text{Thus, }\frac{8}{3}\ne\frac{3}{8} \\ \text{Thus the equation of line is not parallel to the given line} \end{gathered}\)Option C) :
\(\begin{gathered} 8y-3x=32 \\ 8y=3x+32 \\ y=\frac{3}{8}x+\frac{32}{8} \\ y=\frac{3}{8}x+4 \\ \text{Slope is }\frac{3}{8} \\ \frac{3}{8}=\frac{3}{8} \\ \text{ Thus, the equation of line is parallel to the given equation of line} \end{gathered}\)The equation 8y - 3x = 32 is parallel to the line y = 3/8x + 7
Option D) :
\(\begin{gathered} 3x+8y=8 \\ 8y=8-3x \\ y=\frac{8}{8}-\frac{3}{8}x \\ y=1-\frac{3}{8}x \\ \text{Slope is }-\frac{3}{8} \\ \frac{-3}{8}\ne\frac{3}{8} \\ \text{The equation of line is not parallel to the given equation of line.} \end{gathered}\)Answer : C) 8y - 3x = 32