(a) False. If the null hypothesis is rejected using ANOVA, it means that there is significant evidence to suggest that at least one of the means is different from the others.
However, it does not necessarily mean that all the means are different from one another. Additional tests such as pairwise comparisons are needed to determine which specific means are significantly different from one another.
(b) True. When ANOVA is used, the F-statistic is calculated by dividing the variability between groups by the variability within groups. Therefore, if the null hypothesis is rejected, it means that the variability between groups is higher than the variability within groups.
(c) True. Pairwise comparisons are used to determine which specific means are significantly different from one another. If the null hypothesis is rejected using ANOVA, then pairwise comparisons will identify at least one pair of means that are significantly different.
(d) True. When conducting pairwise comparisons, it is important to adjust the significance level to account for the multiple comparisons being made. In this case, there are four groups, so the appropriate level of significance is 0.05/4 = 0.0125. This helps to control the overall type I error rate.
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from a population with a variance of 441, s sample of 361 items is selected. what is the margin of error at 95% condifdence
The margin of error at 95% confidence is approximately 2.16.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
To find the margin of error at 95% confidence, we need to use the following formula:
Margin of error = z * (σ/√n)
where:
z = the z-score associated with the desired level of confidence (in this case, 95% confidence corresponds to a z-score of 1.96)
σ = the population standard deviation
n = the sample size
Given that the population variance is 441, the population standard deviation is the square root of 441, which is 21.
So, the margin of error is:
Margin of error = 1.96 * (21/√361)
= 1.96 * (21/19)
= 2.16 (rounded to two decimal places)
Therefore, the margin of error at 95% confidence is approximately 2.16.
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Find the common difference of the arithmetic sequence.
13,18,23,28,...
Answer: To solve this problem, we will use the formula d = a2 - a1, where d is the common difference and a1 and a2 are two consecutive terms in the sequence.
Step 1: Identify two consecutive terms in the sequence.
In this case, the two consecutive terms are 13 and 18.
Step 2: Substitute the two consecutive terms into the formula d = a2 - a1.
d = 18 - 13
Step 3: Simplify the equation to calculate the common difference.
d = 5
Therefore, the common difference of the arithmetic sequence 13, 18, 23, 28,... is 5.
Step-by-step explanation:
some statistics instructors have students use an online homework system and some do not. final exam scores were recorded for a sample of statistic students who used an online homework system and were compared to the final exam scores from a sample of statistic students who did not use an online homework system. is there evidence that the students who used an online homework system did better on the final?
To determine whether there is evidence that the students who used an online homework system did better on the final exam than those who did not, we can perform a hypothesis test.
State the null hypothesis (H0) and alternative hypothesis (Ha)
H0: There is no difference in the final exam scores between students who used an online homework system and those who did not.
Ha: Students who used an online homework system scored higher on the final exam than those who did not.
Determine the level of significance (alpha). Let's assume a significance level of 0.05.
Collect the data and calculate the sample means and standard deviations for the two groups.
Conduct a t-test for independent samples to determine whether the observed difference in means between the two groups is statistically significant.
If the calculated p-value is less than the significance level (alpha), we can reject the null hypothesis and conclude that there is evidence that the students who used an online homework system did better on the final exam than those who did not. If the p-value is greater than alpha, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that there is a difference in the final exam scores between the two groups.
It's important to note that the results of a hypothesis test depend on the sample size, the variability of the data, and the assumptions made about the underlying population. Therefore, it's important to carefully evaluate the data and assumptions before making any conclusions.
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if testing the claim that σ21≠σ22, what do we know about the two samples if the test statistic is f=1?
When testing the claim that σ21≠σ22, the null hypothesis states that the variances of the two populations are equal, while the alternative hypothesis states that the variances are not equal. To test this claim, we use an F-test, which involves calculating the ratio of the variances of the two samples.
If the test statistic is f=1, this means that the ratio of the variances is equal to 1. This indicates that there is no significant difference between the variances of the two populations. In other words, we cannot reject the null hypothesis that the variances are equal.
However, it is important to note that a test statistic of f=1 does not necessarily mean that the two samples are identical. It is possible for two samples to have slightly different variances that still result in a test statistic of f=1. Additionally, a sample size that is too small or too large can affect the accuracy of the F-test.
Overall, if the test statistic is f=1 when testing the claim that σ21≠σ22, we can conclude that there is not enough evidence to support the alternative hypothesis that the variances are different.
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7 1/4 divided by 3/8
Answer:
14/3
Step-by-step explanation:
Answer:
58/3
Step-by-step explanation:
7 1/4 ÷ 3/8
= 29/4 x 8/3
= 29 x 2/3
= 58/3
Rachel has a bowl shaped like a hemisphere. Which of the following statements about the bowl are accurate?
The statements about the bowl that are accurate include:
A. The area of the opening of the bowl is 63.6 square inches.
E. The volume of the bowl, rounded to the nearest tenth is 575.2 cubic inches.
How to calculate the volume of a hemisphere?In Mathematics and Geometry, the volume of a hemisphere can be calculated by using the following mathematical equation (formula):
Volume of a hemisphere = 2/3 × πr³
Where:
r represents the radius.
By substituting the given parameters into the formula for the volume of a hemisphere, we have the following;
Volume of a bowl = 2/3 × 3.142 × (6.5)³
Volume of a bowl = 575.2 in³
Area of circle = π × (radius)²
Area of bowl = 3.142 × (6.5)²
Area of bowl = 132.7 in².
Volume of a bowl = 575.2/3 = 191.7 in³
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
*MUST ANSWER ASAP PLS*
The ages of the employees in Kathy’s office are: 54, 23, 42, 59, 61, 44, 44, 50, 39, 40, 37, 43, 51, 34, 41,
40, 35, 49, 55, 58, 36, 43.
a. What is the median age?
b. How old are the youngest and oldest employees?
c. What are the lower quartile, upper quartile, and interquartile range?
d. Sketch a box plot using the points you found.
a. The Median age is 43
b. Youngest employee: 34
Oldest employee: 61
c. The lower quartile (Q1) is the median of the lower half of the sorted list, and the upper quartile (Q3) is the median of the upper half. The interquartile range (IQR) is the difference between Q3 and Q1.
How to explain the informationa. The median age is the middle value when the ages are sorted. Since there are 21 employees, the median will be the 11th value:
Median age = 43
b. The youngest employee is the first value in the sorted list, and the oldest employee is the last value:
Youngest employee: 34
Oldest employee: 61
c. The lower quartile (Q1) is the median of the lower half of the sorted list, and the upper quartile (Q3) is the median of the upper half. The interquartile range (IQR) is the difference between Q3 and Q1.
Lower quartile (Q1) = Median of the lower half = (36 + 37) / 2 = 36.5
Upper quartile (Q3) = Median of the upper half = (51 + 54) / 2 = 52.5
Interquartile range (IQR) = Q3 - Q1 = 52.5 - 36.5 = 16
d. To sketch a box plot, we can represent the minimum, maximum, Q1, Q3, and median values on a number line:
Minimum: 34
Q1: 36.5
Median: 43
Q3: 52.5
Maximum: 61
The box plot will have a box from Q1 to Q3 with a line inside representing the median. The whiskers will extend from Q1 to the minimum and from Q3 to the maximum.
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a 95onfidence interval for the ages of six consecutive presidents at their inaugurations is about (,). either interpret the interval or explain why it should not be interpreted_____________________.
Without that information, I cannot interpret or evaluate the validity of the interval. However, I can provide general guidance on how to interpret a confidence interval.
A 95% confidence interval for a parameter (such as the mean age of the six presidents at their inaugurations) is an interval estimate calculated from sample data that has an associated probability of capturing the true population parameter. Specifically, it means that if we were to repeat the sampling process many times and construct 95% confidence intervals each time, approximately 95% of those intervals would contain the true population parameter.
Therefore, if the confidence interval you provided was calculated correctly and is valid, it means that we are 95% confident that the true mean age of the six presidents at their inaugurations falls within the given interval. However, if there are any issues with the data or the assumptions made in calculating the interval, it may not be appropriate to interpret it in this way.
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find the distance between x and y . question content area bottom part 1 the distance between x and y is enter your response here.
To find the distance between x and y, we need to know their coordinates. Let's assume x is located at point (x1, y1) and y is located at point (x2, y2). The distance between them can be calculated using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
The distance formula is derived from the Pythagorean theorem and can be used to find the distance between any two points in a plane. The formula involves taking the square root of the sum of the squared differences in x and y coordinates between the two points.
In order to find the distance between x and y, we need to know their coordinates and then apply the distance formula. It is a useful formula to know when working with geometric figures and can be applied in various real-life situations such as calculating the distance between two cities on a map.
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The distance between x and y can be calculated using the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2).
In order to find the distance between x and y, we need to know the coordinates or positions of x and y. Without this information, we cannot calculate the distance between them. Therefore, we cannot provide a specific answer to this question.
To use this formula, you need the coordinates of the points x and y (x1, y1) and (x2, y2). Plug the coordinates into the formula, then calculate the differences between the x and y values, square them, add them together, and finally, find the square root of the sum. This will give you the distance between x and y.
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a car is driving at 55 kilometers per hour. how far, in meters, does it travel in 3 seconds? myopenmath
The car travels 45.84 meters in 3 seconds.
To solve this problem, we need to convert the speed of the car from kilometers per hour to meters per second since the time given is in seconds.
To do this, we can use the conversion factor that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds.
So, 55 kilometers per hour is equal to (55 x 1000) / 3600 = 15.28 meters per second.
Now, we can use the formula: distance = speed x time
Plugging in the values, we get distance = 15.28 meters per second x 3 seconds = 45.84 meters.
Therefore, the car travels 45.84 meters in 3 seconds.
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find an equation of the tangent line to y=7sin(x) at x=π. (use symbolic notation and fractions where needed.)
To find the equation of the tangent line to the curve y = 7sin(x) at x = π, we first need to find the slope of the tangent line.
We can use the derivative of y with respect to x to find the slope:
dy/dx = 7cos(x)
At x = π, the value of the derivative is:
dy/dx = 7cos(π) = -7
So the slope of the tangent line at x = π is -7.
To find the equation of the tangent line, we also need to know the y-coordinate of the point on the curve where x = π.
y = 7sin(π) = 0
So the point on the curve where x = π is (π, 0).
Now we can use the point slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
Plugging in the values we found, we get:
y - 0 = -7(x - π)
Simplifying, we get:
y = -7x + 7π
So the equation of the tangent line to y = 7sin(x) at x = π is y = -7x + 7π.
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Use the Polygon Angle Sum Theorem to find the measure of x :
The required value of x for this polygon is - 90.
We know that,
Polygons are two-dimensional geometric figures with a fixed number of sides. A polygon's sides are made up of straight line segments that are joined end to end. As a result, the line segments of a polygon are referred to as sides or edges.
The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result.
A triangle with three sides is an example of a polygon. A circle is a plane figure, however it is not regarded a polygon because it is curved and lacks sides and angles.
As a result, we can argue that all polygons are 2d shapes, but not all two-dimensional figures are polygons.
Since,
Sum of interior angles of polygons = 360 degree
Therefore,
130 + x + 20 + 120 + 140 + x - 20 + 150 + x = 360
2x = 360 - 540
x = -180/2
x = -90
Thus,
The value of x = - 90
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Use the formula to find the surface area of the figure.
