The correct option is (A). The correct answer is Ursa Minor, the Little Bear, containing the bright star Polaris.
Whereas stars spin or revolve from the northern hemisphere is the center of the sky, also known as the North Celestial Pole. Additionally, it marks the precise location of the Polaris or Northern Star constellation in full view. In addition, this served as a point of reference for the construction of sundials in earlier times.
When people go outside, especially at night, and try to find the Polaris constellation, it is evident that the stars close to this star formation circle in an east-to-west direction, in contrast to the northern star, which makes no movement whatsoever as the evening wears on.
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Find the general solution of the first-order linear differential equation y' - (ln x)y = 3 x^x.
y(x)=
Note: Use C for the arbitrary constant.
The general solution of the first-order linear differential equation y' - (ln x)y = [tex]3 x^x[/tex] is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]
As per the give,n data the given differential equation is:
y' - (ln x) y = 3 [tex]x^x[/tex]
Here have to determine the general solution of the first-order linear differential equation.
The differential equation is linear if the dependent variable y and its derivative only occur in the first degree.
Then, [tex]$\frac{d y}{d x}-(\ln x) y=3 x^x$[/tex]
This is of the form [tex]$\frac{d y}{d x}[/tex] + P(x)y = Q(x) which is the linear equation.
In order to solve this kind of differential equation, we have to multiply it by an integrating factor.
Here, P = - ln (x), Q(x) = 3 [tex]x^x[/tex]
I F = [tex]e^{\int P d x}[/tex]
I F = [tex]e^{-\int \ln (x)}[/tex]
I F = [tex]e^{-(x \ln x-x)}[/tex]
I F = [tex]e^{x-x \ln x}[/tex]
I F = [tex]\frac{e^x}{e^{x \ln x}}[/tex]
I F = [tex]\frac{e^x}{x^x}[/tex]
Hence, the general solution is
[tex]& y(I F)=\int Q(x)(I F) d x+c \\[/tex]
[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 x^x\left(\frac{e^x}{x^x}\right) d x+c \\[/tex]
[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 e^x d x+c \\[/tex]
[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=3 e^x+c \\[/tex]
[tex]& \Rightarrow y=3 x^x+c x^x e^{-x}[/tex]
Hence, the general solution is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]
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PLS HELP TYY!!The diagram below shows the dimensions of a can of beans.
A can of beans is shown. A dashed line drawn across the top of the can is labeled seven centimeters. The height of the can is labeled eleven and six tenths centimeters.
How much tin was used to make the can rounded to the nearest square centimeter? Use 3.14 for π.
Enter the correct answer in the box.
Answer:
332 cm²
Step-by-step explanation:
You want to know the surface area of a tin can that is 7 cm in diameter and 11.6 cm high.
Surface areaThe area of a cylinder is given by the formula ...
SA = πd(d/2 +h) . . . . . where d is the diameter and h is the height
ApplicationUsing the given values, d=7 and h=11.6, we find the area to be ...
SA = (3.14)(7 cm)(3.5 +11.6 cm) ≈ 332 cm²
About 332 square centimeters of tin are required to make the can.
You roll a 6-sided die.
What is P(greater than 5 or less than 3)?
2/6
2/3
1/2
1/6
1/6
The probability of an event is the number of ways the event can happen divided by the number of possible outcomes. In this case, the possible outcomes are the numbers on the die, which are 1, 2, 3, 4, 5, and 6.
The event of rolling a number greater than 5 or less than 3 can happen in two ways: rolling a 6 or rolling a 1 or 2. So the probability of this event is:
P(greater than 5 or less than 3) = (number of ways the event can happen) / (number of possible outcomes) = 2/6 = 1/3
So the answer is option D. 1/6
A grandmother is now 48 years older than her grandson. 14 years ago she was thirteen times as old as her grandson. How old is the grandmother? How old is the grandson?
Let's call the grandmother's current age G and the grandson's current age S.
