42. Let f be a function from the set A to the set B. Let S and T be subsets of A. Show that
a) f(S ∪ T)=f(S) ∪ f(T).
b) f(S ∩ T) ⊆ f(S) ∩ f(T).
Answers
Start with any random elements of sets and compute LHS and RHS individually.
a) The proof of f(S ∪ T) = f(S) ∪ f(T) is explained below.
b) The proof of f(S ∩ T) ⊆ f(S) ∩ f(T) is expliane dbelow.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Let, The set A = {1, 2, 3, 4, 5} and B = {2, 4, 5}.
Therefore, S = {1, 2, 3} and T = {1, 4, 5}.
Now, f(S ∪ T) = {1, 2, 3, 4, 5} and f(S) ∪ f(T) = {1, 2, 3} ∪ {1, 4, 5}.
Hence, f(S ∪ T)=f(S) ∪ f(T).
Now, f(S ∩ T) = {1} and f(S) ∩ f(T) = {1, 2, 3} ∩ {1, 4, 5} = {1}.
Therefore, f(S ∩ T) ⊆ f(S) ∩ f(T). (⊆ implies improper subset)
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Related Questions
Now you will write an informative paragraph that will help Frankie to understand his financial options and formulate best practices for spending and saving.
Answers
Answer:
Strategies that Frankie should consider:
1.) What he needs vs what he wants (does Frankie need new shoes?)
2.) Opportunity cost (savings Frankie would have to give up if he buys new shoes)
3.) Short-term and long-term goals (Does Frankie needs shoes now, or can he wait?)
Frankie should think about a number of options before purchasing a new pair of shoes. He should first consider whether he actually needs or wants these shoes. He should then think about opportunity cost. How else could he have used that money if he had not purchased the shoes? Could he have utilized his resources more effectively? He must also think about the issue of setting goals. He needs to decide if this is a task for the present or the future.
Also I dont understand how this is math
A triangle has sides with lengths 8, 15, and 17. approximate the acute angles in this triangle to the nearest degree and list in ascending order
Answers
Answer:
28°, 62°
Step-by-step explanation:
As 8,15,17 is a Pythagorean Triple, the triangle must be a right triangle. Hence, we can use our common trig ratios to solve the problem. Let's assume our right triangle has a base of 8, a height of 15, and a hypotenuse of 17.
Here are all the acute angles in order:
[tex]\cos^{-1}(\frac{15}{17})\approx28^\circ[/tex]
[tex]\sin^{-1}(\frac{15}{17})\approx62^\circ[/tex]
I need to figure out how to do linear fuctions... If I could get help that would be great, thanks.
Answers
Answer:
linear function can be found by looking at a linear graph and determining the equation of the line and converting that equation into a function.Step-by-step explanation:
The steps to do this are: Find the y-intercept (this is equal to b in the formula) Find the slope of the line (this is equal to m in the formula)
Several minutes later, Raul decides to measure the water temperature again. He finds that the temperature changed by -0.6°F. What is the temperature of the water now? Show your work.
Answers
The current temperature of the water is given as follows:
71.7 ºF.
How to obtain the current temperature of the water?The defining statement from the problem is given as follows:
He finds that the temperature changed by -0.6°F.
The change by the negative amount of -0.6ºF means that the current temperature of the water is obtained subtracting the previous temperature of the water by 0.6 ºF.
The previous temperature of the water is given as follows:
72.3°F.
Hence the current temperature of the water is obtained subtracting 72.3ºF and 0.6ºF, as follows:
72.3 - 0.6 = 71.7 ºF.
Missing InformationThe previous temperature of the water is given as follows:
72.3°F.
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What is the point of intersection when the system of equations below is graphed on the coordinate plane?
(1, –3)
(–1, 3)
(1, 3)
(–1, –3)
Answers
The point of intersection is (–3.5, 0.5) when the system of equations below is graphed on the coordinate plane.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
The system of equations below
-x + y = 4,
6x + y = -3
As per the given question, the required graph has been attached below.
The point of intersection when the system of equations is graphed on the coordinate plane is (–3.5, 0.5).
This is the point where the two lines cross each other.
Hence, the correct answer would be an option (D).
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The question seems to be incomplete the correct question would be:
What is the point of intersection when the system of equations below is graphed on the coordinate plane? -x+y=4, 6x+y= -3
A. (1, –3)
B. (–1, 3)
C. (1, 3)
D. (–3.5, 0.5)
Fine Floors can install 15 square yards of carpeting in 4 hours 30 minutes. At this rate, how long would it take to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches?
Answers
Answer:
Step-by-step explanation:
To figure out how long it would take Fine Floors to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches, we first need to determine how many square yards of carpeting are needed for the room. We can start by converting the dimensions of the room from feet and inches to yards, since that's the unit of measurement we're working with.
To convert feet to yards, we divide by 3. For example, 11 feet is equal to 11/3 = 3.67 yards. To convert inches to yards, we divide by 36 (since there are 36 inches in a yard). For example, 9 inches is equal to 9/36 = 0.25 yards.
So the length of the room in yards is 3.67 + 0.25 = 3.92 yards, and the width of the room in yards is 13/3 + 4/36 = 4.33 + 0.11 = 4.44 yards.
To determine the total area of the room in square yards, we multiply the length and width: 3.92 * 4.44 = 17.38 square yards.
Now that we know how many square yards of carpeting are needed for the room, we can use that information to calculate how long it would take Fine Floors to install the carpeting. Since we know that Fine Floors can install 15 square yards of carpeting in 4 hours 30 minutes, we can use that as the ratio for our calculation.
To calculate how long it will take to install 17.38 square yards of carpeting, we use the proportion:
(15 sq. yards) / (4 hours 30 minutes) = (17.38 sq. yards) / (x hours)
Cross multiplying and solving for x, we find: x = (4 hours 30 minutes) * (17.38 sq. yards) / (15 sq. yards)
So it would take Fine Floors approximately 5 hours and 11 minutes to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches.
How do logarithmic functions model real-world problems and their solutions? Give a specific example and explain.
Answers
The process of logarithmic functions in real-worlds problems is given below.
And an example of an application of logarithmic function is given.
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
We know,
logarithmic function and exponential function are inverse of each other.
So, whenever we solve the exponential function,
we use the help of logarithmic functions.
To compute the number with bigger exponents,
we use the logarithms.
Because it reduces the size of the numbers.
Let the bacteria is growing exponentially,
b = 2ⁿ.
We know that the bacteria grows every hour.
We want to find time.
Here, we will use the inverse function to the exponential function.
How long will it take them to get 1000 bacteria?
1000 = 2ⁿ
Taking log on both sides,
log(1000) = n log2
n = log(1000)/log(2)
n = 9.96
n ≈ 10 hours.
Therefore, an application of logarithmic function is given above.
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mkaqvzcdwp how to grow a plant in various types
Answers
Answer:
Choose the right container: Select a container that is appropriate for the size and type of plant you want to grow. Make sure the container has drainage holes to allow excess water to drain away.
Use the right soil: Use a well-draining soil mix that is appropriate for the type of plant you are growing. Avoid using soil from your garden, as it may contain pests or diseases that can harm your plant.
Provide proper lighting: Most plants need plenty of sunlight to grow, so choose a location that gets plenty of light. If you are growing plants indoors, you may need to use grow lights to provide adequate lighting.
Water properly: Water your plants regularly, but avoid overwatering, as this can lead to root rot. Check the soil moisture level regularly and water when the top inch of soil is dry.
Fertilize: Use a balanced fertilize to provide your plants with the nutrients they need to grow. Follow the instructions on the fertilize package for the proper amount and frequency of application.
Pest control: Keep an eye out for pests such as aphids, thrips, and mealybugs, and take action if necessary. There are many natural ways to control pests, such as introducing predatory insects or using neem oil.
By following these general tips, you should be able to successful
There are three popular choices when it comes to growing - Hydroponics, Soil and Coco. These methods vary widely according to the source, understanding the source of your media can lead to a grower getting better results.
9. Marcus vegetable is drawing a plan for his garden. He graphs one corner at (-7.2, 2). He reflects (-7.2, 2) across the x-axis. Then Marcus reflects the new points across the y-axis. What shape is the vegetable garden?
Answers
Answer: To reflect a point across the x-axis, you need to change the sign of the y-coordinate. Therefore, the point (-7.2, 2) reflected across the x-axis becomes (-7.2, -2).
To reflect a point across the y-axis, you need to change the sign of the x-coordinate. Therefore, the point (-7.2, -2) reflected across the y-axis becomes (7.2, -2).
The resulting shape is a rectangle with one corner at (-7.2, 2) and the opposite corner at (7.2, -2).
Step-by-step explanation:
What’s the answer ?
Solve |2x - 3| ≥7
Answers
Answer:
x ≤ −2 or x ≥ 5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
An iPhone costs £850 in London, €800 in Paris and $1,000 in New York.
Using £1 = €1.18 and £1 = $1.43, state the lowest price of the iPhone in £.
Answers
Lowest price of an iPhone in Paris is €800 because they stated that one euro is equal to one dollar; when multiplied, the result is 944; this indicates that the iPhone is priced lower in Paris.
What is lowest value of iphone ?It is possible to compare the conversion rates of sterling into the euro and the dollar using the same amount of pounds.
Sterling to Euro : [tex]$750 \times 1.14=6855$[/tex]
Pounds to dollars : [tex]$750 \times 1.39=\$ 1042.5$[/tex]
One phone may be purchased with one pound. The dollar is insufficient to purchase a cell phone, but the euro has enough money to do so. Paris has the lowest pricing for the iPhone from this perspective.
The iPhone SE (2020), which costs Rs 40,000, costs more over a lakh rupees according to the most recent Apple price list for India. Everywhere in the globe, the USA market offers the cheapest prices for iPhones.
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Could someone help answer this? Thanks!
The limit of a function y=f(x) at x=a is sometimes best understood as the approximate height of the function around x=a based on the values around x=a whereas the value of the function f at x=a is the exact height of the function at that point. Consider two functions 1) f(x)=x+1 and g(x)=(x^2-1)/(x-1). Answer the following questions. (a) Discuss the process of finding the limit x->1 f(x). (b) How does it differ from f(1)?
Answers
a) The process to find the limit is given as follows:
f(x): simply replace x by 1.g(x): factor and then replacing.b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.
How to calculate the limit of a function?The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.
Hence:
lim x -> 1 f(x) = 1 + 1 = 2.lim x -> 1 g(x) = (1² - 1)/(1 - 1) = 0/0.For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.
Applying the subtraction of perfect squares, we have that:
x² - 1 = (x - 1)(x + 1).
Then:
g(x) = (x - 1)(x + 1)/(x - 1) = x + 1.
Meaning that the limit is then calculated as follows:
lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.
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Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
Opposite side = 14 in.
Adjacent side = 22 in.
cos θ = ?
Answers
Answer
Since this is a right triangle, we can use the inverse cosine function to solve for the angle θ.
cos θ = Opposite side / Adjacent side
cos θ = 14 / 22
cos θ = 0.6363
θ = cos^-1 (0.6363)
θ ≈ 45.9°
In a equation is it true that when a variable is alone you have to add a number 1 to it?
I’m wondering since I have to add it to my notes.
Answers
Tara is painting her room she brought paint that takes 3 gallons to cover an area of 75 square feet how many gallons of paint will tara need to paint 375 square feet of her room
Answers
Select largest number from 16,48,8
Answers
Answer:
48.
Step-by-step explanation:
8 < 16 < 48
48 > 16 > 8
Answer:
Step-by-step explanation:
Select largest number from 16,48,8
Help PLEASE IN A RUSH!
Which graph represents this system?
y = 3. x + y = 4.
On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0).
On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (4, 0).
On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (2, 6).
On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (3, 7).
Answers
Answer:
first option
Step-by-step explanation:
y = 3 is a horizontal line parallel to the x- axis and passing through all points with a y- coordinate of 3
x + y = 4 ← is the equation of a straight line
find the x and y- intercepts
to find the y- intercept let x = 0 in the equation and solve for y
0 + y = 4 , that is
y = 4 ⇒ (0, 4 ) is a point on line
to find the x- intercept let y = 0 in the equation and solve for x
x + 0 = 4 , that is
x = 4 ⇒ (4, 0 ) is a point on the line
the graph representing the system is
a horizontal line y = 3 and another line passing through (0, 4 ) and (4, 0 )
Anna and Sharon both construct a triangle. Anna begins by drawing a segment with a length of 3 inches. Starting from one vertex, she draws another segment with a length of 5 inches so that the two segments have an included angle of 35°. Sharon constructs her triangle by drawing a segment with a length of 5 inches, measuring a 35° angle, and drawing a ray from one vertex. Then she measures and terminates the ray at 3 inches. Do Anna and Sharon create congruent triangles? Explain.
