When the domain of x is restricted, the function x2 becomes one-to-one, and the inverse function is x.
It is true that limiting a function's domain might cause it to become invertible. Because it is not one-to-one in the example, the function x2 is not invertible across its complete domain of real numbers (i.e., it assigns multiple outputs to some inputs). However, x2 becomes one-to-one and invertible when the domain of x is constrained to or any subset of that interval. The range of x2, which is, is used to define the inverse function in this situation, which is
The function x2 becomes one-to-one when the domain of x is constrained, and the inverse function is
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Linear Equations CHECK POINT 1 University of Arkansas researchers discovered that we underestimate the number of calories in restaurant meals. The next time you eat out, take the number of calories you think you ate and double it. The researchers concluded. that this number should be a more accurate estimate. The actual number of calories in one portion of hamburger and fries and two portions of fettuccine Alfredo is 4240. The actual number of calories in two portions of hamburger and fries and one portion of fettuccine Alfredo is 3980. Find the actual number of calories in each of these dishes. (Source: Consumer Reports, January/February, 2007) Test Your Calorie I.Q.
Answer:
hamburger and fries: 1240 caloriesfettuccine Alfredo: 1500 caloriesStep-by-step explanation:
You want the number of calories in each dish if 1 portion of hamburger and fries with 2 portions of fettuccine Alfredo has 4240 calories, and 2 portions of hamburger and fries with 1 portion of fettuccine Alfredo has 3980 calories.
SetupThe equations describing the calories in each dish can be written using h and f for the calories in a portion of hamburger and in a portion of fettuccine, respectively:
1h + 2f = 4240
2h +1f = 3980
SolutionSubtracting the first equation from twice the second gives ...
2(2h +f) -(h +2f) = 2(3980) -(4240)
3h = 3710 . . . . . . . simplify
h = 1240 . . . . . . . divide by 3
Then the calories in the fettuccine can be found from the second equation:
f = 3980 -2h = 3980 -2480 = 1500
The actual number of calories in a portion of hamburger and fries is 1240.
The actual number of calories in a portion of fettuccine Alfredo is 1500.
__
Additional comment
The attachment shows a calculator solution using matrix methods.
convert the system to an augmented matrix. type each element of the answer in the spaces provided. 2x y
The augmented matrix of the solution to the system of equations is x = 4 and y = -1/2.
The augmented matrix of the system of equations 2x + y = 8 and 3x - y = 7 can be written as follows:
|2x + y = 8 |
|3x - y = 7 |
This can be rewritten in matrix form as:
|2 1 | |x | | 8 |
|3 -1| |y | | 7 |
To solve this system of linear equations, we can use the Gauss-Jordan elimination method. First, we add the first row to the second row to eliminate the x coefficient from the second equation:
|2 1 | |x | | 8 |
|0 -2| |y | | 1 |
Then, we can divide the second row by -2 to get the coefficient of y to be 1:
|2 1 | |x | | 8 |
|0 1 | |y | |-1/2|
Finally, we can subtract the second row from the first row to eliminate the y coefficient from the first equation:
|2 0 | |x | | 8/2|
|0 1 | |y | |-1/2|
Therefore, the solution to the system of equations is x = 4 and y = -1/2.
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What is (f/g)(x)?
f(x) = -x
g(x) = -5x + 2
Write your answer as a polynomial or a rational function in simplest form.
The rational function in the simplest form of (f/g)(x) is x / 5x - 2.
How to solve functions?Composite functions are when the output of one function is used as the input of another. A typical example of a composite function is (f/g)(x).
Therefore, let's solve the rational function in the simplest form.
Hence,
f(x) = -x
g(x) = -5x + 2
(f/g)(x) = f(x) / g(x)
Therefore,
(f/g)(x) = - x / -5x + 2
Hence,
(f/g)(x) = - x / - (5x - 2)
Finally,
(f/g)(x) = x / 5x - 2
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_____ refers to the technology that allows data, collected from sensors in all types of machines, to be sent over the Internet to repositories where it can be stored and analyzed. A. Hadoop B. MapReduce C. Advanced analytics D. Internet of Things
Internet of Things refers to the technology that allows data, collected from sensors in all types of machines, to be sent over the Internet to repositories where it can be stored and analyzed.
Internet of Things refers to the collective network of connected devices and the technology that facilitates communication between devices and the cloud, as well as between the devices themselves.
