The relation ‘equal to’ is an equivalence relation on A.
a) To give an example of an onto function f: A → B, we need to ensure that every element in set B is mapped to from set A. Since set B has three elements (5, 6, 7) and set A has four elements (1, 2, 3, 4), it is impossible to have an onto function from A to B.
This is because there are more elements in A than in B, so at least one element in B will not have a corresponding element in A.
b) A function g: A → B is a one-to-one function if each element of set A is paired with a distinct element in set B. Let us create a table to get the one-to-one function g.
Table of one-to-one function gA1234B5677The function g: A → B can be defined by g(1) = 5, g(2) = 6, g(3) = 7 and g(4) = 7.
Hence, this is a one-to-one function.
c) An equivalence relation is a relation that is reflexive, symmetric, and transitive.
We can define an equivalence relation on set A using the relation ‘equal to’. Every element of set A is equal to itself, i.e., ∀ a ∈ A, a = a.
Hence, this is a reflexive relation on A. Also, if a and b are two elements of A such that a = b, then b = a.
Hence, this is a symmetric relation on A. Also, if a, b, and c are three elements of A such that a = b and b = c, then a = c. Hence, this is a transitive relation on A.
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Show that sin(π/2 + x) = cos x using the compound angle formulas.
Given the trigonometric identity: sin (π/2 + x) = cos x. We are to show that it can be derived from compound angle formulas for sine and cosine functions.
In order to prove the identity using the compound angle formulas, we have to start by recalling the formulas for sin(A + B) and cos(A + B).The compound angle formulas are given as:$$\begin{aligned}\sin (A+B)&=\sin A\cos B+\cos A\sin B\\\cos(A+B)&=\cos A\cos B-\sin A\sin B\end{aligned}$$
Let us set A = π/2 and B = x. Hence, A + B = π/2 + x. Then, we can write:$$\begin{aligned}\sin \left(\frac{\pi}{2}+x\right)&=\sin\frac{\pi}{2}\cos x+\cos\frac{\pi}{2}\sin x \\&= \cos x\end{aligned}$$And, $$\begin{aligned}\cos\left(\frac{\pi}{2}+x\right)&=\cos\frac{\pi}{2}\cos x - \sin\frac{\pi}{2}\sin x \\&= -\sin x\end{aligned}$$
Therefore, sin(π/2 + x) = cos x, as desired.
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Suppose that the mean score for a critical reading test is 580 with a population standard deviation of 115 points. What is the probability that a random sample of 500 students will have a mean score of more than 590? Less than 575? Solve using Excel.
the mean score for a critical reading test, using Excel, the probability that a random sample of 500 students will have a mean score of more than 590 can be calculated to be approximately 0.408.
To calculate the probabilities using Excel, we can utilize the standard normal distribution. First, we need to convert the sample means to z-scores by using the formula: z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). For the sample mean of more than 590, we can calculate the probability of z being greater than the corresponding z-score using the formula "=1-NORM.S.DIST(z-score,TRUE)". In this case, the z-score is (590 - 580) / (115 / sqrt(500)), which gives approximately 0.408.
Similarly, for the sample mean of less than 575, we calculate the probability of z being less than the corresponding z-score using the formula "=NORM.S.DIST(z-score,TRUE)". The z-score is (575 - 580) / (115 / sqrt(500)), which gives approximately 0.084.
Therefore, the probability that a random sample of 500 students will have a mean score of more than 590 is approximately 0.408, and the probability that the sample mean is less than 575 is approximately 0.084.
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Calculate the volume of 2.45 moles of hydrogen gas at STP.
One Mol of any gas occupies a volume of 22.4
We have been given the number of miles of hydrogen and the volume of any gas at STP
Therefore you can use that and substitute it into the formula to calculate the Volume of hydrogen for that number of moles
A recent survey of the alumni of a university indicated that the average salary of 10,000 of its 200,000 graduates was $130,000. The $130,000 would be considered a: a. Population. b. Parameter. c. Sample. d. Statistic.
The $130,000 would be considered as Statistic.
In statistics, a population refers to the entire group of individuals or items of interest, while a sample is a subset of the population. A parameter is a numerical value that describes a characteristic of a population.
In this scenario, the survey results are based on a sample of 10,000 graduates out of a total population of 200,000 graduates. The average salary of $130,000 is calculated from the data collected within this sample. Since it is derived from the sample, it is considered a statistic.
A parameter would be used to describe the average salary of the entire population of 200,000 graduates if data were collected from all of them. However, in this case, the given information only pertains to the subset of the sample.
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help pleaseeeeee ♀️
Answer:
9
my bad I realized mistake
Answer:
perimeter of square =4×side
36 inches =4×side
36 inches/4 =side
9 inches =side
which of the following key characteristics is not true of a quadratic function
Here are the characteristics of Quadratic Functions
Axis of symmetry
x and y-intercepts
Zeroes
vertex
Point symmetric to y-intercept
what’s the answer ??