Answer:
1260 is the answer
Step-by-step explanation:
you solve for the area of the rectangle and multiply it by 3 because there are three sides so 17x20=340x3=1020 then, you solve for the area of a triangle which is 1/2 x base x height so, 1/2 x 16 x 15 = 120 then you multiply that by 2 since there are 2 triangles so 120 x 120=240 finally, you add 1020+240 = 1260
Solve for x. Options are 46,45,40, and 38.
Answer:
45
Step-by-step explanation:
20/x=28/(x+18)
Solving for x, we get that x=45
Cassandra opens a savings account with an initial deposit of $500.The account earns 3.25% simple interest annually. She plans to leave the money in the account for 4 years without making additional deposits or withdrawals. How much simple interest will will Cassandra earn at the end of the 4 years?
Cassandra will earn $65 in simple interest at the cease of the 4 years.
The formulation for simple interest is:
I = P * r * t
Wherein
I is the interest earned, P is the principal amount, r is the interest pricet is the term.In this case Cassandra's preliminary deposit is $500 so that' why the interest rate is some about 3.25% & the time period is four years.
Plugging these values into the formulation, we get:
I = $500 * 0.0325 * 4
I = $65
Therefore, Cassandra will earn $65 in simple interest at the cease of the 4 years.
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(LCM) of 24 and 64
The LCM of 24 and 64 is 192.
Can someone answer check please
Answer:
you got them all correct! good job :)
Step-by-step explanation:
An ice cream shop ordered waffle cones that have a height of 4 in and volume of 3
�
π
in3. The ice cream shop is trying to determine which size ice cream scoop will be the best fit for the waffle cones. Ice cream scoops come in different sizes and have different diameters. The #12 scoop has a 2. 5 in diameter and the #6 scoop has a 3 in diameter. Unfortunately, they are waiting on their order of waffle cones and they don't know the measure of the diameter
The ice cream shop could order a different size scoop with a diameter closer to 1.732 in for an even better fit.
Ice cream scoop will be the best fit for the waffle cones need to find out the diameter of the cones.
We can use the given height and volume of the cones to calculate the diameter using the formula for the volume of a cone:
V = (1/3) × π × r² × h
V is the volume r is the radius (which is half the diameter) and h is the height.
Rearranging the formula to solve for r we get:
r = √((3V) / (πh))
Substituting the given values of V = 3π in³ and h = 4 in we get:
r = √((3π) / (4π))
= √(3/4)
= 0.866 in
So, the diameter of the waffle cones is approximately 1.732 in (twice the radius).
Now we can compare this diameter to the diameters of the #12 and #6 scoops.
The #12 scoop has a diameter of 2.5 in is larger than the cone diameter of 1.732 in so it may not be the best fit.
The #6 scoop has a diameter of 3 in is larger than the cone diameter but closer in size so it may be a better fit than the #12 scoop.
The ice cream shop could order a different size scoop with a diameter closer to 1.732 in for an even better fit.
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what is the volume of a 5 sided pyramid with a height of 10 and the length of each bottom side is 8
Answer:
200cm3
Step-by-step explanation:
Volume is LxWxHL=8cm
W=5 cm
H=10cm
=200cm
the miller school of business at ball state university claims to have a 73% graduate rate from its online mba program. a happy student believes that the 3-year graduation rate is higher than that. a sample of 500 students indicates that 371 graduated within three years. what is the lower limit for the 95% confidence interval for the true graduation rate? use decimals rather than percentages and round your answer to three decimal places.
The lower limit for the 95% confidence interval for the true graduation rate is 0.704.
What is confidence interval?The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level.
We can use the formula for the confidence interval for a proportion:
lower limit = sample proportion - z * √((sample proportion * (1 - sample proportion)) / sample size)
where z is the z-score corresponding to the desired level of confidence (95% in this case), and sample size is 500.
The sample proportion is 371/500 = 0.742.
The z-score for a 95% confidence level can be found using a standard normal distribution table or calculator, and is approximately 1.96.
Plugging in the values, we get:
lower limit = 0.742 - 1.96 * √((0.742 * 0.258) / 500)
lower limit = 0.704
Rounding to three decimal places, the lower limit for the 95% confidence interval for the true graduation rate is 0.704.
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The radius of a circle is 3 m. Find its area in terms of pi
Answer:
9π m²
Step-by-step explanation:
area of circle = πr², where r is the radius.
area = π (3)²
= 9π m²
The results of a survey indicate 70% of seventh-graders watch at least one movie during the weekend. Based on this survey of a group of 50 seventh-graders, how many will watch at least one movie this weekend?
35 seventh-graders will watch at least one movie this weekend based on the survey.
We have,
If 70% of seventh-graders watch at least one movie during the weekend, then the number of seventh-graders who watch at least one movie is:
= 70% of 50
= 70/100 x 50
= 0.7 x 50
= 35
Therefore,
35 seventh-graders will watch at least one movie this weekend based on the survey.
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Find the final value of $2000 investment at an interest rate of 2%compounded quarterly (4 times a year) for 8 years
Answer:
[tex]\Huge \boxed{\boxed{\texttt{\bf{\$2346.09} } } }[/tex]
Step-by-step explanation:
We can use the compound interest formula to get the final value of a $2000 investment at an interest rate of 2% compounded quarterly for 8 years, using:
[tex]\LARGE \boxed{\tt{A = P(1 + \frac{r}{n})^{nt}}}[/tex]
The final amount is A.P stands for the initial principal, in this case $2,000The yearly interest rate is given as r (0.02 for 2%).The value of n determines how many times interest is compounded annually (4 for quarterly).t represents the time in years (8 years).Substituting the values:
[tex]\tt{A = 2000(1 + \frac{0.02}{4})^{4 \times 8}}[/tex][tex]\tt{ A = 2000(1 + 0.005)^{32}}[/tex][tex]\tt{A = 2000(1.005)^{32}}[/tex][tex]\texttt{ A $\approx$ 2346.09 (rounded to 2 decimal places)}[/tex]So, the final value of the investment after 8 years would be approximately $2346.09.
________________________________________________________
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i need help asap plsssss
Answer:
'x' only has one solution
Step-by-step explanation:
First multiply both sides by 'x^2'
40x = -5x^2
(bring both values to one side and factorize to solve for 'x')
5x^2 +40x=0
5x(x+8)=0
5x= 0 ; x+8 = 0
x=0 ; x=-8
x cannot equal to '0' as zero cannot be a denominator.
Hence, x=-8 is the only correct solution.
So, 'x' only has one solution.
which expression is equivalent to cot2β(1−cos2β) for all values of β for which cot2β(1−cos2β) is defined?
After considering the given data we conclude that the given expression upon calculation is equivalent to cot(2β), under the condition that the given expression is cot2β(1−cos2β).
In order to elaborate this given expression we have to use trigonometric identities. Furthermore, the identity cot(2β)(1-cos(2β)) = cot(2β) can be derived applying the following steps:
cot(2β)(1-cos(2β)) = cot(2β) - cos(2β)cot(2β)
= cot(2β) - cos(2β)/sin(2β)
= (cos(2β)sin(2β)/sin(2β)) - cos(2β)/sin(2β)
= (cos(2β)-cos(2β)sin²(2β))/sin(2β)
= cos(2β)(1-sin²(2β))/sin(2β)
= cos(2β)cos²(2β)/sin(2β)
= cot(2β)
Trigonometric identities are considered equalities that have trigonometric functions and are proclaimed as true for each and every value taking place in variables for which both sides of the equality are defined.
These identities are really helpful in the event expressions involving trigonometric functions need to be simplified.
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Two thirds of a certain number plus five equals ten less than the same number, what is the number?
The calculated value of the number is -45
Calculating the value of the number?From the question, we have the following parameters that can be used in our computation:
Two thirds of a certain number Plus five Equals ten less than the same numberRepresent the number with x
So, we have the following equation
2/3x + 5 = x - 10
Collect the like terms
This gives
2/3x - x = -10 - 5
When the like terms are evaluated, we have
1/3x = -15
So, we have
x = -45
Hence, the value of the number is -45
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1. Find the minimum sum of products expression using Quine-McCluskey method of the function F(A, B, C, D) = Σ m( 1, 5, 7, 8, 9, 13, 15) + Σ d( 4, 6, l 1) .
The minimum sum of products (MSP) expression of the given function F(A, B, C, D) can be obtained by using the Quine-McCluskey method. In this case, the MSP expression for the given function is F(A, B, C, D) = A'C'D' + A'BCD + AB'C'D + ABCD.
The MSP expression is a simplified Boolean expression that represents the function in terms of its essential prime implicants.
The Quine-McCluskey method is an algorithm that uses the concepts of prime implicants, essential prime implicants, and petrick's method to simplify Boolean functions. The method starts with finding all the prime implicants of the function and then grouping them to form essential prime implicants. The essential prime implicants are then used to form the MSP expression of the function. The MSP expression obtained using this method is minimal, which means that it has the least number of terms and literals compared to other simplified expressions.
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2. After running the appropriate statistical tests, Jack finds that life satisfaction was __________ in the older adults (M = 4.9, SD = 1.2) than in middle-aged adults (M = 4.1, SD = 1.8), t(58) = 2.03, p = .047, 95% CI [0.01, 1.59], d = .52. A. From these statistical results, what conclusions can Jack make? Comment on whether there are statistically significant differences between the groups and how you know. B. What should Jack decide about the hypotheses? C. What does the "t(58) = 2.03" tell us? D. What can we conclude from the confidence interval? E. What does the effect size tell us?
A. From the statistical results, Jack can conclude that there is a statistically significant difference between the life satisfaction of older adults and middle-aged adults. This is evidenced by the t-value of 2.03 and p-value of .047, which fall below the standard cutoffs for statistical significance. The 95% confidence interval also supports this conclusion, as it does not include zero.
B. Based on these results, Jack should reject the null hypothesis and accept the alternative hypothesis that there is a difference in life satisfaction between older adults and middle-aged adults.
C. The "t(58) = 2.03" indicates the t-value of the statistical test, which is a measure of the difference between the means of the two groups divided by the standard error of that difference. In this case, the t-value of 2.03 suggests that the difference in life satisfaction between the two groups is larger than would be expected by chance.
D. The confidence interval tells us that there is a 95% chance that the true difference in life satisfaction between the two groups falls within the range of 0.01 to 1.59. This suggests that the difference between the two groups is likely not due to chance.
E. The effect size (d = .52) tells us that the difference in life satisfaction between the two groups is moderate in magnitude. This suggests that the difference is not only statistically significant but also practically meaningful.
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what is an equation of the line that passes through the point (6,8) and is perpendicular to a line with equation y
The equation of the line that passes through the point (6,8) and is perpendicular to a line is y = (-2/3)x + 12.
Given the equation, y= 3/2x + 5. Compare it with the general equation of the line,
y = m₁ x + c₁
y= (3/2) x + 5
Therefore, the slope of the given line is m₁=(3/2).
Since it is needed to find the line that is perpendicular to y= 3/2x + 5, therefore, the slope of the two lines can be written as,
(Slope of line 1) × (Slope of line 2) = -1
m₁ × m₂ = -1
(3/2) × m₂ = -1
m₂ = -2/3
Now, the equation of the given line can be written as,
y = m₂x + c₂
y = (-2/3)x + c₂
Substitute the given coordinate in the above equation to get the value of y-intercept(c),
8 = (-2/3)6 + c₂
8 = -4 + c₂
c₂ = 8 + 4
c₂ = 12
Hence, the equation is y = (-2/3)x + 12.
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The complete question is:
What is an equation of the line that passes through the point (6, 8) and is perpendicular to a line with equation y=3/2x 5.