On solving the provided question, we can say that - the value the exponent [tex]10^n\\[/tex] will be 100000
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
from the given exponents we have
[tex]10^n[/tex]
where n = 5
so [tex]10^5 = 100000[/tex]
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Fill in the blanks to write the solutions to the quadratic equation.Fill in the blanks to write the solutions to the quadratic equation.Fill in the blanks to write the solutions to the quadratic equation.Fill in the blanks to write the solutions to the quadratic equation.x^2+2x+10 = 0
The solution to the given quadratic equation is x = -1 + 3i OR x = -1 - 3i
Solving Quadratic equationsFrom the question, we are to solve the given quadratic equation
From the given information,
The quadratic equation is
x² + 2x + 10 = 0
Using the Quadratic formula,
x = [-b ± √(b² - 4ac)] / 2a
From the equation,
a = 1, b = 2, and c = 10
Then,
x = [-b ± √(b² - 4ac)] / 2a
x = [-(2) ± √((2)² - 4(1)(10))] / 2(1)
x = [-2 ± √(4 - 40)] / 2
x = [-2 ± √(-36)] / 2
x = [-2 ± -6i] / 2
x = -1 ± 3i
x = -1 + 3i OR x = -1 - 3i
Hence, the solution is x = -1 + 3i OR x = -1 - 3i
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A 50 Gram Sample of a substance that used to treat thyroid disorders has a K-value of 0.1113. What is the half life? thanks
The half life of the iodine is obtained as 6.2 s.
What is the half life?
Let us recall that the half life would be the time that is taken for about half of the original radioactive isotope that remains in the sample, to become depleted in the thyroid treatment.
Given that we have the fact that the decay constant that we have in the process is given as 0.1113 in the question and we know that;
Half life = 0.693/K
Half life = 0.693/0.1113
Half life = 6.2 s
It would have the half life about 6.2 s.
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The quotient of s and 60
Answer:
60/s or s/60
Quotient means divide so you divide the following, s and 6 by each other.
Step-by-step explanation:
Hope it helps! =D
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown
O 10 units
O 24 units
O 36 units
O 64 units
Answer:
A
Step-by-step explanation:
refer the sketch for step by step answer
Help soon would be greatly appreciated
A home has a replacement value of $324,000. What is the amount
of the insurance if the coverage is:
a.
100% of the replacement value?
b. 90% of the replacement value?
C.
80% of the replacement value?
The insurance company will pay $192, which is the asset's present value.
What is meant by replacement value?The sum of money required to fix your house at the cost of construction materials today, or to replace your possessions at the cost of an equivalent or comparable item today the cost of purchasing a comparable asset to replace an existing one at the going rate on the market.
To be fully insured, your dwelling limit must equal at least 80% of the rebuild value of your house. The average cost of reconstructing a home per square foot in your area can be multiplied by the square footage of your home to determine the replacement cost. Market value and replacement cost are not the same thing.
Therefore,
The distribution of cost over the course of an asset's useful life is known as depreciation. It speaks of the rate at which the value of an asset depreciates over time.
When figuring out depreciation, the original value is utilized. It does not use current market value.
Over the course of the asset's useful life, the value is distributed equally.
In this instance
Depreciation per year = Asset value ÷ Years of useful life
Depreciation per year = 288 ÷ 6 = $48
The asset has been used for 2 years
Amount depreciated = 48 × 2 = $96
Present value = Original value - Depreciation
Present value = 288 - 96 = $192
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a local zoo has 900 pounds of bamboo to feed the giant panda. Each day, the giant panda eats 30 pound of bamboo. An accident happens and 125 pounds of the bamboo cannot be fed to the giant panda Determine the range of the number of days the zoo has more than 500 pounds of bamboo left.
The range of days to have 500 pounds left is 30 - 17.5 days
What is range?The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.
For example the range in the ages 10,15,11,12,18 of students in a class is 18-10 = 8
The maximum days to feed the giant panda if the giant panda feeds on 30pounds per day is 900/30 = 30days
but due to accident 125 pounds are not good
Therefore the new pound of bamboo = 900- 125 = 875 pounds
The range of pounds when the minimum pound is 500 = 875-500 = 375 pounds
therefore no of days on 375 pounds = 375/30 = 12.5
Therefore the range of days to have more thanq 500 pounds = 30-12.5 = 17.5 days
The range of days the zoo has more than 500 pounds of bamboo is 30 - 17.5days
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Mr. Jensen purchased a condo several years ago at a selling price of $295,420. Recently it
was appraised at a value 36.4% lower than that. What is the value of the condo now?
Roun
Answer:
The value of the condo was appraised at 36.4% lower than the selling price, which means it is now worth 100% - 36.4% = 63.6% of the selling price.
The selling price of the condo was $295,420, so the value of the condo now is $295,420 * 63.6% = $<<295420*0.636=188382.72>>188,382.72.
Therefore, the value of the condo now is $188,382.72.
Step-by-step explanation:
If f(-5)=0, what are all the factors of the function f(x)=x^3-19x+30? Use the remainder Theorem.
The requried other factors of the given function are (x - 2) and (x - 3).
What is the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
here,
Given function, f(x) = x³-19x+30,
One of the factors of function is x = -5 or x + 5 = 0
Following the remainder theorem to determine the others factor,
= given function / one of the factor
= [x³-19x+30] / [x + 5]
= (x - 2)(x - 3)
Thus, the requried other factors of the given function are (x - 2) and (x - 3).
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George peels and eats 2 whole satsumas.
He then splits another satsuma into 6 equal segments and eats 1 of these segments.
How many satsumas does he eat in total?
Give your answer as an improper fraction.
The total number of satsumas eated by George are 2[tex]\frac{1}{6}[/tex].
What is fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts namely numerator (upper part) and denominator (lower part).
Given is that George peels and eats 2 whole satsumas. He then splits another satsuma into 6 equal segments and eats 1 of these segments.
The total number of satsumas eated by him can be written as -
2 + 1/6
2[tex]\frac{1}{6}[/tex]
Therefore, the total number of satsumas eated by George are 2[tex]\frac{1}{6}[/tex].
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823× 3.6 weekly math review homework for fifth grade
DUE PLS HELP!! Kayla has $45 and wants to buy three shirts that are originally priced at $18 each. They are on sale for 20% off. After applying 5% tax, does Kayla have enough money to purchase the three shirts?
Complete each statement.
The cost of the shirts after the discount is $43.20.
A 5% tax adds an additional $2.16 so the total bill comes to 45.36.
Kayla does not have enough money to buy the three shirts.
Does Kayla have enough money to purchase the three shirts?The first step is to determine the total cost of the three shirts.
Total cost of the three shirts = cost of one shirt x total number of shirts
$18 x 3 = $54
Cost of the shirt after the sale = (1 - discount/100) x total cost of the shirt
(1 - 20/100) x $54
(1 - 0.2) x $54
= 0.8 x $54
= $43.20
Price after the tax : (1 + tax/100) x cost of the shirt after the discount
(1 + 5/100) x $43.20
(1 + 0.05) x $43.20
1.05 x $43.20 = 45.36
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Clark is building a large gazebo for his backyard. It is in the shape of a regular hexagon. Each side of the
gazebo is 12 feet long. The apothem is 10.4 feet. He needs to purchase stones for the floor. It costs $9.50
per square foot for a special type of interlocking stone. Find the cost of the gazebo's floor.
Round to the nearest ten dollars.
Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.
Given that,
In Clark's backyard, a sizable gazebo is being constructed. It has a typical hexagonal form. The gazebo has 12 feet on each side. 10.4 feet tall is the apothem. He must get stones for the flooring. The price of a particular kind of interlocking stone is $9.50 per square foot.
We have to identify the gazebo's floor's cost.
We know that,
The distance from the center of the regular polygon to the mid point of the side. Here, AB is the chord and AM =BM. O is the center of the circumcircle.
Segments joining the center of a circle to the midpoint of the chord is perpendicular to the chord.
So, OM ⊥AB
In ΔOAB,
AB is the base and OM is the height.
AB = 12 feet
OM = 10.4 feet.
The area of the triangle OAB =1/2×base×height
= 1/2×12×10.4
=62.4 square feet.
A regular hexagon is divided into 6 equilateral triangle having each side 12 feet.
Area of the regular hexagon = 6× area of the one triangle
=6×62.4=374.4 square feet
Cost of inter locking stones = $9.50 per square feet.
Total cost of gazebo's floor = 374.4× 9.50 =$3556.8
Therefore, Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.
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Geometry homework :/
The length of PZ is 7 units.
What is Centroid Property?According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the side midpoints.
Given:
As, Centroid is the point where all median of a Triangle intersect.
Here, we have centroid 'P'.
Now, using the property of Centroid that the Centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.
So, SP = 1/3 SZ => SZ = 3SP
and, PZ = 2/3 SZ => SZ = 3/2 PZ
Then, 3SP = 3/2 PZ
3(3.5) = 3/2 PZ
10.5 x 2 = 3 PZ
21 = 3PZ
PZ = 7 units
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Can anybody awnser the table for me!!
The table is completed as shown below and total earnings of Lori is found.
What exactly is total earnings of a person?
The wages paid for both regular working hours and other working hours, including extra work or tips are referred to as total earnings.
Consider Tuesday
Hours worked = 4
Base salary = 4 × 7 ( $7 per hour given)
= $28
Tips = 18% of food sales = 0.18 × 300 = $54
Total earnings on Tuesday = 28 + 54 = $82
In the similar way the table can be completed as below.
1) The total earnings of Lori for the week = 82+138.9+218.5+173 = $612.4
2) Total earnings in a year = 52 × 612.4 = $31844.8
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Mr.West ate grapes for 11 days. He ate 2 1/11 ounces of grapes each day . How many grapes did he eat ?
Mr.West ate 23 ounces of grapes in 11 days by eating 2 1/11 ounces of grapes each day.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Mr.West ate grapes for 11 days. He ate 2 1/11 ounces of grapes each day.
Therefore, The total number of grapes Mr.West ate is,
= 11×(2 1/11) grapes.
= 11×(23/11) grapes.
= 23 grapes.
So, He ate 23 ounces of grapes in 11 days.
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The function h(t) = -4.9t2 + h0 gives the height (h), in meters, of an object t seconds after it falls from an initial height (h0). The table shows data for a pebble that fell from a cliff. Image description Choose the quadratic equation that models the situation.
The quadratic equation that models the situation is
h(t) = - 4.9t² + 60.
What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c
Given is that the function h(t) = - 4.9t² + h₀ gives the height (h), in meters, of an object (t) secs after it falls from an initial height h₀. The table shows data for a pebble that fell from a cliff as -
TIME (t) HEIGHT (h)
1 55.1
2 40.4
3 15.9
The given function is -
h(t) = - 4.9t² + h₀
For the point (1, 55.1), we can write as follows -
55.1 = - 4.9 x 1 x 1 + h₀
h₀ = 55.1 + 4.9
h₀ = 60
So, we can write the function as -
h(t) = - 4.9t² + 60
Therefore, the quadratic equation that models the situation is
h(t) = - 4.9t² + 60.
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Answer:
c on edge
3.5
Step-by-step explanation:
(4 x 5) + ( 4 x 2) = 4 x (5 + n)
Answer:
Step-by-step explanation:
1. (4x5) is 20
2. (4x 2) is 8
3. 20 plus 8 is 28
4. 28= 4x (5+n)
5. isolate n by dividing 4 on both sides= 28/4= 4+n
6. subtract 4 on both sides to get 7-4=n
7. n=3
Solve for x: 3x + 2 < 14 and 2 x-5> -11.
Therefore the value of x is less than 4 when x is in the inequality 3x + 2 < 14 and greater than -3 when x is in the inequality 2 x-5> -11
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. For instance, let's say you have 225 and want to purchase a new bicycle that costs $250.
What is expressions or values?Expressions are carried out, or evaluated, in order to yield a value. In an evaluation process, values of expressions can be employed as components of surrounding expressions.
To solve for x in the inequality 3x + 2 < 14, we can begin by subtracting 2 from both sides to get 3x < 12. Then, dividing both sides by 3 gives x < 4.
To solve for x in the inequality 2 x-5> -11, we can begin by adding 5 to both sides to get 2x> -6, then divide both sides by 2 to get x > -3
So x can be any number greater than -3 and less than 4
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1) The Cuyahoga River is 306 miles long, but boats can only travel on 134
miles of the total length. Write the ratio of the Cuyahoga's navigable length
to its total length as a fraction in simplest form.
Answer:
67/153
Step-by-step explanation:
The value of 1/2÷1/3=
my mom will kill me please help
If the perimeter of the triangle is 64 units, then the length of the side PR is 24 units.
What is a Triangle?This is referred to as a three-sided polygon that consists of three edges and three vertices and the longest side is referred to as the hypotenuse.
The perimeter of a triangle is the sum of all the sides which is:
P = a + b + c
64 = 3x +4x - 1 + x + 1
64 = 8x
x = 64/8 = 8 units
Therefore the length of side PR is :
3x = 3 (8) = 24 units.
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hello i need help with questions 5 please thank you.
5a) The total cost of buying the car, priced at $32,000 with the harmonized sales tax (HST) of 13%, is $36,160.
5b) Through the lease, the customer saves $14,760.
5c) The lease options for the lessee after returning the car include:
Lease buyoutLease extensionNew lease contractBuying out the vehicle and then reselling it.6a) The after-tax cost of the Honda Civic is $32,199.35.
6b) The value of the vehicle that needs to be financed is $26,199.35.
6c) The monthly payment will be $567.26 for 4 years.
6d) After four years, the total amount paid for the vehicle is $33,228.48.
Financing Options:A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.
A car purchase can also be financed through loans, like home mortgages.
Value of the car = $32,000
Harmonized Sales Tax (HST) = 13%
Cost of the car with HST = $36,160 ($32,000 x 1.13)
Lease Arrangement:Down payment = $1,000
Financing part = $35,160 ($36,160 - $1,000)
Installment payments = 48
Periodic payments = $425
Total lease cost = $21,400 ($1,000 + 48 x $425)
Savings (advantages) from leasing = $14,760 ($36,160 - $21,400)
Jordan's Car:The value of the Honda Civic = $28,495
Harmonized Sales Tax (HST) = 13%
After-tax cost = $32,199.35 ($28,495 x 1.13)
Annual interest rate = 1.9% compounded monthly
Down payment = $6,000
Financing part = $26,199.35 ($32,199.35 -$6,000)
Financing period = 4 years
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 1.9%
PV (Present Value) = $26,199.35
FV (Future Value) = $0
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 12
Results:
Monthly Payments (PMT) = $567.26
Sum of all periodic payments = $27,228.48
Total Interest $1,029.13
Total amount paid over 4 years = $33,228.48 ($27,228.48 + $6,000)
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The total cost (t) after 8% sales tax is added to an item's price (p): 1.08p= t
The total cost of the item after the sales tax of 8 % is given by the equation t = 1.08p , where p is the initial price of the item
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost price of the item be represented as t
Let the initial cost price of the item be represented as p
Now , the sales tax percentage = 8 %
So , the equation will be
The total cost price of the item t = sales tax percentage ( initial cost price of the item ) + initial cost price of the item
Substituting the values in the equation , we get
The total cost price of the item t = 8 % ( p ) + p
On simplifying the equation , we get
The total cost price of the item t = ( 8/100 ) p + p
The total cost price of the item t = 0.08p + p
The total cost price of the item t = 1.08p
Hence , the equation is t = 1.08p , where p is the initial price of the item
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HELP! WILL GIVE BRAINLIEST
Answer:
Radical Approximation
of A=5√2
of B=2√13
of C is 3√7
Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and 51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?
If we compare the given values then we can find that database B is more likely to have a smaller standard deviation.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.
While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Given that the values in database A are 0 from 100 and have a mean of 50 and Database B has entries from 49 to 51 and also has a mean of 50.
We are required to find the database whose standard deviation is lower.
Standard deviation measures the variation of values. It is calculated after finding the mean. The square of a standard deviation is known as a variance.
Database A has values from 0 to 100 and has a mean of 50. Because the values are somewhat very larger than 50 and database B has values from 49 to 51, there are more chances that the standard deviation of database B will have a smaller value than the standard deviation of database A.
Hence if we compare the given values then we can find that database B is more likely to have a smaller standard deviation.
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Write each percent as a fraction and as a decimal.
7/10%
I NEED THIS BY 2:30PM
The value of 10% as a fraction and a decimal will be 1/10 and 0.1.
How to calculate the percentage?From the information, we want to write the percentage as a fraction as well as a decimal. A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100.
10% as a fraction will be calculated by dividing 10 by 100. This will be:
= 10 / 100
= 1 / 10
10% as a decimal will be calculated by dividing 10 by 100 and giving it in decimal form.
= 1/10
= 0.1
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. Complete question
Write 10% as a fraction and a decimal
a funeral
(since the element in the domain is repeated.
1) {(-1, 8), (0, 15), (1,-4), (2, 0)} 2) {(-5,2), (5,2), (0, -3), (3,-8)} 3) {(-2, 7), (6, 2), (-2,-3), (0, 9)}
it is a function
because there is not any
Points which have the
X-Coordinate and differen
y-Coordinates.
4) {(7,2), (4,-6), (2,-2), (4, -9)} 5) {(2, 3), (2, 4), (2, 5), (2,6)}
Practice: Determining if a Relation is a Function the Siven
6) {(1,-4), (2,-4), (3,-4), (4-4)}
2) {(-5,2), (5,2), (0, -3), (3,-8)} is a function.
3) {(-2, 7), (6, 2), (-2,-3), (0, 9)} is not a function.
4) {(7,2), (4,-6), (2,-2), (4, -9)} is not a function.
5) {(2, 3), (2, 4), (2, 5), (2,6)} is not a function.
6) {(1,-4), (2,-4), (3,-4), (4-4)} is a many to one function.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
We know a relation is a function if it is one-to-one and many-to-one.
But a function can not be one to many means the same value of x can not lead to different values of y.
2) {(- 5, 2), (5, 2), (0, -3), (3,- 8)} is a fuction as different values of x leads to different values of y.
3) {(-2, 7), (6, 2), (-2,-3), (0, 9)} is not a function as the input - 2 leads to two different outputs 7 and - 3.
4) {(7, 2), (4, -6), (2, -2), (4, -9)} is also not a function as input 4 leads to two different outputs - 6 and - 9.
5) {(2, 3), (2, 4), (2, 5), (2,6)} is not a function as input 2 leads to different outputs.
6) {(1, - 4), (2, - 4), (3, - 4), (4, - 4)} is a function and it is a many-one function.
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Brain Builders
Use the graph for Exercises 24 and 25.
24. Before leaving the grocery store, Kenny wrote the
y-coordinate first and the x-coordinate second when telling
his sister where to meet him. To his surprise, she was at
the right location. If his sister did not make an error, where
did the siblings meet? Explain how you know.
The siblings met at the point (4,7). This can be determined by looking at the graph and seeing that the point (4,7) is the only point with an x-coordinate of 4 and a y-coordinate of 7.
What is coordinate?Coordinate refers to the pair of numbers used to identify the position of a particular point on a graph, map, or other two-dimensional plane. Each coordinate consists of an x-coordinate and a y-coordinate that indicate the horizontal and vertical position of the point, respectively. Coordinates can be used to plot points, draw shapes, and determine distances between points. For example, the coordinates (4, 7) would tell you that the point is located four units to the right and seven units up from the origin point. Coordinates can also be used to describe the location of a point in three-dimensional space, with the addition of a z-coordinate.
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what is reference angle for 7pi/4
The reference angle of 7pi/4 is pi/4
What is reference angle?The acute angle formed by the terminal arm or side and the x-axis is known as the reference angle.
There is always a positive reference angle. The reference angle is, in other words, the angle formed by the terminal side and the x-axis. It must always be positive and less than 90 degrees.
considering angle 7 pi/4, the angle is pi/4 away from 2 pi.
7 pi/4 + pi/4 = 8 pi/4 = 2 pi
We can therefore conclude that 7 pi/4 is an angle on the third quadrant and the reference angle is pi/4.
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When the Bureau of Labor Statistics conducts a survey, it begins by partitioning the U.S. adult population into 2007 groups called primary sampling units. Assume that these primary sampling units all contain the same number of adults. If you randomly select one adult from each primary sampling unit, is the result a simple random sample? Why or why not? If it is not a simple random sample, what type of sample is it?
The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.
What is Probability and Non-Probability Sampling?It is not always possible to interview or survey an entire population. Therefore, in many research studies, a portion of the population that is expected to represent the population is drawn and surveyed instead. The portion that is drawn is called the sample, and the method used to draw the sample is called the sampling method. Broadly, there are two types of sampling methods. The probability sampling method is a method wherein all members of the population have an equal probability to be selected to be included in the sample. The non-probability sampling method is a method wherein not all members of the population have an equal probability to be selected to be included in the sample. Instead, members are recruited into the sample based on the researcher's subjective and personal judgment.
Simple Random Sampling Method:
Simple random sampling method, sometimes abbreviated as SRS, is the purest form of probability sampling. Figuratively, it is like putting the names of the entire population in a hat and drawing each member from the hat with a blindfold. Therefore, every member of the population has an equal chance of being included in the sample.
Two-stage Cluster Sampling Method:
In the first stage of a two-stage cluster sampling method, the population is first divided into subgroups called clusters. For instance, the population is divided into subgroups based on geographic location. Unlike strata in stratified sampling, clusters are heterogeneous and each cluster is supposed to represent the heterogeneity of the population. These clusters are also known as primary sampling units or PSUs. In the second stage, the simple random sampling method is used to draw individuals from each of the PSUs to be included in the study sample.
Hence, The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.
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