A bijection between two sets is constructed below and also proved that it is both one-one and onto.
What is meant by one-one function?The phrase "one-to-one function" should not be mistaken with "one-to-one correspondence," which is used to describe bijective functions, in which each element in the codomain is a precise mirror image of a single element in the domain.
Any function that can work with the operations of two algebraic structures is said to be a homomorphism between them. An injective homomorphism is also referred to as a monomorphism for any commonly occurring algebraic structures, particularly vector spaces.
Let t∈T
Then,
t=2k+1, for some k∈Z
Let s=3k
Then,
s∈S and f(s)=2(s/3)+1
=2k+1
=t
Therefore, for every t∈T there exists s∈S such that f(s)=t
Thus, f is onto.
Hence,
f:S ----> T is a bijective mapping
⇒|S|=|T|
Now, we have to define a mapping f:S ---?T
By f(x)=2(x/3)+1, ∀x∈S
Given,
S={3k|k∈Z} and T={2k+1:k∈Z}
We have to prove:
|S|=|T|
Let x, y∈ S with f(x)=f(y)
Then,
2(x/3)+1=2(y/3)+1
2(x/3)=2(y/3)
(x/3)=(y/3)
x=y
So, f is one-one
Now, we have proved that f is both one-one and onto.
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Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the bone density test scores that can be used as cutoff values separating the lowest 3% and highest 3%, indicating levels that are too low or too high, respectively.
The bone density scores are -1.88, 1.88
What is Standard Normal Deviation ?A normally distributed deviation is a standard normal deviate. A standard normal random variable is a realization of a random variable with an expected value of 0 and a variance of 1.
The z score for the lowest 3%(0.03) calculated from the standard normal table = -1.88
X1 = 0+1× (-1.88 ) = -1.88
Similarly, The z score for the highest 3%(0.03) calculated from the standard normal table = +1.88
X2 = 0+1× (1.88 ) = +1.88
So
The bone density scores are -1.88, 1.88
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Find a low-rank approximation Compute the optimal rank-2 approximation of the symmetric matrix 3.75 -1.25 0.25 -1.75 -1.25 3.75 -1.75 0.25 A= given that the columns of 0.25 -1.75 3.75 -1.25 -1.75 0.25 -1.25 3.75 of A are eigenvectors A2 = Save & Grade 10 attempts left Save only Additional attempts available with new variants
Previous question
Answer: 53.213
Step-by-step explanation:
On a coordinate plane, a parabola with a dashed boundary line opens down. It goes through (negative 8, 0), has a vertex at (negative 6, 2), and goes through (negative 4, 0). Which inequality in standard form represents the shaded region? y less-than negative x squared minus 12 x minus 32 y less-than negative one-half x squared minus 6 x minus 16 y less-than negative one-half x squared + 6 x minus 16 y less-than negative x squared + 12 x minus 32.
The inequality y < -1/2x² - 6x - 16 corresponds to the right representation.
Along with passing through (-8, 0), (-6, 2), and (-4, 0), it also has a vertex there.
We need to find its equation.
We must take into account the provided details on the parabola's properties and its points in order to choose the proper inequality to symbolize the shaded area of the parabola.
The vertex of the parabola is at (-6, 2), and it opens downward. This indicates that the equation for the parabola is of the type y = a(x - h)² + k, where (h, k) denotes the vertex.
In this case, h = -6 and k = 2.
Plugging in the values of the vertex into the equation, we have:
y = a(x - (-6))² + 2
y = a(x + 6)² + 2
Now we can use one of the points that the parabola passes through to solve for the value of 'a'.
The point (-8, 0) lies on the parabola. Substituting these values into the equation:
0 = a(-8 + 6)² + 2
0 = a(-2)² + 2
0 = 4a + 2
4a = -2
a = -1/2
Substituting the value of 'a' into the equation:
y = (-1/2)(x + 6)² + 2
Expanding and rearranging the equation:
y = (-1/2)(x² + 12x + 36) + 2
y = (-1/2)x² - 6x - 18 + 2
y = (-1/2)x² - 6x - 16
Therefore, the correct inequality that represents the shaded region is:
y < -1/2x² - 6x - 16
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Suppose the odds of rain today are 5:9
What would be the probability that it will rain today?
The probability is the odds thus the probability it will rain today will be 5/9.
What is probability?Probability is also known as chance because, if you flip a coin, the chance that it will strike on its head or tail is just a chance that either a head will make an appearance or not.
As per the given,
The odds of rain today are 5:9
Odds will be the equivalent of probability because probabilities is the same as chances.
The probability will be 5/9 or 5:9.
Hence "Since probability implies odds, so possible that it will rain tonight is 5/9.".
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the task of framing a building has been estimated to take an average of 25 days with a standard deviation of 4 days. what duration should be used if there is to be a 90% confidence that the duration will not be exceeded? what is the probability that the duration will actually exceed 23 days?
The required probability that the duration will actually exceed 23 days is 22.66%.
What is Probability distribution?A probability distribution is a factual capability that depicts every one of the potential qualities and probabilities for an irregular variable inside a given reach.
According to question:We have,
μ = 25, σ = 4,
For 90% confidence interval, Z = 1.645
Then,
Z =( x -μ )/σ =(x - 25)/4
1.645 = (x - 25)/4x
x = 4(1.645) + 25 = 31.58 days
when duration increase by 3 days
So, Z = 3/4 = 0.75
Probability = 22.66%
Thus, required probability is 22.66%.
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consider the angle the bottom of the ladder makes with the ground. how fast is the angle changing (in radians) when the ladder is 5.4 feet away from the house?
The angle is changing 0.05136 radians when the ladder is 5.4 feet away from the house.
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Here, we have
The angle the bottom of the ladder makes with the ground.
d∅/dt = d∅/dx × dx/dt.....(1)
bur, x = 24cos∅
dx/d∅ = -24sin∅
d∅/dx = 1/(-24sin∅)
Now, equation (1) becomes,
d∅/dt = 1/(-24sin∅)× dx/dt
If the ladder is 5.4 feet away from the house then,
sin∅ = √24² - 5.4²/24
d∅/dt = -1/√24² - 5.4² ×0.12
d∅/dt = 0.05136 radian
Hence, the angle is changing 0.05136 radians, when the ladder is 5.4 feet away from the house.
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You plan to put anti-theft devices on each garment in your store. You have 575 garments and it takes an employee 30 seconds to tag a garment. How many hours will it take 3 employees to tag all garments?.
The number of hours it will take 3 employees to tag all garments is 1.60 hour
How to determine the number of hours it will take 3 employees to tag all garments?.From the question, we have the following parameters that can be used in our computation:
Number of garments = 575
Time taken by an employee on a garment = 30 seconds
This means that the variation is an inverse variation
If the time taken by an employee on a garment is 30 seconds
Then the time taken by 3 employees on a garment is
Time taken = 30 seconds/3
Evaluate
Time taken = 10 seconds
For 575 garments, we have
Time taken = 10 seconds * 575
Evaluate
Time taken = 5750 seconds
Express in hours
Time taken = 1.60 hour
Hence, the time taken is 1.60 hour
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if a giraffe has two eyes, a monkey has two eyes, and an elephant has two eyes, how many eyes do we have?
Write 14/5 as a mixed number
Answer:
2 4/5
Step-by-step explanation:
14 = 10 + 4
10/5 = 2
4/5
9. There were 15 questions on the last quiz in
Mrs. Lorenzo's class. A student answered
13 questions correctly. Write the ratio of
correct answers to total questions as a
decimal. (Lesson 1)
Answer:
13:15
1:1.5
0.5:0.575;is the ratio of
correct answers to total questions as a
decimal.
What is the value formula?
The value formula is: Value = Place Value × Face Value
We know that the value in mathematics is nothing but the worth of each digit depending on where it lies in the number.
We calculate the value of number by multiplying the place value and face value of the digit.
The value formula is:
Value = Place Value × Face Value
Place value is the value of the column in which the number is. Each column in a number holds a different place value.
For exa., consider a number 456. Here, the place value of the digit 5 is tens and the place value of 4 is hundreds.
The face value of any digit is the same digit.
For a number 120 , the face value of 1 is 1, face value of 2 is 2.
Therefore, the formula for the Value = Place Value × Face Value
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What does 1/2 of a number mean?
1/2 of a number means one - half of a number.
The irreducible fraction that results from dividing one by two or from dividing any number by its double is known as a half (plural: halves).
Conversely, division by one-half is equivalent to multiplication by two, or "doubling," while multiplying by one-half is equivalent to division by two, or "halving."
In measurements, recipes, equations, etc., one half is frequently used. One part of something that is divided into two equal pieces is said to be divided in half.
For instance, a triangle's S-area is calculated.
S = base / 2 * perpendicular height.
The typical decimal extension of one half is 0.5, and it frequently appears as 0.49999999. In any even base, it has a similar pair of expansions.
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The organizers of a school playestimate that half the students who attend will bring an adult guest. If s represents the number of students expected to attend the play, which expression represents the total expected attendance
Answer: 1/2s + s = total expected attendance.
Step-by-step explanation: If s is the number of expected students and half of them are estimated to bring a guest than you would find half of s and add it to s to get the total expected attendance.
What shape is the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base?
A triangle shape is formed by the cross-section of a triangular pyramid sliced by a plane that is perpendicular to its base
A triangular pyramid is a geometric solid having a triangle for a base and three triangles with the same vertex on each side. That is, the triangular pyramid is made up of four triangles. Pyramids made of triangles might be straight or inclined. It resembles a pyramid with four triangular faces that meet at one vertex and a triangular base.
Let's first draw the triangular pyramid. Now, mark the base. Then, denote the plane passing perpendicular to the base. From the diagram we can tell, the plane cuts this pyramid to form a triangle cross-section.
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How do you draw a 1 1 scale bar?
To draw a figure with 1 : 1 scale, draw the the figure in actual size
The scale factor can be defined as the ratio between the original size of the figure and the new size of the figure.
While scale factoring the shape of the object will be same but the size changes
Here the given ratio = 1 : 1
The means the scale factor = 1/1
= 1
When the scale factor is equal to one, the the size of the original object and the size of the new object will be same
Therefore, 1 : 1 scale bar is the drawing with actual size of the object
I have solved the question in general, as the given question is incomplete
The complete question is
How do you draw a figure with 1 : 1 scale bar ?
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a sporting goods store manager was selling a kayak set for a certain price the manager offered markdowns 10 percent, and 30 percent marking the one-day sale price as 328 find the original selling of the kayak
Using percentages, we know that $515.87 approx is the purchase price at the start.
What is the percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.
Although "pct," "pct," and occasionally "pc" are also employed as acronyms, the percent symbol "%" has been most usually used to denote it.
A% is a number that has neither dimensions nor a specified unit of measurement.
For example, if you properly completed 75 out of 100 questions on a test, you would have received a 75% grade (75/100).
So, in mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Let x represent the initial asking price ( in dollars ),
After 10% is deducted, 10% of x less the new selling price, or x - 0.1x, equals 0.9x.
Having reduced the price by 30%,
The final selling price equals 90% less than 90%.
= 0.9x - 0.3 × 0.9x
= 0.9x - 0.27x
= 0.63x
The answer to the query is:
0.63x = 325
x = 325/0.63
x = 515.87
Therefore, using percentages, we know that $515.87 approx is the purchase price at the start.
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Correct question:
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set $325. Find the original selling price of the ski set. It was marked down 10% and 30%
Find the unit vector (in component form)
12) a = (12, -35)
Unit vector in the direction of a
Compare the square root of 30 and fifty ninths using >, <, or =.
fifty ninths is less than the square root of 30
the square root of 30 is less than fifty ninths
fifty ninths is equal to the square root of 30
the square root of 30 is greater than fifty ninths
The square root of 30 is less than fifty-ninths mathematically it can be written as √30<√59. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the numbers are the square root of 30 and the square root of 59. The values will be compared below,
√30 = 4.8
√59 = 7.68
The inequality will be written as,
√30<√59
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PLEASE HELP 35 POINTS MATH
Answer:
31
Step-by-step explanation:
-4+16+19=31
What is the LCD of
17x/(x+1)(x+1) and x² /x² -1
Answer:
To find the least common denominator (LCD) of two fractions, we need to find the least common multiple of the denominators of the fractions. The first fraction is 17x / (x + 1)(x + 1), and the second fraction is x² / x² - 1. The denominators of these fractions are (x + 1)(x + 1) and x² - 1, respectively.
To find the least common multiple of (x + 1)(x + 1) and x² - 1, we need to first factor each denominator. The denominator (x + 1)(x + 1) can be factored as (x + 1)², and the denominator x² - 1 can be factored as (x + 1)(x - 1). The least common multiple of these two denominators is (x + 1)², which is the LCD of the two fractions. Therefore, the LCD of 17x / (x + 1)(x + 1) and x² / x² - 1 is (x + 1)².
Step-by-step explanation:
Spiral Review
Find the slope of the line that passes through the points. Need a review? Go back to lesson 3.2 or use the formula below.
If necessary, leave your answer as a fraction, not a mixed number.
a. (-1, 7) and (5, 7)
b. (1, 2) and (5, 0)
NEED HELP NOW!!
Answer: b
Step-by-step explanation:
becuase of the fromula
Jerry makes souvenirs to sell in his shop. For one batch of souvenirs, he spends 200 dollars for materials and hopes to make 1,000 dollars in profit. He writes the equation pn−200 = 1,000 to represent the price, p, in dollars, for each souvenir and the number of souvenirs, n, that he needs to sell to make 1,000 dollars in profit. He knows that he can make at most 400 souvenirs from the materials.
To make 1,000 dollars in profit, he needs to sell each souvenir with a price of $3.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
pn−200 = 1,000
Substitute n =400
400p - 200= 1000
400p = 1000 + 200 = 1200
p= 1200/400 = 3
=> To make 1,000 dollars in profit, he needs to sell each souvenir with a price of $3.
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correlation and regression are two closely related topics in statistics. for each of the following statements, indicate whether the statement is true of correlation, true of regression, true of both correlation and regression, or true of neither correlation nor regression.
Outliers can have an impact on correlation and regression, which may result in the calculation of inaccurate parameters.
Given that,
In statistics, correlation and regression are frequently used interchangeably.
Regression models the impact of one variable on another, whereas correlation assesses the strength of the link. The following is the solution:
Correlation
Correlation and Regression
Correlation
The degree and type of the association between variables, which cannot be deduced from the regression equation, can be determined using the correlation coefficient.
Both Outliers can have an impact on correlation and regression, which may result in the calculation of inaccurate parameters.
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PLEASE HELP WITH MY MATH HOMEWORK
ill give brainliest
Answer:
The answer is that the ball was in the air for 0.56 seconds when it was 54 feet above the ground. This was determined by using the Quadratic Formula to solve the equation 54 = -16s^2 + 96s for the variable s.
Step-by-step explanation:
To solve this equation, we can use the Quadratic Formula, which states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
In this case, a = -16, b = 96, and c = -54. Plugging these values into the Quadratic Formula, we get:
s = (-96 +/- sqrt(96^2 - 4 * -16 * -54)) / (2 * -16)
= (96 +/- sqrt(9216 + 4352)) / -32
= (96 +/- sqrt(13,568)) / -32
Since we want the time (in seconds) that the ball was in the air, we need to find the positive solution to this equation. Thus, we have:
s = (96 + sqrt(13,568)) / -32
= (96 + 120) / -32
= 0.5625 seconds
Rounding this value to the nearest hundredth of a second, we get 0.56 seconds. This means that the ball was in the air for 0.56 seconds when it was 54 feet above the ground.
To solve this equation, we used the Quadratic Formula. This method allowed us to find the time (in seconds) that the ball was in the air by solving for the value of the variable s in the given equation. This helped Vue answer his question by providing a numerical value for the amount of time that the ball was in the air when it was 54 feet above the ground.
how many integers must you pick in order to be sure that at least two of them have the same remainder when divided by 14?
Because of this, we need to choose 15 integers in such a way that we can ensure that when they are divided by 14, at least two of them will provide the same residual.
In order to be sure that at least two of them have the same remainder when divided by 14.
Generally, If you divide a number by 14, the result is a fraction. There are 14 remainders that might occur, and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and, 13.
So if we pick a number and divide it by 14, the remainder can be one of 14 (0 memory 13). So if we select 14 numbers, we have the option to select 14 unique memories ranging from 0 to 13.
Finally, if we choose another integer, we will have the same reminders according to the drawer principle, because there are only 14 reminders and 15 > 14.
Therefore, we should choose the number of 15 so that at least two numbers have the same remainder when divided by 14.
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You have a surfboard at the store you work at that has a price tag of $800.
You were told that it will cost $745 when it goes on sale this Friday.
You are asked to make a poster describing the sale. They want the poster to say
Surfboards
____% off
Today only!
Calculator the % of sale.
Answer:
Hope this is helpful
Step-by-step explanation:
50% off Today Only!
The ratio of Pablo's age to Richard's age is 6: 7. The ratio of Pablo's age to Tristan's age is
5: 4. Find the ratio of Pablo's age to Richard's age to Tristan's age.
Answer:
The ratio of Pablo's age to Richard's age to Tristan's age is 6:7:4.
Step-by-step explanation:
The ratio of Pablo's age to Richard's age is 6: 7 and the ratio of Pablo's age to Tristan's age is 5: 4. To find the ratio of Pablo's age to Richard's age to Tristan's age, we can first find the ratio of Richard's age to Tristan's age by multiplying the ratios of Pablo's age to Richard's age and Pablo's age to Tristan's age. The product of these ratios is 6/7 * 5/4 = 30/28. Since the ratio of Pablo's age to Richard's age is 6:7, we can add this ratio to the ratio of Richard's age to Tristan's age to find the ratio of Pablo's age to Richard's age to Tristan's age. Thus, the ratio of Pablo's age to Richard's age to Tristan's age is 6:7:4.
This shows a graph.
Where is the function increasing?
The function increases when x > 0
The function increases when x > 1
The function increases when x > 2
The function increases when x > -3
The function of the graph increases at x > 2
What is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
The graph starts from point (-3, 1) and remained at 1 while x changed from -3 to 2. above point 2 which is x > 2 y is seen to first change to 2 when x got to 3.
So the function increases when x > 2.
In conclusion the function increases when x > 2
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suppose 30% of all households in a certain town own 3 or more vehicles. what is the probability that a random sample of 60 households will have exactly 20 households with 3 or more vehicles?
X ~ Bin ( n , p)
The probability that a random sample of 60 households will have exactly 20 households with 3 or more vehicles is 0.90931
What is mean and standard deviation?
Continuous data, not categorical data, are summarised using the standard deviation in conjunction with the mean. Additionally, the standard deviation, like the mean, is typically only acceptable when the continuous data does not have outliers or is not highly skewed.A common way to assess variability in statistics is the standard deviation (SD). It displays the degree of variance from the average (mean). When the SD is low, the data tend to be close to the mean, while when it is high, the data are dispersed over a wide range of values.Using Normal Approximation to Binomial
Mean = n * P = ( 60 * 0.3 ) = 18
Variance = n * P * Q = ( 60 * 0.3 * 0.7 ) = 12.6
Standard deviation = √(variance) = √(12.6) = 3.5496
P ( X = 20 )
Using continuity correction
P( n - 0.5 < X < n + 0.5 )
= P ( 20 - 0.5 < X < 20 + 0.5 )
= P ( 19.5 < X < 20.5 )
Using EXCEL,
P ( 19.5 < X < 20.5 )
= P(X < 20.5) - P(X < 19.5)
= BINOM.DIST ( 20.5 , 60 , 0.30, TRUE) - BINOM.DIST ( 19.5 , 60 , 0.30, TRUE)
= 0.7622 - 0.66916
= 0.0931
Hence, the probability that a random sample of 60 households will have exactly 20 households with 3 or more vehicles is 0.90931
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HELP ME HELP ME!!!! WHAT IS 1+1