⚘Kindly refer to the attachments for complete solutions!!~
Suppose two trains, say A and B are initially 125 miles apart on the same east-west track. Train A is initially to the west of train B. Train A begins to head due east at 25 mph, and train B begins to head due west at 20 mph. To the nearest minute, how long will it take for the two trains to collide?
Answer:
\(167\ \text{minutes}\text{ or }166\ \text{minutes}\ \text{and}\ \text{40}\ \text{seconds}\)
Step-by-step explanation:
Distance between the two trains is 125 miles.
So, when they will collide they would have covered a distance of 125 miles together.
The time that will pass for both the trains will be same but the distances covered will be different as their speeds are different.
\(\text{Distance}=\text{Speed}\times \text{Time}\)
\(25t+20t=125\\\Rightarrow t=\dfrac{125}{45}\\\Rightarrow t=\dfrac{25}{9}\ \text{hours}=\dfrac{25}{9}\times 60\times 60=10000\ \text{s}=166.67\ \text{minutes}\\\approx 167\ \text{minutes}\\=166\ \text{minutes}\ \text{and}\ \text{40}\ \text{seconds}\)
\(167\ \text{minutes}\text{ or }166\ \text{minutes}\ \text{and}\ \text{40}\ \text{seconds}\)
The sum of Lisa's age and Myra's age is 40. In 10 years, Lisa will be 3
times as old as Myra. How old is each person now?
Answer:
Lisa: 35Myra: 5Step-by-step explanation:
You want Lisa's and Myra's ages if the sum of their ages is 40 and in 10 years, Lisa will be 3 times as old as Myra.
10 years henceThe current sum of their ages is 40. In 10 years, 10 will be added to each of their ages, so the sum will be 60.
At that time Lisa's age is 3 times Myra's age, so will be 3/(3+1) = 3/4 of the total.
Lisa's age in 10 years = (3/4)(60) = 45
Lisa is 35 now, and Myra is 5 now.
__
Additional comment
We could write some equations, but we find a mental solution based on ratios to be quick and easy. Here is a solution using equations:
L + M = 40
(L +10) = 3(M +10) . . . . . . age relation in 10 years
(40 -M) +10 = 3M +30 . . . . substitute for L
20 = 4M . . . . . . . . . add M-30
M = 5; L = 40-M = 35
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A circular window is drawn on architectural plans where each unit is a foot on a coordinate grid. the window is modeled by the equation (x – 4)2 (y – 12)2 = 9. the equation indicates that the center of the window is feet from the ground and the distance the window spans is feet.
The equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.
What is the general equation of a circle?The equation of a circle is given by the formula,
\((x-a)^{2} + (y -b)^{2} = r^{2}\)
where (a,b) is the coordinate of the center of the circle, and r is the radius of the circle.
According to the given equation, if we compare this equation with the general equation of the circle.
\((x-4)^{2} + (y-12)^{2} = 9\)
\((x-a)^{2} + (y -b)^{2} = r^{2}\)
\((x-4)^{2} + (y -9)^{2} = 3^{2}\)
On observing this equation we will get that the value of (a,b) is (4,12).
Thus, The equation indicates that the center of the window is 12 feet from the ground
window span = diameter of circle
window span = 2r
= 2 × 3 (radius = 3)
= 6
Hence, The equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.
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Find the unit rate. Then write which is the better buy. $0.90 for 2 pens or $1.75 for 5 pens
Answer:
2 pens for $0.90 is better
Step-by-step explanation:
Which is the most accurate measurement for the line segment?
Answer:
Step-by-step explanation:
So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length. The length of a line segment can be measured either in metric units such as millimeters, centimeters, or customary units like feet or inches.
Please help me solve the question from below. It is from IM3 Algebra
The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.
To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:
log₂(x - 1) = x³ - 4x
Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.
For the point (2, 0):
log₂(2 - 1) = 2³ - 4(2)
log₂(1) = 8 - 8
0 = 0
The equation holds true for the point (2, 0), so (2, 0) is one solution.
