According to the question the distance of the railway track is 200 km and the area representing the country map is 8 km² in real life.
Explain Area?The surface area of an object is the sum of all the shapes that make up its surface. This kind of rectangle's area is calculated by multiplying its length and breadth.
(a)If the scale of the map is 1 : 500,000, this means that 1 unit on the map represents 500,000 units in real life. The real length of a railway track, which is shown on the map as a 40 cm track, needs to be determined.
Let x be the actual distance in km. Then, we can establish the ratio shown below:
1 cm on the map represents 500,000 cm in real life, or
1 cm on the map represents (500,000/100,000) km in real life (since there are 100,000 cm in 1 km).
Thus, 1 cm on a map corresponds to 5 km real life.
Therefore, 40 cm on the map represents 40 x 5 = 200 km in real life.
So, the actual distance of the railway track is 200 km.
(b) If the area of the country is 40,000 km², we need to find the area on the map that represents this area in real life.
Since the scale of the map is 1 : 500,000, this means that 1 cm on the map represents 500,000 cm² in real life.
To find the area on the map that represents 40,000 km² in real life, we can set up the following proportion:
1 cm on the map represents 500,000 cm² in real life, or
1 cm² on the map represents (500,000/100,000,000) km² in real life (since there are 100,000 cm² in 1 km²).
So, 1 cm² on the map represents 0.005 km² in real life.
Therefore, the area representing the country on the map is 40,000/0.005 = 8,000,000 cm² or 8 km² in real life.
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Match each sum or difference with the correct simplified expression.
(x-5)-(x + 1)
(x-5)+ (x + 1)
(x-5)+ (x-1)
(x-5)-(x-1)
Intro
-4
2x-6
-6
2x-4
Answer:
Step-by-step explanation:
[tex](x-5)-(x + 1)=x-5-x-1=-6[/tex]
[tex](x-5)+ (x + 1)=x-5+x+1=2x-4[/tex]
[tex](x-5)+ (x-1)=x-5+x-1=2x-6[/tex]
[tex](x-5)-(x-1)=x-5-x+1=-4[/tex]
A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 59° and AC = 9.3.
Calculate the length of AB rounded to 3 SF.
Please help me i need the answers pleasee
Starting with the graph of f(x)=9^x , write the equation of the graph that results when:
(a) f(x) is shifted 2 units upward. y=-----------
(b) f(x) is shifted 4 units to the right. y=----------
(c) f(x) is reflected about the x-axis and the y-axis. y=------------
Answer: (a) To shift the graph of f(x)=9^x 2 units upward, we can add 2 to the function. Therefore, the new equation is:
y = 9^x + 2
(b) To shift the graph of f(x)=9^x 4 units to the right, we can replace x with (x - 4). Therefore, the new equation is:
y = 9^(x - 4)
(c) To reflect the graph of f(x)=9^x about the x-axis and the y-axis, we can replace x with (-x) and take the negative of the function. Therefore, the new equation is:
y = -9^(-x)
Step-by-step explanation:
what function is equivalent to the following:
the cofunction of sin
Trigonometric ratios connect angles and sides of right triangle. The cofunction of sinθ = cosecθ.
What is trigonometric ratios?Trigonometric ratios are mathematical proportions that connect the angles and sides of a right triangle. The hypotenuse, adjacent, and opposing sides are the three sides of a right triangle, which is a triangle having one angle of 90 degrees.
For example, imagine a triangle made up of wires of length L.
The same wire can be used to create a square if all sides are the same length.
The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.
As we can say, the surroundings are one-dimensinal. As a result, you can measure in meters, kilometers, millimeters, etc.
Inches, feet, yards, and miles are other globally recognized units of circumference measurement.
Hence, The function equivalent to sinθ = cosecθ.
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The average retail price of gasoline (all types) for the first half of 2005 was 212.2 cents. What would the standard deviation have to be in order for a 11% probability that a gallon of gas costs less than $1.80? Round z-value calculations to two decimal places and final answer to the nearest cent.
cadens savings account had $70 in its first year. each year since the , his account accumulated interest amounting to 10% of the valance in the previous year.
let f(n) be cadens account balance at the nth year of the saving
f is a sequence what kind of sequence is it
The supplied question's response based on the savings account is A geometric sequence is the sequence f.
What is Geometric sequence?A geometric sequence is a set of numbers where each term is obtained by multiplying the one before it by a predetermined quantity known as the common ratio. The following is the generic formula for a geometric sequence:
[tex]a, ar, ar^2,ar^3,ar^4,...[/tex]
There are two types of geometric sequences: finite and endless. While an infinite geometric sequence has no end, a finite geometric sequence has a set number of terms.
Because each term is created by multiplying the term that came before by a constant ratio of 1.1, the sequence f is a geometric sequence. (which accounts for the interest that has accrued on the preceding balance using the formula 1 + 0.1).
The first term is for $70, and each succeeding term is equal to the first term times 1.1. As a result, the nth term of the series can be
written as: [tex]f(n)=\$ \times 1.1^{n-1}[/tex]
where n is how long it has been since the first year of saving.
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1. Solve the following system of equations graphically. Make sure to check the solution.
y = 1/2x - 3
y = 3/4x + 2
Answer:
Step-by-step explanation:
You spin the spinner once. 123 What is P(odd or divisor of 54)? Simplify your answer and write it as a fraction or whole number.
After answering the given question, we can conclude that As a result, the probability of receiving an odd or a divisor of 54 is one, or 100% confidence.
What is probability?Probability is a gauge of how likely an occurrence is to occur. It is represented by a figure between 0 and 1, with 0 representing an unlikely occurrence and 1 representing an inevitable event. Switching a fair coin and coin turns has a chance of 0.5 or 50% because there are two equally likely results. (Heads or tails). Probability theory is a branch of mathematics that studies random occurrences rather than their characteristics. It is applied in many areas, including statistics, economics, science, and engineering.
There are three equally probable results from the spinner: 1, 2, and 3. To determine the likelihood of receiving an odd or divisor of 54, we must tally the number of events that meet this requirement.
54 has divisors of 1, 2, 3, 6, 9, 18, 27, and 54. Only one, three, and nine are unusual. As a result, the potential results that are either odd or divisors of 54 are 1, 3, and 2.
P(odd or divisor of 54) = P(1) + P(2) + P(3) + P(9) = 1/3 + 1/3 + 1/3 + 0 (because 9 is not a spinning choice) = 1
As a result, the chance of receiving an odd or a divisor of 54 is one, or 100% confidence.
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HELP PLS THIS IS DUE TOMORROW PLSSSSSSSS
Are ARST and ANSP similar? Use pencil and paper. Find the
measure of the angles in each triangle.
Which two angles must be congruent? What type of angles are they? (1 point)
The measure of the angles in triangle ARST are: 28 degrees, 28 degrees, 124 degrees, 124 degrees. The measure of the angles in triangle ANSP are: 28 degrees, 51 degrees, 101 degrees, 129 degrees.
What is angle?An angle is a geοmetric figure fοrmed by twο rays οr lines with a cοmmοn endpοint, called the vertex. Angles are typically measured in degrees οr radians and are used tο describe the amοunt οf turn οr rοtatiοn between twο intersecting lines οr οbjects. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), οbtuse (greater than 90 degrees), straight (exactly 180 degrees), οr reflex (greater than 180 degrees).
Here,
To find the measure of the angles in each triangle, we need to solve for the value of x in both equations.
For the first equation, we can simplify it as follows:
x + 14 = 2x
Subtracting x from both sides, we get:
14 = x
For the second equation, we can simplify it as follows:
3x + 9 = 2x + 23
Subtracting 2x and 9 from both sides, we get:
x = 14
Now that we know x = 14, we can find the measure of the angles in each triangle.
In triangle ARST, we have:
angle A = x + 14
= 14 + 14
= 28 degrees
angle R = 2x
= 2(14)
= 28 degrees
angle S = 180 - (angle A + angle R)
= 180 - (28 + 28)
= 124 degrees
angle T = 180 - (angle A + angle R)
= 180 - (28 + 28)
= 124 degrees
In triangle ANSP, we have:
angle A = x + 14
= 14 + 14
= 28 degrees
angle N = 3x + 9
= 3(14) + 9
= 51 degrees
angle S = 180 - (angle A + angle N)
= 180 - (28 + 51)
= 101 degrees
angle P = 180 - (angle N)
= 180 - 51 = 129 degrees
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2. You check 50 cartons of eggs. Eight of the cartons have at least one
cracked egg. What is the experimental probability that a carton of ega
has no cracked eggs?
Answer: 3/20 and 15%
Step-by-step explanation:
evaluate the expression -5+7-(-3)
Answer:
the answer is 5........
Answer: I rechecked and confirmed the answer. The answer is 5.
At this year's State Fair, there was a dice rolling gamne. If you rolled two dice and got a sum of 2 or 12, you won $12. If you rolled a 7, you won $5. Any other roll was a loss. It cost $1 to play one game with one roll of the dice. What is the expectation of the game? Round your answer to the nearest cent.
The expectation of this game is approximately dollars.
the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.
How to solve the probability?
To find the expectation of the game, we need to calculate the probability of winning and losing and multiply them by their corresponding payoffs.
First, let's calculate the probability of rolling a sum of 2 or 12. There is only one way to roll a sum of 2 or 12, which is by rolling a pair of ones or a pair of sixes, respectively. So, the probability of rolling a sum of 2 or 12 is:
P(2 or 12) = P(1,1) + P(6,6) = (1/6) * (1/6) + (1/6) * (1/6) = 1/18
Next, let's calculate the probability of rolling a 7. There are six ways to roll a sum of 7, which are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, the probability of rolling a 7 is:
P(7) = P(1,6) + P(2,5) + P(3,4) + P(4,3) + P(5,2) + P(6,1) = 6 * (1/6) * (1/6) = 1/6
Finally, the probability of losing is:
P(loss) = 1 - P(2 or 12) - P(7) = 1 - 1/18 - 1/6 = 11/18
Now, we can calculate the expectation of the game as follows:
E(X) = (12 * P(2 or 12)) + (5 * P(7)) - (1 * P(loss))
= (12 * 1/18) + (5 * 1/6) - (1 * 11/18)
= 2/9 + 5/6 - 11/18
= 0.22
So, the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.
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ASAAPP ONE QUESTION ONLY
Answer:
mWX = 106°-------------------------------
Angles at vertex V and Y are of same measure since they intercept same arc WX:
6x - 7 = 10x - 4710x - 6x = 47 - 74x = 40x = 10Angle measure of V and Y is:
6*10 - 7 = 60 - 7 = 53°Arc measure of WX is double the inscribed angle:
mWX = 2*53° = 106°Solve using the substitution method
2x -y = 7 and -6x + 3y = 21
There is no solution to the given system of equations. Therefore, the system is inconsistent.
How to solve the equation using substitution method?
To solve this system of equations using the substitution method, we need to solve one of the equations for one of the variables, and then substitute that expression into the other equation. Let's solve the first equation for y:
2x - y = 7
-y = -2x + 7
y = 2x - 7
Now we substitute this expression for y into the second equation:
-6x + 3y = 21
-6x + 3(2x - 7) = 21
-6x + 6x - 21 = 21
-21 = 21
This is a contradiction, and there is no solution to the system of equations. Therefore, the system is inconsistent.
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pls help lol it’s due tomorrow
A rectangular basket has a height of 6 inches, a width of 4 inches, and a length of 12 inches. What is the volume of the basket? Show how you found your answer.
V= l x w x h
V= B x h
The volume of a rectangular box or basket can be calculated using the formula:
V = l x w x h
where l is the length, w is the width, and h is the height of the box or basket.
In this case, the height of the basket is 6 inches, the width is 4 inches, and the length is 12 inches. Therefore, we can substitute these values into the formula and calculate the volume:
V = l x w x h
V = 12 x 4 x 6
V = 288 cubic inches
Therefore, the volume of the rectangular basket is 288 cubic inches.
The volume of the basket is 288 cubic inches.
What is Volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
The volume of a rectangular prism can be calculated
= length x width x height.
Given that the height is 6 inches, the width is 4 inches, and the length is 12 inches, the volume of the basket can be calculated as:
Volume = Length x Width x Height
Volume = 12 inches x 4 inches x 6 inches
Volume = 288 cubic inches
Therefore, the volume of the basket is 288 cubic inches.
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Please help with this
The probability that a passenger is traveling for business is 67.1%.
The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.
How to calculate the probabilityThe probability that a passenger is traveling for business can be calculated by adding the number of passengers traveling for business and dividing by the total number of passengers:
P(traveling for business) = (274 + 397) / 1000 = 0.671
Therefore, the probability that a passenger is traveling for business is 0.671 or approximately 67.1%.
b. The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business can be calculated as follows:
P(laptop | traveling for business) = number of passengers with a laptop and traveling for business / number of passengers traveling for business
P(laptop | traveling for business) = 236 / 671 = 0.352
Therefore, the probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.
c. It should be noted that to determine if there is an association between bringing a laptop on a flight and traveling for business, we can compare the proportion of passengers who bring a laptop when traveling for business versus when not traveling for business. If the proportions are different, it suggests an association.
P(laptop | traveling for business) = 0.352
P(laptop | not traveling for business) = 0.093
The proportions are different, which suggests an association between bringing a laptop on a flight and traveling for business.
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PLEASE I REALLY NEED HELP PLEASE
A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.
A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.
A) The annual rate of change or APR between 1991 and 2000 is approximately -0.1091.
B) The correct answer to part A in percentage form is approximately -10.91%.
C) The value of the car in 2003 is $7,750.
What is annual rate?
The car depreciated from $45,000 to $12,000 in 9 years. Using the formula for annual rate of change or annual percentage rate (APR):
r = [tex](Vf/Vi)^{1/n}[/tex] - 1
where Vf is the final value, Vi is the initial value, n is the number of years, and r is the annual rate of change or APR.
Substituting the given values:
r = [tex]($12,000/$45,000)^{1/9}[/tex] - 1
r ≈ -0.1091
Therefore, the annual rate of change or APR between 1991 and 2000 is approximately -0.1091.
B) The correct answer to part A in percentage form is approximately -10.91%.
What is APR?
To express the answer as a percentage, multiply the annual rate of change by 100 and round to the nearest 0.01%:
r = -0.1091 × 100
r ≈ -10.91%
Therefore, the correct answer to part A in percentage form is approximately -10.91%.
C) The value of the car in 2003 is $7,750.
What is the value?
To find the value of the car in 2003, we need to use the same percentage rate of decrease from 2000 to 2003. Since 2003 is 3 years after 2000, the value will be:
value = $12,000 × (1 + r)³
value ≈ $7,729.18
Rounding to the nearest 50 dollars, the value of the car in 2003 is $7,750.
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A parallelogram has an area of 14.4 square feet. The base is 4.5 centimeters. What is the height?
We know that the area of a parallelogram is given by the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given the area and the base, and we need to find the height.
We can rearrange the formula to solve for h: h = A/b
Plugging in the given values, we get:
h = 14.4 sq ft / 4.5 cm
Note that the units are different for area and base, so we need to convert them to the same units. Let's convert the base to feet, since the area is given in square feet:
h = 14.4 sq ft / (4.5 cm / 30.48 cm/ft) [converting cm to ft]
h = 14.4 sq ft / 0.148 ft
h ≈ 97.3 cm
Therefore, the height of the parallelogram is approximately 97.3 cm.
How many different committees can be formed from 12 teachers and 43 students if the committee consists of 2 teachers and 2 students
Answer: 59598
Step-by-step explanation:
It would be 12C2 for the teachers
and 43C2 for the students
12C2=66
43C2=903
66*903=59598
how many degrees is a obtuce angel
Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
the product of 6 less than a number and 2 more than the number
The complete verbal phrase translates to
(Do not perform the calculation.)
The expression represents the product of two terms = (x - 6) × (x + 2)
What do you mean by Linear Equation ?An equation in mathematics that is linear has a variable whose maximum power is 1. Alternatively said, it is an algebraic equation of the following form:
ax+ b = 0
where an is a constant that cannot equal zero, b is a constant, and x is a variable. Another way to express a linear equation in its general form is as follows:
y = mx + b
where the y variable is the dependent variable, the independent variable is x, the slope is m, and the y-intercept is b.
The product of 6 less than a number and 2 more than the number can be translated into the mathematical expression:
(x - 6) × (x + 2)
Here, x represents the unknown number, and the expression represents the product of two terms: "6 less than a number" (x - 6) and "2 more than the number" (x + 2).
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4) Two Truths and a Lie. Use what you know about the patterns in area models to determine which two area models correctly represent a factorable polynomial in the form of ax^2 + bx + c where c = 40. The middle “b” term is unknown
The correct area models are 4e and none of the given models for 4d and 4c.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The area model of 4c is incorrect because the last term of the polynomial, which is 40, is represented by the bottom right box of the area model. However, in the given area model, the box representing 40 is in the upper row.
The area model of 4e is correct because it represents the polynomial as the product of two binomials, where the factors are (x-5) and (x-8).
When multiplied using the distributive property, the resulting polynomial is x² - 13x + 40, which matches the given polynomial form.
The area model of 4d is incorrect because it does not properly represent a factorable polynomial.
It only includes three boxes, representing the three terms of the polynomial, but it does not show how the terms can be factored into binomials.
Therefore, the correct area models are 4e and none of the given models for 4d and 4c.
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Pls help, Micheal tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to the function that models the data.
This means that after two years since the purchase, the boat was worth $24.57.
What is worth?In general, worth refers to the value or monetary equivalent of something. It can be used to describe the financial value of assets such as property, stocks, or commodities, or to describe the value of something in terms of its usefulness, importance, or significance.
Michael tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to find the function that models the data.
16.75
19.5
4
3
22.9
27.25
2
1
32
0
Years Since Purchase
To better understand the exponential function that models the data, let's break it down:
y = 10.92 * 1.50ˣ
The constant "10.92" represents the initial value of the boat when it was purchased. This means that the boat was worth $10.92 when Michael first bought it.
The constant "1.50" represents the growth factor of the boat's value. This means that each year, the value of the boat increases by a factor of 1.50.
The variable "x" represents the number of years since the boat was purchased. The function takes this input and returns the value of the boat at that time.
For example, if we plug in x=1 into the function, we get:
y = 10.92 * 1.50¹
y = 16.38
This means that after one year since the purchase, the boat was worth $16.38. Similarly, if we plug in x=2 into the function, we get:
y = 10.92 * 1.50²
y = 24.57
This means that after two years since the purchase, the boat was worth $24.57.
It's important to note that the exponential function assumes that the growth rate remains constant over time. In reality, the value of the boat may be affected by other factors such as wear and tear, maintenance, and market fluctuations. Nevertheless, the exponential function provides a useful model for understanding the trend in the data and making predictions about the future value of the boat.
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A DVD rotates through an angle of 20pi radians in 1 second. At this speed, the DVD will make ____ revolutions in 1 minute!
Lynne read 2.5 chapters of her book on Tuesday, 4.25 chapters on Wednesday, and 5 chapters on Thursday. How many chapters did she read in total during those three days? I think you have to add them
Answer:
11.75
Step-by-step explanation:
2.5 + 4.25 + 5
Answer:
11.75 chapters in total
Step-by-step explanation:
Given:
2.5, 4.25, 5
The question ask for total
2.5 + 4.25 + 5 = 11.75
Select "Growth" or "Decay" to classify each function.
y=200(0.5)2t = DECAY
y=12(2.5)t6 = GROWTH
y=(0.65)t4 = DECAY
just took the test
y=200(0.5)2t this functiοn represents decay, y=12(2.5)t6 this functiοn represents grοwth and y=(0.65)t4 this functiοn represents decay.
What is functiοn?In mathematics, a functiοn is a relatiοnship between twο sets οf elements, called the dοmain and the range, such that each element in the dοmain is assοciated with a unique element in the range.
In general, we can determine whether a functiοn represents grοwth οr decay by examining the base οf the expοnential term.
If the base is greater than 1, the functiοn represents grοwth.
If the base is between 0 and 1, the functiοn represents decay.
Here are the classificatiοns fοr each οf the given functiοns:
y=200(0.5)2t
The base οf the expοnential term is 0.5, which is between 0 and 1. Therefοre, this functiοn represents decay.
y=12(2.5)t6
The base οf the expοnential term is 2.5, which is greater than 1. Therefοre, this functiοn represents grοwth.
y=(0.65)t4
The base οf the expοnential term is 0.65, which is between 0 and 1. Therefοre, this functiοn represents decay.
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Complete Question:
Select "Growth" or "Decay" to classify each function.
Function Which ones are growth or decay
f(x)=(1.05)t4
y=100(0.4)t
f(x)=14(10)t12
Use substitution to determine whether the given number is a zero of the given
polynomial.
3; f(x) = -x^4 -8x²-x-5
also
As f(3) is not equal to zero, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.
How to determine whether a given number is a zero of the a polynomial?Given the polynomial in the question;
f(x) = -x⁴ -8x²-x-5
Given number: 3
To check if 3 is a zero of the polynomial f(x) = -x⁴ -8x²-x-5, we need to substitute x = 3 into the polynomial and see if the result will give zero.
f(x) = -x⁴ -8x²-x-5
plug i x = 3
f(3) = -3⁴ - 8(3)² - 3 - 5
= -81 - 72 - 3 - 5
= -161
Therefore, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.
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To the nearest whole number, what is the mean of the
number of stamps for these four friends?
F. 92
G. 124
H. 203
J. 217
K. 234
To find the mean of the number of stamps for these four friends, we need to add up the total number of stamps and divide by 4 (the number of friends).
Samir has 60 stamps. Lisa has 2 1/2 times as many stamps as Samir, which can be calculated as follows: 2 1/2 * 60 = 150
Kwame has 443 stamps.
Jake has 159 fewer stamps than Kwame, which can be calculated as follows: 443 - 159 = 284 To find the total number of stamps, we add up the number of stamps each friend has: 60 + 150 + 443 + 284 = 937
To find the mean, we divide by 4: 937 / 4 = 234.25
Therefore, to the nearest whole number, the mean of the number of stamps for these four friends is 234.
Therefore, the answer is K. 234.
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What was the age distribution of prehistoric Native Americans? Suppose an extensive anthropological studies in the southwestern United States gave the following information about a prehistoric extended family group of 84 members on what is now a Native American reservation.
Age range (years) 1-10 11-20 21-30 31 and over
Number of individuals 35 22 20 7
For this community, estimate the mean age expressed in years, the sample variance, and the sample standard deviation. For the class 31 and over, use 35.5 as the class midpoint. (Round your answers to one decimal place.)
x =
years
s2 =
s =
years
Mean age: 16.1 years, Sample variance: 50.47 square years and Sample standard deviation: 7.10 years for the given problem.
To estimate the mean age, we need to find the midpoint of each age range and multiply it by the number of individuals in that range. Then we add up these products and divide by the total number of individuals:
Mean age = [(1+10)/2 x 35 + (11+20)/2 x 22 + (21+30)/2 x 20 + 35.5 x 7] / 84
= (5.5 x 35 + 15.5 x 22 + 25.5 x 20 + 35.5 x 7) / 84
= 16.1
Therefore, the estimated mean age of this extended family group is 16.1 years.
To calculate the sample variance, we need to find the deviation of each age from the mean, square each deviation, and add up these squared deviations. Then we divide this sum by the total number of individuals minus one:
s2 = [(1-16.1)2 x 35 + (11-16.1)2 x 22 + (21-16.1)2 x 20 + (35.5-16.1)2 x 7] / (84-1)
= (2254.05 + 537.08 + 220.89 + 253.68) / 83
= 50.47
Therefore, the estimated sample variance is 50.47 square years.
We simply take the square root of the sample variance to calculate the sample standard deviation:
s = [tex]\sqrt{s2}[/tex]
= s[tex]\sqrt{50.47}[/tex]
= 7.10
Therefore, the estimated sample standard deviation is 7.10 years.
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