Answer:
answer A shows a rotation
A because B is a mirror, c is a translation
PLEASE HELP ASAP!!!!!!!!!!!!!!!
Answer:
the answer is D
Step-by-step explanation:
y=[tex]x^{2}[/tex]+1
How many odd three-digit numbers have three digits different?
Answer:
320 odd three.
Step-by-step explanation:
9 but we cannot place the digits that are used in the two other digits and we can place only 7 digits. However, the result is not correct, because there are 320 odd three-digits numbers with different digits.
help me please it’s math
Answer:
1) 345 2) 62 3) 36 4) 51 5) 96 6) 142
Step-by-step explanation:
I hope you and your 3rd or 4th grader self enjoy the answers i gave you.
please help, tysm if you do :D
Answer:
3c + 14d
Step-by-step explanation:
Hello There!
We can simplify this expression by combining like terms
Now what are like terms?
They are terms that have the same variable ex. 4a and 2a are like terms as they have the same variable (a)
Now lets look back at the expression and see if there are any like terms
which there are (4c and -c) and (6d and 8d)
so lets combine them
4c - c =3c
6d + 8d = 14d
so the simplified version would be 3c + 14d
Answer:
B) 3c+14d
Step-by-step explanation:
We use the addition property for the following question
First we rearrange the following problem and we get
4c-c+6d+8d
The easiest way is to just add and subtract or if you want have a better understanding, you can factor our the like terms which gives us
(4-1)c+(6+8)d
and then we can simplify to get
3c+14d
Expert Answer Please Find The Area Of A Circle With R=13.8 Explain Answer!
Answer:
if r= to 13.8 so the answer is 598.28
After t seconds a ball thrown in the air from ground level reaches a given
height (h) in feet. Given the equation h = -1612 + 144 + 100 at what time does the
ball reach 100 feet?
Answer:
9 sec.
Step-by-step explanation:
I think you wrote the equations incorrectly. It probably is
[tex]h = -16t^{2} + 144t + 100[/tex]
If that is true, then [tex]100 = -16t^{2} + 144t + 100[/tex]
0 = -16[tex]t^{2}[/tex] + 144t
-16t(t - 9) = 0
t = 0 or t = 9
How many possible pairs of people can we have in a group of 23(think c or p)
Answer:
Step-by-step explanation:
To determine the number of possible pairs of people in a group of 23, you can use the concept of combinations. The formula to calculate combinations is given by:
C(n, r) = n! / (r!(n - r)!)
where C(n, r) represents the number of combinations of choosing r items from a set of n items, and the exclamation mark (!) denotes the factorial of a number.
In this case, you want to find the number of combinations of 2 people chosen from a group of 23. Using the formula, the calculation would be:
C(23, 2) = 23! / (2!(23 - 2)!)
= 23! / (2! * 21!)
= (23 * 22 * 21!) / (2 * 1 * 21!)
= (23 * 22) / (2 * 1)
= 23 * 11
= 253
Therefore, there are 253 possible pairs of people that can be formed in a group of 23.
find an equation of the tangent plane to the given parametric surface at the specified point. x = u + v, y = 5u², z = u − v; (2, 5, 0)
The equation of the tangent plane to the parametric surface at the point (2, 5, 0) is x + 20y + z - 102 = 0.
To find the equation of the tangent plane to the given parametric surface at the point (2, 5, 0), we need to compute the partial derivatives and evaluate them at the given point.
The parametric surface is defined by the equations:
x = u + v
y = 5u^2
z = u - v
First, we find the partial derivatives with respect to u and v:
∂x/∂u = 1
∂x/∂v = 1
∂y/∂u = 10u
∂y/∂v = 0
∂z/∂u = 1
∂z/∂v = -1
Next, we evaluate the partial derivatives at the given point (2, 5, 0):
∂x/∂u = 1
∂x/∂v = 1
∂y/∂u = 10u = 10(2) = 20
∂y/∂v = 0
∂z/∂u = 1
∂z/∂v = -1
At the point (2, 5, 0), the partial derivatives are:
∂x/∂u = 1
∂x/∂v = 1
∂y/∂u = 20
∂y/∂v = 0
∂z/∂u = 1
∂z/∂v = -1
The equation of the tangent plane can be written as:
(x - x₀) (∂x/∂u) + (y - y₀) (∂y/∂u) + (z - z₀) (∂z/∂u) = 0,
where (x₀, y₀, z₀) is the given point.
Substituting the values, we have:
(x - 2)(1) + (y - 5)(20) + (z - 0)(1) = 0.
Simplifying further, we get:
x - 2 + 20(y - 5) + z = 0.
