Any method of sampling in which every individual is equally likely to be selected.
What does "simple random sampling" mean?
Simple random sampling is a sort of probability sampling in which a subset of participants from a population is randomly chosen by the researcher.
There is an equal opportunity for selection for every person in the population. Then, data are gathered from as many of the individuals in this chosen subset as is feasible.
A simple random sampling is a method of sampling where each potential participant has an equal chance of being chosen. In other words, the likelihood that any given person will be chosen is 1/n if there are n people.
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piecewise linear functions common core algebra 2 homework answers
Piecewise linear functions, f(x) as common core algebra, Evaluate each of the following :
(1) f(-3) = 12
(2) f(4) = 2
(3) f(0)= 8
(4) f(3)= 8
What is Piecewise linear functions ?A piecewise linear function is a function defined on the interval [xₘᵢₙ ,xₘₐₓ]. A piecewise linear function is a function that consists of straight line segments. This is a piecewise function whose pieces are affine (linear) functions. Graphs of piecewise linear functions consist of line segments and rays.
We have given that,
f(x) = 5x - 3 ; x< -2
= x+8 ; -2≤x< 3
= 1/3(x) + 7 ; x ≥3
we see here that , f(x) is a piecewise linear function defined on interval [-2,3).
Now, we solve the following
(1) f(-3) , here x = -3< -2 i.e we take f(x) =5 x -3
=> f(-3) = 15 - 3 = 12
(2) f(4) , x= 4 >3 so, f(x) = 1/3(x) + 7
=> f(4) = 1/3(4) + 7 = 14/7 = 2
(3) f(3) , x = 3 so, f(x) = 1/3(x) + 7
=> f(3) = 1/3(3) + 7 = 8
(4) f(0) , x = 0 or -2 < x < 3 so, f(x) = x+8
=> f(0) = 0+8 = 8
Hence, we evaluate the given functions.
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Complete question:
piecewise linear functions common core algebra 2 homework answers
5x - 3 x<-2 1. For f (x) = x+8 -25x<3 answer the following questions. -x+7 x23 (a) Evaluate each of the following by carefully applying the correct formula: (1) f ( -3 ) (ii) f (4) (iii ) f ( 3 ) (iv ) f (0 )
if the list price is $70 and the percent of discount is 10%. What is the amount of discount
Answer: 7
Step-by-step explanation: You would multiply 70 by 10 to get 700, then divide it by 100 to get 7. So, it would be 7 dollars.
Answer: 7
Step-by-step explanation:
Determine the coordinates of W(−7, 4) after a reflection in the line y=9
The coordinate of the reflection about the line y = 9 is thus (7, 4)
What is reflection?Reflection is a transformation in which an object is flipped over a line.
How to find the coordinates of W(−7, 4) after a reflection in the line y = 9?We know that to reflect W(-7, 4) over the line y = 9, the distance of the point W and its reflection from the line y = 9 must be the same.
The distance of point W(-7, 4) from the line y = 9 is d = 9 - (- 7) = 9 + 7 = 15
So, the x - coordinate of the reflection from the line y = 9 is x = 15 - 9 = 7
Since the y - coordinate of the point W, does not change, the coordinate of the reflection about the line y = 9 is thus (7, 4)
So, the coordinate of the reflection about the line y = 9 is thus (7, 4)
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Drag the tiles to the correct boxes to complete the pairs.
Match the one-to-one functions with their inverse functions.
f(x)=-17
f(x)=x-10
Inverse Function
f-¹(x) = 5x
ƒ-¹ (x) = ²
f-¹ (z) = x + 10
f-¹ (z) = 3(z+17)
f(x) = √2x
Function
f(x) = //
The inverse of a function is f^-1(x) = 3(x + 17)/2 and f^-1(x) = x + 10
What is function ?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.
Functions can be roughly categorized into four sorts. based on the element Numerous to one function, onto function, one to one and onto function, into function.
1.f(x) = 2x/3 - 17
Finding the inverse
y = f(x)
= 2x / 3 - 17
Exchange the variables, x for y and y for x
x = 2y / 3 - 17
Isolate the variable y
Adds 17 both sides
x + 17 = 2y / 3
Multiply by 3 both sides
3(x+17) = 2y
Divide by 2 both sides
y = 3(x + 17)/2
let f^-1(x) = y
f^-1(x) = 3(x + 17)/2
2. f(x) = x - 10
Finding the inverse
y = f(x)
= x - 10
Exchange the variables, x for y and y for x
x = y - 10
Isolate the variable y
Adds 10 both sides
y = x + 10
Multiply by 3 both sides
3(x+17) = 2y
let f^-1(x) = y
f^-1(x) = x + 10
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the sample mean is the point estimator of
the sample mean is the point estimator of μ
Sample Mean:
The Sample Mean is the average mathematical value of a sample’s values. It is a statistical indicator used to analyze various variables over time. Statisticians and researchers obtain it by dividing the total sum of values of all data fragments and then dividing it by the total number of data sets.
Point Estimate:
p=x/
p is the point estimate for the population proportion, x is the number of
successes, n is the sample size
p= + /2
for the population proportion
x= + /2
for the population mean
= − /2
is the margin of error
the sample mean is the point estimator of μ
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Which of the following is not a criterion for congruence of ∆ s a SAS B ASA C SSA D SSS?
(C) SSA is not a requirement for triangle congruence.
What is the congruence of triangles?
Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
We can move, flip, twist, and turn these triangles to produce the same effect.
When relocated, they are parallel to one another.
Two triangles are congruent if they satisfy all five conditions for congruence.
Right angle-hypotenuse-side (RHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).
We know that SSA is not the criteria for the congruence of the triangles.
Therefore, (C) SSA is not a requirement for triangle congruence.
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One basketball costs $2 more than another. The sum of their costs is $146. How much does each basketball cost?
Answer:
$72 and $74
Step-by-step explanation:
Let the cheaper ball cost x.
x + x + 2 = 146
2x = 144
x = 72
x + 2 = 74
Answer: $72 and $74
What is 2 divided by 3? Explain the steps pleas.
The value of 2 divided by 3 is 0.67
How to evaluate the quotient expression?From the question, we have the following parameters that can be used in our computation:
2 divided by 3
To start with, we need to represent the expression properly as a quotient
So, we have the following representation
2 divided by 3 = 2/3
Evaluate the quotient expression using a calculator
This gives
2 divided by 3 = 0.67
Hence, the solution to 2 divided by 3 is 0.67
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HELP PLEASEJG
Problem: What is the actual distance between two cities if it is drawn to scale of 1:3,000,000 and it is 3 cm on the map?
Answer:
distance between two cities will be 9 000 000 km
Answer:
Step-by-step explanation:Scale of a map is 1:3000000 i.e, 1cm on map =30km so distance of towns on map =3.5cm Actual distance = 3.5×30=105km
You bought 4 cakes to split between 7 teachers what fraction of a cake does each teacher get?
4/7
4 ÷ 7 = 4/7
fraction means division
The rate of change of the line represented by each table
Answer: m = 3
Step-by-step explanation:
Let pick 2 points ( 0,3) ( 2,9)
Y increased by 6, x increase by 2
Slope is 6/2 = 3
Which graph has a slope of 4/5?
Answer: Second graph from top.
Step-by-step explanation:
Slope is written in change in y over change in x. In other words, "rise over run" so the slope of 4/5 means rise 4 units and move 5 units right. The graph that meets this requirement is the second graph, as shown in the attachment.
C'D'
is a translation of
CD
. Write the translation rule.
-
Translation is one of the four types of mathematical transformations that may be applied to a function graph.
(x, y) = (x + a, y + b)
Describe translation.In mathematics, a translation is the up, down, left, or right movement of a form. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more routes have been altered. There is no change in the form because it is just being moved from one location to another.
Rule of TranslationWhen the shape is moved towards the left by k units, then replace x with x - k.
When the shape is moved towards the right by k units, then replace x with x + k.
When the shape is moved up by k units, then replace y with y + k.
When the shape is moved down by k units, then replace y with y - k.
Example: What are the new coordinates when the translation (x, y) → (x - 2, y + 3) is applied to the point (2, 5).
Solution:
The coordinates of old point (preimage) are (x, y) = (2, 5). Now, applying the given translation to this point,
x - 2 = 2 - 2 = 0
y + 3 = 5 + 3 = 8
Thus, the coordinates of the translated point (image) are (0, 8).
This was the example of translation.
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Select the values that make the inequalityt > -1 true.
(Numbers written in order from least to greatest going across.)
The values that make v ≥ 1 inequality true are 2, 3, 4, 5....
What is inequality in mathematics?
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
The inequality is given as:
v ≥ -1
The values of c for which the given inequality → v ≥ -1 is true will belong to the set (say A) -
A = [-1, - ∞)
Therefore, we have to select all numbers which fall in this set. The numbers are
-1, 0, 1, 2, 3,....
Rewrite properly as:
v ≥ 1
The above means that the true values of v are values greater than 1.
Hence, the values that make v ≥ 1 inequality true are -1, 0, 1 , 2, 3, 4, 5....
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PLS HELP ME NEED FOR MATH PLS
y = 25x + 263 this equation represents how much money she will have, including her saving.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
We have,
The saved amount of $263 by Jenna,
and also she earns $25 per day
if x represents the number of days she works,
and let's take y as the total amount she will have.
Then the equation becomes:
y = 25x + 263
Hence, y = 25x + 263 this equation represents how much money she will have, including her saving.
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Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.
Which table contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces?
The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.
How to obtain the viable solutions?The variables for this problem are given as follows:
The input variable b represents the number of books ordered.The output variable w represents the total weights of the books, in ounces.To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.
Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.
Missing InformationThe table is given by the image shown at the end of the answer.
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a survey was taken of a random sampling of residents of new york city and los angeles to compare how many of them own a car. a 4-column table with 3 rows. the first column has no label with entries l a residents, n y c residents, total. the second column is labeled own a car with entries 3,251; 1,478, 4,729. the third column is labeled do not own a car with entries 869; 6,182; 7,051. the fourth column is labeled total with entries 4,120; 7,660; 11,780. which statement about the two-way frequency table is true?
The true statement is;
There is a greater percentage of Los Angeles residents who own a car than New York City residents who do
Given,
Following is the presentation of the values:
The number of residents in Los Angeles own a car = 3251
The number of residents in New York City own a car = 1478
Total residents who own a car = 4729
Los Angeles residents who do not own a car = 869
New York City residents who do not own a car = 6182
Total residents who do not own a car = 7051
Total Los Angeles residents sampled = 4120
Total New York City residents sampled = 7660
Total residents of both cities sampled = 11780
Here,
Percentage of Los Angeles residents who own a car = (3251/4120)×100 = 78.9%
Percentage of New York City residents who own a car = (1478/7660)×100 = 19.3%
Then,
The total number of people in the poll who own a car = 4729
Therefore,
The correct option is that there is a greater percentage of Los Angeles residents who own a car than New York City residents who do.
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Answer: B
Step-by-step explanation:
the manager of a clothing factory checks a random sample 500 shirts for defects he finds that 8 are defective the factory produces 2625 shirts on friday
The expected number of defective shirts produced by the factory on Friday is of:
42 shirts.
How to obtain the expected amount?The expected number of defective shirts produced by the factory on Friday is obtained as the multiplication of the sample proportion by the total number of shirts produced on Friday.
The manager of a clothing factory checks a random sample 500 shirts for defects he finds that 8 are defective, hence the sample proportion is given as follows:
p = 8/500 = 0.016.
The factory produces 2625 shirts on Friday, hence the expected number of defective shirts is given as follows:
E(X) = 0.016 x 2625 = 42 shirts.
Missing InformationThe problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the expected number of defective shirts produced by the factory on Friday.
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I RLLY NEED HELP ASAP
the virus that causes bird flu is being spreading through your community quickly. you and your roommate received a flu shot over two months ago. your roommate gets sick and then the doctor confirms it is the bird flu. explain if you have a high, average or low probability of getting the bird flu and why you selected your answer. the virus that causes bird flu is being spreading through your community quickly. you and your roommate received a flu shot over two months ago. your roommate gets sick and then the doctor confirms it is the bird flu. explain if you have a high, average orlow probability of getting the bird flu and why you selected your answer.
It is possible for humans to contract bird flu viruses. There have been outbreaks of two strains, H5N1 and H7N9, that have affected some populations in Asia, Africa, the Pacific, the Middle East, and portions of Europe. Other unusual forms of avian flu that have affected humans in the US have also been reported. The majority of humans who contract bird flu have had direct contact with diseased birds or surfaces that have been contaminated by the saliva, mucus, or droppings of infected birds.
By what means is the avian flu spread?Through their saliva, mucus, and excrement, infected birds spread the bird flu virus. Inhaling the virus or getting it in one's eyes, nose, or mouth can result in human infection with bird flu viruses.
How might we stop the spread of the avian flu?After contacting birds or surfaces that could be contaminated with their saliva, mucus, or feces, whether they are wild or domesticated, avoid touching your mouth, nose, or eyes.
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which of the following represents the average rate of change to the function g(x) = 3/2x + 1 over the interval -2 < x < 8
The average rate of change to the function is (d) 3/2
How to determine the average rate of change to the function?From the question, we have the following parameters that can be used in our computation:
g(x) = 3/2x + 1
Also, we have the interval to be
-2 < x < 8
This interval can be expressed as
a = -2 and b = 8
So, we start by calculating g(-2) and g(8)
Substitute the known values in the above equation, so, we have the following representation
g(-2) = 3/2 * (-2) + 1
g(-2) = -2
Also, we have
g(8) = 3/2 * (8) + 1
g(8) = 13
The average rate of change to the function is then calculated as
Rate = [g(8) - g(-2)]/[8 + 2]
So, we have
Rate = (13 + 2)/(8 + 2)
Evaluate
Rate = 3/2
Hence, the average rate is 3/2
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HELP ME I WILL GIVE 20 POINTS PLS
the given proportional relationship y=0.5x with proportional constant is 1/2.
what is proportional relationship?
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.
Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.
For every 1 scoop of ice cream, cup of milk is needed 1/2, and for every 5 scoops of ice cream, 2 cups of milk 2 1/2 are needed.
So the equation will be y = kx
or y = 0.5(x)
Here proportional constant is 1/2 or 0.5.
For 18 scoops of icecream, milk will be needed is 18/2 = 9 cups of milk.
Hence, we can say that the given proportional relationship y=0.5x with a proportional constant is 1/2.
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(PLEASE HELP)
Consider circle O with diameter GB. Line AD is tangent to circle O at point A and line DB is tangent to circle O at point B. The measure of ∠GBA is 38°. Chord GC bisects ∠G. Determine each measure
The angles GBD, GBD and G measures 90 , 90, 52 degree respectively.
GB is the diameter given.
AD is the tangent given.
The tangent makes 90 degree angle with diameter.
hence the angle GBD will be : 90°
Similarly, GBA will also be 90°
The angle GBA is given as 38°
Hence the angle G will be = 90 - 38 =52
All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its centre.
The radius must typically be a positive integer. A degenerate situation is a circle with radius equal to zero (one point). Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.
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Which of the following choice are the factors of X² 5x 6?
Answer:
Step-by-step explanation:
Assuming that you mean x² + 5x + 6
the factors are (x + 2) and (x + 3).
You roll a 6- sided die what is p (greater than 3 or factor of 14)
Answer:
7
Step-by-step explanation:
Find the coordinates of the circumcenter of the triangle with the given vertices.
A(0, 0), B(0, 8), C(6, 0)
x =3 and y = 4 , these two perpendicular bisectors will come together. These are the triangle's circumcenter's coordinates.
What is perpendicular in triangle?
The sides of a triangle are divided into two equal portions by the perpendicular, which is parallel to the sides drawn from the opposing vertices.
The circumcenter of a triangle is the location where the three perpendicular bisectors of the triangle meet.
A(0, 0), B(0, 8), C(6, 0)
Circumcenter , P(x,y)
AP = BP = CP
AP² = BP²
(x - 0 )² + ( y - 8 )² = ( x- 0)² + ( y - 0 )²
x² + y² + 64 - 16y = x² + y²
64 - 16y = 0
16y = 64
y = 4
BP = CP
BP² = CP²
(x - 0)² + ( y- 0 )² = ( x- 6)² + ( y - 0)²
x² + y² = x² 36 - 12x + y²
36 - 12x = 0
12x = 36
x = 3
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how many ways can i select 3 objects out of 30
Answer:
10 times.
Step-by-step explanation:
because 10 x 3 = 30.
If the 3 objects are selected from 30. Then the number of combinations will be 4,060.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
A won and a punctuation mark are used to represent the combination of all positive integers that are less than or equal to the provided positive integer.
The 3 objects are selected from 30. Then the combination is given as,
⇒ ³⁰C₃
⇒ [30!][(30 - 3)! x 3!]
Simplify the expression, then we have
⇒ [30 x 29 x 28 x 27!] / [(27! x 3 x 2 x 1)]
⇒ (30 x 29 x 28) / (3 x 2 x 1)
⇒ 24,360 / 6
⇒ 4,060
If the 3 objects are selected from 30. Then the number of combinations will be 4,060.
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Car A travels 702 miles on 12 gallons of gasoline. Car B travels 873 miles on 15 gallons of gasoline. Hugo wants to buy a car with lower fuel consumption. Find out the distance each car could travel per gallon of gasoline. Then, tell which of the two cars (A or B) Hugo should buy.
Hugo will buy car B.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Car A travels 702 miles on 12 gallons of gasoline.
And, Car B travels 873 miles on 15 gallons of gasoline.
Now,
Since, Car A travels 702 miles on 12 gallons of gasoline.
And, Car B travels 873 miles on 15 gallons of gasoline.
Hence, The distance of car A for travels in per gasoline = 702 / 12
= 58.5 miles
And, The distance of car B for travels in per gasoline = 873 / 15
= 56.2 miles
Since, Hugo wants to buy a car with lower fuel consumption.
Clearly, The car B consume lower fuel.
Hence, Hugo will buy car B.
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i've asked 55 students on monday whether they did their homework over the weekend. 17 of them said they did. find a 67% confidence interval for the proportion of students who will tell me that they did their homework over the weekend.
We are 67% confident that the proportion of students who are tell me that they did their homework over the weekend.0.087 with a margin of error of 0.0175
Find the confidence interval ?In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.
Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
87/1000 = 0.087
We have a 67% confidence level that the percentage of left-handed students is 0.087, with a 0.0175 margin of error.
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how healthy are the employees at direct marketing industry? a random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period). use these data to create a 95% confidence interval for the population mean days absent for sickness.
The sample mean is 5.0833 and the standard deviation is 3.476 and the confidence interval is (2.87, 7.29).
In the given question, a random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period).
Using these data to create a 95% confidence interval for the population mean days absent for sickness
2 5 3 7 10 0 6 8 5 11 3 1
a) We have to find the sample mean and the standard deviation (round to two decimal places).
The sample mean;
X = 2+5+3+7+10+0+6+8+5+11+3+1/12
X = 61/12
X = 5.0833
Now the standard deviation
SD = √[{x(1)-X)^2+(x(2)-X)^2…………….(x(12)-X)^2}/N]
After solving using that formula;
SD = 3.476
b) 95% confidence in interval for the population mean days absent for sickness.
Lower Bound = X - t(α/2)*s/√n
Upper Bound = X + t(α /2)*s/√n
where
α /2 = (1 - confidence level)/2 = 0.025
X = sample mean = 5.083333333
t(α/2) = critical t for the confidence interval = 2.20098516
s = sample standard deviation = 3.476108936
n = sample size = 12
df = n - 1 = 11
Thus,
Lower bound = 2.874719086
Upper bound = 7.291947581
Thus, the confidence interval is (2.87, 7.29).
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The right question is:
How healthy are the employees at direct marketing industry? A random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period). Use these data to create a 95% confidence interval for the population mean days absent for sickness.
2 5 3 7 10 0 6 8 5 11 3 1
a) Find the sample mean and the standard deviation (round to two decimal places)
b) 95% confidence in interval for the population mean days absent for sickness.
