The fraction of the entire cake that each friend who arrived late received is = 1/30.
Division of fractions:The whole cake was divided into 6 pieces
The portion of the cake left is one portion which is = 1/6
He shared 1/6 cake equally among 5 friends which is
=1/6 ÷ 5
=1/30
Therefore, the fraction of the entire cake that each friend who arrived late received is = 1/30
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Becca visited 80 vendors at a job fair, and she took a pamphlet from 40% of them. How many pamphlets did Becca take?
how many were there? well, really there were "x", which oddly enough is the 100%, we also know that 40% of "x" is 80, so
\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 80& 40 \end{array} \implies \cfrac{x}{80}~~=~~\cfrac{100}{40} \\\\\\ \cfrac{ x }{ 80 } ~~=~~ \cfrac{ 5 }{ 2 }\implies 2x=400\implies x=\cfrac{400}{2}\implies x=200\)
Use the given right triangle to find ratios, in reduced form, for sin A, cos A, and tan A.
The ration will be sinA =\(\frac{P}{H}\) =\(\frac{33}{65}\) , cosA = \(\frac{B}{H}\)=\(\frac{56}{65}\) & tanA = \(\frac{P}{B}\)= \(\frac{33}{56}\).
What are a right triangle's three sides?The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use particular terminology to define the sides of right triangles. A right triangle's hypotenuse is always side opposite the right angle.
Would a right triangle have a 90- or 180-degree angle?When one of a triangle's angles is exactly 90 degrees, the triangle is said to be right-angled. The remaining two angles together equal 90 degrees.. The sides that make up the right angle are perpendicular and the triangle's base. The third side, also referred to as the hypotenuse, is the longest of the three sides.
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Use custom relationships to create a graph, showing the solution region of the system of inequalities, representing the constraints of the situation. Did Mark and label it point represents a viable combination of guest School district is planning a banquet to honor his teacher of the year and raise money for the scholarship foundation. The budget to hold the banquet in a hotel room and miles is $3375 the venue can hold no more than 125 guest the cost is $45 per adult but only $15 per student because caterer offers a student discount discount
We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.
What is banquet?
A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.
To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.
Let's define the variables:
Let x be the number of adult guests.
Let y be the number of student guests.
Now, let's write the system of inequalities representing the constraints of the situation:
The total number of guests cannot exceed 125: x + y ≤ 125
The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375
To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.
The boundary lines of each inequality are:
x + y = 125 (the line that connects the points (0, 125) and (125, 0))
45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))
To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.
The resulting graph should look like this:
The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.
We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.
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a recipe for polvorones , which are mexican pink sugar cookies needs 3/4 cups of white sugar and 1/3 cup of cane sugar .which model can be used to find the total amount of sugar in cups the recipe needs
Answer:2
Step-by-step explanation:I DONT REALLY GIVE A THING I NEED POINTS.
Please answer this correctly without making mistakes I want ace expert and genius people to answer this correctly without making mistakes
Answer:
6936 pints and 1156 cups
Step-by-step explanation:
Answer:
7514 pints
Step-by-step explanation:
i rechecked and this was correct?
29-(11-2³)+6²÷4 simplify each Expression
The simplified form of the expression 29 - ( 11 - 2³ ) + 6² ÷ 4 is 35
What is the simplified form of the given expression?Given the expression in the question;
29 - ( 11 - 2³ ) + 6² ÷ 4
To simply, replace 2 raised to the power of 3 with 8 and 6 raised to the power of 2 by 36
29 - ( 11 - 2³ ) + 6² ÷ 4
29 - ( 11 - 8 ) + 36 ÷ 4
Now, remove the parenthesis by performing the operation inside the parenthesis.
29 - ( 11 - 8 ) + 36 ÷ 4
29 - 3 + 36 ÷ 4
Now, divide 36 by 4
29 - 3 + 36 ÷ 4
29 - 3 + 9
Next, add -3 and 9
29 + 6
Add 29 and 6
35
Therefore, 35 is the simplified form of the expression.
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which of these statements best compares the pair of line segments with the vertex
Answer:
Line segments have two endpoints and a vertex is a common endpoint where two line segments meet.
Step-by-step explanation:
A line segment is defined as a portion of a line that has two endpoints.
A vertex is defined as the common endpoint of two or more rays or line segments.
find the line of best fit for the set of data
The line of best fit for the set of data in this problem is given as follows:
y = 0.613x + 4.142.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) of the data-set in the calculator.
The points for this problem are given as follows:
(-2, 2.9), (-3.5, 2), (1.4, 4.8), (-4.2, 1.5), (0,4), (2.8, 6), (-1.5, 3.5).
