17. Is the operation of forming Cartesian products commutative? Explain why or why not.
Choose the correct answer below.
OA. The operation of forming Cartesian products is commutative because order does not matter in
the definition of a Cartesian product.
OB. The operation of forming Cartesian products is not commutative because part of the definition of
a Cartesian product is the order of the elements generated by the two sets.
OC.
The operation of forming Cartesian products is commutative because a Cartesian product is
multiplication and multiplication is commutative.
O D. The operation of forming Cartesian products is not commutative because multiplication is not
commutative.
Answers
The operation of forming Cartesian products is not commutative because part of the definition of a Cartesian product is the order of the elements generated by the two sets.
==========================================================
Explanation:
Let's go over an example. We'll have these two sets
A = {1,2}
B = {3,4}
The cartesian product is this set of ordered pairs
A x B= {(1,3), (1,4), (2,3), (2,4)}
Each (x,y) pair has x as a value from the first set mentioned (A), and y a value from the second set mentioned (B). It might help to make a 2 by 2 table.
If we swap the order of set A and B then we have
B x A = {(3,1), (4,1), (3,2), (4,2)}
We can see that A x B does not equal B x A in this case. Therefore, the cartesian product operation is not commutative. The order matters.
Side note: Two sets are equal when they are subsets of each other.
Related Questions
X+2y=8, -3x-2y=12 how do you solve the system of equations with cramers rule
Answers
Using Cramer's rule, the solution to the system of equations is given as follows:
x = -10, y = 9.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
There are multiple ways to solve a system of equations, and one of them is Cramer's Rule, in which we use the determinants of matrices to find the solutions.
In the context of this problem, the system is:
x + 2y = 8.-3x - 2y = 12.The matrix for the system is:
[tex]M = \left[\begin{array}{cc}1&2\\-3&-2\end{array}\right][/tex]
Hence it's determinant is:
|M| = 1(-2) - (-3)(2) = -2 + 6 = 4.
The matrix for x is given by:
[tex]M_x = \left[\begin{array}{cc}8&2\\12&-2\end{array}\right][/tex]
Hence it's determinant is:
|Mx| = 8(-2) - 2(12) = -16 - 24 = -40.
The matrix for y is given by:
[tex]M_y = \left[\begin{array}{cc}1&8\\-3&12\end{array}\right][/tex]
Hence it's determinant is:
|My| = 12 - (-3)(8) = 12 + 24 = 36.
Then the solutions are given as follows:
x = |Mx|/M = -40/4 = -10.y = |My|/M = 36/4 = 9.More can be learned about a system of equations at https://brainly.com/question/24342899
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A rectangle garden is 9ft longer than wide. It’s area is 580ft2. What are it’d dimensions?
Answers
The dimensions of the rectangular garden are 20 feet and 29 feet respectively.
How to determine the dimensions of the rectangleIt is vital to note that the formula for the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of a rectanglew is the measure of the width of a rectangleFrom the information given, we have that;
Area = 580ft²
Length = 9 + width
L = 9 + w
Substitute the values into the formula, we have;
580 = (9 +w)(w)
expand the bracket
580 = 9w + w²
Make into quadratic equation
w² + 9w - 580 = 0
Factorize the equation
w² + 29w - 20w - 580 = 0
Factor the common terms
w( w + 29) - 20(w + 29) = 0
Then,
w + 29 = 0
w = -29
and w - 20 = 20 feet
We have the expression of length as l = 9 + w
Length, l = 9 + 20
Length, l = 29 feet
Thus, the values are 20 feet and 29 feet
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Pls help
Find the surface area of the cylinder.
Answers
In the picture there is a cylinder with height 5 inches and diameter 4 inches. The surface area of cylinder is 87.62.
Given that,
In the picture there is a cylinder with height 5 inches and diameter 4 inches.
The surface area of a cylinder is the area that is enclosed by the flat bases and the curving surface of the cylinder. The cylinder's total surface area includes the area of the curving surface as well as the areas of the two circle-shaped bases of the cylinder.
The surface area of cylinder is 2πr²+2πrh
r is radius which is diameter/2
r=4/2=2
h is 5
Surface area of cylinder= 2πr²+2πrh
=2π×2²+2π×2×5
=8π+20π
=28π
=28×3.14
=87.92
Therefore, the surface area of cylinder is 87.62.
