Answer:
Step-by-step explanation:
Work for finding the equation, feel free to skip it:
So first off, to write the equation, we will use an equation in slope intercept form: y = mx + b, where y is the numbers of pages she has read, m is the number of pages she reads per hour, x is the number of hours she read, and b is the number of pages she has already read.
To find the slope(The number of pages she reads per hour), we can subtract the number of pages she had read at 2 hours from the number of pages she had read at 4 hours:
297 - 195 = 102.
This tells us she read 102 pages over 2 hours. Thus, over 1 hour, she had read 102/2 = 51 hours. This is m. So our equation so far is y = 51x + b
To find b, we can take 195(the pages she had read after 2 hours), and subtract it by the pages she can read over 2 hours(51 * 2), giving us the amount of pages she had already read(b):
195 - (51*2) = 195 - 102 = 93.
So our equation is:
y = 51x + 93.
Work for finding how many hours it will take Kya to read the whole book:
Y is the total number of pages Kya has read when we plug in x hours. However, if we already know the total number of pages in a book, we can plug in that number for Y, and then solve for x to find how many hours it takes for Kya to read the book:
399 = 51x + 93
Subtracting 93 from both sides gets us:
51x = 306
=
x = 6
This means it takes 6 hours for Kya to read the whole book.
Since Kya has already been reading for 4 hours, the time she has left is:
6-4 = 2
So it takes Kya 2 more hours to finish reading the 399 pages in the book.
Hope this helps!
What is a power of 3 equation called?
A power of 3 equation is called as cubic equation.
The term equation in math is known as a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Here we need to find the term that has been used for power of 3 equation.
Here we have to know that the power of 3 equation is known as cubic equation.
in other terms the polynomial equation which has a degree of three is called a cubic polynomial equation or trinomial polynomial equation.
As we all know that the power of the variable is the maximum up to 3, therefore, we get three values for a variable, say x.
The general form of the power of 3 equation is written as
=> ax³ + bx² + cx + d = 0
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Question
To be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
What is the maximum time (in seconds) that she can take on her last lap and still make the team?
The maximum time (in seconds) that she can take on her last lap and still make the team will be 52 seconds.
How to calculate the mean?From the information, to be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
The maximum time (in seconds) that she can take on her last lap and still make the team will be:
= (60 × 5) - (63 + 62 + 65 + 58)
= 300 - 248
= 52
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Write the equation of a line that is perpendicular to y=14x - 4 and passes through the point (28, 16)
Write a linear function for the values given in the table below
A function whose equation is of the form y = ax + b, where a and b are constants, a does not equal zero, and x is any real number, and whose graph is a straight line.
Given an equation y = 14x -4 there is an equation that is perpendicular to this given equation.
from the slope-intercept of a linear equation:
The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.
thus the slope of the given equation is 14
The slope of the required equation = 1/14
Since both equations are perpendicular
From the slope intercept of the required line equation of a line:
y = 1/14x + c...(2)
Since, it passes through the point (28, 16)
Thus, 16 = 1/14 *28 + c
c = 16
from equation 2
y = 1/14 x + 14
from the table, two given coordinates of a linear function are (4, 36) and (6, 56)
thus slope of the line = (y₂ - y₁) / (x₂ - x₁)
Slope of the line = 20/2 = 10
Equation of a line:
y = 10x +c
Since, it passes through the point (4, 36)
Thus, 36 = 40 + c
c = -4
Therefore, the required equation from the table is y = 10x - 4
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Does anyone know the question to this ?? :(
Answer:
The ratio of the new area to the old area will be 16:1
Step-by-step explanation:
I remember learning this in class. The radius is quadrupled, which means the radius is 4 times bigger. This will make the new area 16 times bigger than the old area.
Let's check
Area of circle: 3.14 x r^2
Area of the circle when radius 6:
3.14 (6)^2 = 113.04 ft^2
Area of the new circle when the radius is quadrupled:
3.14 (24)^2 = 1808.64 ft^2
1808.64 divided by 113.04 = 16
So, the ratio of the new area to the old area will be 16:1
how do i do this question
Answer: Okay this is the formula for slope: y=mx+b 2 would be the slope and -1 would be the y intercept so select b.
Step-by-step explanation:
Which area model represents the factorization x2+3x+2=(x+2)(x+1)?
The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)
What is an equation?An equation is an expression that shows how numbers and variables relate with each other.
A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.
The standard form of a quadratic equation is:
y = ax² + bx + c
where a, b and c are constants.
Given the polynomial:
x² + 3x + 2
Factorizing the polynomial:
x² + 2x + x + 2
= x(x + 2) + 1(x + 2)
= (x + 1)(x + 2)
The factorization gives (x + 1)(x + 2)
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I need help.
professional?
- needed
The equation of the linear function after a translation down 9 units is given as follows:
f(x) = x - 11.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the y-intercept, representing the value of y at which the graph cross the y-axis.The graph of the function crosses the y-axis at y = -2, hence the intercept b is given as follows:
b = -2.
When x increases by 2 units, from x = 0 to x = 2, y increases by 2 units, from y = -2 to y = 0, hence the slope is calculated as follows:
m = 2/2.
Then the function is of:
y = x - 2.
After the translation down 9 units, 9 is subtracted from the function, hence:
f(x) = x - 2 - 9
f(x) = x - 11.
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5. It takes a truck 4 hours to drive 240 miles. What was the truck's miles per hour? How far would the truck go in 1 days (think carefully)?
Answer:
Step-by-step explanation:
a.4 hours drive 240 miles, so the speed is 240÷4=60 miles per hour
b.1 days have 24 hours, then, it will go 60 ×24 = 1440 miles in 1 days
Answer:
1440
Step-by-step explanation:
240+4= 60
distance = rt
r= rate
t = time
IN ONE DAY
60 times 24= 1440
(24 for 24 hours)
The cost of an online newspaper is 7. 99 per month. If you buy a one year subscription the cost is 89. 88. How much do you pay each month if you choose the one year subscription
If we chosen the one year subscription we have to pay 7.49 per each month.
What is Linear Equation ?
Linear Equation can be defined as the equation in which the highest degree of the variable is one.
Given,
The cost of an online newspaper is 7.99
And if we bought the one year subscription the cost is 89.88
Let the the cost of the each month if we bought the one year subscription be x .
for one year the cost is 89.88
for one month could be
that is, x = 89.88/12
x = 7.49
Hence , If we chosen the one year subscription we have to pay 7.49 per each month.
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The price of an item has dropped to $42 today. Yesterday it was $60 . Find the percentage decrease.
Answer:
70% Decrease
Step-by-step explanation:
70% Decrease
The percentage decrease in price of an item is 30 %
Step by step solution:
The percentage decrease in price = [(original value - decreased value)/original value]*100
percentage decrease[tex]=\frac{(original value - decreased value}{original value} * 100[/tex]
percentage decrease=[tex]=\frac{60 - 42}{60} *100[/tex]
[tex]=\frac{18}{60} *100[/tex]
[tex]=0.3 *100[/tex]
30 %
Therefore, the percentage decrease in price of an item is 30 %
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Can I add myself on Wikipedia?
One cannot add themselves directly to Wikipedia as this can cause harm to the platform and community in a later run. As one can start adding content and details on the page based on their personal opinions.
Therefore we can say that the answer is that we cannot edit or create our own Wikipedia page, because that would be a conflict of interest ,more on this later.
But the thing which one can do is to add themselves in the line ,to list themselves on Wikipedia’s repository of articles which are out there looking for creators who can help maintain the site.
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Parabola Skate Rental rents skate boards for $4.50 per hour with a rental fee of $35. Arc Hawk Skate Rental rents skate boards for $5.25 per hour with a rental fee of $25.
Give an example when renting from Parabola's would be a better deal than renting from Arc of Hawk's? Justify your answer.
An example of when renting from parabolas would be a better deal than renting from Arc of Hawk's is when the rental period is 8 hours.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
The total cost of renting parabolas would be 8 × $4.50 + $35 = $43.
The total cost of renting from Arc Hawk's would be 8 × $5.25 + $25 = $45.75
So Parabola is cheaper by $2.75
In general, any rental period of 8 hours or less would be a better deal with Parabola's, as per hourly rate is cheaper and the rental fee is higher than Arc Hawk but still, the total cost is lesser.
As the rental period increases beyond 8 hours, the per-hour rate difference becomes negligible and Arc Hawk becomes cheaper.
It is important to compare the cost for the same rental period, to accurately determine which rental company offers a better deal.
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Consider your construction of pentagon ABCED. What segments, if any, are perpendicular? Explain how you made your determination
Answer:
Sine AB is perpendicular to sides AE and BC/
Step-by-step explanation:
The slope is the change in y over the change in x.
Line segment AE has a slope of 3/4
(0,4)(4,7)
The y values are 7 and 4.
The x values are 4 and 0.
You find the change by subtracting
[tex]\frac{7-4}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]
Line segment BC has the same slope
((3,0)(7,3)
The y values are 3 and 0.
The x values are 7 a d 3.
You find the change by subtracting
[tex]\frac{3-0}{7-3}[/tex] = [tex]\frac{3}{4}[/tex]
Since line segments Ae and BC has the same slope. They are parallel.
Line segments that are perpendicular will have opposite reciprocals slopes. In this case the slope should be - [tex]\frac{4}{3}[/tex].
Let's look at line segment AB
(0,4)(3,0)
The y values are 0 and 4.
The x values are 3 and 0.
You find the change by subtracting
[tex]\frac{0-4}{3-0}[/tex] = [tex]\frac{-4}{3}[/tex]
Since the slopes are opposite reciprocals, side AB is perpendicular to sides AE and BC
Blair bought 3 1/6 pounds of nuts and 1 5/6 pounds of milk, what is total weight of the nuts and milk that Blair bought
Answer:
Step-by-step explanation:
3 [tex]\frac{1}{6}[/tex]
+ 1 [tex]\frac{5}{6}[/tex]
_______
4 [tex]\frac{6}{6}[/tex] = 5 pounds
[tex]\frac{6 }{6}[/tex] = 1 add this to the 4 and you have 5 pounds total
Solve for x in this triangle. Round your answer to the nearest tenth. 17 х° 6
Answer:
x ≈ 70.6°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{17}{6}[/tex] , then
x = [tex]tan^{-1}[/tex] ( [tex]\frac{17}{6}[/tex] ) ≈ 70.6° ( to the nearest tenth )
The function f is defined by f(x) = x^2 + 3x - 10. If f(x-2) = x^2 + bx + c, what are the values of b and c?
______________________________
When you put the answer could you put the steps that you took, so I could use it on other problems
Thanks
Distributive Property
Factoring
FOIL (First Outside Inside Last)Functions
Function NotationApplicationStep 1: DefineLet's organize what is given to us in the problem.
We are given a function f, defined as f(x) = x² + 3x - 10.
We are asked to find the values of b and c in f(x - 2) = x² + bx + c.
Step 2: SolveIn order to solve the question, we first must find the full function of f(x - 2):
[tex]\displaystyle\begin{aligned}f(x - 2) & = (x - 2)^2 + 3(x - 2) - 10 \\& = \underbrace{x^2 - 4x + 4}_{\text{FOIL}} + \underbrace{3x - 6}_{\text{Distribute}} - 10 \\& = \boxed{ x^2 - x - 12 } \\\end{aligned}[/tex]
∴ [tex]\displaystyle \boxed{ f(x - 2) = x^2 - x - 12 }[/tex]
Now, we can correlate our variables to the f(x - 2) function by comparing them side-by-side:
[tex]\displaystyle\begin{aligned}f(x - 2) & = x^2 - x - 12 \\& = x^2 + bx + c \\& \Rightarrow \boxed{ b = -1 ,\ c = -12 }\end{aligned}[/tex]
∴ we have found the values of b and c.
Answer∴ the value of b is equal to -1 and the value of c is equal to -12.
___
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___
Topic: Algebra I
Unit: Factoring
In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequencies of students from each grade who participate in the community service activity.
According to the given bar chart options A, B and C are the correct.
How do you find relative frequency?Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.
Given that, the bar chart shows the relative frequencies of students from grades 6 to 12 who participate in the community service activity.
Relative Frequency = Subgroup frequency/ Total frequency.
Relative Frequency = f/ n.
From the given bar chart we can see that
The maximum number of participating students was in grade 9.
The number of participating students in grade 6 was equal to the number of participating students in grade 7.
The relative frequency of all participating students in grades 6 and 7 combined was 0.60.
Therefore, options A, B and C are the correct answers.
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Complete question is in attachment:
in macy's department store, every item has a 30% discount or markdown. If the original price of a pair of Adidas sneakers cost $140, how much would the final price of the sneaker be after the discount is taken off
$98 is the final price of the sneaker be after the discount is taken off
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that in macy's department store, every item has a 30% discount or markdown.
The original price of a pair of Adidas sneakers cost $140
We need to find the final price of the sneaker be after the discount is taken off
Let us find 30% of 140
Convert 30% to decimal value by dividing with 100
30/100×140
0.3×140=42
So 30% of 140 is 42.
After removing discount the amount will be 140-42=98
Hence, $98 is the final price of the sneaker be after the discount is taken off
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Arya has 5 cupcakes and wants to
share them with 8 friends equally.
How many cupcakes will each frien
receive?
Each friend of Arya will receive 0.625 cupcakes.
To divide 5 cupcakes equally among 8 friends, we can use simple division. We would divide the total number of cupcakes (5) by the total number of friends (8) to find the number of cupcakes each friend would receive. In this case, 5 divided by 8 is equal to 0.625. This means that each friend will receive 0.625 cupcakes. However, since cupcakes are not divisible it is not possible to divide 5 cupcakes equally among 8 friends. In this case, either Arya will have to make more cupcakes or they will have to decide on a different way to divide the cupcakes.
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Use the number line to find the difference of-3(-1.5).
Answer:
=4.5
Step-by-step explanation:
the rule is
positive - negative changes to positive + positive so
3- (-1.5) changes to 3 + 1.5 which equals 4.5
(-2) (-3) less greater than equal than 8- (-2)
The true statement is 6 less than 10
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
(-2) (-3) less greater than equal than 8- (-2)
We start by evaluating each expression
So, we have the following representation
(-2) (-3) = 6
8- (-2) = 10
Substitute the known values in the above equation, so, we have the following representation
6 less greater than equal than 10
6 is less than 10
So, we have
6 less than 10
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Convert 12 m/s in
to km/h
By using the conversion factor: 1 km/h = 0.277778 m/s, we get 12 meter per second is equal to 43.2 km/h.
What is velocity?Velocity is a vector quantity that represents the rate of change of an object's position. It is defined as the displacement of an object divided by the time it takes for that displacement to occur. In other words, velocity tells you how fast an object is moving in a certain direction.
What is the unit and formula for velocity?The standard unit for velocity is meters per second (m/s) or kilometers per hour (km/h) in the International System of Units (SI). In imperial system of units, it is expressed in feet per second (ft/s) or miles per hour (mph).
The formula for velocity is:
velocity = displacement / time
To convert 12 m/s to km/h, you can multiply 12 by the conversion factor:
12 m/s * (1 km/h / 0.277778 m/s) = 43.2 km/h
So 12 meters per second is equal to 43.2 kilometers per hour.
Another way to do the conversion is by applying the formula :
Speed (km/h) = Speed (m/s) x 3.6
12 x 3.6 = 43.2
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The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 15 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours
Over the course of the three hours, 41.25 gallons of water passed through the pipe in total.
We know that the rate of flow for the first hour was 50% slower than the rate of flow for the second hour. So, if the rate of flow in the second hour was 15 gallons per hour, the rate of flow in the first hour would be:
15 gallons/hour * (100% - 50%) = 15 gallons/hour * 50% = 7.5 gallons/hour
We also know that 25% more water flowed through the pipe in the third hour than in the second. So the rate of flow in the third hour would be:
15 gallons/hour * (1 + 25%) = 15 gallons/hour * 1.25 = 18.75 gallons/hour
To find the total number of gallons of water that flowed through the pipe during the entire three hours, we can multiply the rate of flow for each hour by the number of hours:
First hour: 7.5 gallons/hour * 1 hour = 7.5 gallons
Second hour: 15 gallons/hour * 1 hour = 15 gallons
Third hour: 18.75 gallons/hour * 1 hour = 18.75 gallons
Adding these values we can find the total amount of water that flowed through the pipe during the entire three hours
7.5 gallons + 15 gallons + 18.75 gallons = 41.25 gallons
So, in total 41.25 gallons of water flowed through the pipe during the entire three hours.
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PLEASE HELP ME WITH PROBLEM C
1) The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average rate of 3/4 feet per year.
a) Write an equation in Slope-Intercept form to represent the growth of the trees over time. Let x represent the number of years and let y represent the height (in ft.) of the tree.
Y=3/4x+3
b) What does the y-intercept represent in your equation
Y=3. 3 stands for feet tall
c) Determine the height of the tree in 3 years.
a) To write an equation in slope-intercept form to represent the growth of the Magnolia trees over time, we can use the formula y = mx + b, where x represents the number of years, y represents the height of the tree in feet, m represents the slope (or rate of growth) of the tree, and b represents the y-intercept (or the height of the tree at x = 0).
In this case, the slope (m) of the tree is 3/4 feet per year and the y-intercept (b) is 3 feet, as the trees are initially 3 feet tall when they are purchased. Plugging these values into the formula gives us:
y = (3/4)x + 3
This equation represents the growth of the Magnolia trees over time.
b) The y-intercept of an equation in slope-intercept form represents the value of y when x is equal to 0. In this case, the y-intercept of the equation y = (3/4)x + 3 is 3 feet. This means that when x is equal to 0 (when no years have passed), the height of the tree is 3 feet.
c) To determine the height of the tree in 3 years, we can substitute 3 for x in the equation y = (3/4)x + 3 and solve for y. This gives us:
y = (3/4)(3) + 3
= 9/4 + 3
= 21/4
= 5.25 feet
Therefore, the height of the tree in 3 years is approximately 5.25 feet.
A farmer plants corn and wheat on a 180-acre farm
The farmer needs to sow 135 acres of corn and wheat, and 45 acres of wheat.
What is linear equation ?A linear equation is the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "linear equation in two variables" is the term used to describe the previous sentence, where y and x are variables. Two variables make up bivariate linear equations. Examples include the linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
180 acres total land area
The corn acres should be C.
The wheat acres should be W.
A 180-acre property is planted with wheat and corn by a farmer.
Equation 1: C + W = 180
Corn is grown on three times as many acres as wheat:
Equation 2 is created by substituting C = 3W into Equation 1. The result is:
45 acres is W.
For corn, 135 acres equals C.
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Josefina wants to prove that figures d and d are similar.
What seguence of transformation could Josefina perform to prove the figures are similar?
The left shift required to translate from D to D" is 6 units and scale factor for dilation of D" from D' is 2.5.
What is Scale factor?The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.
Compare the corresponding vertex of the given figures.
It is given as,
(-5, 0) → (1, 0)
It can be concluded that the graph of D is shifted (1 - (-5)) = 6 units towards left.
The scale factor is given as,
Length of side of D" ÷ Length of side of D'
⇒ 10 ÷ 4 = 2.5
Hence, the required shift and the scale factor are obtained as 6 units and 2.5 respectively.
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can anyone solve it use translation if found necessary.
On solving the provided, we can say that - here in graphs by solving the equation - [tex]x^2 + y^2 = > 2^2 = > 4[/tex]
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
here from graph,
x= 0
and y = 2
so, in equation
[tex]x^2 + y^2 \\2^2\\4\\[/tex]
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A wheelchair ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 23-foot ramp, to the nearest tenth of a degree, if its fi nal height is 6 feet.
The angle of elevation of the ramp is 28.6 degrees.
If the ramp's final height is 6 feet, calculate the ramp's angle of elevation to the nearest tenth of a degree.The angle of elevation of the ramp is the angle formed by the ramp to the horizontal ground.It is also known as the angle of inclination. To find the angle, the following equation is used:Tan = (Change in Height) / (Length of Ramp)
Therefore, using the given information, the angle of elevation of the 23-foot ramp is:
Tan = (6 feet) / (23 feet)
Tan = 0.26
= 14.5° (to the nearest tenth of a degree)
Therefore, the angle of elevation of the 23-foot ramp is 14.5°.
The angle of elevation of the 23-foot ramp is 15.7 degrees to the nearest tenth of a degree.This can be found using the equation for finding the angle of elevation of an incline, which is tan θ = rise/run.In this case, the rise is 6 feet (the final height of the ramp) and the run is 23 feet (the length of the ramp).Therefore, the equation becomes tan θ = 6/23, and the angle of elevation can be found by solving for θ.Using a calculator, this value turns out to be 15.7 degrees.To learn more about the angle of inclination refer to:
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How do you find the equation of a vector given the point and direction?
To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).
The equation of a vector is typically written like this:
v = (x, y, z)
To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation. For example, let's say you are given the point (1,2,3) and the direction of the vector is (2,3,4). The components of the vector, v, would be x = 2, y = 3, and z = 4, so the equation for that vector would be:
v = (2, 3, 4)
To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).
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Charlotte is a customer-satisfaction expert at a large pizza company. She took a random sample of 1{,}0001,0001, comma, 000 delivery orders and constructed a one-sample zzz interval to estimate the proportion of delivery orders that take more than an hour to arrive. She decides to repeat this process, but this time she'll use a sample of 4{,}0004,0004, comma, 000 orders. Assume that the point estimates from each sample are approximately equal.What is true about the margins of error from these two samples
The smaller sample's margin of error will be almost twice as great as the larger sample's margin of error.
Calculating the margin of error for a given sample from a population:
Let the level of significance be and the standard deviation of the population be σ and the sample size be n, then we have:
MOE(Margin of Error)= [tex]z_{a/2}\times\frac{\sigma}{\sqrt n}[/tex]
Using the above formula to calculate the margin of errors for two specified samples
For first sample:
Sample size = n(1) = 1000
MOE(1) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {1000}}[/tex]
For second sample:
Sample size = n(2) = 4000
MOE(2) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {4000}}[/tex]
(since it was given that they have same point estimates, so same standard deviation)
Their ratios are given by
MOE(2)/MOE(1) = [tex]\frac{z_{a/2}\times\frac{\sigma}{\sqrt {4000}}}{z_{a/2}\times\frac{\sigma}{\sqrt {1000}}}[/tex]
MOE(2)/MOE(1) = [tex]\sqrt{\frac{1000}{4000}}[/tex]
MOE(2)/MOE(1) = 1/2
MOE(1) = 2*MOE(2)
Thus, the margin of error from the smaller sample will be about double of the margin of error from the larger sample.
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