There are some Advantages of IOT:
It can assist in the smarter control of homes and cities via mobile phones. It enhances security and offers personal protection.
Automating activities saves us a lot of time. Information is easily accessible, even if we are far away from our actual location, and it is updated frequently in real time.
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Write an expression for a polynomial function whose graph intercepts the horizontal axis at -7,8 and 15
The polynomial function with the given intercepts of the hirzontal axis can be written as:
p(x) = (x + 7)*(x - 8)*(x - 15)
How to write the polynomial?We know that a polynomial of degree N whose leading coefficient is 1 and has the zeros {x₁, x₂, ...}
Then the polynomial can be written as:
p(x) = (x - x₁)*(x - x₂)*...
Here the zeros (also called intercepts of the horizontal axis, like on this case) are {-7, 8, 15}
Then wecan write the polynomial with these zeros as:
p(x) = (x - (-7))*(x - 8)*(x - 15)
p(x) = (x + 7)*(x - 8)*(x - 15)
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in a given year, approximately 30% of children and adolescents in the united states display serious psychological disturbances and need clinical treatment.
It can be concluded that in 2018, approximately 21.7% of children and adolescents in the United States displayed serious psychological disturbances and needed clinical treatment.
The percentage of children and adolescents in the United States displaying serious psychological disturbances is calculated by dividing the number of children and adolescents with serious psychological disturbances by the total number of children and adolescents in the United States. This can be expressed mathematically as:
% = (Number of children and adolescents with serious psychological disturbances / Total number of children and adolescents in US) x 100
Using estimates from 2018, approximately 48.5 million children and adolescents in the United States, and 10.5 million of them displaying serious psychological disturbances, the percentage of children and adolescents in the United States displaying serious psychological disturbances in 2018 can be calculated as:
% = (10.5 million / 48.5 million) x 100 = 21.7%
Therefore, it can be concluded that in 2018, approximately 21.7% of children and adolescents in the United States displayed serious psychological disturbances and needed clinical treatment.
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What is the circumference of the circle in terms of π?
circle with a segment drawn from one point on the circle through the center to another point on the circle labeled 7 yards
3.5π yards
7π yards
21.98π yards
49π yards
Circumference of circle = 7π yards
The correct option is B.
What is circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Given,
Segment drawn from one point on the circle through the center to another point = diameter of circle = 7 yards
Circumference of the circle = π × Diameter
= 7π yards
Hence, 7π yards is the circumference of the circle
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Answer:
b
Step-by-step explanation:
Mick drew the following steps using parallel lines. What is the measure of z?
Answer:
Step-by-step explanation:
The top left angle = 52⁰ - also right angle = 52⁰. ( alternate angles of parallel l;ines).
So, x = 180 - 2(52) = 180-104
= 76 degrees.
which if the following definitions is not correct? which if the following definitions is not correct? raw data is data that have been collected but are not processed, cleaned or analyzed. statistics is the branch of math that deals with collection, analysis and interpretation of large masses of data. you generally use some form of statistics to get to a useful data visualization. qualitative data is data that cannot be counted easily using numbers. social scientists often used qualitative data which includes text, observations, interviews, and open questions. the y-axis is the horizontal number line and the x-axis is the vertical number line in a chart.
Qualitative data is data that cannot be counted easily using numbers is not have the correct definitions.
Qualitative data is used to address the research questionnaire regarding whats and how many(s) or also for research procedures to quantify a problem. This data can be used to compare or count data on a numerical scale.
This type of research typically involves in-depth interviews, focus groups, or observations in order to collect data that is rich in detail and context. This data is used for Qualitative research which is very helpful when understanding social reality and the attributes, beliefs, and motivations of people.
The main importance of this kind of project come into the limelight when someone is trying to understand the reason behind one's beliefs or behaviors.
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2 x – 3 y = 7
–4 x + y = –5
What is the x -value of the solution to this system of equations?
Answer:
x = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
2x - 3y = 7 → (1)
- 4x + y = - 5 → (2)
multiplying (2) by 3 and adding to (1) will eliminate y
- 12x + 3y = - 15 → (3)
add (1) and (3) term by term to eliminate y
- 10x + 0 = - 8
- 10x = - 8 ( divide both sides by - 10 )
x = [tex]\frac{-8}{-10}[/tex] = [tex]\frac{4}{5}[/tex] (= 0.8 )
let f (x, y) be the statement x trusts y, where the domain of discourse for both x and y is all people. (a) use quantifiers to express each of the following propositions in symbols. (i) nobody trusts ralph. (ii) everybody trusts fred. (iii) somebody trusts everybody.
The required expressions are ¬ ∃x(F(x, Ralph)), ∀xF(x, Fred), and ∀x∃yF(x,y). Here, ¬ means negation, ∃ means existential quantifier, and ∀ means universal quantifier.
One or more variables that are defined on a particular domain are expressed by a predicate. By giving the variable a value or by quantifying it, it is possible to turn a predicate with variables into a proposition.
There are two quantifiers used in this they are (i) existential quantifier which is represented by ∃ and (ii) universal quantifier which is represented by ∀.
For, the proposition, "Nobody trusts Ralph", the quantifier is written as ¬ ∃x(F(x, Ralph)).
For the proposition, "Everybody trusts Fred", the quantifier is written as ∀xF(x, Fred).
For the proposition, "Somebody trust everybody", the quantifier is written as ∀x∃yF(x,y).
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If an item that originally cost $18 is decreased to $12, what is the percentage of decrease in the item?
Which difference is 4.517?
The difference between 4.507 and 4.517 can be expressed as -0.010.
What is difference in mathematics?The concept that will be used here is substraction. The outcome of subtracting one integer from another is difference. While we frequently discuss differences in how objects appear, feel, or even taste, mathematics demonstrates how much two numbers vary from one another in terms of quantity. Difference is what is left behind after subtracting one number from another.
the outcome of subtraction of two numbers. the difference between two numbers. For instance: There is a 5 difference between 8 and 3.
We were to find the difference between 4.507 and 4.517 whichg implies the substraction between the values and can be done as
(4.507 - 4.517)= -0.010
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complete question:
What is the difference between 4.507 and 4.517
amanda got a train ticket valid for the five cities listed below. she can choose to visit some or none of these cities. she doesn't have time to visit all of them. amsterdam, brussels, lille, paris, rotterdam
As per the permutation method, the number of possible way for here travel is 5.
The term permutation in math is known as an arrangement of objects in a definite order and the members or elements of sets are arranged here in a sequence or linear order.
Here we have given that Amanda got a train ticket valid for the five cities listed below.
There are Amsterdam, brussels, Lille, Paris, Rotterdam.
So, the given number of ways is 5.
Then the value of n = 5 and the value of r = 1 because here we have given that she can choose to visit some or none of these cities which means that she must chose at least one city.
Then the number of ways is calculated as,
=> ⁵P₁ = 5!/ (5 - 1)!
=> ⁵P₁ = 5!/4!
=> ⁵P₁ = 5
Complete Question:
Let us consider that Amanda got a train ticket valid for the five cities listed below. she can choose to visit some or none of these cities. she doesn't have time to visit all of them.
They are Amsterdam, brussels, Lille, Paris, Rotterdam
Find out the number of ways to visit each cites using permutation method.
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Determine constants and such that the given piecewise function is continuous for all .
F(x)= -6 if x < -1
Ax + 2. if -1 ≤ x ≤ 2
-x^2 + Bx + 14. if x > 2
Round your answers to one decimal place, if necessary.
Answer: To make the piecewise function continuous for all x, we need to make sure that the function values and the function slopes at the boundaries (-1 and 2) are the same for each piece.
For x = -1:
F(-1) = -6 (from the first piece)
F(-1) = A(-1) + 2 = -A + 2 (from the second piece)
So, to make the function continuous at x = -1, we need to set -6 = -A + 2, which gives us A = -8.
For x = 2:
F(2) = -x^2 + Bx + 14 (from the third piece)
F(2) = A(2) + 2 = 2A + 2 (from the second piece)
So, to make the function continuous at x = 2, we need to set -4 + 2B + 14 = 2A + 2, which gives us B = -5.
Now we can write the function with the constants that we found :
F(x) = -6 if x < -1
-8x + 2 if -1 ≤ x ≤ 2
-x^2 - 5x + 14 if x > 2
This function is continuous for all x and the values and slopes match at x = -1 and x = 2.
Step-by-step explanation:
10. Some people who have never smoked develop lung cancer. Does this disprove the evidence?
(1 point)
I
The fact that some people who smoked never develop lung cancer does not disprove the evidence.
Why can some people smoke and not develop lung cancer ?The fact that some people who have never smoked develop lung cancer does not disprove the evidence linking smoking to lung cancer.
Smoking is a major risk factor for lung cancer, and the overwhelming majority of people who are diagnosed with the disease are smokers or former smokers. However, it is important to note that other factors, such as exposure to radon and other pollutants, can also increase the risk of lung cancer, and that some people may be more genetically susceptible to the disease. So, it is possible for people who have never smoked to develop lung cancer as well.
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Olivia earns $12 an hour at the grocery store. She kept track of her hours per week and how much she earned in the following table. Graph the values in the table on the coordinates plane shown. what will you label the x-axis?
Answer:
12 times y = x
Step-by-step explanation:
I see on you paper you want to do intervals of 2 so just take 12 and multiply it by the desired number. Equation: 12 x # = the y axis point. This is where #=x-axis and plugging it in the equation gives you the y point.
#15 find the measure of angle P. I need help with this problem
The measure of ∠P is 96°.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
∠P and ∠R are alternate angles.
Alternate angles are equal.
So,
∠P = ∠R
2x = x + 48
2x - x = 48
x = 48
Now,
∠P = x + 48
∠P = 48 + 48
∠P = 96
Tus,
The value of ∠P is 96°.
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The image includes the questions
Answer:
a.
b. 35/100 of 76 = 26 to 27 remained
c.
d. statistic
e. experiment
f. I don't think so
Step-by-step explanation:
For the rectangular parking area of the shopping
center shown, which one of the following equations
says that the area is 30,000 yd² ?
A. x(4x +300) = 30,000
B. x+(4x +300)=30,00
Equation
(Type A, B, C, or D.)
says that the area is 30,000 yd².
CO
C. 2x + 2(4x + 300) = 30,000
D. x² (4x+300)² = 30,000²
1.Q
fale
W
CI
RE
4x+300
TORP
COBECOBOBEE
LED
LD
ME
C
MAGI
WAL
(0)
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7100
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For the rectangular parking area of the shopping center shown, an equation which says that the area is 30,000 yd² is: A. x(2x + 200) = 30,000.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.From the information provided about the rectangular parking area of the shopping center shown in the image attached below, we have the following dimensions:
Length = x
Width = 2x + 200
Substituting the given points into the area of rectangle formula, we have the following;
30,000 = x × (2x + 200)
30,000 = x(2x + 200) ⇒ (required equation).
30,000 = 2x² + 200x.
2x² + 200x - 30,000 = 0.
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when the population mean and standard deviation are known, we can generally assume the following about the sample mean and standard deviation (check all that apply
When σ is known, hypothesis tests are performed for one population mean. The one-mean z-test, or simply z-test, is a hypothesis test carried out for a single population mean when the population standard deviation is known.
A data distribution's spread is measured by standard deviation. It calculates the average separation between each data point and the mean.
Whether we consider the data to be a population unto itself or a sample of a broader population affects the method we use to calculate standard deviation.
Statistics is the parent topic for the Population Mean notion. In a nutshell, statistics addresses the issues of gathering data as well as its analysis, interpretation, and presentation. The population mean formula calculates the average of all the values in the population or set of data.
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4 Four boys and five girls went to the movies together. Between them they
had $120 to spend. Tickets cost $8 each. How much money did they have
to buy refreshments?
A sunflower is measured at the beginning of June and is 40cm tall. The sunflower
grows by 25% each month for three months. What height is the sunflower to the nearest
centimetre at the beginning of September?
Answer:
78cm 78.125
Step-by-step explanation:
Answer: 78.13
Step-by-step explanation:
you start with 40cm and find 25% of that and add it to 40cm. Or you can do 1.25x40=50 That would be July, so repeat to get 50x1.25=62.5 to get august, then again to get 62.5x1.25=78.13
PLEASE HELP FOR 30 POINTS ITS A UNIT TEST!!!!!!!
The coordinates of the vertices of a polygon are shown on the graph below.
What is the name of the polygon?
hexagon
octagon
quadrilateral
triangle
Answer: Quadrilateral
Step-by-step explanation:
hexagon: 6 sides
octagon: 8 sides
quadrilateral: 4 sides
triangle: 3 sides
The quadrilateral is the only one that makes sense.
Will Mark brainliest
Write an equation in point slope form for the line that passes through the given point and is perpendicular to the graph of each equation.
(3, - 2) ; y = 2/3x + 4
An equation in point slope form for the line that passes through the given point and is perpendicular to the graph of each equation is y=2/3 x²+4x
How to find the equation?A mathematical equation is a formula that uses the equals sign ('=') to express the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, an equation in English is any well-formed formula consisting of two expressions related by an equals sign, while an equation in French is defined as containing one or more variables.
step 1
y=2/3+4
y=2/3 x²+4x
y=m x+ b
step 2
y= y coordinate
m=slope
x=x coordinate
b=y intercept
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Consider the weighted voting system [20: 9,7,5,3,1] Find the weight of the coaltion P1,P2,P3
The weight of the coalition P1, P2, P3 is 36
How to determine the weight coalitionFrom the question, we have the following parameters that can be used in our computation:
weighted voting system [20: 9,7,5,3,1]
The variable P1, P2 and P3 are the first three values
So, we have
P1 = 20
P2 = 9
P3 = 7
The weight of the coalition P1, P2, P3 is the sum of the points
So, we have
Coalition = 20 + 9 + 7
Coalition = 36
Hence, the weight coalition is 36
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Find f(-5) if f(x) = |x + 1|
Answers are 4, 5, or 6
Answer:
f(-5) = 4
Step-by-step explanation:
[tex]f(x)=|x+1|\\f(-5)=|-5+1|=|-4|=4[/tex]
Cement cost $76 per cubic yard. What is the cost of cement for a sidewalk that is 4" thick, 3' wide, and 40' long.
If cement costs $76 per cubic yard, the total cost of cement for a sidewalk with a volume of 480 inches³ is $1,013.
How is the total cost determined?The total cost of cement for the sidewalk is determined using unit conversions and multiplication.
After determining the volume in inches and converting it to yards, the result is multiplied by the unit cost of cement per cubic yard.
Dimensions of the Sidewalk:
Length = 40 inches
Width = 3 inches
Thickness = 4 inches
Volume = 480 inches³ (40 x 3 x 4)
36 Inches = 1 Yard
480 cubic inches = 13.33 cubic yards
Cost of cement per cubic yard = $76
Cost of the sidewalk = $1,013 ($76 x 13.33)
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a) Using the 2" zn rule, construct a frequency distribution for these data. Select the correct choice below and fill in the answer boxes to complete your choice.O A. Credit Card Balances Frequency $0 to less than $1,000 $1,000 to less than $2,000 $2,000 to less than $3,000 $3,000 to less than $4,000 $4,000 to less than $5,000 $5,000 to less than $6,000 O B. Credit Card Balances Frequency $0 to less than $1,200 $1,200 to less than $2,400 $2,400 to less than $3,600 $3,600 to less than $4,800 $4,800 to less than $6,000 Credit Card Balances$2,368 $5,789 $1,754 $5,927 $5,815 $349 $3,522 $3,888 $5,323 $1,039 $1,247 $2,429 $461 $1,464 $4,505 $2,667 $5,425 $669 $911 $750 $1,007 $1,706 $300 $410 $4,650 $3,770 $4,502 $4,056 $1,020 $158 $168 $4,565 $1,557 $924 $524 $1,669
If k is the number of classes and n is the number of observation then for class intervals, select the smallest k such that 2k >= n using statistics.
n = 36
2^5 = 32< 36
2^6 = 64 > 36
So k = 6
a) Frequency distribution: Answer A.
Class interval Frequency
0 to less than 1000 11
1000 to less than 2000 9
2000 to less than 3000 3
3000 to less than 4000 3
4000 to less than 5000 5
5000 to less than 6000 5
b) Relative frequency distribution: Answer B.
Class interval Relative frequency
0 to less than 1000 11 / 36 = 0.306
1000 to less than 2000 9 / 36 = 0.250
2000 to less than 3000 3 / 36 = 0.083
3000 to less than 4000 3 / 36 = 0.083
4000 to less than 5000 5 / 36 = 0.139
5000 to less than 6000 5 / 36 = 0.139
c) Cumulative relative frequency:
Class interval Cumulative Frequency
less than 1000 11
less than 2000 20
less than 3000 23
less than 4000 26
less than 5000 31
less than 6000 36
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Help I need to do corrections but they need to be turned in by 4pm today
Answer: I think it is -7 I'm not exactly sure but that's what I think please take someone else's answer just in case.
Step-by-step explanation: