Question 1 Give an explicit example of a function from Z to N that is: a) One-to-one but not onto. b) Onto but not One-to-one. c) One-to-one and onto. d) Neither One-to-one nor onto.
Answers
a) One-to-one but not onto: An example is f(x) = x + 1, where integers map to natural numbers. It's one-to-one, but not onto since there is no integer x for which f(x) = 1.
b) Onto but not one-to-one: An example is f(x) = |x|, mapping integers to natural numbers. It's onto as every natural number can be obtained, but not one-to-one since different integers with opposite signs map to the same natural number.
c) One-to-one and onto: An example is f(x) = 2|x| - 1, mapping integers to natural numbers. It's both one-to-one and onto as different integers always produce different natural numbers, and every natural number can be obtained.
d) Neither one-to-one nor onto: An example is f(x) = x^2, mapping integers to natural numbers. It's neither one-to-one nor onto because different integers can produce the same square value, and there are natural numbers that cannot be obtained as the square of any integer.
a) An example of a function from the set of integers (Z) to the set of natural numbers (N) that is one-to-one but not onto is f(x) = x + 1. This function takes an integer x and maps it to the natural number x + 1. It is one-to-one because different integers will always produce different natural numbers. However, it is not onto because there is no integer x for which f(x) = 1.
b) An example of a function from Z to N that is onto but not one-to-one is f(x) = |x|. This function takes an integer x and maps it to its absolute value. It is onto because for every natural number n, there exists an integer x (positive or negative) such that f(x) = n. However, it is not one-to-one because different integers with opposite signs will map to the same natural number.
c) An example of a function from Z to N that is both one-to-one and onto is f(x) = 2|x| - 1. This function takes an integer x, computes its absolute value, multiplies it by 2, and then subtracts 1. It is one-to-one because different integers will always produce different natural numbers. It is also onto because every natural number can be obtained by choosing an appropriate integer.
d) An example of a function from Z to N that is neither one-to-one nor onto is f(x) = x^2. This function takes an integer x and maps it to the square of x. It is not one-to-one because different integers can produce the same square value (e.g., f(-2) = f(2) = 4). It is not onto because there are natural numbers that cannot be obtained as the square of any integer (e.g., 3).
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Related Questions
Ali takes a full-time position as a makeup artist in Atlanta. Her starting salary is $29,000. Her taxes are 28%. What is her net monthly income?
b. $3,840
c. $2,088
d. $1,740
Answers
The correct answer is (c) Ali has a monthly net income of $2,088 after paying 28% in taxes.
.
To calculate Ali's net monthly income, we first need to find out the amount of tax she pays, and then we can subtract it from her annual income to get her net annual income. We'll then divide it by 12 to get her monthly net income.
Calculations: Ali's tax rate is 28%. 28% of 29,000 is 8,12029,000 - 8,120 = 20,88020,880 / 12 = 1,740
Therefore, Ali's net monthly income is $1,740. The correct answer is option D, $1,740. ($29,000 salary x 28% taxes = $8,120 in taxes annually; $8,120 / 12 months = $677 in taxes per month; $29,000 - $677 = $2,088 net monthly income).
Net income refers to the amount of money that a company or an individual has earned after deducting all the expenses and taxes from their gross income. In the context of a company, net income is also called profit, and it is an important measure of a company's financial performance.
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Bearing a to b is 280 what is bearing b to A
Answers
Answer:
please see photo attached for detailed analysis.
translate this sentence into an equation 59 is the sum of 23 and vidya height use the variable v to represent vidyas height
Answers
The translated formula is 59 = 23 + v, where v represents Vidya's height.
To translate the sentence "59 is the sum of 23 and Vidya's height" into an equation using the variable v to represent Vidya's height, we can use the following formula:
59 = 23 + v
Here, we are saying that the number 59 is equal to the sum of 23 and Vidya's height (which we are representing with the variable v).
To summarize, we can say that we have translated the given sentence into an equation using the formula 59 = 23 + v, where v represents Vidya's height.
What is the mathematical variable?
a symbol (often a letter) used in algebra to represent a variable with an undetermined numerical value. The following variables are frequently used: t (time), r (radius), s (arc length), x and y (real-number unknowns), and z (complex-number unknowns).
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On a coordinate plane, a triangle has points A (negative 5, 3), B (negative 2, 4), C (negative 2, 2). Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin? (4, 2) (2, 4) (–4, –2) (–2, –4)
Answers
Answer:
A. (4, 2)
Step-by-step explanation:
I got it right on edge:)
The coordinate of B (-2, 4) changes to (4,2) after Rotation, the correct option is A.
What is Rotation?Rotation is a type of transformation in Geometry, where the original figure is rotated about a point by some angle.
The triangle ABC has coordinates A (- 5, 3), B (-2, 4), C (- 2, 2).
It is rotated 270 degrees about the origin.
The coordinate when rotated 270 degrees about the origin is changed from (x,y) -----> (y ,-x)
The coordinate of B (-2, 4) changes to (4,2)
Therefore, the correct option is A.
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My parents recently moved to the Poconos, they got 30 or more inches of
snow from this last snow storm. It took my Dad 2 hours to clear 10 feet of
their driveway. If he spent 5 hours out there clearing snow, how much of
their driveway did he clear?*
Answers
Answer:
25ft
Step-by-step explanation:
2hr=10ft
5hr=25ft
5-2=3 so you have to find what they did for the 3 hours which is another 2 plus half so 25ft.
Simplify w x 12 x 3
Helppp
Answers
Answer:-x • (w2 - 12)
——————————————
3w
In regression analysis, the error term ε is a random variable with a mean or expected value of.
Answers
In regression analysis , the error term ε is a random variable with expected value of 0.
What is regression analysis?
A set of statistical procedures known as regression analysis is used to estimate the relationships between a dependent variable and one or more independent variables.
Main Body:
In regression analysis, the model in the form is called regression model.
The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as regression equation.
So the answer to error term is 0.
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Help pls this is so hard lololololol
Answers
Answer:
it is c i belive
Step-by-step explanation:
37-90=53.53=180-53=127
did not learn this yet but i am smart
If we have an effect, would error variance go away?
Answers
No, the presence of an effect does not necessarily imply that error variance will go away.
Why could not error variance go away?The presence of an effect does not necessarily imply that error variance will go away. In fact, error variance is an inherent part of any statistical model and represents the amount of variation in the response variable that is not explained by the predictor variables.
Even if a predictor variable has a significant effect on the response variable, there may still be some unexplained variation in the response that is attributable to error variance.
It is important to take into account and control for error variance in any statistical analysis, as it can affect the precision and accuracy of the estimates of the model parameters and can also influence the interpretation of the results.
One way to control for error variance is to use appropriate statistical methods, such as analysis of variance (ANOVA), regression analysis, or other modeling techniques that take into account the variability in the data.
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Please answer this equation 4x+1-1 > -8
Answers
Answer:
+1-1=0
4x>-8
x>-2
Step-by-step explanation:
Answer:
x>−2
Step-by-step explanation:
Each parking space will be 19 feet by 8 feet. what is the maximum number of parking spaces that will fit in the lot? 10 30 35 40
Answers
The maximum number of parking spaces that will fit in the lot given the area of the parking lot is 30.
what is the maximum number of parking spaces that will fit in the lot?The parking lot has the shape of a rectangle. The area of a rectangle is length x width
The area of the available parking space = length of the lot - [width of the lot - (width of the alley x 2)
80 x (77 - 10 - 10) = 4560 ft²
Maximum number of parking spaces = 4560 / (19 x 8) = 30
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Give the information asked for to each problems Ax Styles Tags Assignments Calendar In each of the following state the Start Value Growth Value 1. C-5f + 32 Calts FE 2. Y= 4000 - 250x 3 х -3 0 6 у -9 3 -1 -5 3 4. x -4 4 8 Olo у 3 15 21 5. A financial account begins with $5900. Each week $300 is deducted. 6. Also point to the start value Apps Hus Type here to search
Answers
Explanation:
1) C = 5/9 f + 32
The start value is the constant = 32.
The start value = 32
Growth value = rate of change
Growth value = 5/9
2) y = 4000 - 250x
The start value is the constant = 4000
The start value = 4000
8. You have $15 in five-dollar bills and one-dollar bills. Let x represent the number of five-dollar bills you
have and y represent the number of one-dollar bills you have.
a. Write an equation that represents all the possible combinations of five-dollar lbills and one-dollar
bills you could have with $15.
b. Graph this equation to show all the different dollar bill combinations.
c. What do the ordered pairs on the graph represent?
d. How many one-dollar bills would you have if you have 2 five-dollar bills?
e. How many five-dollar bills would you have if you have 10 one-dollar bills?
f. Find and describe the x'and y-intercepts for this context.
Answers
Answer:
Below
Step-by-step explanation:
a.
5x + y = 15
b.
I can't put a graph here, but it is a straight line through (3, 0) and (0,15).
c.
The ordered pairs on the graph represent the possible combinations of 5 dollar bills (x-coordinate) and 1 dollar bills (y-coordinate) you can have summing to $15.
The valid pairs are: (3, 0), (2, 5), (1, 10), (0, 15)
d.
If you have 2 $5 bills, you will have 5 $1 bills (from the pair (2, 5)).
e.
If you have 10 $1 bills, you will have 1 $5 bill (from the pair (1, 10)).
f.
The x-intercept is (3, 0); this ordered pair is when we have 3 $5 bills and no $1 bills.
The y-intercept is (0,15); this ordered pair is when we have 15 $1 bills and no $5 bills.
6x+4 = -6+ 4x +18 solve for x
Answers
Answer:
4
Step-by-step explanation:
6x+4=12+4x6x-4x=12-42x=8x=4Answer:
7/4 or 1.75 or 1 3/4
Step-by-step explanation:
try to use a scientific calculator and then that will be your answer that I came up with.
What constant term is necessary to complete the perfect square trinomial pictured in the algebra tiles? x2 8x
Answers
The constant term that is necessary to complete the perfect square trinomial pictured in the algebra tile is 16.
What is a perfect square trinomial?A perfect square trinomial is an algebraic statement with three terms of the type ax²+bx+c. It is calculated by multiplying a binomial with itself.
For the given trinomial to be a perfect square trinomial, the value of the constant term should be such that the value of the term expression must be similar to (a+b)². Therefore,
\((a+b)^2=a^2+2ab+b^2\)
\(=x^2+8x+16\)
Now, if we compare the two equations we will understand that the first term of the perfect square trinomial is x, and thus, the last term should 16.
\((x+4)^2=x^2+8x+16\)
Hence, the constant term that is necessary to complete the perfect square trinomial pictured in the algebra tile is 16.
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16 is the constant term is necessary to complete the perfect square trinomial pictured in the algebra tiles will be (x + 4).
What is a perfect square?
A perfect square is a number that may be written as the product of two integers or as the integer's second exponent.
The perfect square obtained from the given equation is (x + 4).;
On squaring we get;
\((x + 4)^2 = x^2 + 8x + 16.\)
16 is the only constant term in the equation.
Hence 16 is the constant term that is necessary to complete the perfect square.
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using f '(x) = lim h→0 f(x + h) − f(x) h with x = 0, we have f '(0) = lim h→0 f(0 + h) − f(0) h
Answers
f'(0) is the derivative of the function f(x) evaluated at x = 0, and it provides information about the instantaneous rate of change of the function at that specific point.
In the context of calculus, the derivative measures the rate of change of a function at a specific point. By taking the limit as h approaches 0, we are considering the instantaneous rate of change or the slope of the tangent line at x = 0.
The expression f'(0) represents the value of the derivative of the function f(x) at x = 0. This value indicates how the function is changing at that particular point. The limit h→0 ensures that we are approaching the point of interest as closely as possible, allowing us to capture the exact rate of change at x = 0.
Overall, f'(0) is the derivative of the function f(x) evaluated at x = 0, and it provides information about the instantaneous rate of change of the function at that specific point.
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Hi,please help !
(see image!)
Answers
The perimeter of each shape are as follows:
a. 4x + 18 units
b. 6y + 4x units
c. 5x units
d. 16x + 12 units
The area of the square is 9x² units²
How to find the area and perimeter of a figure?The perimeter of a shape is defined as the total length of its boundary. In other words, the perimeter of a shape is the sum of the whole sides of the figure.
Therefore, let's find the perimeter of the shapes as follows:
a.
perimeter = x + 9 + x + 9 + x + x
perimeter = 4x + 18
b.
perimeter = 3y + 3y + 2x + 2x
perimeter = 6y + 4x
c.
perimeter = 2x + 2x + x
perimeter = 5x
d.
perimeter = 4x + 1 + 2x + 3x + 5 + 2x + 1 + 3x + 5 - 2x + 4x + 1 - (2x + 1)
perimeter = 16x + 12
Area of the square = l²
where
l = side lengthTherefore,
Area of the square = (3x)²
Area of the square = 9x²
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How many triangles can be constructed with angles measuring 90ş, 60ş, and 60ş?.
Answers
No triangle can be constructed with the given angles of 90 degrees, 60 degrees, and 60 degrees, as the sum of the angles exceeds the total of 180 degrees required for a valid triangle.
To determine the number of triangles that can be constructed with angles measuring 90 degrees, 60 degrees, and 60 degrees, we need to consider the conditions for triangle construction.
In a triangle, the sum of all angles must be equal to 180 degrees. Since we already have two angles of 60 degrees each, the sum of these angles is 60 + 60 = 120 degrees.
To form a valid triangle, the sum of all three angles must be equal to 180 degrees. However, in this case, the sum of the given angles (90 + 60 + 60 = 210 degrees) exceeds 180 degrees. Therefore, it is not possible to construct a triangle with angles measuring 90 degrees, 60 degrees, and 60 degrees.
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A lot measuring three-fourths of an acre is for sale. how many square feet is this?
Answers
Answer:
32,670 ft²
Step-by-step explanation:
An acre is 43,560 square feet. You want 3/4 of that area.
3/4 AcreThe area of the lot will be ...
(3/4)(43,560 ft²) = 32,670 ft² . . . . 3/4 acre
A company manufactures two products. A and B on two machines, I and II. It has been determined that the company will realize a profit of $3/unit of product A and $5/unit of product B. To manufacture a unit of product A requires 11 min on machine I and 7 min on machine II. To manufacture a unit of product B requires 19 min on machine I and 11 min on machine II. There are 5 hr of machine time available on machine 1 and 3 hr of machine time available on machine II in each work shift. How many units of each product should be produced in each shift to maximize the companies profit?
Answers
Answer:
product A on machine 1 would make 27 units (rounded down) 81 dollars profit.
product A on machine 2 would make 25 units (rounded down) 75 dollars profit.
product b on machine 1 would make 15 units (rounded down) 75 dollars profit.
product b on machine 2 would make 16 units (rounded down) 80 dollars profit.
Step-by-step explanation:
a1 refers to product a on machine 1
a2 refers to product a on machine 2
same rule applies for product b 1 and 2
The volume (in m3) of water in my (large) bathtub when I pull out the plug is given by f(t)=4−t2 (t is in minutes). This formula is only valid for the two minutes it takes my bath to drain.
(a) Find the average rate the water leaves my tub between t=1 and t=2
(b) Find the average rate the water leaves my tub between t=1 and t=1. 1
(c) What would you guess is the exact rate water leaves my tub at t=1
(d) In this bit h is a very small number. Find the average rate the water leaves my tub between t=1 and t=1+h (simplify as much as possible)
(e)
What do you get if you put in h=0 in the answer to (d)?
Answers
(a) The average rate the water leaves the tub between t=1 and t=2 is -3 m^3/min.
(b) The average rate the water leaves the tub between t=1 and t=1.1 is -23.1 m^3/min.
(c) The estimated exact rate at t=1 is -2 m^3/min.
(d) The average rate the water leaves the tub between t=1 and t=1+h is -2 - h m^3/min.
(e) The result when h=0 in part (d) is -2 m^3/min.
(a) To find the average rate the water leaves the tub between t=1 and t=2, we need to calculate the change in volume divided by the change in time. The change in volume is f(2) - f(1) = (4 - 2^2) - (4 - 1^2) = 1 m^3. The change in time is 2 - 1 = 1 min. Therefore, the average rate is 1 m^3/min.
(b) Similarly, for t=1 to t=1.1, the change in volume is f(1.1) - f(1) = (4 - 1.1^2) - (4 - 1^2) ≈ 0.69 m^3. The change in time is 1.1 - 1 = 0.1 min. The average rate is 0.69 m^3/0.1 min ≈ 6.9 m^3/min.
(c) At t=1, we can estimate the exact rate by calculating the derivative of the function f(t) = 4 - t^2 with respect to t. The derivative is -2t, so at t=1, the rate is -2 m^3/min.
(d) When h is a very small number, we can approximate the average rate by taking the derivative at t=1. The derivative is -2t, so the average rate between t=1 and t=1+h is approximately -2 m^3/min.
(e) When we substitute h=0 in the answer to part (d), we get -2 m^3/min, which is the exact rate of water leaving the tub at t=1.
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In your Math Notebook, Solve the Following
Two-Step Equations:
1. 2x + 5 = 19
2. 5x – 1 = 9
3. 7x + 3 = 11
Help pleaseee and hurry!!! 40 points!!!!
Answers
Write an expression that represents the height of a tree that begins at 6.7 feet and increases by 2.6 feet per year. Let t represent the number of years.
Answers
The expression for the height of a tree with a starting height of 6.7 feet and annual growth of 2.6 feet is h=6.7+2.7t.
What is a function?It is described as a particular kind of relationship, and each value in the domain is associated with exactly one value in the range according to the function. They have a predetermined domain and range.
It is given that, the term used to describe a tree's height starts at 6.7 feet and grows by 2.6 feet per year.
Expressions are made up of variables and constants together with mathematical operators.
Let's say that h is a tree's height and that t is the number of years.
For the specified condition, the resulting expression,
h=6.7+2.7t
Thus, the expression for the height of a tree with a starting height of 6.7 feet and annual growth of 2.6 feet is h=6.7+2.7t.
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Jason is asked to graph this system of equations:
3x+y=2
2y+6x=4
How many times will the lines intersect?
Answers
Hello!
· {3x + y = 2 · {y = 2 - 3x
· {2y + 6x = 4 · {2(2 - 3x) + 6x = 4
· {y = 2 - 3x · {y = 2 - 3x
· {4 - 6x + 6x = 4 · {4 - 12x = 4
· {y = 2 - 3x · {y = 2 - 3x
· {12x = 4 + 4 · {12x = 8
· {y = 2 - 3x · {y = 2 - 3 • 8/12
· {x = 8/12 · {x = 8/12
· {y = 2 - 2 · {y = 0
· {x = 8/12 · {x = 8/12
Good luck! :)
what is the solution of the system? use the elimination method. {4x 2y=182x 3y=15 enter your answer in the boxes.
Answers
The solution of the system is x = 4 and y = 1.
To solve the system of equations using the elimination method, we can eliminate one variable by adding or subtracting the equations.
In this case, we can eliminate the variable "x" by multiplying the first equation by -2 and adding it to the second equation.
1. Multiply the first equation by -2:
-8x - 4y = -36
2. Add the modified first equation to the second equation:
-8x - 4y + 2x + 3y = -36 + 15
Simplifying the equation gives:
-6x - y = -21
3. Solve the new equation for one variable. Let's solve for y:
-y = -21 + 6x
y = 21 - 6x
4. Substitute the value of y into one of the original equations. Let's use the first equation:
4x + 2(21 - 6x) = 18
Simplifying the equation gives:
4x + 42 - 12x = 18
-8x = -24
x = 3
5. Substitute the value of x back into the equation for y:
y = 21 - 6(3)
y = 21 - 18
y = 3
Therefore, the solution to the system of equations is x = 3 and y = 3.
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If y = x + 5 is changed to y = 3x + 5, how would the graph of the new function compare with the first one?
Answers
Answer:
y= –2x
Step-by-step explanation:
1. x–3x=–2x
2. 5–5=0
3.y=–2x+0
4. y= –2x
Calculate the length of AC in ABAC to 1 decimal place.
Answers
The length of AC in triangle BAC is equal 10.7 units
Cosine RuleIn trigonometry, the cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
The formula is given as
AC² = AB² + BC² - 2(AB)(BC) cos AC
AC² = 6² + 7² - 2(6)(7)cos110
AC = 10.7
Using cosine rule, the length of AC is 10.7 unit.
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While moving up on the rope-way, I noticed that the seat place in the opposite direction was numbered as 95. Behind it was number 0, then 1, 2 and so on. My seat place was numbered as 66. What number should I meet when I am in the middle of my one-way route?
Answers
The seat in the middle of the one-way route is 34
The seats are given as:
\(First= 0\) --- the first seat behind the seat number 95
\(Last= 66\) --- my seat
The seat number half-way would be:
\(Half = \frac{Last - First}{2} + 1\)
This gives
\(Half = \frac{66- 0}{2} + 1\)
Subtract 0 from 66
\(Half = \frac{66}{2} + 1\)
Divide 66 by 2
\(Half = 33 + 1\)
Add 33 and 1
\(Half = 34\)
Hence, the seat in the middle of the one-way route is 34
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What is the formula of arc length of a curve?
Answers
Answer:
Arc Length=∫ba√1+[f′(x)]2dx. Note that we are integrating an expression involving f′(x), so we need to be sure f′(x) is integrable. This is why we require f(x) to be smooth.
Step-by-step explanation:
have a nice day
Kent bought a $500, 20-year u. S. Treasury bond that paid six percent annual yield when he was 22. How much would that bond be worth 20 years later when it matured?.
Answers
The bond would be worth amount of $1,000 when it matured after 20 years, since it pays a 6% annual yield, which means it will double in value over the 20-year period.
500 x (1 + 0.06) ^ 20 = 1000
500 x 3.51 = 1,755
1,755 - 500 = 1,255
1,255 / 2 = 627.5
627.5 + 500 = 1,127.5
1,127.5 x 2 = 2,255
2,255 - 1,755 = 500
500 x 2 = 1,000
The bond is worth $500 when Kent buys it at 22 years old, and will pay a 6% annual yield. This means that the value of the bond will double over the 20-year period. To calculate the value of the bond at maturity, we need to use the formula: 500 x (1 + 0.06) ^ 20 = 1000. This means that the bond will be worth $1,000 when it matures 20 years later. We can also arrive at this result by breaking down the calculation into smaller steps. First, we multiply the initial bond value by the interest rate (500 x 1.06) to get the value after one year. Then, we repeat this step for the remaining 19 years (500 x 3.51) to get the total value after 20 years (1,755). We then subtract the initial bond value (500) from this to get the total interest earned (1,255). We then divide this interest by two (627.5) and add it to the initial bond value (500) to get the value after 20 years (1,127.5). We then multiply this by two (2,255) and subtract the total interest earned (1,755) to get the final value (500). This is double the initial bond value, so the bond will be worth $1,000 when it matures.
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