Answers
Answer:
Yes, Anna and Sharon both created triangles that are congruent. Their triangles are congruent because they have 2 corresponding, congruent side-lengths and an included angle that is congruent. Therefore, their triangles are congruent by SAS (Side-Angle-Side).
please help it’s due in half an hour
Answers
Answer:
(a) They asked for one value of x
but I'll give you both
They're 2 and -2
(b)g(-1) = 4
Step-by-step explanation:
For (a) they're are looking for the value of x that is corresponding to 1 on the y axis
If you observe from your graph only -2 and 2 will have a corresponding value of 1 therefore they're the answers
for (b) Just look for the corresponding value of -1(x -axis) on the y axis which is 4
Mr. Fraser signs up for a math class in the
summer, and at the end of each week there is
a 5 questions multiple choice test. Each
question has four options/answers.
On week 3, out of curiosity, he decides to
randomly pick the answer for each of the five
questions (he doesn't even read the
questions-just circles one of the four
options!)
What is the probability that he will pass using
this method? Do you think he will regret this
experiment?
Answers
Therefore , the solution of the problem of probability comes out to be
Probability = 0.25 or 25% that he will pass using this random option picking method.
Define probability.Probability is the likelihood or potential for something to event. For instance, there is only one way to get a head and a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) must equal 12. Classical: (equally likely results) (equally probable outcomes) S, the sample location (the collection of all distinct outcomes that could occur), Definition of Relative Frequency and Subjective Probability.
Here,
Given : t the end of each week there is a 5 questions multiple choice test.
and
Has 4 options.
Probability that he will pass using this random option picking method.
=> Probability = Favourable events / Total no of outcomes
=> Probability = 1 /4
=> Probability = 0.25 or 25%
Therefore , the solution of the problem of probability comes out to be
Probability = 0.25 or 25% that he will pass using this random option picking method.
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We are asking everyone to focus on reducing their average transaction time by 10%. The average transaction time for this location is 6 minutes and 52 seconds."So we have to get the average transaction time down to __________."
Answers
Answer:
Step-by-step explanation:
The average transaction time of this location reduced to 371 seconds.
Mr Paul has 4 bars of chocolate. He distributes 1/3
of each bar to 4 children.
a) Write the fraction of chocolate distributed.
b) Write the fraction of cholates left with Mr. Paul
Answers
a) The fraction of chocolate distributed is given as follows: 4/3.
b) The fraction of chocolates left with Paul is given as follows: 8/3.
How to obtain the fractions?The fractions are obtained applying the proportions used in the context of this problem.
He distributes 1/3 of each bar to 4 children, hence the total number of bars distributed is given as follows:
4 x 1/3 = 4/3.
(multiplication of fractions, multiply the numerators and the denominators, keeping the quotient).
The total number of bars that Paul had initially is given as follows:
4 bars.
Then the fraction of chocolate remaining with Paul is given by the subtraction of the total amount of bars by the amount given to the children, as follows:
4 - 4/3 = 12/3 - 4/3 = 8/3 bars.
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Please help
Match the items.
a. Multiplicative Inverse
b. Additive Inverse
c. Commutative Property of Multiplication
d. Distributive Property
e. Additive Identity Property
f. Associative Property of Addition
1. 5.6=6-5
2. -8+0= -8
3. (3+5) +9=3+ (5+9)
4. 5.1=1
5. 7+(-7)=0
6. 5(x−4)=5x−20
Answers
The matching of the items as follows ,a - 4 , b - 5, c - 1 , d - 6 , e - 2 , f - 3
What is a number ?
number is used to represent the quantity of number and it is even used for calculations.
a) Multiplicative inverse
if the product the given number and reciprocal of the given number is 1.
so,
5 * 1/5 = 1
as LHS = 5 * 1/5 = 1
RHS = 1
Hence , a - 4
b ) Additive inverse
if the summation of the given number and opposite sign of given number results 0 .
7 + (-7) = 0
LHS = 7+ (-7) = 0
RHS = 0
hence , b - 5
c ) Commutative Property of Multiplication
if a.b = b.a hence it is in Commutative Property of Multiplication .
so, 5.6 = 6.5
hence , c - 1
d) Distributive property
if a ( b + c ) = a*b + a*c than it is in distributive property .
hence , d - 6
e) Additive Identity Property
if a+ 0 = a hence it is Additive Identity Property
so , b - 2
f ) Associative Property of Addition
if (a+b) + c = a + (b+c ) hence it is in Associative Property of Addition
so , f - 3.
