The expected value is 160 and SE for the number of students in the sample is 9.78
a)Given: students of which 25000 of which 10000 are older than 25 and 25000-10000=15000 are not older than 25.
we represent 400 students by drawing 400 tickets from a box that contains 15000 tickets labeled 0 and 10000 tickets labeled 1
Expected value and standard deviation of a box:
First, we determine the expected value of the box, which is the sum of all values on the tickets by the number of tickets.
[tex]expected value box=\frac{15000*0+10000*1}{25000}\\\\ =\frac{10000}{25000} =\frac{2}{5}[/tex]
expected value box=0.4
let us next determine the standard deviation using the shortcut formula:
SD=(big number-small number)*√fraction with small number*fraction with a small number.
[tex]SD=(1-0)*\sqrt{\frac{10000}{25000} *\frac{15000}{25000} \\\\SD=1*\sqrt{\frac{2}{5} *\frac{3}{5} } \\SD=1*\sqrt{\frac{6}{25} } =\frac{\sqrt{6} }{5}[/tex]
SD=0.4899.
Expected value sum=Number of draws*expected value box
=400*0.4
Expected value sum=160
standard error of the sum is the product of the square root of the number of draws and the standard deviation of the box.
SE Sum=√number of draws*SD box
SE Sum=√400*0.4899
=20*0.4899
SE Sum=9.78
b)EXpected value and standard error:
The expected value of the percentage is the expected value of the sum divided by the number of draws.
Expected value percentage=Expected value sum/Number of draws*100%
160/400*100
=0.4*100%
Expected value percentage=400%
The standard error of the percentage is the standard error for the sum divided by the sample size:
SE%=SE for number/Number of draws*100%
=9.798/400*100%
=0.0245*100%
SE% =2.45%
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to serve one person at a local restaurant it takes 10 minutes to serve pot five people it takes 18 minutes right and solve an equation to find the number of minutes it will take to serve a party of eight
By finding an evaluating a linear equation we will see that it takes 24 minutes to serve a group of 8 people.
How long takes to serve a party of eight?
Let's assume that the relation between the number of people and the time it takes to serve them is linear.
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
Here we have two points:
1 person, 10 minutes, written as (1, 10)
5 people, 18 minutes, written as (5, 18)
Then the slope is:
a = (18 - 10)/(5 - 1)
a = 8/4 = 2
Then the linear equation is:
y = 2x + b
To find the value of b, we can replace the values of one of the points, I will use (1, 10) so we will get:
10 = 2*1 +b
10 = 2 + b
10 - 2 = b
8 = b
The linear equation is:
y = 2x + 8
For 8 customers, the time will be:
y = 2*8 + 8
y = 24
It will take 24 minutes to serve 8 people.
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(7,5), (x, 2); m =
3
Answer: (6,2)
Step-by-step explanation:
(7,5) (x,2) m=3 x=?
y=mx+b
y=3x+b (1)
To find the coefficient b we take the coordinate that belongs to this line (7,5): x=7 y=5
5=3(7)+b
5=21+b
5-21=21+b-21
-16=b
Thus, b=-16
Hence, y=3x-16
To find the x we take the coordinate that belongs to this line (x,2): y=2
2=3x-16
2+16=3x-16+16
18=3x
Divide both parts of the equation by 3:
6=x
Thus, x=6
Find the equation of the line with slope 0 and passing through (-5,16). Write the equation in standard form.
Lines with a slope of zero can be thought of as y = 0x + b, which simplifies to just "y = b".
In this case, your equation is y = 16.
If you want to force it explicitly into standard form, you could write it at
0x + 1y = 16
The figures shown below are similar and the labeled sides are corresponding.
If the perimeter (P₂) of figure 2 is 25 ft then what is perimeter (P₂) of figure 1?
P1=feet
The Perimeter of the Pentagon in Figure 1 is 40ft
What is Pentagon?
A pentagon is a two-dimensional polygon having five sides and five angles. "Penta" means "five," and "gon" means "angles" in Greek, therefore when we mix the two words "penta + gon," we obtain the term "pentagon."
Solution:
Permieter of Pentagon = 5 * side
In Figure 1, the length of a side is 8 ft,
Then the Perimeter will be 8*5 = 40ft.
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In choosing what music to play at a charity fund raising event, Cory needs to have an equal number of piano sonatas from Haydn, Mozart, and Schubert. If he is setting up a schedule of the 15 piano sonatas to be played, and he has 52 Haydn, 18 Mozart, and 21 Schubert piano sonatas from which to choose, how many different schedules are possible? Express your answer in scientific notation rounding to the hundredths place.
Answer: Cory can have 6 different schedules
Step-by-step explanation:
Add them all together and divide by fifteen
If A and B are independent events with P(A)=0.5 and P(B)=0.1, find P(A AND B).
The probability of event A and event B of the independent events will be 0.05.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the conditional probability is given as,
P(A and B) = P(A) x P(B)
Event A and event B are independent events. The probability of event A is 0.50 and the probability of event B is 0.10.
Then the probability of event A and event B of the independent events is given as,
P(A and B) = P(A) x P(B)
P(A and B) = 0.50 x 0.10
P(A and B) = 0.05
The probability of event A and event B of the independent events will be 0.05.
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any help on this question
Using law of logarithm and exponent rules, the value of the unknown is 5
Logarithmlogarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2.
Logₐ x = n or aⁿ = x
Where b is the base of the logarithmic function.
This can be read as “Logarithm of x to the base b is equal to n”.
In this case, we just need to solve for the value of b
4 = logₐ(625)
4 = 1 / log625(a)
multiply both sides by log₆₂₅(x)
log₆₂₅(a) / 4 = 1/4
applying log rules
a = 5
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Which additional piece of information would show that quadrilateral W X Y Z is a rhombus?
The additional fact that would prove that quadrilateral WXYZ is a parallelogram is '' XY = YZ''.
What is quadrilateral ?
A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.
Properties include: There are four vertices . There are four sides . 360° is the total of all interior angles. There are two diagonals in them.
Trapezium is one of the five unique quadrilateral shapes. Parallelogram. Rectangle. Rhombus. Square
These bisectors intersect each other at 90 degrees.
And it means that they are perpendicular.
Since they are perpendicular, we find that there 4 congruent triangles, XY is parallel to WZ, and WX is parallel to YZ.
Additionally, opposite angles are equal.
These two latter findings are the characteristics of the parallelogram.
Hence, the additional fact that would prove that quadrilateral WXYZ is a parallelogram is '' XY = YZ''.
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What is the equation in slope-intercept form of the line that passes through the points (6,1) and (3,3)?
y=−2/3x+5y
y=−2/3x−10y
y=2/3x+2y
y=2/3x−2
The equation in slope intercept form of the line that passes through the points (6,1) and (3,3) is y = - 2 / 3 x +5
How to find equation in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation in slope-intercept form of the line that passes through the points (6,1) and (3,3) can be represented as follows;
let's find the slope
m = 3 - 1 / 3 - 6
m = - 2 / 3
Hence, let's find the y-intercept as follows;
using (3, 3)
y = - 2 / 3 (x) + b
3 = - 2 / 3 (3) + b
3 + 2 = b
b = 5
Therefore, the equation of the line is y = - 2 / 3 x +5
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what is the importance of knowing the history of the earth
Knowing the history of the Earth is of the utmost importance to understand how it got to now and to know where we are going.
¿What is the history of the Earth?The history of the Earth is nothing more than the set of events, occurrences and phenomena that the same happened from its origin to the present.
Knowing the history of the Earth is very important because:
It gives us knowledge about the development of the Earth and different associated elements.It allows us to understand different elements of the universe. It allows us to study and analyze different events associated with man and life.¡Hope this helped!
Answer:
The history of the Earth is nothing more than the set of events, occurrences and phenomena that the same happened from its origin to the present.
5(g + 8) - 7 = 117 - g = 14
14 is the answer
Parts of a Right Triangle
In a right triangle, the sides that meet to form the
right angle are called the legs. The side opposite the
right angle is called the hypotenuse. The hypotenuse is
always the longest of the three sides. It is important
that you can correctly identify the sides of a right tri-
angle, regardless of what position the triangle is in.
leg
leg
60
1. Name the legs.
Practice
AABC is a right triangle.
TRIANGLES AND THE PYTH
hypotenuse
leg
leg
hypotenuse
hypotenuse
2. Name the hypotenuse.
leg
leg
APQR is a right triangle.
3. Name the legs.
4. Name the hypotenuse.
AHLM is a right triangle.
5. Name the legs.
6. Name the hypotenuse.
Review of Squares
and Square Roots
Before you study the Pythagorean theorem, le
first review squares and square roots. Just like add
tion and subtraction are inverses, so are squares
and square roots. In other words, they "undo" e
other. To square a number, you multiply it by itsel
For example, 52 means two factors of 5, or 5 times
5, which is 25. Written algebraically, it looks
this: 52= 5 x 5 = 25. A common mistake is to s
that you multiply by 2, since 2 is the exponent (the
small raised number). But the exponent tells you
how many times to multiply the base (bot
number) by itself.
Twenty-five is a perfect square. It can be writer
as the product of two equal factors. It would be he
1) The legs of △ABC are AB and BC.
2) The name of hypotenuse is AC.
3) The legs of △PQR are PR and RQ.
4) The name of hypotenuse is PQ.
5) The legs of △HLM are LH and ML.
6) The name of hypotenuse is MH.
What is a triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The right angle of △ABC is ∠ABC. Thus AB and BC meet at right angle. Therefore AB and BC are legs of △ABC.
The opposite side of ∠ABC is AC. Therefore the hypotenuse is AC.
The right angle of △PQR is ∠PRQ. Thus PR and RQ meet at right angle. Therefore PR and RQ are legs of △PQR.
The opposite side of ∠PRQ is PQ. Therefore the hypotenuse is PQ.
The right angle of △HLM is ∠HLM. Thus HL and LM meet at right angle. Therefore HL and LM are legs of △HLM.
The opposite side of ∠HLM is MH. Therefore the hypotenuse is MH.
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you have a bag of ping pong balls. you arrange all but 2 of the balls in an equilateral triangle. then you put all the balls back into the bag and create a new equilateral triangle where each side has one more ball than the first arrangement but this time you are 11 balls short. how many balls were in the first arrangement?
Answer:
The “edge” effect of a tetrahedral container with edge length of 1,000 mm would be 2*r*√3 (r = radius of ball, see diagram below). For a ping pong ball with a diameter of 40 mm, the edge effect would be 2*20*√3 = 69.28 mm. Subtract that from 1,000 mm and you get 930.72 mm of “available space” along the bottom row. Divide 930.72 mm by 40 mm per ball and you get 23.27. So you wouldn’t be able to fit 24 balls along the base, you’d only be able to fit 23 balls. With 23 balls, the total number that a tetrahedron could contain (T) would be T = n(n+1)(n+2)/6 = 2,300 balls, not 2,600.
C
18. Andrew works at Grub Burger and earns
$8.00 an hour. Create a graph of the
relationship between x, the number of hours
and y, the total amount Andrew earns. Then
write an equation to represent the relationship.
EARNINGS ($)
50
45
40
30
25
20
15
10
5
1 2 3 4 5 6 7 8 9 10
HOURS
The graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.
What is the graph of the equation?
The graph of an equation is the group of all points on a number line or the coordinate plane that are solutions of an equation (= statement that two amounts are equal).
0 hours- $0
4 hours- $32
8 hours- $64
12 hours- $96
First find the equation of this problem to represent the relationship, which is y = 8x.
Next, you substitute the number of hours into x to get y, which is the amount of money.
Hence, the graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.
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Determine the value for m in the equation 1.3m = 0.78.
A. 10.14
B. 6.50
C. 0.60
D. 0.06
Answer:
0.60
Hope this helps, I believe in you!
Answer: The answer is C 0.60
Step-by-step explanation:
Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)=(x²-64)^{1/11} on the domain [-8,9]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The absolute maximum is , which occurs at x= (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.)
B. There is no absolute maximum.
The critical points for the equation [tex]f(x)=(x^{2} +64)^{\frac{1}{11} }[/tex] is
[tex](x,f(x))[/tex] = [tex](0,2^{\frac{6}{11} })[/tex] = [tex](0,1.46)[/tex]. at x=0
The absolute maximum is at [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] = [tex](9,1.6)[/tex], at x=9.
What is the absolute maximum of an equation?
The highest conceivable values for f are represented by the absolute maximum (sometimes called the global maximum) of a function f(x) (x). Let's imagine the function's critical value, x=c, is present within its domain. If the inequality f(c) [tex]\geq[/tex] f(x), x is a domain, then the function f(x) is said to satisfy an absolute maximum when x=c.
To find the critical points, we find the value of f'(x) and equate to 0.
[tex]\frac{d}{dx} (\sqrt[11]{x^{2}+64} )=0[/tex]
we get x=0.
We see that f'(x) exists for all x between [-8,9].
We also find the endpoints, that is -8 and 9.
Then we calculate f(x) at critical points and endpoints.
We calculate f(x) at 0, -8, and 9.
We get,
for x=0, f(x)= [tex]2^{\frac{6}{11} }[/tex]
for x=-8, f(x)= [tex]2^{\frac{7}{11} }[/tex]
for x=9, f(x)= [tex]\sqrt[11]{145}[/tex]
We see that the value is maximum at x=9, and f(x) becomes [tex]\sqrt[11]{145}[/tex].
Hence we get the absolute maximum is [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] = [tex](9,1.6)[/tex]
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There were 202 tickets sold during the first hour of sales for the opening match of the
World Cup. Tickets for the cheap seats cost $50, and the best seats cost $556. Use algebra
to find out how many tickets of each type were sold if the total receipt was $42,990,
Answer:
137 cheap tickets sold, and 65 best seats sold
Step-by-step explanation:
x+y=202
50x+556y=42900
x=202-y
50(202-y)+556y=42900
10100-50y+556y=42900
10100+506y=42900
506y=32890
y=65
x=202-65
x=137
x= Cheap tickets, y= expensive tickets
Which of the following algebraic steps will solve the equation -6t = 2/3 and what is the solution?
Answer:
C. DIvide both sides by -6 to get 1/9.
Step-by-step explanation:
Kim ran a 26-mile marathon.
She ran 1/7 of the marathon during
the first hour. How many miles did
Kim run during the first hour?
Answer:3.71 miles
Step-by-step explanation:
Write the linear equation in slope-Intercept form that passes through the given points.
4. (1.3) and (-3,-5)
6. (-12, 14) and (6,-1)
5. (1, 4) and (6, -1)
Answer:
1.3,-12,16
Step-by-step explanation:
A circle has a circumference of 20 m.
Work out the radius of the circle.
Give your answer correct to 1 decimal place.
The required radius of the circle is given as 3.18 m.
Given that,
A circle has a circumference of 20 m. the radius of the circle is to be determined.
Perimeter is the measure of the figure on its circumference.
Here,
The perimeter of the circle = 20m
2πr = 20
r = 20/2π
r = 3.18 m
Thus, the required radius of the circle is given as 3.18 m.
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Solving distance, rate time problem
A total of 396 miles and 2.2 hours will pass between the two trains on the Long.
How to calculated the Distance and rate time?For additional information on how to handle rate-time-distance or motion problems, scroll down the page.
Moving away from one another are the two trains.
85x + 95x = 396
To solve you combine like terms. The like terms are 85x and 95x
85x + 95x = 180x
Right now, you
180x = 396
Now multiply by 180.
180 divided by 396 equals 2.2.
X= 2.2
That's how you do things, in my opinion.
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1.) ΔECD ≅ ΔECX
CD=?
By the congruence property CD ≅ CX
Congruent examples include what?
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Which five types of congruence are there?
If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) (RHS).
Given that:
ΔECD ≅ ΔECX
so ED ≅ EX
CD ≅ CX
by the congruence property
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A lioness has 4 cubs that weigh 1.7 kg, 2.1 kg, 3 kg, and 2.7 kg. Each cub eats 1.25 kg of food a day. How much food will be needed to feed all the cubs for one year?
The quantity of food that would be needed to feed all the cubs for one year is 1825 kg
Calculating the quantity of food that would be needed to feed cubsFrom the question, we are to determine how much food would be needed to feed all the cubs for one year
From the given information,
"Each cub eats 1.25 kg of food a day"
Assume there are 365 days in a year.
Since there are 4 cubs,
The quantity of food that would feed the cubs for one year = 365 × 4 × 1.25
The quantity of food that would feed the cubs for one year = 1825 kg
Hence, the quantity of food needed is 1825 kg
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TEXT ANSWER
An airplane has stopped to refuel. Fuel is being added to the plane's gas tank at a constant
rate. After 13 minutes, there are 32,882 gallons of fuel in the plane; after 31 minutes, there
are 34,902.5 gallons in the plane. Write the y = mx + b equation that describes this
scenario.
W
You can refer to time 31:05 in the video above for a solution to a very similar example.
Please show your work below.
H
Normal
Enter your answer here
√x
E BIUS X₁ X²
22 Ix
Practice.
A JA
The function in f(t) form that describes the amount of fuel in the plane at time t will be:
f(t) = 112.25t + 31.425.75
What is the Equation of line?
The equation of the line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
we have given that;
After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Now,
Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (32882 - 34902.5) / ((31 - 13)
m = 2020.5 / 18
m = 112.25
Thus, The equation of the line with slope 112.25 is,
⇒ y - 32885 = 112.25 (x - 13)
⇒ y - 32885 = 112.25x - 1459.25
⇒ y = 112.25x - 1459.25 + 32885
⇒ y = 112.25x + 31.425.75
Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be:
f(t) = 112.25t + 31.425.75
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Given dy/dt=2y and y(2)=200. Find y(7).
The required value of y(7) is given as y (7)= 4412711.8.
Given that,
Given dy/dt=2y and y(2)=200.
The action of bringing concurrently shorter components into a single system that acts as one is known as integration.
Here,
dy/dt = 2y
dy/y = 2dt
integrate,
logy = 2t + c
[tex]y = e^{2t + c}[/tex]
put t = 2 and y = 200
C = 1.3
Now,
[tex]y= e^[2t + 1.3][/tex]
Substitute t = 7
[tex]y= e^[14 + 1.3]\\y = e^{15.3}[/tex]
y = 4412711.8
Thus, the required value of y(7) is given as y (7)= 4412711.8.
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I need help
Arc QR =
Arc RS=
QPS =
PSR =
SRQ =
Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:
Arc QR = 48°
Arc RS = 96°
Arc QPS = 216°
Arc PSR = 186°
Arc SRQ = 144°
What is the Inscribed Angle Theorem?The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.
Find arc PSR:
Arc PSR = 2(93) [based on the inscribed angle theorem]
Arc PSR = 186°
Find arc QR:
Arc QR = 360 - arc PQ - arc PSR
Substitute
Arc QR = 360 - 126 - 186
Arc QR = 48°
Arc RS = arc PSR - arc PS
Arc RS = 186 - 90
Arc RS = 96°
Arc QPS = 126 + 90
Arc QPS = 216°
Arc PSR = arc PS + arc RS
Arc PSR = 90 + 96
Arc PSR = 186°
Arc SRQ = arc RS + arc QR
Arc SRQ = 96 + 48
Arc SRQ = 144°
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Answer: 48 96
Step-by-step explanation:
Arc QR = 360 - 126 - 186
Arc QR = 48°
Arc RS = arc PSR - arc PS
Arc RS = 186 - 90
Arc RS = 96°
Given ΔPHS ≅ ΔCNF, find the values of x, y, and z.
In the given congruent triangle ΔPHS ≅ ΔCNF, the values of x, y, and z are 24° , 37/3° , 61/4° respectively
What is a congruent triangle ?
The meaning of congruent in Maths is addressed to those figures and shapes that can be repositioned or flipped to coincide with the other shapes. These shapes can be reflected to coincide with similar shapes.
Two shapes are congruent if they have the same shape and size. We can also say if two shapes are congruent, then the mirror image of one shape is the same as the other.
Two triangles are said to be congruent if their sides have the same length and angles have same measure. Thus, two triangles can be superimposed side to side and angle to angle.
In mathematics, the term "congruent" refers to figures and forms that may be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes. If two forms are similar in size and shape, they are congruent. We may also state that if two forms are congruent, then their mirror images are identical .Triangles that line up. A triangle is a closed polygon with three line segments that intersect at each of its three angles.
When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles may be placed side by side and angle by angle on top of one another.
Since both the triangles are congruent this means the side , angles of both the triangles are equal
therefore,
∠ H = ∠ N
∠ S = ∠ C
∠ P = ∠ F
which means,
6x-29° = 115°
6x=144°
x=24°
∠ S = 180° - ∠ H - 36°
∠ S = 180°-6x+29°-36°
∠ S = 173°-6x
173°-6x=4z-32°
173°-144°+32° = 4z
61/4° = z
3y-1° = 36°
y= 37/3°
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can someone help me with this thank you
Step-by-step explanation:
we know that the two angles with x are equal since they are made with the same lines
so
8x+36=5x+51
solve for x
a. subtract 36 from both sides
8x=5x+15
b. subtract 5x on both sides
3x=15
c. divide by 3
x=3
now to find z
we know a line equals 180
so
(8x+36)+z=180
plug in 3
8(3)+36+z=180
24+36+z=180
60+z=180
z=120
The table represents some points on the graph of a linear function.
Which equation represents the same relationship?
x-2y-1=0
2x-y +7=0
y+3= 1/2 (x - 5)
y-15 = 2(x-31)
The equation that represents the same relationship is equation 1: x-2y-1=0
How to find the equation?We should know that an equation is a mathematical statement that shows the equality of two sides o a statement.
From the given equation:
x-2y-1=0
If we input the various values of x such as -5, 7,31,42 into the equation we are going to obtain the corresponding values of y as indicated in the table
x-2y-1=0
Rewrite the equation
x-1=2y
⇒2y=x-1
=2y=-5-1
y=-3
Also, 2y=7-1
2y=6
y=3
Input the value 31 into the equation or x
2y=31-1
2y=30
y=15
Input the value 45 or x in the equation
2y=45-1
2y=44
y=22
In conclusion, the equation x-2y-1=0 represents the the same relationship in the table
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