For the point (1.1187, -3.075):
log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)
log₂(0.1187) = 1.4013 - 4.4748
-3.075 = -3.0735 (approx.)
The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.
Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.
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Find the first three terms of the sequence below.
Tn = 3n^2- 4n - 3
Answer:
Look on the internet , It's easy
Solve the equation for all exact solutions where appropriate. Round approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures. sin cos 0 - sin = 0 Choose the correct answer below. O A. {90°n, where n is any integer; B. {270°n, where n is any integer} C. {180°n, where n is any integer} OD. {0°}
To solve the equation sin(cos(0)) - sin(0) = 0, we first observe that cos(0) = 1. Substituting this value, we get sin(1) - sin(0) = 0. Since sin(0) = 0, we have sin(1) = 0.
The solutions to sin(x) = 0 are x = nπ, where n is an integer. Therefore, the only solution to the given equation in the interval [0,360°] is 0°.
However, if we consider all possible values of x, then the solutions are given by x = 180°n, where n is any integer. This is because sin(x) = sin(180° - x), and so sin(180°n + x) = sin(x) for all integers n and all angles x. Therefore, the answer is (C) {180°n, where n is any integer}.
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true or false? about 60% of u.s. women older than 16 years are either currently employed or looking for work.
Answer: True
Step-by-step explanation:
Simple.
How do you simplify the expression 1+tan^2θ?
The tangent theta is a Trigonometric function, the simplified value of 1 + tan²θ is sec²θ.
What is Trigonometry function ?Trigonometric functions are also called circular functions. They are easily defined as functions of triangle angles. This means that the relationships between the angles and sides of triangles are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant. Also read the triangle identity here.
We have given an expression, 1 + tan²θ
we know that , tanθ = sinθ /cosθ
sin²θ + cos²θ =1 and 1/cosθ = secθ
Now, 1 + tan²θ = 1 + sin²θ/cos²θ
taking LCM cos²θ
=> 1 + tan²θ = (cos²θ + sin²θ )/cos²θ
=> 1 + tan²θ = 1/cos²θ
=> 1 + tan²θ = sec²θ
Hence, the required expression is sec²θ.
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a pizza shop runs a special where you can buy a large pizza with one cheese, one vegetable, and one meat for $9. You have a choice of seven Cheese's, 11 vegetables, and 6 Meats. Additionally, you have a choice of Three crusts and two sauces. How many different variations of the pizza special are possible?
The possible number of pizza special is (7 x 11 x 6 x 3 x 2 = 2772 variations.
Find the next three terms in the pattern 7, 5, 3, 1, −1, .... and complete the description of the pattern.
Answer:
2
Step-by-step explanation:
Answer:
7,5,3,1,-1,-3,-5,-7
Step-by-step explanation:
7,5,3,1,-1,-3,-5,-7
Hope this helps!
solve the equation (3x-5)=16
with working
=
Answer:
x=7
Step-by-step explanation:You can plug in the value for x and solve to see if true.
A 24ft. ladder is leaning against a house while the base is pulled away at a constant rate of 1ft/s. At what rate is the top of the ladder sliding down the side of the house when the base is: (a) 1 foot from the house? (b) 10 feet from the house? (c) 23 feet from the house? (d) 24 feet from the house? 10. A boat is being pulled into a dock at a constant rate of 30ft/min by a winch located 10 ft above the deck of the boat.
The Pythagorean Theorem is used to find the rate at which the top of a 24ft. ladder is sliding down the side of a house when the base is at a certain distance from the house. It states that the rate of change of the distance between the boat and the dock is given by 30ft/min. To find the rate of change of the height of the boat, we can plug in known values to solve for dh/dt, which is about 28.96 ft/min.
The Pythagorean Theorem is used to find the rate at which the top of a 24ft. ladder is sliding down the side of a house when the base is at a certain distance from the house. The distance between the base of the ladder and the house is x and the length of the ladder is L. The height h of the ladder on the wall can be found by using the Pythagorean Theorem. The rate at which the top of the ladder is sliding down the side of the house when the base is 1 foot away from the house is 2.41 feet per second.
The rate at which the top of the ladder is sliding down the side of the house when the base is 10 feet away from the house is 2.41 feet per second. The Pythagorean Theorem states that the rate of change of the distance between the boat and the dock is given by 30ft/min. To find the rate of change of the height of the boat, we can use the Pythagorean Theorem, which states that the rate of change of the distance between the boat and the dock is given by 30ft/min. To find the rate of change of the height of the boat, we can plug in the known values to solve for dh/dt, which is about 28.96 ft/min. This means that the boat is approaching the dock at a rate of 28.96 ft/min.
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33.5 ÷ 10² i need help on this question i will give you 30 points
Answer: 0.335
Step-by-step explanation:
all 10 to the 2nd power is its multiplying its self twice so if theirs a 3 its gonna be 10x10x10 i did 33.5 ÷ 100
Given that YZ bisects VW, and VX = 46, find XW
Answer:
XW = 134
Step-by-step explanation:
The fact that YZ bisects VW means that the angles VX and XW are supplementary, that is, they add to 180º. So
VX + XW = 180
We have that VX = 46. So
46 + XW = 180
XW = 134
eight concrete specimens are constructed from a new formulation, and the compressive strength of each is measured.
The populace is the concrete produced by a certain procedure. This population is conceptual since the concrete won't exist until the sampling procedure has created it.
What is the difference between tangible and conceptual population?
It is frequently crucial to ascertain the type of population we are working with when asked to perform a sample of it. Sometimes we want to learn more about a lot of different things, like people, apple trees, cereal boxes, etc. Physical things make up the majority of this population. But occasionally, we work with a population that is determined by how well a certain method works (like flipping a coin). We cannot influence that population, but we are aware of its behavior. The population is the broad category of topics about which we are interested in learning more. Since we are dealing with concrete objects that we can touch and interact with, it is more particularly a tangible population.
Similar to the bag of marbles, we have a 50/50 probability of seeing each result. The population does not yet exist with the coin, which is the problem. To get a result, we must flip a coin. Although it is only a notional population, we nonetheless regard "all of the coin flips" as the conceptual population.
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List five tasks that a layer can perform. is it possible that one (or more) of these tasks could be performed by two (or more) layers?
Error control, flow control, segmentation and reassembly, multiplexing, and connection setup are five tasks that a layer can perform.
Flow control: It is the efficient management of data flow between two or more devices like computers or nodes of a network.
Error control: The identification and correction of errors that occur during the transmission of data is called error control.
Segmentation and reassembly: Data to be transmitted is divided into small parts or chunks for convenience. This process is called segmentation. The combining of these chunks to reform the original data is called reassembling.
Multiplexing: The process of combination of digital data streams in one signal over a shared medium is known as multiplexing.
Connection setup: Establishing a connection between two devices that are connected to the same network is called connection setup.
All these tasks can be duplicated at different layers.
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suppose that professor degroot has a policy of giving as to the top 10% of student scores on his final, regardless of the actual scores. if the distribution of scores on his final exam turns out to be normal with mean 69 and standard deviation 9, how high does your score have to be to earn an a?
Your score must be greater than or equal to 81 in order to receive an A grade. The mean value comes out to be 80.52.
Here, we are given that professor Degroot has a policy of giving A grade to the top 10% of student scores on his final.
This means in order to earn an A grade, your score should be in the top 10%.
⇒ Z score should be 0.09
we can look at the z tables to find that this value is at z = 1.28
Now, we know z score is calculated as-
z = (X - μ)/ σ
where X = observed value
μ = sample mean
σ = standard deviation
substituting the given values in the formula we get-
1.28 = (X - 69)/ 9
1.28 × 9 = X - 69
11.52 = X - 69
X = 11.52 + 69
X = 80.52
Thus, your score must be greater than or equal to 81 in order to receive an A grade.
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What i the um of the fraction? Ue the number 18 equivalent fraction to help find the anwer -3/41/2
fractions with the same denominator added together
You must add the numerators and keep the same denominator when adding fractions with the same denominator. Since the denominators of the two fractions are the same, we must add the numerators while maintaining the same denominator, which is 4.
What are the parts of fraction?
A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.
The number below the bar is called the denominator . It tells the number of equal parts into which the whole has been divided. The number above the bar is called the numerator. It tells how many of the equal parts are being considered.
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The formula P = 14.7e⁻⁰.²¹ˣ gives the average atmospheric pressure P, in pounds per square inch, at an altitude x, in miles above sea level. Find the average atmospheric pressure of a city that is 1 mile above sea level.
The average atmospheric pressure of a city that is 1 mile above sea level is approximately 14.383 pounds per square inch. This can be found using the formula P = \(14.7e^(-0.021x)\), where x represents the altitude in miles.
The given formula P = \(14.7e^(-0.021x)\) represents the relationship between the average atmospheric pressure P and the altitude x in miles above sea level. To find the average atmospheric pressure of a city that is 1 mile above sea level, we substitute x = 1 into the formula.
P = \(14.7e^(-0.021 * 1)\)
Simplifying the expression inside the exponential function:
P = \(14.7e^(-0.021)\)
Using a calculator, we can evaluate the exponential function:
P ≈ 14.7 * 0.979
P ≈ 14.383
Therefore, the average atmospheric pressure of a city that is 1 mile above sea level is approximately 14.383 pounds per square inch.
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which of the following is a quadratic inequality
y>x3+x2
y
y2+3x+4
Answer:
y>x3+x2
Step-by-step explanation:
it has the greater than sign
How do 3/6 and 7/15 compare?
Answer:
To compare them first you need to see if these fractions are equal.
Step-by-step explanation:
Select the formula reference in the last column of the table and enter the the gross profit percentage for each year: (Round your answers to the nearest tenth percent, X×%
2
. [Clok the ican to vew the formulas] (a.) 365 days + Inventory turnover (b.) Annual dividend per share + Earnings per share (c.) Annual dividend per share + Market price per share (d.) (Cash including cash equivalents + Short-term investments + Net current receivables) + Total current liabilities (e.) Cost of goods sold + Average merchandise inventory (f.) Current assets - Current liabilities (g.) Gross profit + Net sales revenue (h.) Market price per share of common stock + Earnings per share (i.) Net credit sales + Average net accounts receivables (i.) (Net income + Income tax expense + Interest expense) + Interest expense (k.) Net income + Net sales (L.) (Net income + Interest expense) + Average total assets (m.) (Net income - Preferred dividends) + Average common stockholders equity (n.) (Net income - Preferred dividends) + Weighted average-number of common shares outstanding (o.) Total current assets + Total current liabilities (p.) Total liabilities + Total assets WRN Athletic Supply, Inc. Five-Year Financial Summary (Partial; adapted)
Gross Profit ratio(%) = Gross Profit / Net Sales * 100
= Net Sales - Cost of Goods Sold / Net Sales * 100
(1) Year 2016 :-
Gross Profit Ratio = $1,34,000 - $1,05,994 / $1,34,000 * 100 = 20.9%
(2) Year 2017 :-
Gross Profit Ratio = $1,63,000 - $1,27,955 / $1,63,000 * 100 = 21.5%
(3) Year 2018 :-
Gross Profit Ratio = $1,92,000 - $1,48,800 / $1,92,000 * 100=22.5%
(4) Year 2019 :-
Gross Profit Ratio = $2,17,000 - $1,65,788 / $2,17,000 * 100= 23.6%
(5) Year 2020 :-
Gross Profit Ratio = $3,10,000 - $2,35,290 / $3,10,000 * 100 = 24.1%
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This is an incomplete question. Here is the full question.
determinant of matrix in python giving wrong answers true or false
The statement "determinant of matrix in Python giving wrong answers" is generally false, as long as you're using the correct method for calculation and providing a valid input matrix. It
What's determinant of a matrixThe determinant of a matrix is a scalar value that can be used to determine if a matrix is invertible or not.
In Python, the NumPy library provides a function to calculate the determinant of a matrix. However, if the input matrix is not a square matrix, the function will return an error.
Additionally, if the matrix is singular, the determinant will be zero, but due to the limitations of floating-point arithmetic, the function may return a very small non-zero value instead.
This can lead to the function giving wrong answers, either indicating that a matrix is invertible when it is not, or vice versa. It is important to check the validity of the matrix before calculating its determinant, and to be aware of the limitations of floating-point arithmetic.
One possible solution is to use symbolic computation libraries like SymPy to calculate the exact determinant of a matrix.
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Which equation represents a line which is parallel to the line y = 2/7x – 5?a) 7x - 2y = -2b) 2x + 7y = -42c) 7y - 2x = 21d) 7x + 2y = 10
Answer
C. 7y - 2x = 21
Expalnation
You must know that for two lines to be parallel to each other, they must have the same slope.
The standard form of equation of a line is expressed as y = mx+c
m is the slope of the line
Comparing to the given equation y = 2/7x – 5, you will see that
m = 2/7
This means that the equation that will be parallel to this line must also have a slope of 2/7.
Fromm the option given, we need to find the equation that has a slopw of 2/7.
Looking at option A
7x - 2y = -2
First we must write this in standard form y = mx+c as shown
To do this, we need to make y the subject of the formula:
7x - 2y = -2
-2y = -2-7x
-2y = -7x-2
Divide through by -2
-2y/-2 = -7x/-2 -2/-2
y = 7/2x + 1
The slope of this line is 7/2, this shows that the line is not parallel to the given line since their slope are different
Let us look at option C:
7y - 2x = 21
Rewrite the equation
7y = 21 +2x
Divide through by 7
7y/7 = 21/7 + 2/7 x
y = 3 + 2/7 x
y = 2/7 x + 3
We can see that the slope of this line is also 2/7 which is equivalent to the slope of the given line.
Hence the equation of the line parallel to y = 2/7x – 5 is 7y - 2x = 21
Answer:
c). 7y - 2x = 21.
Step-by-step explanation:
Given line is y = 2/7x - 5
Parallel lines have the same slope.
The equation is in slope-intercept form so,
the slope of the given line is 2/7.
We need to convert the given choices to slope / intercept form:
a) 7x = 2y = -2
2y = 7x + 2
y = 7/2x + 1
- so, it's not this one.
b) 2x + 7y = -42
7y = -2x - 42
y = -2/7x - 6 . No.
c) 7y - 2x = 21
7y = 2x + 21
y = 2/7 + 3.
It's this one.
1) A live action role-playing game (LARP) is a form of role-playing game where the participants physically portray their characters in a fictional setting, while interacting with each other in character. There are game rules to dictate the interactions between players and to determine the winner of the games. A local gamemaster would like to determine how many people in the area would be interested in participating in his LARPing event. He sent out a survey to 1500 people in the area and asked if they would be interested in participating. 432 people said that they would be interested in participating in a LARPing event. (a) State the parameter our confidence interval will estimate. (b) Identify each of the conditions that must be met to use this procedure, and explain how you know that each one has been satisfied. (c) Find the appropriate critical value and the standard error of the sample proportion. (d) Give the 95% confidence interval. (e) Interpret the confidence interval constructed in part (d) in the context of the problem.
Based on the given information, it is explicitly mentioned whether the sample was randomly selected. This means that, based on the sample data, we can estimate the range within which the true proportion of interested participants is likely to fall with 95% confidence.
What is sample?In statistics, a sample refers to a subset of a population that is selected for analysis or study in order to make inferences about the entire population. It is often not feasible or practical to collect data from an entire population, so a sample is used as a representative subset to gather information and draw conclusions about the larger population.
Here,
(a) The parameter that the confidence interval will estimate is the proportion of people in the area who are interested in participating in the LARPing event.
(b) The conditions that must be met to use a confidence interval procedure for a proportion are:
Random Sample: The survey respondents must be randomly sampled from the population of interest. This ensures that the sample is representative of the population.
Large Sample Size: The sample size must be sufficiently large, typically with at least 10 successes and 10 failures in the sample. This ensures that the sampling distribution of the sample proportion is approximately normal.
Independence: The responses of the survey respondents must be independent of each other. This means that one respondent's answer should not influence the answer of another respondent.
Based on the given information, it is not explicitly mentioned whether the sample was randomly selected or whether the sample size is large enough, and whether the responses are independent. This information would need to be provided or assumed in order to determine if the conditions for using a confidence interval procedure for a proportion have been met.
(c) The appropriate critical value can be found using a table or calculator. For a 95% confidence interval, the critical value is 1.96. The standard error of the sample proportion can be found using the formula:
SE = √(p(1-p)/n)
where p is the sample proportion and n is the sample size. Plugging in the values from the problem, we get:
SE = √(0.288(1-0.288)/1500)
= 0.020
(d) The 95% confidence interval can be calculated using the formula:
sample proportion ± (critical value) x (standard error)
Plugging in the values from the problem, we get:
0.288 ± 1.96 x 0.020
= 0.288 ± 0.0392
The 95% confidence interval is (0.2488, 0.3272).
(e) The interpretation of the confidence interval constructed in part (d) would be: We are 95% confident that the true proportion of people in the area who are interested in participating in the LARPing event lies between the lower and upper bounds of the confidence interval. The larger the confidence interval, the less precise our estimate, but the higher our level of confidence in the range.
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What is the number −37,860,000 written in scientific notation?
Select one:
A. -3786 x 104
B. -0.3786 x 108
C. -37.86 x 106
D. -3.786 x 107
Answer:
The answer is D - 3.786x10^7
PLEASE HURRY AND HELPPPP!!
In order to prove that the diagonals of a rhombus are perpendicular to each other using the following figure, which triangle congruency postulate is used?
Answer:
SSS Postulate
Step-by-step explanation:
Just took the test ;)
Use the given conditions to write an equation for the line. Passing through (−3,7) and parallel to the line whose equation is 5x−8y−7=0 The equation of the line is (Simplify your answer. Type an equation using x and y as the variables. Use integers or fraction
The equation of the line passing through (-3, 7) and parallel to the line 5x - 8y - 7 = 0 is: 5x - 8y = -11.
To find the equation of a line parallel to the line with equation 5x - 8y - 7 = 0 and passing through the point (-3, 7), we need to determine the slope of the given line first.
The given line is in the form Ax + By + C = 0, where A = 5, B = -8, and C = -7. The slope of this line can be found by rearranging the equation in slope-intercept form (y = mx + b), where m represents the slope.
Rearranging the equation 5x - 8y - 7 = 0, we have:
5x - 7 = 8y
(5/8)x - 7/8 = y
From this equation, we can determine that the slope of the given line is 5/8.
Since the line we want to find is parallel to this line, it will have the same slope of 5/8.
Now we can use the point-slope form of a line to write the equation of the line passing through (-3, 7) with a slope of 5/8:
y - y₁ = m(x - x₁),
where (x₁, y₁) is the given point and m is the slope.
Substituting the values (-3, 7) and m = 5/8 into the equation, we have:
y - 7 = (5/8)(x - (-3))
y - 7 = (5/8)(x + 3)
Now we can simplify the equation:
y - 7 = (5/8)x + (5/8)(3)
y - 7 = (5/8)x + 15/8
Bringing the constant term to the other side, we have:
y = (5/8)x + 15/8 + 7
y = (5/8)x + 15/8 + 56/8
y = (5/8)x + 71/8
Therefore, the equation of the line passing through (-3, 7) and parallel to the line 5x - 8y - 7 = 0 is:
y = (5/8)x + 71/8.
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