From the first piece of information given, we know that:
G = S + 48
From the second piece of information given, we know that:
G - 14 = 13S
We can use the first equation to substitute for G in the second equation:
(S + 48) - 14 = 13S
S + 34 = 13S
34 = 12S
S = 34/12
S = 2.8 years
So the grandson is 2.8 years old.
Now we can use this information to find the grandmother's age:
G = S + 48
G = 2.8 + 48
G = 50.8 years
So, the grandmother is 50.8 years old and the grandson is 2.8 years old.
One numbe is 5 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 513 . Find the numbers
Answer:
x = 56
First number = 56
Second number = 280
Third number = 156
Total 331
Step-by-step explanation:
which of the following is the solution to the compound inequality? 3x+5> or -2x-7>5
The solution of the compound inequality 3x + 5 > -1 or -2x-7 > 5 is x > -2 or x < -6.
How to solve compound inequality?Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
A compound inequality is an inequality that combines two simple inequalities.
Therefore,
3x + 5 > -1 or -2x-7 > 5
Let's solve the inequality individually
3x + 5 > -1
3x > -1 - 5
3x > -6
x > -6 / 3
x > -2
Therefore,
-2x - 7 > 5
-2x > 5 + 7
-2x > 12
x > 12 / -2
x < -6
Hence,
x > -2 or x < -6
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Select all the correct locations on the image. Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
Out of the given functions, a ,b, c, d , the function with complex roots are b and d.
What are complex roots?
Complex roots, also known as non-real roots, are roots of an equation that are not real numbers but instead are complex numbers. Complex roots are usually represented in the form of a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
The functions which have complex roots are b and d.
hence, out of the given functions, a ,b, c, d , the function with complex roots are b and d.
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Select the correct answer.
Rita is reviewing her electricity bills for the past year. The monthly bills were:
$92, $98, $90, $99, $96, $91, $89, $106, $95, $102, $96, $99.
Which measure should Rita use to find the average monthly bill for the year?
A.
range
B.
interquartile range
C.
median
D.
mean
I'm pretty sure the answer is D.mean absolute deviation.
I hope it'll help you.
Solve for the indicated value, and graph the situation showing the solution point. The formula for measuring sound intensity in decibels D is defined by the equation D=10log(II0) using the common (base 10) logarithm where I is the intensity of the sound in watts per square meter and I0=10−12
is the lowest level of sound that the average person can hear. How many decibels are emitted from a jet plane with a sound intensity of 8.1⋅102
watts per square meter?
Round your answer to three decimal places.
The jet plane emits ___ decibels at 8.1⋅102 watts per square meter.
149.0848502 decibels are emitted from a jet plane with a sound intensity of 8.1*10²
How to find the number of decibels?Decibels are units for expressing the ratio between two physical quantities, usually amounts of acoustic or electric power, or for measuring the relative loudness of sounds.
Number of watts per square meter
d = 10*log(I/IO)
IO = 10⁻¹²
Therefore: d = 10 * log(I/10⁻¹²
jet plane has a sound intensity of 8.1*10² watts per square meter.
Therefore: d = 10*log((8.1*10²) / 10⁻¹²)
10²/10⁻¹² = 10²⁽⁻¹²⁾ = 10⁽²⁺¹²⁾ = 10¹⁴
Therefore: d = 10 * log(8.1 * 10¹⁴)
log(8.1 * 10¹⁴) = 14.90848502
10 * that = 149.0848502 decibels
That's the value of d.
In conclusion, 149.0848502 decibels are emitted from a jet plane with a sound intensity
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Which of the following correlation coefficients indicates the strongest relationship between two variables?
a. -.90 b. -.50 c. +.80 d. +.25
c. +.80 is correct.
lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
Input (x) 1 2 4 5
Output (y) 6 12 18 24 30
1
6 12
2 3
18
4
24
5
30
The output is determined by the pattern of the input.