Expanding and rearranging the terms, the equation of the tangent plane to the parametric surface at the point (2, 5, 0) is:
x + 20y + z - 102 = 0.
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Find the length of side x in simplest radical form with a rational denominator
Answer:
x = 8/√3
Step-by-step explanation:
We solve that above question using the trigonometric function of sin
Sin theta = Opposite/Hypotenuse
Theta = 60°
Opposite = 4
Hypotenuse = x
Hence,
Sin 60 = 4/x
Cross Multiply
sin 60 × x = 4
x= 4/sin 60
in rational form
sin 60 = √3/2
Hence, x = 4/ √3/2
= 4 ÷ √3/2
= 4 × 2/√3
= 8/√3
Q9.
£4000 is invested at 2% compound interest.
(a) What is the value of the investment after 3 years?
Answer:
£4244.83
Step-by-step explanation:
Use the compound amount formula:
A = P(1 + r)^t. Here, P = £4000, r = 0.02 and t = 3 yrs
So: A = £4000(1 + 0.02)^3, which comes to:
A = £4000(1.061) = £4244.83
When you find volume of a 3-D shape, you are finding the measurement of the outside of the shape.
Group of answer choices
True
False
Jace went shopping for a new video game. The listed price of the video game was $41,
but the price with tax came to $44.28. Find the percent sales tax.
Answer:
It would be 8% .
Good luck ^^
In this scenario, your supervisor asked you to conduct an appropriate analysis to see if the relationship between conscientiousness and performance best described as a linear or curvilinear function. You collected data from 300 incumbents from the technology design company. The data includes the conscientiousness responses from the Revised NEO Personality Inventory (NEO-PI-R) and supervisory ratings of overall job performance.
How would you conduct an analysis to answer your supervisor’s question? Please describe the statistical steps.
If you find that a linear assumption is wrong, what would be an implication of the result to validity evidence and selection decision-making for your organization?
To determine whether the relationship between conscientiousness and performance is best described as linear or curvilinear, a statistical analysis can be conducted.
To begin the analysis, calculate the correlation coefficient between conscientiousness scores and job performance ratings. This will provide an initial indication of the relationship's direction and strength. A positive correlation suggests a linear or curvilinear relationship, while a weak or non-existent correlation may indicate no clear relationship.
Next, perform a regression analysis to model the relationship between conscientiousness and performance. Fit a linear regression model and assess the goodness of fit using metrics like R-squared.
If the linear model yields a high R-squared value and the residuals exhibit random patterns, it suggests a linear relationship between the variables. However, if the linear model produces a low R-squared and the residuals show a non-random pattern, it indicates a potential curvilinear relationship.
If the analysis indicates that the linear assumption is incorrect and a curvilinear relationship exists, it has implications for validity evidence and selection decision-making. Traditional selection methods that rely solely on linear relationships may not accurately predict job performance for individuals with extreme levels of conscientiousness.
Validity evidence may need to be re-evaluated, and selection procedures could be adjusted to consider the curvilinear nature of the relationship. Incorporating additional assessments or modifying selection criteria may be necessary to capture the nuances of the relationship and make more informed selection decisions.
In summary, to determine the nature of the relationship between conscientiousness and performance, conduct a statistical analysis involving correlation and regression. If a curvilinear relationship is found, it can impact the validity of selection decisions and require adjustments to selection procedures to accommodate the non-linear nature of the relationship.
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Determine the range of the function [tex]\displaystyle f(x)=a\sqrt[3]{bx-c}+d[/tex].
Hi there!
[tex]\large\boxed{(-\infty, \infty)}}[/tex]
We are given the function:
[tex]f(x) = a\sqrt[3]{bx-c}+d[/tex]
This is the transformation form of a cubic root function. Recall these properties of cubic root functions:
Domain: -∞ < x < ∞ (all real numbers)
Range: -∞ < x < ∞ (all real numbers)
Therefore, the range of the given function is all real numbers, or on (-∞, ∞).
If a car can travel 78 miles using 3 gallons of gas, what is the unit rate?
Answer:
26
Step-by-step explanation:
Well since a car can travel 78 miles Using 3 gallons
78/3=26
26 miles for each gallon
Answer:
26
Step-by-step explanation:
The unit rate refers to the distance the car can travel using 1 gallon of gas. One way to solve this is to create an algebraic equation like [tex]78=3x[/tex]. Then, to find the unit rate isolate x by dividing both sides by 3. This means that the unit rate is 26.
PLZZZ HELP MEE BIG BRAIN PLP PLZZ
Represent each linear situation with an equation in slope-intercept form.
A family bucket meal at Chicken Deluxe costs twenty-six dollars plus $1.50 for every extra piece of chicken added to the bucket.
Answer:
y = 1.5x + 26Step-by-step explanation:
Total cost is $26 add x-pieces each $1.50:
y = 1.5x + 26A sinusoidal graph has a maximum point at (-22, 9) and a midline of y = -5. Determine the range of the graph. Be sure to show calculations or explain your answer. /2
2. If the range of a sinusoidal function is -5.6 ≤ y ≤ 3.8, determine the equation of the midline and the amplitude of the graph.
Please explain thanks!
1. The range of the graph is 28.
2. The equation of the midline is y = -0.45, the amplitude of the sinusoidal graph is 4.7.
How to determine the range of a sinusoidal graph with a maximum point at (-22, 9) and a midline of y = -5?1. To determine the range of a sinusoidal graph with a maximum point at (-22, 9) and a midline of y = -5, we need to find the minimum point of the graph.
Since the midline is y = -5, the average of the maximum and minimum values of the graph will be -5. In other words, the midpoint between the maximum point and the minimum point will lie on the midline.
Let's assume the minimum point is (x, y). Since the maximum point is (-22, 9), the midpoint between the maximum and minimum points can be calculated as:
Midpoint = (x + (-22))/2, (y + 9)/2
Setting the midpoint equal to the midline value, we have:
-5 = (x - 22)/2, (y + 9)/2
Simplifying the equations:
x - 22 = -10
y + 9 = -10
Solving for x and y, we get:
x = 12
y = -19
Therefore, the minimum point is (12, -19).
The range of the graph can be calculated as the difference between the maximum and minimum y-values:
Range = 9 - (-19)
= 28
Therefore, the range of the graph is 28.
How to find the range of a sinusoidal function is -5.6 ≤ y ≤ 3.8?2. If the range of a sinusoidal function is -5.6 ≤ y ≤ 3.8, we can determine the equation of the midline and the amplitude of the graph.
The midline of the graph is the horizontal line that divides the range equally. In this case, the midline will be the average of the maximum and minimum values:
Midline = (3.8 + (-5.6))/2
= -0.9/2
= -0.45
Therefore, the equation of the midline is y = -0.45.
The amplitude of a sinusoidal function is half the range of the graph. In this case, the amplitude can be calculated as:
Amplitude = (3.8 - (-5.6))/2
= 9.4/2
= 4.7
Therefore, the amplitude of the graph is 4.7.
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4, what is the length of EF? Please help
Answer:
EF = 8
Step-by-step explanation:
BC is half of AB, which means that DE will be half of EF. So if DE is 4, which is half of EF, then EF must be 8.
hope this helped! :)
The highest value on the domain of the function is called its ____ ____. (2 words)
starts with ab
Answer:
It is called the maximum value.
Step-by-step explanation:
The highest value on the domain of the function is called its maximum value.
What is domain and range of the function?The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:
Domain = the set of all x-coordinates = {1, 2, 3, 4}
Range = the set of all y-coordinates = {2, 3}
The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph. There is no point above the maximum value of the function. Thus the highest point on the graph is known as the maximum value of the domain of the function.
The maximum value is one of the extreme values of the domain of the function. The other extreme value is known as the minimum value. It is on one side of the graph and the maximum value is on the other side of the graph.
Therefore, the highest value on the domain of the function is called its maximum value.
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A water supply system is to be installed at a distance of 54 meters using 6 meters long PVC pipe with a diameter of 100mm. determine the number of length of PVC pipe to be used? a. 7 b. 8 c. 9 d. 10
To determine the number of lengths of PVC pipe to be used, we need to divide the total distance to be covered (54 meters) by the length of each PVC pipe (6 meters) and round up to the nearest whole number.
Number of lengths of PVC pipe = Total distance / Length of each PVC pipe
Number of lengths of PVC pipe = 54 meters / 6 meters
Number of lengths of PVC pipe = 9
Therefore, the number of lengths of PVC pipe to be used is 9.
So, the answer is option c. 9.
The moment of inertia depends on the distribution of masses relative to the axis of rotation. It is a measure of an object's resistance to rotational motion. The formula for the moment of inertia varies depending on the specific shape and distribution of masses.
If you can provide more details about the arrangement of masses and the axis of rotation, I can help you derive the expression for the moment of inertia in terms of m and l.
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find the amount to be paid at the end of 3years in each case. a) principal =1,200 at12% p.a
Answer:
$1632
Step-by-step explanation:
Given data
Principal= $1200
Rate= 12%
Time= 3 years
The simple interest expression is given as
A= P(1+rt)
substitute
A=1200(1+0.12*3)
A=1200(1+0.36)
A=1200*1.36
A=$1632
Hence the amount is $1632
B. use the figur on the right side to classify the pair of Angeles.
________1.<5 and <1
________2.<6 and <3
________3.<7 and <2
Please please help please
Yikes i dont know this but thanks for the coins C: