Based on the information provided, the archaeological sample's estimated age is = 0.214136 years
Half life given is 5730
t₆.₅ = Ln2/k
k= ln 2/ 5730
The rate constant ,
k = 0.00012 year⁻¹
Given that 23 % of the 14C remains
then |A1|/|A2| = 0.23
As we know ,
|A1|/|A2| = e ⁻₍kt₎
Hence, on solving the equation we get ,
ln(0.23)= -1.46967
t = -0.31471/ --1.46967
= 0.214136 years
The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay).
The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite life's in exponential growth is time's doubling.
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Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that is also compounded semiannually at 10%. At the end of six years, the balance in Merle's account is (use the tables in the handbook):
A.
$73,604.00
B.
$53,604.00
C.
$80,406.00
D.
$98,636.72
E.
None of these
The correct option D. $98,636.72; is the amount in Merle's account after six years.
Explain the term compounded semiannually?Interest compounded semiannually indicates that its compound interest rate is determined on the bases of the principal combined with the outcomes of the compound interest rate as from previous term's computation, and this will occur twice a year.The formula for the compound interest is-
A = P * (1 + r/nt)^nt
In which,
A = amount after compounding.P = principal amountr = rate of interestt = total time in yearsn = number of time amount compoundedFrom the beginning to end of the third year:
A = P(1 + 0.05 )^6
A = 40,000 × 1.05^6
A = $53,603.83
Now, add $20,000 to the amount obtained.
A = $53,603.83 + $20,000
A = $73,603.83
Thus, at the end of sixth year:
A = 73,603.83 x 1.05^6
A = $98,636.16
Therefore, the balance in Merle's account after six years is $98,636.16.
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Mr. Lincoln is making slime for his kindergarten class. He has 3 cups
of glue. Each batch of slime uses 2/3 cup of glue. How many batches
of slime can Mr. Lincoln make? Show your work
In linear equation, 5 batches of slime can Mr. Lincoln make.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Based on the given conditions, formulate = 3 ÷ 2/3
= 3 * 3/2
= 3 * 3/2
= 9/2
the smallest integer greater than or equal to = 9/2 : 5
= 5
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A ladder is leaning against a vertical wall makes an angle of 20° with the ground. The foot of the ladder is 3 m from the wall. Find the length of ladder (Round to the nearest whole number).
If you choose the 20 degree acute angle, the distance between the foot of the ladder and the wall represents the [Select] leg. Since we are given the [Select] leg and solving for the hypotenuse, we need to use [Select] to solve for the length of the ladder. The length of the ladder when solved is [Select] meters.
Options for blank #1: adjacent, opposite, hypotenuse
Options for blank #2: adjacent, opposite, hypotenuse
Options for blank #3: sine, cosine, tangent
Options for blank #4: 3, 1, 9, 4
The length of the ladder is approximately 3 m. The correct option is the first option 3
Calculating the length of a ladderFrom the question, we are to calculate the length of the ladder.
From the given information,
The ladder makes an angle 20° with the ground
and
The foot of the ladder is 3 m from the wall
This scenario gives a right triangle where the hypotenuse is the ladder and the adjacent is the distance of the foot of the ladder from the wall.
Let the length of the ladder be x
Thus,
Using SOH CAH TOA
We can write that
cos 20° = 3 / x
x = 3/(cos 20°)
x = 3.19
x ≈ 3 m
Hence, the length is approximately 3 m
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An agent is paid a commission of 2% on the total sales in a year and a bonus of 0.5% on the excess of sales over Rs. 9,00,000. Find how much he receives as commission if the bonus amounts is Rs. 1500.
Ans:Rs.42500
The amount of commission the agent receives if the bonus amount is Rs. 1,500, is Rs. 24,000.
How the commission is computed:To find the commission received by the agent, we first determine the excess sales using the bonus rate and bonus amount.
The excess sales are added to Rs. 900,000 to determine the total sales for the year.
The commission rate is applied to the total sales to ascertain the amount of the commission the agent received.
Commission on the total annual sales = 2%
Bonus on the excess of sales over Rs. 900,000 = 0.5%
Bonus amount = Rs. 1,500
Excess sales over Rs. 900,000 = Rs. 300,000 (Rs. 1,500/0.5%)
Total sales = Rs. 1,200,000 (Rs. 900,000 + Rs. 300,000)
Commission amount = Rs. 24,000 (Rs 1,200,000 x 2%)
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I NEED HELP ASAP!!
Alex rides his bike to visit two
friends and returned home. Interpret the graph to answer questions about his activities.
1. How long did it take Alec to get to his friends house?
2. How long did he stay at his first friends house?
3. How long did it take alec ti ride his bike from his first friends house to his second friends house?
4. How much longer did alec stay at his first friends house than at his second friends house?
5. In which parts of the graph is alec riding his bike toward his home?
6. In which parts of the graph is alec traveling the fastest?
7. How long was alec away from his house?
Answer:
1 hour
Step-by-step explanation:
Answer: 1hour
Step-by-step explanation: lol
In ΔWXY, \overline{WY} WY is extended through point Y to point Z, \text{m}\angle YWX = (3x+17)^{\circ}m∠YWX=(3x+17) ∘ , \text{m}\angle XYZ = (10x-5)^{\circ}m∠XYZ=(10x−5) ∘ , and \text{m}\angle WXY = (3x+2)^{\circ}m∠WXY=(3x+2) ∘ . Find \text{m}\angle WXY.m∠WXY
The value of ∠WXY = 20.
What is Exterior angle theorem?
The exterior angle theorem describes the connection between the two remote angles in a triangle and the external angle created by an extended side outside the triangle.
Given: Measure of angle YWX = (3x + 17) °
Measure of angle WXY = (3x + 2) °
Measure of angle XYZ = (10x − 5) °
Therefore, m∠XYZ = m∠YWX + m∠WXY (exterior angle theorem)
⇒ (10x − 5) ° = (3x + 17) ° + (3x + 2) °
Solve for x,
⇒ 10x - 5 = 3x + 17 + 3x + 2
⇒ 10x - 6x = 17 + 7
⇒ 4x = 24
⇒ x = 6
∴ ∠WXY = (3x + 2) = 18 + 2 = 20
Hence, value of ∠WXY = 20.
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The tree diagram represents an
experiment consisting of two trials.
.5 - A - A - .4 - c
.5 - B - .3 - c
.7 - D
P(A) =
Answer:
P(A) =0.5 obviously since it didn't say like P(AC) or P(AD)
what is the potential difference between the center of the sphere and the surface of the sphere?
Possible distinction between the center of the sphere and surface of the sphere is
A notable distinction is made by the fact that the surface is three-dimensional, while the sphere's centre is a (non-dimensional) point, and that their values are independent of one another.If the sphere is a conducting hollow sphere, its centre and surface have the same potential. A perfect conductor has no electric field at all.A dielectric sphere's core has zero potential, while the surface has a potential of KQ/(R).The sphere is one of the most significant mathematical figures. Spheres and nearly-spherical objects can be seen in both nature and industry.
Soap bubbles and other bubbles have a spherical shape when they are in an equilibrium state. The celestial sphere is a fundamental concept in astronomy, and the Earth is usually represented as spherical in geography.
The majority of pressure vessels, curved mirrors and lenses, and other manufactured items are based on spheres. Because spheres roll effortlessly in all directions, the majority of balls used in sports and toys are spherical, just like ball bearings.
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we want to test the hypothesis: the fraction of people with severe depression is higher in country a than in country b. we have chosen the statistic of interest to be (fraction of depressed people in country a divided by fraction in country b). we call this ratio r. what is the null hypothesis?
The null hypothesis is R = 0
In this question we have been given a hypothesis that the fraction of people with severe depression is higher in country a than in country b.
We need to test the hypothesis.
Suppose that we have chosen the statistic of interest to be PAPB.
Let the ratio R be the fraction of depressed people in country a divided by fraction in country b
We need to find the null hypothesis.
We know that the null hypothesis as statement says that there is no relationship between two measured variables/phenommena.
In this case, for null hypothesis the ratio must be zero.
Therefore, for given situation the null hypothesis is R = 0
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The complete question is:
We want to test the hypothesis: the fraction of people with severe depression is higher in country A than in country B.
We have chosen the statistic of interest to be PAPB (fraction of depressed people in country A divided by fraction in country B). We call this ratio R.
What is the null hypothesis?
Group of answer choices
1 R=0
2 R=1
f(x) = x + 1, and g(x) = 2x.
then
g(f(x)) = [? ]x+[?]
Answer: 2x + 2
Step-by-step explanation:
The composition of two functions f and g, denoted g(f(x)), is a new function that is obtained by substituting the function f(x) into the function g(x) in place of x.
In this case, f(x) = x + 1 and g(x) = 2x. Substituting f(x) into g(x) in place of x gives us g(f(x)) = 2(x + 1) = 2x + 2.
Therefore, the final expression for g(f(x)) is 2x + 2. The coefficient of x is 2, and the constant term is 2.
Differentiate implicitly to find dy/dx. 2x^2+8xy+6y^2+13y-2=0 dy/dx= Find dy/dx using implicit differentiation. 3x^3=2y^2-9y dy/dx= Use implicit differentiation to find dy/dx. 3y^2=5x-2/5x+2 dy/dx
The first derivative of the implicit functions are listed below:
y' = - 4 · (x + 2 · y) / (8 · x + 12 · y + 13) y' = 9 · x² / (4 · y - 9) y' = 23 / (30 · y)How to use implicit differentiation
In this problem we have an implicit function of the form f(x, y) = 0, whose first derivative shall be found by implicit differentiation. Now we proceed to present the procedure. First, write the entire expression:
2 · x² + 8 · x · y + 6 · y² + 13 · y - 2 = 0
Second, use the derivative rules:
4 · x + 8 · y + 8 · x · y' + 12 · y · y' + 13 · y' = 0
4 · x + 8 · y + (8 · x + 12 · y + 13) · y' = 0
y' = - 4 · (x + 2 · y) / (8 · x + 12 · y + 13)
The same procedure is used in the next two implicit functions:
3 · x³ = 2 · y² - 9 · y
9 · x² = 4 · y · y' - 9 · y'
9 · x² = (4 · y - 9) · y'
y' = 9 · x² / (4 · y - 9)
3 · y² = 5 · x - (2 / 5) · x + 2
6 · y · y' = 5 - 2 / 5
6 · y · y' = 23 / 5
y' = 23 / (30 · y)
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Find the value of x.
Answer:
[tex]120^{\circ}[/tex]
Step-by-step explanation:
Using the exterior angle theorem, [tex]x=50^{\circ}+70^{\circ}=120^{\circ}[/tex].
Answer:
Step-by-step explanation:
we know the inside total angles for triangle is 180 degrees.
We are given the two internal angles as 70 and 50 degrees.
So the equation can be written as
70+50+y = 180
y= 60
Also, we know that straight line is 180 degrees. Now we can write the second equation as follow:
60+x = 180
x = 120 degrees
please help me find the answer
Answer:
the last one is obviously represent a linear of function
Evaluate the expression.343 ^ { 4 / 3 }
In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. the expression.343 ^ { 4 / 3 } is 7,625
In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 = 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.The expression 343^ {4/3} can be broken down into 343 to the power of 4 divided by 3. Before we evaluate the expression, we must understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 can be calculated using the formula 343 x 343 x 343 x 343. This results in 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.
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a campfire girls troop has 14 members. in how many different ways can the leader appoint 3 members to clean up camp?
The leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp in 364 ways.
The number of members in the campfire girls troop
= 14
The number of members the leader of the campfire girls troop can appoint at a time = 3
The number of ways to appoint r members out of n members
= nCr = n!/(r)!×(n-r)!
Therefore, the number of ways in which the leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp
= 14C3 = 14!/(3)!×(14-3)! = 364 ways
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EASY 7TH-GRADE MATH
You mix 1/4
cup of red paint for every 1/2
cup of blue paint to make 3 gallons of purple paint.
a. How much red paint do you use? How much blue paint do you use?
Question 2
b. You decide that you want to make light purple paint. You make the new mixture by adding 1/4
cup of white paint for every1/4
cup of red paint and 1/2
cup of blue paint. How much red paint, blue paint, and white paint do you use to make 1 1/2
gallons of the lighter purple paint?
PLEASE HELP THIS IS OVER DUE
The amount of red paint used is 3/4 gallons
The amount of blue paint used is 1 1/2 gallons.
The amount of red paint used is 3/8 gallons
The amount of blue paint used is 3/4 gallons
The amount of white paint used is 3 /8 gallons
How much of each paint was used?In order to determine the quantity of each type of paint needed, multiply the fraction of each type of paint used by the total gallons of purple paint.
Amount of red paint used = 1/4 x 3 = 3/4 gallons
Amount of blue paint used = 1/2 x 3 = 3/2 = 1 1/2 gallons
The quantity of each type of paint used to make the lighter purple shade:
Amount of red paint used = 1/4 x 1 1/2
1/4 x 3/2 = 3/8 gallons
Amount of blue paint used = 1/2 x 3/2 = 3/4 gallons
Amount of white paint used = 1/4 x 1 1/2
1/4 x 3/2 = 3 /8 gallons
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Find X and Y I WILL MARK BRAINLIEST
Answer:
x = 40°
y = 35°
Step-by-step explanation:
Let us take two triangles ∆ABC and ∆ADE
We know that, in a triangle the sum of all angles is equal to 180°
So,
For the traingle ABC
m∠A = 80°m∠B = 60°m∠C = x°Now,
m∠A + m∠B + m∠C = 180°
80° + 60° + x° = 180°
140° + x° = 180°
x° + 140° - 140° = 180° - 140°
x = 40°
For the triangle ADE
m∠A = 80°m∠D = 65°m∠E = y°Now,
m∠A + m∠D + m∠E = 180°
80° + 65° + y° = 180°
145° + y° = 180°
y° + 145° - 145° = 180° - 145°
y = 35°
Thus, The value of x and y is 40° and 35° respectively
Data that are left-skewed would include:
O values that are unusually low.
O values that are unusually high.
O values that are symmetrically distributed.
O values that are all less than the median.
Data that are left-skewed would include values that are unusually high.
What is meant by symmetry of data?A data is symmetric when it has a mirror image on both sides of the mean. For a symmetric data the mean = mode = median.
What is left-skewed data?If the data is asymmetric, it can either be left-skewed or right-skewed. A left-skewed data has mots of its values greater than the mean. In this case the mean < median < mode. Left-skewed data mostly contains very less amount of values with smaller magnitudes.
Hence, data that are left-skewed would include values that are unusually high.
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Michael picks cucumbers from his garden and bags them up to give to his neighbors. He starts with 40 bags of cucumbers and gives out 8 bags per hour until there are none left. Use the Segment tool to plot a graph representing the number of bags of cucumbers Michael has left to give away from the time he starts giving them away until he has no bags left.
You would start at points (0, 40) and then move to (1, 32), (2, 24), (3, 16), (4, 8), and (5, 0) because he gives out 8 bags per hour.
What is a line graph?
An informational shift over time is graphically represented by a line graph. It is a graph that was created by connecting points with line segments.
Michael starts with 40 bags of cucumbers and gives out 8 bags per hour until there are none left.
Michael starts giving them away until he has no bags left.
To create the graph we need coordinate points to locate on the graph.
So initially he has 40 bags and gives away 8 bags for every 1 hour.
The number of bags will be represented on the y-axis, and the number of hours will be represented on the x-axis.
The coordinates are:
x-axis y-axis
0 40
1 32
2 24
3 16
4 8
5 0
Hence, you would start at points (0, 40) and then move to (1, 32), (2, 24), (3, 16), (4, 8), and (5, 0) because he gives out 8 bags per hour.
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Match the plot with a possible description of the sample.
60 70 80 90 100
Choose the correct answer below
A. Wait time (in minutes) for a sample of doctors offices
B.Ages (in years) of a sample of residents of a retirement home.
C. Highest yearly temperatures (F) for a sample of deserts.
D. Time (in hours_ spent watching TV in a day for a sample of teenagers.
Ages (in years) of a sample of retirement home inhabitants is option B. For the lowest wait time, the maximum frequency is anticipated to be right-skewed. A desert cannot have a maximum annual temperature of 60°F, and it is not conceivable to watch 60+ hours of TV in a single day.
Residents of senior living facilities are typically 84 years old. While there are many couples in these communities, the majority of people who live in independent living are women. Some people move in at or near the minimum age (often around 65), but most people do so between the ages of 75 and 84. Residents come from all different backgrounds.
Many people are choosing senior living in a community environment, including teachers, nurses, small business owners, big business CEOs, university professors, housewives, lawyers, engineers, musicians, and more. Current residents will attest that the rich diversity of origins fosters amazing interactions and relationships. And contrary to popular belief, the majority of residents of independent living are quite active.
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Correct Question:
Match the plot with a possible description of the sample.
60 70 80 90 100
Choose the correct answer below
A. Wait time (in minutes) for a sample of doctors offices
B. Ages (in years) of a sample of residents of a retirement home.
C. Highest yearly temperatures (F) for a sample of deserts.
D. Time (in hours_ spent watching TV in a day for a sample of teenagers.
The table shows values for functions f(x) and g(x) .
x=-2
x=-1
x=0
x=1
x=2
The solution to the equality of the functions f(x) and g(x) are;
At x = 0 and x = 1
How to find the point where the functions are equal?We are given the functions as;
f(x) = 3ˣ and g(x) = 2x + 1
Now, we want to find the point at which the functions f(x) and g(x) are equal. This is;
f(x) = g(x)
Thus, from the graph, we can see that;
When x = 0, f(x) = 1 and g(x) = 1
Similarly, when x = 1, f(x) = 3 and g(x) = 3
Thus, these are the points where f(x) is equal to g(x)
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how to find asymptotes of a rational function
Step-by-step explanation:
you devide the upper half of a fraction with the part under it. for example
6x2+x+1
_______=6. that is asymptote
x2+2
when you multiply 6 and lower half of a fraction you get 6x2+12
if you substract that from 6x2+x+1 you get x-11
if you make x-11=0 the number that x represents is the point where the function crosses the asymptote
Please help. Math- Thank you
The simplified expression, when using the Quotient rule is b. 1 / 8⁴.
What is the Quotient Rule ?The Quotient Rule allows us to be able to carry out operations on quotients. The rule is such that when dividing quotients with the same base, you should subtract the quotients. For multiplication, you add the quotients.
8 ⁵ / 8 ⁹ will therefore be:
= 8 ⁵ ⁻ ⁹
= 8 ⁻⁴
8 ⁻⁴ is the equivalent of 1 / 8⁴ because when a number is taken to a negative power, then that number becomes a denominator to 1.
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The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes 8 hours for a car moving at 45 mph How long does the trip take for a car moving at 30 mph?
Time ∝ 1/Speed
Time = k/Speed
k = Time x Speed
The time taken for the trip for the car moving at 30 mph is 12 hours.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 7 is an equation.
We have,
Time ∝ 1/Speed
This can be written as,
Time = k/Speed
k = Time x Speed
Now,
The trip takes 8 hours for a car moving at 45 mph.
This means,
k = 8 x 45
k = 360
Now,
The time taken at the speed of 30 mph.
Time = k / Speed
Time = 360/30
Time = 12 hours
Thus,
The time taken for the trip for the car moving at 30 mph is 12 hours.
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Evaluate the iterated integral. The first integral is 0 to 2 and the second integral is 2 to 3. xy^2 dx dy. Please show step by step with detail. Thanks
The value of the iterated integral is equal to 24. In general, when evaluating iterated integrals, it is important to remember to integrate with respect to the outer variable first, and then with respect to the inner variable. This will ensure that the resulting value of the integral is correct.
To evaluate this iterated integral, we need to integrate with respect to the outer variable first, and then with respect to the inner variable. In this case, the outer variable is x and the inner variable is y.
We can write the iterated integral as:
∫₀² ∫₂³ xy² dx dy
To find the value of this integral, we first need to evaluate the inner integral with respect to x. We can do this by taking the integral of xy² with respect to x from 0 to 2, which gives us:
∫₀² xy² dx = [x³y² / 3]₀² = (2³ * 3²) / 3 = 24/3
Now that we have found the value of the inner integral, we can evaluate the outer integral with respect to y. We can do this by taking the integral of 24/3 with respect to y from 2 to 3, which gives us:
∫₂³ (24/3) dy = [24y / 3]₂³ = (24 * 3) / 3 = 24
Therefore, the value of the iterated integral is equal to 24.
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what is the rate of change?
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{50}~,~\stackrel{y_1}{45})\qquad (\stackrel{x_2}{70}~,~\stackrel{y_2}{61}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{61}-\stackrel{y1}{45}}}{\underset{run} {\underset{x_2}{70}-\underset{x_1}{50}}} \implies \cfrac{ 16 }{ 20 } \implies {\Large \begin{array}{llll} \cfrac{4 }{ 5 } \end{array}}[/tex]
what is the probability that a person selected at random will live on campus or have a low intention of attending the fair?
The probability that a person selected at random will live on campus OR have a low intention of attending the Fair is 0.584.
The data of Intention of Attending the Fall Career Fair is given below:
High Medium Low TOTAL
On Campus 99 102 22 223
Off Campus 78 80 43 201
>20 mi. Away 18 32 26 76
TOTAL 195 214 91 500
We have to find the probability that a person selected at random will live on campus OR have a low intention of attending the Fair.
Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = P(on campus) + P(low) - P(on campus and low)
Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 223/500 + 91/500 - 22/500
Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 292/500
Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 0.584
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The right question is:
The data shown below is for a sample of LSU students to evaluate their intention of attending the Fall 2023 Career Fair based on where they live.
Intention of Attending the Fall Career Fair
High Medium Low TOTAL
On Campus 99 102 22 223
Off Campus 78 80 43 201
>20 mi. Away 18 32 26 76
TOTAL 195 214 91 500
What is the probability that a person selected at random will live on campus OR have a low intention of attending the Fair?
What equals number nineteen
13+16 are the numbers that equals to 19.
What is equal number?The equal sign in the mathematics describes by equality between the values,. Of the equations, or expressions are the written on both sides. There symbol for equal to is two be the small horizontal lines placed to parallelly. We place the to the 'equal to' sign is between two things that are to the same or equal.
As we know,
If two things are equal or if one thing is equal to the another, they are the same or in the size, number, standard, or values .
As per the question we have to find equal number of 19.
So 13+6 are the equal number that equals to 19.
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1. The line of best fit for a data set is y = 1.1x + 3.4. Find the residual for each of the coordinate pairs, (x, y).
a. (5,8.8)
b. (2.5,5.95)
c. ((0,3.72)
d. (1.5,5.05)
e. (-3,0)
f. (-5,-4.86)
The residual for each of the coordinate pairs, (x, y) are-
a) -3.1; b) -0.2; c) 0.32; d) 0; e) -0.1; f) -6.96.
Explain the term line of best fit?A straight line which minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis as well as a tool for forecasting indicators and price changes.For the stated question;
Data is given by the line of best fit as;
y = 1.1x + 3.4
Then, the residual for the given coordinates are found as;
Residual = y - (1.1x + 3.4)
a. (5,8.8)
Residual = 5.8 - (1.1(5) + 3.4)
Residual = -3.1
b. (2.5,5.95)
Residual = 5.95 - (1.1(2.5) + 3.4)
Residual = -0.2
c. ((0,3.72)
Residual = 3.72 - (1.1(0) + 3.4)
Residual = 0.32
d. (1.5,5.05)
Residual = 5.05 - (1.1(1.5) + 3.4)
Residual = 0
e. (-3,0)
Residual = 0 - (1.1(-3) + 3.4)
Residual = -0.1
f. (-5,-4.86)
Residual = -4.86 - (1.1(-5) + 3.4)
Residual = -6.96
Thus, the residual for each of the coordinate pairs, (x, y) are found.
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write an equation for the graph shown in the form $y=ax b.$
The required straight equation will be y = -0.5x + 27.5 passes through the points (-5, 0) and (5, 2).
What are equations in a straight line?
A straight line's equation is given by y=mx+c, where c is the height at which the line intersects the y-axis (often referred to as the y-intercept) and m is the gradient.
According to the given graph,
We can see two points are (-5, 0) and (5, 2)
The linear equation will be: y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Here
x₁ = -5, y₁ = 0
x₂ = 5, y₂ = 2
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
Substitute values in the equation, we get
⇒ y - 0 = (2 - 0)/(8-4)(x-(-5))
⇒ y - 30 = (2)/(-4)(x + 5)
⇒ y - 30 = -1/2(x + 5)
⇒ y = (-1/2)x - 5/2 + 30
⇒ y = -0.5x + 27.5
Thus, the required equation will be y = -0.5x + 27.5 passes through the points (-5, 0) and (5, 2).
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Write an equation for the graph shown in the form y=ax+b.