What is pattern?Pattern is a repeated design or motif used to create a visually pleasing effect. Patterns are often seen in nature, architecture, clothing, and artwork. Patterns can be used to create shapes, textures, and decorations. They can add interest and depth to a design. Patterns can be made up of geometric shapes, lines, curves, and combinations of those elements. They can be created with a variety of materials and techniques, including weaving, printing, embroidery, and painting. Patterns can be used to create continuity, emphasize a focal point, or provide a sense of balance. Patterns can be used to draw the eye to a particular area, or to create a sense of order and organization.
In this example, each output number is the sum of the two numbers before it. Therefore, the output is 6 (1 + 2), 12 (2 + 4), 18 (4 + 5), 24 (5 + 6), and 30 (6 + 8).
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assess reasonableness a monument will be at the circumcenter of a triangular plot of land at the state capital. on the coordinate grid, the vertices of the triangular plot of land are a(1, 5) , b(7, 5) , and c(8, 0) .
Yes, this is reasonable. The circumcenter of a triangle is found by taking the average of the x-coordinates of the three points and the average of the y-coordinates of the three points, so for this triangle, the circumcenter would be at (5.67, 2.67).
The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.
1. Calculate the average of the x-coordinates of the three vertices: (1 + 7 + 8) / 3 = 16 / 3 = 5.67
2. Calculate the average of the y-coordinates of the three vertices: (5 + 5 + 0) / 3 = 10 / 3 = 2.67
3. Therefore, the circumcenter of the triangle is (5.67, 2.67).
The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.
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in a survey collecting data about the salaries earned by recent college graduates, li found that her salary was in the 78th percentile. that means that 78% of recent college graduates earn less than or equal to what li does. [1 point]
Li earns more than 78percentage of recent college graduates, and is in the 78th percentile of salaries earned.
1. Calculate the total number of recent college graduates surveyed: Multiply the total number of responses to the survey by 100 to get the total number of graduates surveyed.
2. Calculate the number of recent college graduates who earn less than or equal to Li's salary: Multiply the percentile (78%) by the total number of graduates surveyed to get the number of graduates who earn less than or equal to Li's salary.
3. Calculate the percentage of recent college graduates who earn less than or equal to Li's salary: Divide the number of graduates who earn less than or equal to Li's salary by the total number of graduates surveyed to get the percentage of graduates who earn less than or equal to Li's salary. The result will be 78%.
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Which graph represents a proportional relationship? Explain
Graph A.
Proportional relationships have to go through the origin, (0,0).
I WILL GIVE BRAINLIEST!!!!
To make 4 cups of punch, David needs 3 cups of cranberry juice. David wants to make 72 cups of punch.
How many cups of cranberry juice will he need?
Work Shown:
4/3 = 72/x
4x = 3*72
4x = 216
x = 216/4
x = 54
Explanation:
Each fraction in the first step is of the form A/B, where A is the amount of punch and B is the amount of cranberry juice. Both measured in cups. In the 2nd step, I cross multiplied. Afterward, divide both sides by 4 to isolate x.
Find the sum and product of Eigen value of matrix A = 3 1 4 0 2 6 0 0 5
The sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.
What is the eigenvalue?
Eigenvalues are the special set of scalar values that are associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed characteristic roots.
To find the eigenvalues of matrix A, we can solve the characteristic equation |A - λI| = 0, where λ is a scalar and I is the identity matrix.
|A - λI| = 3- λ 1 4 0 2- λ 6 0 0 5- λ
= (3-λ)(5-λ) - 24 = λ^2 - 8λ - 15
Setting λ^2 - 8λ - 15 = 0, we can find the eigenvalues of the matrix by solving the quadratic equation.
λ^2 - 8λ - 15 = 0
λ = (8 ± √(8^2 + 4*15))/2
λ = (8 ± √(64 + 60))/2
λ = (8 ± √124)/2
So the eigenvalues of matrix A are λ_1 = (8 + √124)/2 and λ_2 = (8 - √124)/2
The sum of eigenvalues is λ_1 + λ_2 = (8 + √124)/2 + (8 - √124)/2 = 8
The product of eigenvalues is λ_1 * λ_2 = (8 + √124)/2 * (8 - √124)/2 = -15
Hence, the sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.
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Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 8, 10}, and C = {1, 2, 3, 4, 7, 8}. List the elements of each set. (Enter your answers using roster notation. Enter EMPTY or ∅ for the empty set.) (a) AC $$ Incorrect: Your answer is incorrect. (b) B ∪ C (c) C ∪ CC
The elements of each set are given as follows:
a) A and C: {1, 3, 7}.
b) B U C = {1, 2, 3, 4, 6, 7, 8, 10}
c) C U C' = U.
How to realize the operations with sets?The intersection operation between two sets is composed by the elements that belong to both sets, hence:
A and C: {1, 3, 7}.
(as the elements 1, 3 and 7 belong to both of the sets).
The union operation between two sets is composed by the elements that belong to at least one of the sets, hence:
B U C = {1, 2, 3, 4, 6, 7, 8, 10}
The union between a set and it's complement is always the universal set, hence:
C U C' = U.
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answer? Drag the tiles to the correct boxes to complete the pairs.
Match each expression to its simplified form
The expression are matched to the simplest form as shown below
simplest form Equation
12 - 1/2r (13 - 3/2 r) - (1 - r)
r - 13/6 (7r - 3/2) - (2/3 + 6r)
13r + 20 (6r + 7) + (13 + 7r)
-12 + r (-8 - r) + (2r - 4)
How to find the simplest for m of each equation'The simplest form is solved by evaluating each of the equation in the problem
Evaluating the expressions
(6r + 7) + (13 + 7r)
collecting like terms
6r + 7r + 13 + 7
13r + 20
(13 - 3/2 r) - (1 - r)
opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)
13 - 3/2 r - 1 + r
collecting like terms
13 - 1 - 3/2 r + r
12 - 1/2 r
(-8 - r) + (2r - 4)
collecting like terms
-8 - 4 - r + 2r
-12 + r
(7r - 3/2) - (2/3 + 6r)
opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)
7r - 3/2 - 2/3 - 6r
collecting like terms
7r - 6r - 3/2 - 2/3
r - 13/6
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5. how much are you willing to pay to play the following game? you start with $1. you flip a fair coin. if it lands on heads, you double your winnings and flip again. if it lands on tails, the game is over and you collect the money you've won. you continue playing until you land on tails. (asked by point72)
I'm willing to pay up to $1 to play the game. If I get lucky and the coin lands on heads multiple times, I could potentially win more than $1.
The game is quite simple. I start with $1 and then flip a fair coin. If I get heads, I double my winnings and flip the coin again. I will keep flipping the coin until I get tails, at which point the game is over and I collect the money I have won. Depending on how lucky I get, I could potentially win more than $1. Therefore, I am willing to pay up to $1 to play the game. The expected value of this game is $1.50. This is because, on average, I will get heads 50% of the time and tails 50% of the time. So, if I get heads every time, I will double my winnings each time and end up with $2. If I get tails every time, I will end up with $1. Therefore, the expected value is the average of these two outcomes, which is $1.50. There is also some risk involved in this game. If I get unlucky and get tails on my first flip, then I will only get my money back and not make any profit. Therefore, I have to be willing to take on some risk if I want to try and make a profit. It is important to note that this game does not guarantee a profit. The expected value may be $1.50, but I could end up making less or more than that depending on how lucky I get. Therefore, I have to be willing to accept some uncertainty if I want to play this game.
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After giving a test to a group of students, below is the summary of grades by gender. A B C Total Male 16 17 11 44 Female 14 6 3 23 Total 30 23 14 67 If a student is randomly chosen, find the probability that the student is female or earned grade C. Leave your answer as a reduced fraction.