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There is a raffle for the class of 30
students. There are 3 prizes that are gift
cards for the value of $5, $10 and $25.
How many ways can there be 3 winners of
this raffle?
Answers
Answer:
Having 3 students pick a raffle
Step-by-step explanation:
help with this math assignment pls
Answers
From the classification angles, it was possible to find the arcs:
UL=40, UY= 90, TY=50, YLE =270, LE=140 and UET=220.
UETIf UE= 180 and TE=40, you have:
UET=UE+TE
UET=180+40
UET=220
Classification AnglesThey are a lot of classifications for angles like complementary angles, supplementary angles, right angles, and others. See below:
complementary angles - two angles whose sum is equal to 90°.supplementary angles - two angles whose sum is equal to 180°.right angles - angles whose measure is 90°.opposite angles - opposite angles consequently they are congruent.The question gives mTE=40, and it asks:
ULUL is opposite the arc TE, therefore its value is also 40.
UYThe figure shows a right angle, then UY is equal to 90.
TYIf UY is equal 90, YE is equal to 90 too, because they are supplementary. If YE=90 and TE=40, you have:
TE+TY=90
40+TY=90
TY=90-40
TY=50
YLEYLE = YE+UE. The figure shows YE=90 and UE represents a semicircle (180). Thus,
YLE= 90+180=270
LEIf UE= 180 and UL=40, you have:
UE=UL+LE
180=40+LE
LE=180-40
LE=140
UETIf UE= 180 and TE=40, you have:
UET=UE+TE
UET=180+40
UET=220
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suppose that a randomly generated list of numbers from 0 to 9 is being used to simlulate an event that has a probability of success of 30% which of these groups of numbers could represent a success
Answers
Any event for which, the 3 numbers between 0 and 9 are outcomes could represent the success.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.Given is that suppose that a randomly generated list of numbers from 0 to 9 is being used to simulate an event that has a probability of success of 30%.
For the success rate of 30%, this means the probability of that specific event would be 0.3.
So any event for which, the 3 numbers between 0 and 9 are outcomes or are the number of favorable events could represent the success.
Therefore, any event for which, the 3 numbers between 0 and 9 are outcomes could represent the success.
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Find the difference between Mary's weight when she was 10 year's old and when she was born
Answers
The difference between Mary's weight when she was 10 year's old and when she was born will be;
⇒ 72 pounds
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
When Mary was born, she weighed 8 pounds.
And, When she was 10 years old, she weighed 10 times as much.
Now,
Since, When she was 10 years old, she weighed 10 times as much.
Hence, When she was 10 years old, she weighed = 10 × 8 pounds
= 80 pounds
And, When Mary was born, she weighed 8 pounds.
Thus, The difference between Mary's weight when she was 10 year's old and when she was born is,
⇒ 80 - 8 pounds
⇒ 72 pounds
So, The difference between Mary's weight when she was 10 year's old and when she was born is 72 pounds.
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The complete question is this,
When Mary was born, she weighed 8 pounds. When she was 10 years old, she weighed 10 times as much. How much more did Mary weigh when she was 10 years old than she was born?
Use the rule x+8 to write a sequence of numbers. Then write the sequence as a list of ordered pairs. Start with and substitute at least six values for .
Answers
Answer:
Here is a sequence of numbers using the rule "x+8":
x+8=9 (x=1)
x+8=10 (x=2)
x+8=11 (x=3)
x+8=12 (x=4)
x+8=13 (x=5)
x+8=14 (x=6)
Here is the sequence of ordered pairs:
(1, 9)
(2, 10)
(3, 11)
(4, 12)
(5, 13)
(6, 14)
A pizza shop sold 18 medium pizzas. The number of large pizzas sold was 3 times as many as the number of medium pizzas sold. How many pizzas did the pizza shop sell altogether?
Answers
Answer:
18 × 3 = 54
18 + 54 = 72
Therefore, the answer is 72.
The weight of the square is 10 grams. How much heavier is the circle than the square?
Answers
The weight of the circle is heavier than the weight of the square by the weight of the triangle
How to find how much weightier is the circle as compared with the squareExamining the weights, can lead to a linear equation, the equation will have the follows parameters
let t represent triangle
let c represent circle
let s represent square
6s + 3t = 3s + 3c
6s - 3s + 3t = 3s + 3c
3s + 3t = 3c
divide through by 3
s + t = c
10 + t = c
From the equation 10 + t = c we can say that the weight of the circle is a triangle weight more than the square
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