Inserting these points into a calculator, the line of best fit is given as follows:
y = 0.613x + 4.142.
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Exercise 1.2
A person has G¢60 to spend on two goods, X and Y, whose respective prices are GH¢6 and GH¢4.
(a) Draw a budget line showing all the different combinations of the two goods that can be bought within the given budget.
(b) What happens to the original budget line if the budget is increased by 20%?
(c) What happens to the original budget line if the price of X is halved?
(a) The maximum combination of X and Y is (10, 15).
(b). The new maximum combination of X and Y is (12, 18).
(c). The new maximum combination of X and Y is (20, 15).
To draw the budget line, we need to determine the different combinations of goods X and Y that can be bought within the given budget.
The budget line represents all the possible combinations of X and Y that can be purchased with G¢60.
Let's assume the quantity of good X is represented on the x-axis and the quantity of good Y is represented on the y-axis.
The combinations, we can start with the maximum quantity of each good that can be purchased with the given budget.
Given that the price of X is GH¢6 and the price of Y is GH¢4, we can calculate:
Maximum quantity of X = G¢60 / GH¢6 = 10
Maximum quantity of Y = G¢60 / GH¢4 = 15
Now, we can plot the budget line connecting this point with the origin (0, 0).
The budget line represents all the combinations of X and Y that can be purchased with G¢60.
|
15 +---------------------
|
|
|
10 + /
| /
| /
| /
Y | /
| /
5 + /
| /
| /
| /
0 +-----------------------
0 5 10 15 X
(b) If the budget is increased by 20%, the new budget will be 120% of the original budget.
New budget = 120% of G¢60 = 1.2 × G¢60
= G¢72
To draw the new budget line, we repeat the steps from part (a) using the new budget of G¢72.
Maximum quantity of X = G¢72 / GH¢6 = 12
Maximum quantity of Y = G¢72 / GH¢4 = 18
Plotting the new budget line:
|
18 +---------------------
|
|
|
12 + /
| /
| /
| /
Y | /
| /
6 + /
| /
| /
| /
0 +-----------------------
0 6 12 18 X
(c) If the price of X is halved, the new price of X will be GH¢6 / 2 = GH¢3.
To draw the new budget line, we keep the budget and the price of Y the same as in the original scenario.
Only the price of X changes.
Maximum quantity of X = G¢60 / GH¢3 = 20
Maximum quantity of Y = G¢60 / GH¢4 = 15
Plotting the new budget line:
|
15 +---------------------
|
|
|
20 + /
| /
| /
| /
Y | /
| /
5 + /
| /
| /
| /
0 +-----------------------
0 5 10 15 X
Note that the slope of the budget line changes in both cases, reflecting the changes in the budget and the price of X.
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Write 3 1/2 cups as a multiplication expression using the unit, 1 cup, as a factor.
I ABSOLUTELY NEED HELP BY TOMORROW!!! I AM GIVING 100 POINTS
3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.
How to Write 3 1/2 cups as a multiplication expression using the unit, 1 cup, as a factor.To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:
3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup
Since there are 1 cup in each term, we can rewrite it as:
3 cups + (1/2) cup
Now, we can express each term as a multiplication expression:
3 cups = 3 * 1 cup = 3
(1/2) cup = (1/2) * 1 cup = 1/2
Putting it all together, the multiplication expression is:
3 * 1 cup + (1/2) * 1 cup = 3 + 1/2
Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.
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Example: Divide 3 loaves between 5 people First, divide two of the loaves into thirds... each person gets one third each, with one third left over Then divide the left-over third from the second loaf into fifths So, each person gets: 1/5 and the third loaf into fifths each person gets one fifth each each person gets a slice (one fifteenth) 1/15 3/5 The Egyptians used the approximated process to work on the area of a circle as shown in the picture. 1.4 Show the representation of the fractions on the second row. (2) 1.5 Show the algorithm/abstract strategy to justify the 3/5 found as the answer. (3)
The algorithm justifies the answer of 3/5 as the fraction each person gets.
Representation of the fractions on the second row:
From what you described, two of the loaves were divided into thirds.
This means each person receives one third, and there is one third remaining. Then, this remaining third from the second loaf was further divided into fifths.
Therefore, each person receives one fifth from this remaining third.
So, the representation of the fractions on the second row would be:
Each person receives 1/3 (one third) from the two loaves.
Each person receives 1/5 (one fifth) from the remaining third.
Algorithm/Abstract strategy to justify the 3/5 found as the answer:
To find the final answer of 3/5, we can follow the steps you provided:
Divide two loaves into thirds, giving each person 1/3.
Divide the remaining third from the second loaf into fifths, giving each person 1/5.
Combining the fractions, each person has 1/3 + 1/5.
To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15. We can convert 1/3 and 1/5 to have a denominator of 15:
1/3 = 5/15 (multiplying numerator and denominator by 5)
1/5 = 3/15 (multiplying numerator and denominator by 3)
Now, we can add the fractions:
5/15 + 3/15 = 8/15
Therefore, each person receives 8/15 of a loaf.
Simplifying this fraction, we get 3/5.
Hence, the algorithm justifies the answer of 3/5 as the fraction each person gets.
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Which of the following rational functions is graphed below?
A. F(x) =(x-2)/(x+5)
B. F(x) =1/(x-2)(x + 5)
C. F(x) =1/(2x + 5)
D. F(x)= 1/(x+2)(x-5)
The graph of the rational equation is solved and f ( x ) = 1/ ( x + 2 ) ( x - 5 )
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 1/ ( x + 2 ) ( x - 5 )
The function will have increasingly large values as the denominator approaches zero. When x -2, the denominator is positive and the function tends to the upside. When x -2 x 5, the function is negative. When x 5, the function becomes positive once more.
Hence , the rational function is f ( x ) = 1/ ( x + 2 ) ( x - 5 )
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The complete question is attached below :
Which of the following rational functions is graphed below?
A. F(x) =(x-2)/(x+5)
B. F(x) =1/(x-2)(x + 5)
C. F(x) =1/(2x + 5)
D. F(x)= 1/(x+2)(x-5)
The James family purchased a home for $180,000 five years ago and obtained an 80% LTV loan. Now the property has appreciated 25%. In addition, the loan has been paid down $11,000. What is the James’s current equity in the home?
$92000 is the James’s current equity in the home.
What is equity?Equity, also known as shareholders' equity or owners' equity for privately held businesses, is the sum of money that, in the event of a company's liquidation, would be distributed to its shareholders after all of the company's assets have been sold and its debt has been fully repaid.
In an acquisition scenario, it is equal to the sum of the company's sales less any liabilities that were not transferred to the new owner.
A company's book value can also be represented by shareholder equity. A payment-in-kind arrangement may occasionally include equity. Furthermore, it represents the proportionate ownership of a company's shares.
James’s current equity = (180000 × 1.25) - ((180000 × 0.8) -11000)
= 92000
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When a percentage of the smallest and largest values are deleted from a data set, the mean of the remaining data values is the _____ mean.
What is the surface area (S.A) of the circle shown below in terms of π
r = 4 inches.
h = 6 inches.
Answer:
64π
Step-by-step explanation:
To calculate the surface area (S.A) of the circle with a radius (r) of 4 inches and a height (h) of 6 inches, we need to consider both the curved surface area (lateral surface area) and the area of the circular base.
The curved surface area, also known as the lateral surface area, is calculated using the formula:
L.A = 2πrh
Substituting the given values, we have:
L.A = 2π(4)(6)
L.A = 48π square inches
The area of the circular base is calculated using the formula:
A = πr^2
Substituting the given radius, we have:
A = π(4^2)
A = 16π square inches
To find the total surface area (S.A), we need to sum the lateral surface area (L.A) and the area of the circular base (A):
S.A = L.A + A
S.A = 48π + 16π
S.A = 64π square inches
Therefore, the surface area (S.A) of the given circle is 64π square inches.
The Weasley brothers estimate that they will need a thousand galleons just to set up their joke shop, Weasley's Wizarding Wheezes. The first products they are manufacturing are pygmy puffs, and they realize that the cost of making a single box of pygmy puffs is 3 galleons. The brothers would like to estimate the cost, in galleons, of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p. Which of the following equations is the correct equation representing this scenario?
1. ()=3−1000
2. ()=3+1000
3. ()=1000−3
4. ()=1000+3
The most appropriate choice for linear equation will be given by -
Total cost of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p
C(p) = 3p + 1000
Second option is correct
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Initial cost of manufacturing Weasley's Wizarding Wheezes by the Weasley brothers = 1000 galleons
Cost of producing one pygmy puff = 3 galleons
Cost of producing p boxes of pygmy puffs = 3p galleons
Total cost of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p
C(p) = 3p + 1000
Second option is correct
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Complete Question
The Weasley brothers estimate that they will need a thousand galleons just to set up their joke shop, Weasley's Wizarding Wheezes. The first products they are manufacturing are pygmy puffs, and they realize that the cost of making a single box of pygmy puffs is 3 galleons. The brothers would like to estimate the cost, in galleons, of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p. Which of the following equations is the correct equation representing this scenario?
1) C(p) = 3p - 1000
2) C(p) = 3p + 1000
3) C(p) = 1000p - 3
4) C(p) = 1000p + 3
a student claimed that the function shown in the table is exponential. do you agree or disagree? explain
The correct statement that F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."
To determine whether the function shown in the table is exponential, we need to analyze the relationship between the x-values and y-values.
The table shows x-values that are increasing by a power of 2 (1, 2, 4, 8, 16, 32, 64) and y-values that are increasing by a constant rate of 1 (0, 1, 2, 3, 4, 5, 6).
The constant ratio between consecutive x-values indicates exponential growth or decay.
In this case, the function is growing exponentially because the y-values are increasing at a constant rate.
Based on this information, we can conclude that the function is exponential.
Therefore, we agree with statement F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."
The other statements are incorrect because they do not accurately describe the relationship between the x-values and y-values in an exponential function.
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2x2+3y=-2 solve for y
Answer:
y=(-2/3)x^2-(2/3)
Step-by-step explanation:
2x^2+3y=-2
3y=-2x^2-2
y=(-2/3)x^2-(2/3)
Answer:
y= -2
Step-by-step explanation:
2x2+3y=-2
4+3y=-2
Subtract 4 from both sides
3y=-6
Divide both sides by 3
y= -2
In my case, x means multiplied by not a variable.
Find the lateral area of the prism. 8cm 6cm, I 1 13cm I 10cm Lateral Area = [?]cm² 2008-2012 International Academy of Science, All Rights Reserved. Aid Enter
The lateral area of the prism is 270cm²
What is the lateral area of a prism?
The lateral area of a prism is defined as the sum of the areas of its lateral faces.
How to determine the lateral area of a prismUsing the formula;
Lateral area = (a+ b+ c) h
Where a, b, c, are all the lateral faces and h is the height
Lateral area = (8 + 6 + 13) × 10 = 27 × 10 = 270cm²
Therefore, the lateral area of the prism is 270cm²
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2) What is the area of the parallelogram?
A. 16 square centimeters
B. 30 square centimeters
C. 60 square centimeters
D. 120 square centimeters
(20 points)
height= 6 cm
base= 10 cm
to find:the area of the parallelogram.
solution:\(formula = bh\)
\(a = 6 \times 10\)
\(a = 60 {cm}^{2} \)
therefore, the area of the parallelogram is 60 square centimeters.
answer= option c.
. What is (f + g)(x)?
=
-
f(x) = x3 - 2x + 3
g(x) = 2x² + 4x - 4
-
Answer:
\(3x^3 + 2x - 1\)
Step-by-step explanation:
\(x^3 - 2x + 3 + 2x^3 + 4x - 4\)
Combine like terms:
\(3x^3 + 2x - 1\)
Hope that helped
Smallest successive composites with gap
17, 73, 2, 19
Answer:
Well, the smallest successive composites with gap 17, 73, 2, and 19 would have to be:
1. $341 = 11 \times 31$
2. $458 = 2 \times 299$
3. $460 = 2^2 \times 5 \times 23$
4. $479 = 13 \times 37$
For which of the following displays of data is it not possible to find the mean histogram frequency, table, stem, and leaf plot doc plot
The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.
A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.
A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.
A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.
A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.
In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
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The figure below shows a shed in the shape of a rectangular prism.
Note that the shed has a floor.
Answer:
Step-by-step explanation:
a). Volume of a rectangular prism = Length × width × height
= 13 × 8 × 12
= 1248 cubic ft
Surface area of a rectangular prism = (lb + bh + hl)
Here, l = length, b = width and h = height of the rectangular prism
Surface area of the given prism = (13×8 + 8×12 + 12×13)
= 356 square ft
b). If the shed is made of metal,
Metal needed to make the shed = Volume
c). The shed is used for the storage.
Measure would be used → Surface area
3 mi 1,622 yd − 3 mi 1,038 yd =
mi
yd
Answer: 584 yds
Step-by-step explanation:
3mi-3mi=0
1622-1038=584yds
can u find all angles
Answer:
I think it's 118°73°49° not really sure
sorry
Ravi is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Ravi has been adding money. Suppose that x and y are related by the equation
y=550+40x
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of money in the account?
What was the starting amount of money in the account?
Answer:
1. The change per week is $40 as it is the coefficient.
2. The starting amount is $550 as it is the constant.
1. The change per week in the amount of money in the account is $40.
2. The starting amount of money in the account is $550.
Given that,
Ravi is putting money into a checking account.
Suppose that x and y are related by the equation;
y = 550 + 40x
Now, the change per week in the amount of money in the account, look at the coefficient of the x-term in the equation y = 550 + 40x.
In this case, the coefficient of x is 40.
Therefore, the change per week in the amount of money in the account is $40.
Now, for the starting amount of money in the account, look at the y-intercept of the equation y = 550 + 40x.
The y-intercept is the value of y when x is 0.
In this case, when x is 0, the equation becomes;
y = 550 + 40(0)
y = 550.
Therefore, the starting amount of money in the account is $550.
So, the change per week in the amount of money in the account is $40, and the starting amount of money in the account is $550.
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Could you [please help me with the question in the screenshot thank you
The bias of the estimator is 1/45, so correct option is A.
Describe Proportion?In mathematics, a proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities, expressed as a fraction or a division of one quantity by another.
For example, the proportion "a/b = c/d" means that the ratio of a to b is equal to the ratio of c to d. This can also be written as "a : b = c : d", where the colon (:) represents the ratio symbol.
Proportions can be used to solve a variety of problems, such as finding unknown quantities in a ratio or comparing quantities that have different units. For instance, if a recipe calls for 2 cups of flour for every 3 cups of water, we can use proportions to determine how much flour and water we need if we want to make a larger or smaller batch.
The estimator for the true proportion of residents in support of the bypass road construction is given by:
p = (X + √2025/2) / 2025
We can see that this estimator involves adding √2025/2 to X, and then dividing the sum by 2025. Since √2025 = 45, we can simplify the estimator as:
p = (X + 45/2) / 2025
Now, we can find the expected value of the estimator:
E[p] = E[(X + 45/2) / 2025]
= (E[X] + 45/2) / 2025
To find the bias of the estimator, we need to compare its expected value to the true value of the parameter being estimated. Since we are estimating the proportion of residents in support of the bypass road construction, the true value of the parameter is the population proportion, denoted by p.
If the estimator is unbiased, then its expected value must equal the true value of the parameter, i.e., E[p] = p. Therefore, we have:
E[p] = (E[X] + 45/2) / 2025 = p
Solving for E[X], we get:
E[X] = 2025p - 45/2
Thus, the bias of the estimator is:
Bias[p] = E[p] - p
= (E[X] + 45/2) / 2025 - p
= [(2025p - 45/2) + 45/2] / 2025 - p
= (2025p - p) / 2025
= 44/2 x 2025
= 1/45
Therefore, the bias of the estimator is 1/45. Answer: A.
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The bias of the estimator is 1/45. The appropriate choise for the posed query is option (a).
What is proportion?In mathematics, a proportion is the assertion that both ratios are equal. A ratio is the division of one quantity by another or the comparison of two quantities given as a fraction.
The ratio "a/b = c/d," for instance, denotes that the ratio of a to b is equivalent to the ratio of c to d. This can also be expressed as "a: b = c: d," where the ratio sign is denoted by the colon (:).
Numerous issues can be resolved using proportions, like comparing amounts with various units or locating unknown values in a ratio. For instance, we may use proportions to calculate the amount of flour and water needed to make a larger or smaller batch of a recipe if it calls for 2 cups of flour and 3 cups of water.
The estimator for the actual percentage of residents in favour of building the bypass route is provided by:
p = (X + √2025/2) / 2025
As we can see, this estimator multiplies X by 2025/2 before dividing the result by 2025.
Since √2025 = 45, The estimator may be distilled down to:
p = (X + 45/2) / 2025
We can now determine the estimator's expected value:
E[p] = E[(X + 45/2) / 2025]
= (E[X] + 45/2) / 2025
We must contrast the estimator's expected value with the actual value of the parameter being estimated in order to determine its bias. The population proportion, given by p, is the genuine value of the parameter because we are calculating the percentage of residents who support the construction of the bypass route.
If the estimator is impartial, then its predicted value must match the parameter's true value, or E[p] = p. As a result, we have:
E[p] = (E[X] + 45/2) / 2025 = p
Solving for E[X], we get:
E[X] = 2025p - 45/2
As a result, the estimator's bias is:
Bias[p] = E[p] - p
= (E[X] + 45/2) / 2025 - p
= [(2025p - 45/2) + 45/2] / 2025 - p
= (2025p - p) / 2025
= 44/2 x 2025
= 1/45
As a result, the estimator's bias is 1/45. Answer: A.
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Simplify -3a + 5b - c given a = 2, b = -1 and c= 10
Answer:
-21
Step-by-step explanation:
-3a + 5b - c
-3(2)+5(-1)-(10)=-21
3 2/3 x 1/5= please help
Answer: 11/15
Step-by-step explanation: