Answer:
No solution, because the slopes are the same and the y-intercepts are different.
Step-by-step explanation:
The two equations are:
y = 1/4x + 1 and y= 1/4x - 1
Since the left sides are equal we can equate the right sides:
1/4x + 1 = /4x - 1
1/4x cancels out of the equation and we get the absurdity:
1 = -1
This indicates no solution to the system of equations
Answer:
No solution, because the slopes are the same and the y-intercepts are different.
We can see that the slopes are the same (1/4) and the y-intercepts are different (1 and -1)
India's Population at the end of the year 2019 was 1.37 billion. The country's growth in
population can be modeled by the function G(x) = 1.37(1.003), where x is the number of
years since 2019.
What is the country's annual growth factor?
Find the constant percent rate of change and interpret in the context.
The formula (y2y1)/(x2x1) (y 2y1)/(x 2x1) can be used to determine the constant rate of change.
What is constant rate?When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant. The slope exist as a another name for the constant rate of change. The rate of change for linear functions will be constant. One quantity changes in respect to another when something changes at a consistent rate. For instance, a pigeon may go 25 miles in every half-hour of flight. This constant rate can be expressed as a ratio. The equation y = mx + b, where m and b are constants, can be used to express a linear function, which has a constant rate of change.To learn more about constant rate, refer to:
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Jorimiah scored 85 points in a basketball game. That was 1/8 of the points that he scored for the season. How many points did jorimiah score in the season.
Jorimiah score 680 points in the season.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Jorimiah scored 85 points in a basketball game.
That was 1/8 of the points that he scored for the season.
let Jorimiah score x points
So, 1/8 of x= 85
x= 85(8)
x= 680 points.
Hence, he score 680 points.
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You can solve the equation 3x + 2 = 8 by graphing y = 3x + 2 and y = 8 and finding their point of intersection.
Use the drop-down menus to complete the statements below.
The solution of 3x + 2 = 8 is
A. 2
B. 8
C. (2,8)
D. (8,2)
(2, 8) is a solution of
1. only y = 3x + 2
2. only y = 8
3. both y = 3x + 2 and y = 8
4. neither y = 3x + 2 nor y = 8
Answer:
A. and 3
Step-by-step explanation:
3x+2=8
3x=6
x=2
Solve the inital value problem dy/dt= ey-t sec(y)(1+t2) y(0)=0. Solve the inital value problem.
The solution of the initial value problem is [tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex].
What is initial value problem?Initial value issues are a specific kind of calculus issue. Calculus initial value issues include differential equations with a known beginning condition that identifies the function's value at a certain point. Finding the function that best describes the system is the goal of these puzzles, and this can be accomplished by integrating the differential equation.
There is always an unknown constant present when doing an integration with an indeterminate integral or without initial conditions. The constant of integration is what is commonly indicated by the letter C.
Given that the initial value problem is:
dy/dt= e^(y-t) sec(y)(1+t2)
This can be re written as follows:
dy/ dt = e^(y-t) (1 + t^2) / sec (y)
Separate the derivative in terms of y and t and take integration:
[tex]\int{e^{-y}cos(y)} \, dy = \int {e^{-t}(1 + t^2)} \, dt[/tex]
Integrate the following:
[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + c\\[/tex]
The initial conditions given are y(0) = 0, substitute the value of the variables as 0:
[tex]\frac{e^{0}}{2} [sin0 - cos0] = -e^{0} [0^2 + 2(0) + 3] + c\\\\\\\frac{1}{2} [-1] = 3 + c[/tex]
c = 5/2
Hence, the solution of the initial value problem is:
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#SPJ4[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex]
15 pt = _______ qt
240
15/16
7 1/2
30
Answer:
7.5qt is the correct answer
find the phase shift of the sin function
y = -2 sin (2x - π/pi)
The phase shift of the sin function , y = -2 sin (2x - π)-3 is =π/-3.
What is phase shift ?Amplitude: The amplitude of a wave is a maximum displacement of a particle from its rest position
Period: The ratio of wavelength to the velocity.
Phase shift: The phase shift represents the amount a wave has shifted horizontally from the the usual position.
here, we have,
The equation of a wave is
f(x) = a sin(bx - c)+d
Where
amplitude = |a|
phase shift = c/d
now,
Given equation of wave is
f(x) =-2 sin (2x - π)-3
Here a=-4, b=2, c = π, d = -3
i.e.
phase shift = c/d
=π/-3
Therefore, phase shift =π/-3.
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Manoj and shira asked to find an explicit formula for the sequence -9, -27, -81, -243.
manoj said the formula is h(n) = -9*3^n, and
shira The formula is h(n) =-3*3^n. Which one of them is right?
A. Only manoj
B. Only shira
C. Both manoj and shira
D. Neither manoj nor shira
Option (A) Only Manoj is the correct answer. the correct formula for the sequence -9, -27, -81, -243 is [tex]h(n) = -9 * 3^n[/tex], as proposed by Manoj.
The formula for a sequence represents a pattern in the terms of the sequence. By finding an explicit formula for a sequence, we can generate any term of the sequence without having to list out all of the terms.
In this case, the sequence -9, -27, -81, -243 follows a pattern where each term is obtained by multiplying the previous term by 3. This can be represented by the formula [tex]h(n) = -9 * 3^n[/tex], where n is the index of the term in the sequence and [tex]3^n[/tex] represents 3 raised to the power of n.
In contrast, Shira's formula [tex]h(n) = -3 * 3^n[/tex] results in a different sequence, -3, -9, -27, -81, which does not match the given sequence.
Therefore, the correct formula for the sequence -9, -27, -81, -243 is[tex]h(n) = -9 * 3^n[/tex], as proposed by Manoj.
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eric walks around a man-made circular lake (pictured above) four times. how far (in miles) has he walked?
The amount of total distance walked has walked by Eric in a man-made circular lake is 75.36 miles.
A circle's circumference is the length of its perimeter. The circumference of a circle can be calculated using length units such as centimeters, meters, or kilometers by opening a circle and measuring the boundary in the same way that we would measure a straight line.
Circumference = D* π
Total distance walked four times = 4.C
= 4 * D * π
= 4 * 6 * 3.14
= 75.36 miles
So, the total distance is 75.36 miles.
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A primary credit cardholder has a current APR of 19.99%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent?
1.67%
0.17%
16.67%
19.99%
Anyone who needs the answer its 1.67%
19.99/12
The monthly Period interest rate is 1.67( nearest hundredth)
What is APR?Annual percentage rate (APR) refers to the yearly interest rate you'll pay if you carry a balance on your credit card. Some credit cards have variable APRs, meaning your rate can go up or down over time.
To convert annual rate to monthly rate, when using APR, simply divide the annual percent rate by 12.
The APR of the card holder is 19.99%
Therefore the monthly Period interest will be calculated as ;
19.99/12
= 1.67% ( nearest hundredth)
therefore the monthly periodic interest is 1.67%
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Two friends shop for fresh fruit. Jackson buys a watermelon for $8.25 and 5 pounds of cherries. Tim buys a pineapple for $2.15 and 4 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more Jackson spent.
please its to tonight at 11:59pm
Answer:
Step-by-step explanation:
Jackson -
8.25 + 5p
Tim -
2.15 + 4p
8.25 - 2.15 = 6.1
5p - 4p = 1p or p
simplified expression
6.1 + p is how much more Jackson spent
(I’m sorry if it’s wrong not 100 percent sure)
the graph to the right shows the relationship between the number of baseballs produced per day, q, and the daily cost of production, c.
The graph shows an inverse relationship between the number of baseballs produced per day and the cost of production. As the number of baseballs produced per day increases, the cost of production decreases.
1. The graph shows a downward-sloping line, which indicates an inverse relationship between the number of baseballs produced per day, q, and the daily cost of production, c.
2. As q increases, c decreases.
3. This inverse relationship means that as the number of baseballs produced per day increases, the cost of production decreases.
The graph shows an inverse relationship between the number of baseballs produced per day and the cost of production. As the number of baseballs produced per day increases, the cost of production decreases.
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The square shape wall whose length is 10m has a door of length 2m and breadth 1m. It also has a window of length 1m and breadth 0.5m. What will be the cost of painting the wall at Rs.5 per meter.
The cost of painting the wall is Rs.48.75 .
How to find the cost to paint the wall?The square shape wall whose length is 10m has a door of length 2m and breadth 1m. It also has a window of length 1m and breadth 0.5m.
Therefore, the cost of painting the wall can be calculated as follows:
cost of painting per meters = Rs0.5 per metre square
Therefore, the area of the wall to be painted will exclude the window and the door.
Hence,
area of wall of the wall to be painted = area of the wall - area of the window - area of the door
Therefore,
area of wall of the wall to be painted = 10² - (1 × 0.5) - (2 × 1)
area of wall of the wall to be painted = 100 - 0.5 - 2
area of wall of the wall to be painted = 97.5 metres²
Therefore,
1 metres square = Rs0.5
97.5 metres squared = ?
cross multiply
cost to paint the wall = 0.5 × 97.5
cost to paint the wall = Rs.48.75
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Is the estimated intercept Bo meaningful in this case? O A. Yes. B. No.
Yes the estimated intercept B meaningful in this case
The estimated intercept, also known as the constant, is the point at which the regression line intersects the y-axis.
In this case, the meaning of the estimated intercept Bo is crucial in understanding the results of the regression analysis.
The intercept represents the expected value of the dependent variable when all independent variables are equal to zero.
In conclusion, the estimated intercept can be a meaningful and valuable tool in regression analysis, but it is important to consider the context of the data and the relationships between the variables before interpreting the results.
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casey and darnell went to the movies a total of 11 times last month. darnell went one less than twice as many times as casey did. how many times did each boy go to the movies last month?
Casey went too movie for 4 times and Darnell went to movie for 7 times.
Casey and Darnell went to the movies a total of 11 times last month, Darnell went one less than twice as many times as Casey did.
Let us say that Casey went to movie for X times,
So, the amount of times that Darnel went for movie is 2X-1
It is given that they went for a total of 11 times.
We can make a simple algebraic equation by using the above data.
X + 2X - 1 = 11
3X = 12
X = 4
So, Casey went to movie for 4 times and Darnell went to movie for 7 times.
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use the properties of logarithms to expand the following expression. logy7xz3
The expanded logarithmic expression is 7log y + log x + 3log z.
The use of a logarithm can be utilised to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Log interpretation is not that tough. It suffices to know that an exponential equation can also be written as a logarithmic equation in order to comprehend logarithms.
Exponent and logarithm are inverses of one another. This is explained in the section below. John Napier, a mathematician, first developed logarithms as a technique to perform computations simply, and other scientists, engineers, etc. immediately embraced this idea.
The given logarithmic equation is:
log ([tex]y^{7}xz^{3}[/tex])
Now, we can use the properties of logarithms to expand this fully.
log (abc) = log a + log b+ log cTherefore,
log ([tex]y^{7}xz^{3}[/tex]) = log ([tex]y^{7}[/tex]) + log (x) + log ([tex]z^{3}[/tex])
log (a²) = 2log aTherefore,
log (y⁷) = 7 log y
log (z³) = 3 log z
Therefore, the expanded logarithmic expression is 7log y + log x + 3log z.
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g(x)= (x+10)^2 find the inverse function
The inverse of the function is given by x=√y-10
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here; g(x)= (x+10)²
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.
Thus y=(x+10)²
√y=x+10
x=√y-10
Hence, The inverse of the function is given by x=√y-10
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the price of an item has been reduced by 15%. the original price was $91 find the price of the item now.
Answer:
77.35
Step-by-step explanation:
I'm sorry because I don't know how to explain it...
Simon, Sarah and Matthew are given a total of £300. They share it in the ratio 10:11:9. How much does each receive?
Based on given ratio of 10:11:9, the share for each person is as follows:
Simon = £100Sarah = £110Matthew = £90.What is ratio?Ratio is the relative size of one value or variable compared to another.
Ratios show how much each quantity is contained in another.
Ratios are fractional values obtained as the quotient of one value divided by another, and are depicted in fractions, decimals, or percentages.
The total shareable amount = £300
The sharing ratio = 10:11:9
The sum of ratios = 30
Simon's share = £100 (10/30 x £300)
Sarah's share = £110 (11/30 x £300)
Matthew's share = £90 99/30 x £300)
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a group of eight kids lines up in random order. each ordering of the kids is equally likely. there are five girls and three boys in the group. what is the probability that all the boys are ahead of all the girls?
Using the arrangements formula, it is found that there is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.
The number of possible arrangements of the n elements is the factorial of n, that is:
[tex]A_{n} = n![/tex]
The total number of outcomes is the arrangement of 8 elements, hence:
T = 8! = 40320
The desired number of outcomes is all-girls(5!), then all-boys(3!), hence:
D = 5! × 3! =120× 6=720
Hence, the probability is:
p = D/T =720/40320 = 0.0178
There is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.
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use the method of corners to find the point(s) that maximize the objective function p = 3x y
For the function P = 3x + y, there is no solution present to maximize it.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The given objective function -
P = 3x + y
Subjected to the constraints -
5x + 7y ≥ 35
3x + 4y ≤ 12
x ≥ 0, y ≤ 0
First consider the inequality 5x + 7y ≥ 35.
The equation of the above inequality is as follows -
5x + 7y = 35
Find two points that satisfies the above equation.
Take x = 0, then -
5(0) + 7y = 35
7y = 35
y = 5
The first point is (0,5).
Take y = 0, then -
5x + 7(0) = 35
5x = 35
x = 7
The second point is (7,0).
Substitute (x,y) = (0,0) and see the direction of the region for 5x + 7y ≥ 35.
5(0) + 7(0) ≥ 35
0 ≥ 35
This is not true.
Therefore, the region is non-origin side.
Now consider the inequality 3x + 4y ≤ 12.
The equation of the above inequality is as follows -
3x + 4y = 12
Find two points that satisfies the above equation.
Take x = 0, then -
3(0) + 4y = 12
4y = 12
y = 3
The first point is (0,3).
Take y = 0, then -
3x + 4(0) = 12
3x = 12
x = 4
The second point is (4,0).
Substitute (x,y) = (0,0) and see the direction of the region for 3x + 4y ≤ 12.
3(0) + 4(0) ≤ 12
0 ≥ 12
This is true.
Therefore, the region is origin side.
Plot the graph.
From the graph it can be seen that there are no corner points and no feasible region.
Therefore, there is no solution for the function.
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Ethan and enoch hare a reward of $133 in a ratio of 2:5. How much doe each boy get?
So, Ethan gets $38 and Enoch gets $95.
We can find the amount each boy gets by using the ratio to find how much of the total $133 reward belongs to each.
Since the ratio is 2:5, this means that for every 7 parts, 2 of those parts belong to Ethan and 5 of them belong to Enoch.
So, if we divide the total reward of $133 into 7 equal parts, each part would be $133 / 7 = $19.
Since Ethan is entitled to 2 parts of the reward, he would get $19 x 2 = $38.
And since Enoch is entitled to 5 parts of the reward, he would get $19 x 5 = $95.
So, to summarize:
Ethan gets $38
Enoch gets $95
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So, Ethan gets $38 and Enoch gets $95.
We can find the amount each boy gets by using the ratio to find how much of the total $133 reward belongs to each.
Since the ratio is 2:5, this means that for every 7 parts, 2 of those parts belong to Ethan and 5 of them belong to Enoch.
So, if we divide the total reward of $133 into 7 equal parts, each part would be $133 / 7 = $19.
Since Ethan is entitled to 2 parts of the reward, he would get $19 x 2 = $38.
And since Enoch is entitled to 5 parts of the reward, he would get $19 x 5 = $95.
So, to summarize:
Ethan gets $38
Enoch gets $95
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Shawn's Pizzeria made 5 pizzas with pepperoni and 18 pizzas without pepperoni. What is the ratio of the number of pizzas with pepperoni to the number of pizzas without pepperoni?
Answer: 5 : 18 = 10 : 36
Step-by-step explanation:
The ratio is already in lowest terms so we found an equivalent ratio by multiplying both terms by 2.
Answer:
5 to 18
Step-by-step explanation:
precalculus and i dont understand it much
The equation of the graph is (a) [tex]\frac{2x^2-8}{x^2+x-6}[/tex]
How to determine the equation of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph and the list of options
Next, we test the graph with the options
On the graph, we have:
f(0) = 1.3
f(-1) = -1
From the list of options, the equation that has the above properties is option (a)
Hence, the equation is (a)
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6. Consider the ordered pairs.(0,0) (1.5,4.5) (3,9) (4.5,13.5). Write two rules. One for the x terms in the given ordered pair and one for the y terms. Describe the relationship between the corresponding terms.
the rule for x terms is 1.5x - 1.5 and the rule for y terms is 4.5y - 4.5.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given, the ordered pairs.(0,0) (1.5,4.5) (3,9) (4.5,13.5)
For x term:
The rule for x term that is 0, 1.5, 3, 4.5
First term = 0
difference = 1.5
From the general formula of Arithmetic sequence:
an = a + (n – 1)d.
thus,
Equation = 0 + (x -1 ) d
Equation = 1.5x - 1.5
For y term:
The rule for y term that is 0, 4.5, 9, 13.5
First term = 0
difference = 4.5
From the general formula of Arithmetic sequence:
an = a + (n – 1)d.
thus,
Equation = 0 + (x -1 ) d
Equation = 4.5x - 4.5
Therefore, The x-term rule is 1.5x-1.5, while the y-term rule is 4.5y-4.5.
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Help please, I was not in class when the lesson was happening and now I’m very confused.
Thank you :)
11. The measure of ∠EBF = 20°
12. The measure of ∠DBE = 32°.
13. The measure of ∠GBC = 56°.
What is the angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given that m∠EBF = 60°, m∠EBG = 2m∠EBF
The m∠EBF is the sum of the angles and the angles are m∠EBG and m∠EBF.
Therefore,
m∠EBF = m∠EBG + m∠EBF
Putting m∠EBF = 60° and m∠EBG = 2m∠EBF in aboue equation:
60° = 2m∠EBF + m∠EBF
3m∠EBF = 60°
Divide both sides by 3:
∠EBF = 20°.
12.
Given that, m∠ABE = 64°.
From the diagram, m∠ABD = m∠DBE.
The m∠ABE is the sum of the angles and the angles are m∠ABD and m∠DBE.
m∠ABE = m∠ABD + m∠DBE
64° = 2m∠DBE
Divide both sides by 2:
m∠DBE = 32°
13.
Given that, m∠GBH = 28°.
From the diagram, m∠GBH = m∠HBC.
m∠HBC = 28°.
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Complete the table for different values of x in the polynomial expression -7x^2 +32x+240. Then, determine the optimal price that the taco truck should sell its tacs for. Assume whole dollar amounts for the tacos
If the taco truck were to sell its tacos for $1, it would earn a profit of $267. However, if they were to sell their tacos for $-1, they would incur a loss of $202.
[tex]x | -7x^2 + 32x + 240[/tex]
[tex]-1 | -7(-1)^2 + 32(-1) + 240 = 6 + 32 - 240 = -202[/tex]
[tex]0 | -7(0)^2 + 32(0) + 240 = 240[/tex]
[tex]1 | -7(1)^2 + 32(1) + 240 = -5 + 32 + 240 = 267[/tex]
The optimal price that the taco truck should sell its tacos for is $0. This is because when x is equal to 0, the value of the polynomial expression is at its highest point. This means that the taco truck will earn the most profit when they sell their tacos for $0.
However, it is important to note that this is not a realistic scenario and the taco truck would need to sell its tacos for a positive whole dollar amount.
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Li and Amber are writing number patterns. Both patterns start at 2. Li uses the rule "Add 1, then multiply by 3." Amber uses the pattern "Add 2, then multiply by 2." Write the first five ordered pairs with an x-coordinate representing the number Li's pattern and the y-coordinate representing the corresponding numbers in Amber's pattern.
Based on the information provided the coordinates would be
What is Li's sequence?To know her sequence, let's apply the rule given"Add 1, then multiply by 3"
2 + 1 = 3 x 3 = 9
3+1 = 4 x 3 =12
4 +1 = 5 x 3 =14
5 + 1 = 6x3 = 18
What is Amber's sequence?Let's apply the rule given "Add 2, then multiply by 2"
2+ 2 = 4x2= 8
3+2= 5x2= 10
3+3= 6x 2= 12
4+3=7x 12 = 14
Based on this, the coordinates are (2,2), (9,8), (12,10), (14,12), (18,14).
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Describe the relationship you would expect between the data. Explain.
1. age of the automobile and the odometer reading
The age of the automobile and the odometer reading will be in direct proportion and both variables will have a strong positive correlation.
What is the age of Automobiles:The age of automobiles indicates the lifetime of the Automobiles from their manufacturing day to the present workday. For example, if the car was made in 2010 and working till 2020 then the age of the car will be 10 years.
Odometer reading:Odometer is a machine or instrument which is used to calculate the distance traveled by a vehicle in its lifetime. The reading of the Odometer shows the distance covered by the car in the number of milages.
Here the more age of the automobile increases the more the distance covered by the automobile will increased hence the reading of the Odometer will increase.
As we know in mathematics, if two quantities are in relation such as one quantity is increased then the other quantity will also increase then two quantities are said to be in Direct proportion.
So here we can conclude that the age of the automobile and the odometer reading will be in direct proportion Since both are increases both variables will have a strong positive correlation.
Therefore,
The age of the automobile and the odometer reading will be in direct proportion and both variables will have a strong positive correlation.
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what is the ordered pair for -5x + y = -10
Answer:
x = (2, 0), y = (0, -10)
There are 30 tudent in cla 8B. 3 tudent tudy both German and French. 12 tudent tudy only German. 15 tudent tudy only French
Answer:
Step-by-step explanation:
1. Total number of students in class 8B: 30
2. Number of students studying both German and French: 3
3. Number of students studying only German: 12
4. Number of students studying only French: 15