The probability that the student is female or earned grade C is 0.6
How to find the probability?You should recall that probability is the chance of occurrence of an event E
P(E) = (Number of required outcome)/(number of possible outcomes)
The given parameters are
We'll use this table (below) to answer the questions
A B C Total
Male 16 17 11 44
Female 14 6 3 23
Total 30 23 14 67
Total number of female = 23Total number in grace C = 14Total number of students = 67Pr(E) = 23/67 + 14/67
Simplifying the fractions to have
37/67 = 0.55
Therefore this is approximately rounded to 1 decimal place as 0.6
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Which of the following conditions or set of conditions must be met for a parallelogram to be a rectangle?
A. Diagonals are perpendicular.
B. Diagonals are congruent.
C. All sides are congruent.
D. The length of a diagonal is equal to the length of a side.
A parallelogram can only be a rectangle if the following conditions are satisfied: B) The diagonals must be congruent, and A) the diagonals must be congruent and perpendicular.
What is meant by parallelogram?A unique kind of quadrilateral known as a parallelogram is defined by having both pairs of its opposite sides parallel and equal. The opposing sides of a parallelogram are all parallel and of equal length. a quadrilateral parallelogram. Rhombus: An equal-length parallelogram with four sides. A parallelogram is a square. Always. This is accurate. A square is a quadrilateral with two sets of parallel sides, four right angles, and four congruent sides.Since not all parallelograms have equal sides, not every parallelogram is a rhombus. The opposite is true, though, when every rhombus is a parallelogram.Every rectangle is a parallelogram, but not every parallelogram is a rectangle, is the correct statement.Therefore,
One feature of a parallelogram is that its diagonals are divided in half. A rectangle also has congruent diagonals.
In addition to being congruent, the diagonals in a square are perpendicular to one another.
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Problem: Given an integer amount of money, you have to determinate which is the minimum amount of coins needed to arrive at the exact total. You have an infinite number of each, and may choose more than one. Coins available are $1, $5, $10, $25. Choose the highest-value coin available that does not exceed the total and repeat until you arrive at the desired amount.:
The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.
1. Start by subtracting the largest coin value from the total amount.
2. If the difference is greater than 0, add the coin to the total and repeat the process.
3. If the difference is 0, move onto the next smallest coin value.
4. Repeat the process until the total amount is reached.
5. Once the total amount is reached, the minimum amount of coins needed to arrive at the total will be displayed.
The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.
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WHATS THE ANSWER? WILL APPRECIATE SOO MUCH !!
(s+12)^3
I am wasting space here as you can tell but no fr the answer is (s+12)^3
a 2.5 nm torque is applied to a flywheel for 10.0 seconds. if the flywheel is initially at rest and its moment of inertia is 2.0 kg m2, determine its angular momentum. group of answer choices
The angular momentum of the flywheel is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s.
1. Determine the angular momentum of the flywheel:
Angular momentum = Torque × Time × Moment of Inertia
= 2.5 Nm × 10.0 s × 2.0 kg m2
= 50 kg m2/s
The angular momentum of an object can be determined from the product of the applied torque, the time interval, and the moment of inertia. The moment of inertia is the rotational inertia of an object, which is the resistance to changes in its angular velocity. The angular momentum of the flywheel in this question is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s. This means that the flywheel will have an angular momentum of 50 kg m2/s after the 10-second interval when the torque is applied. The angular momentum of the flywheel will remain constant until another torque is applied to change it.
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aisha, benoit, and carleen are each thinking of a positive integer. aisha's number and benoit's number have a common divisor greater than 1. aisha's number and carleen's number also have a common divisor greater than 1. benoit's number and carleen's number also have a common divisor greater than 1. is it necessarily true that the greatest common divisor of all three numbers is greater than 1? if it is necessarily true, explain how you know it's true. if it isn't necessarily true, convince us by showing us three numbers for which it's false -- in other words, show us three integers such that every pair have a common divisor greater than 1, but all three numbers don't have a common divisor greater than 1. hint(s):
No, it is not true that GCD(A, B, C).
What is the greatest common divisor?
The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF). For instance, since both 15 and 10 can be divided by 5, 5 is the biggest common factor between both.
Here, we have
Given: Aisha's number and Benoit's number have a common divisor greater than 1. Aisha's number and Carleen's number also have a common divisor greater than 1. Benoit's number and Carleen's number also have a common divisor greater than 1.
We have to determine if is it necessarily true that the greatest common divisor of all three numbers is greater than 1.
Here, we solve this with an example.
A = 6 = 2*3,
B = 14 = 2*7,
C = 21 = 3*7
There is no GCD greater than 1 that divides all of A, B and C.
Hence, No, it is not true that GCD(A, B, C).
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Describe how you can determine the domain and range of f(x) = −8x7 + 1.9x6 − 7x5 + 0.12x3 + 22x2 + 4.
The domain of a function is the set of possible values that can be plugged into it.
What is the Domain and Range of a Function?The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The collection of all possible inputs and outputs constitutes a function's domain and range, respectively. Important features of a function are the domain and range. The domain accepts all potential input values from the set of real numbers, and the range accepts all function output values.
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1. Jeremy's father is paying for a $30 meal. He has a 20% off coupon for the meal. How much money will the coupon save Jeremy's dad?
2. Jeremy's father is paying for a $30 meal. He has a 20% off coupon for the meal. After the discount, a 6% sales tax is applied. How much will Jeremy's father pay in sales tax?
3. Jeremy's father is paying for a $30 meal. He has a 20% off coupon for the meal. How much in total did Jeremy's father pay for the meal (including tax)?
1. The coupon will save: $6.
2. The sales tax is of: $1.44.
3. The total price paid for the meal is of: $25.44.
How to obtain the total cost?The total cost is obtained applying the proportions in the context of this problem.
The initial fee for the meal is of:
$30.
With the coupon of 20% off, the amount paid is of:
0.8 x 30 = $24.
Meaning that the amount saved is of:
30 - 24 = $6.
After the sales tax, the total price is of:
1.06 x 24 = $25.44.
Meaning that the tax is of $1.44.
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Write the solution set in interval notation and graph the inequality.
Set-Builder Notation: {x | 5/7
The set X can therefore be written as follows: The expression "A is the set of elements x such that x is a natural number less than 7" can be translated as "A is the set of elements x such that x is a natural number less than 7." A = x: x N, x 7 is another way to express the above set.
What is the Set Builder Form or Rule Method?If a set's components share a characteristic, the characteristic can be used to define the components. For instance, the natural numbers 1, 2, 3, 4, 5, and 6 in the set A have a trait in common that all of their members fall below the number 7. This trait is not shared by any other natural numbers. The set X can therefore be written as follows:The expression "A is the set of elements x such that x is a natural number less than 7" can be translated as "A is the set of elements x such that x is a natural number less than 7."A = x: x N, x 7 is another way to express the above set.The expression "the set of all natural numbers smaller than seven" can also be used to denote set A.The common property of the elements of a set is described in this instance inside braces. A set-builder form, often known as a rule technique, takes this simple structure.The Complete Question is Set Builder .
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Test market data shows that changing the price of a product changes the demand. Does this table indicate that purchase price is a function of demand? Why or why not?
The table indicates that purchase price is a function of demand, as each demand is mapped to a single purchase price.
When does a relationship represents a function?To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.
The input and output variables for this problem are given as follows:
Input: demand.Output: purchase price.In the table, there are no repeated demand values, meaning that the purchase price is a function of the demand, as there are no inputs mapped to multiple outputs.
Missing InformationThe table is given by the image presented at the end of the answer.
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The number of miles y is proportional to the number of hours x as shown in the graph.
An equation to represent this proportional relationship is y = 65x.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
y represents the number of hoursx represents the number of miles.m represents the slope.Next, we would determine the linear equation representing the line which passes through the points (3, 195) and (6, 390) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 195 = (390 - 195)/(6 - 3)(x - 3)
y - 195 = 195/3(x - 3)
y - 195 = 65(x - 3)
y = 65x - 195 + 195
y = 65x
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