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an airplane covers 1259km in an hour find the distance it will cover 23/6 hours
Answers
Answer:
4826.166666km
Step-by-step explanation:
d=distance
[tex]\frac{1259km}{1h} =\frac{d}{23/6h}[/tex]
= [tex]\frac{1259km}{1h}= \frac{6d}{23}[/tex]
= [tex]1259=\frac{6d}{23}[/tex]
= [tex]1259*23=6d[/tex]
= [tex]28,957=6d[/tex]
= [tex]\frac{28,957}{6}=d[/tex] ≈4826.166666
Admissions to Carowinds cost $45 per person. Each person spent $10 for a meal. There is a parking fee of $12 for an entire family. How many people went on the trip ito Carolwinds if the total amount spent was $287?
Answers
Step-by-step explanation:
5 people went on the Carowinds trip.
The temperature has been dropping 2 degrees Celsius per hour since midnight. If the temperature is 13 degrees at midnight, what is the temperature at 3:00AM?
Answers
If the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.
Temperature at midnight = 13 °
Temperature drop per hour = 2 °
We need to find the temperature at 3:00 AM
Number of hours till then = 3 hours.
Temperature drop will be calculated by using multiplication.
Temperature drop = 2 × 3 = 6°
Temperature ate 3:00 AM = 12 - 6 = 6°
Therefore, we get that, if the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.
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if graph of g(x)is the graph of the parent function f(x)=x translated 3 units upward,then the y-intercept of the function g(x) is __
Answers
Answer: (0,3)
Step-by-step explanation:
The y-intercept for f(x)=x would be (0,0). Therefore, if we translate it up by three to get g(x), then the y coordinate would go up by 3, resulting in (0,3).
graph g(x). please and thank you!
Answers
Answer: The graph is below
======================================================
Explanation:
If x = 0, then,
g(x) = -x+1
g(0) = -0+1
g(0) = 0+1
g(0) = 1
Therefore, x = 0 leads to y = 1. The point (0,1) is on the g(x) line.
Now try x = 1
g(x) = -x+1
g(1) = -1+1
g(1) = 0
The point (1,0) is also on the g(x) line.
Draw a line through the points (0,1) and (1,0)
Then erase the portion that is to the left of x = -4
This is because g(x) is only graphed when x > -4; i.e. we're only graphing stuff to the right of x = -4.
We'll have an open hole when x = -4 since we aren't including it as part of the graph.
See below.
Question 4 of 10 The function a(b) relates the area of a trapezoid with a given height of 12 and one base length of 9 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)-12.b+9 Which equation below represents the inverse function b(a), which takes the trapezoid's area as input and returns as output the length of the other base?
Answers
The answer to the given function is [tex]B(a)= a/6-9[/tex].
What is a trapezoid?A trapezoid, also referred to as a trapezium, is an open, flat object with 4 straight sides and 1 set of parallel sides. A trapezium's bases are its parallel sides, while its legs are its non-parallel sides.
Given :
[tex]A(b)= 12( b+9)/2[/tex]
where, A(b) is the trapezoid's area
and b is the other base value
On solving the above equation further we get ;
[tex]A= 6(b+9)[/tex]
[tex]A/6= b+9[/tex]
this implies we get;
b= [tex]A/6-9[/tex]
Now convert this into function notation we get
[tex]B(a)= a/6-9[/tex]
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amy eans £10 per hour. she gets a raise, and her new hourly rate is £11.5. what is the percentage change in her hourly rate?
Answers
Answer:
The percentage change is 15%
Step-by-step explanation:
Can I have brainliest?
(a)At Cheng's Bike Rentals, it costs $42 to rent a bike for 9 hours.How many dollars does it cost per hour of bike use? dollar per hour (b)A color printer prints 14b pages in 6 minutes.How many minutes does it take per page? minute per page
Answers
Answer:
a. 4.67 dollars per hour
b. 0.43 minutes per page
Explanation:
Part a.
To know the cost per hour of bike use, we need to divide the total cost by the number of hours, so:
[tex]\frac{Cost}{Hours}=\frac{\text{ \$42}}{9\text{ hours}}=\text{ \$4.67 per hour}[/tex]So, the cost is 4.67 dollars per hour
Part b.
In the same way, the number of minutes per page can be calculated as the division of the number of minutes by the number of pages, so:
[tex]\frac{\text{ Minutes}}{Pages}=\frac{6\text{ minutes}}{14\text{ pages}}=0.43\text{ minutes per page}[/tex]So, it takes 0.43 minutes per page.
0.43 mins per page
Find the equation of a line that contains the points (-2, 2) and (-6,-5). Write the equation in slope-intercept form, usingfractions when required
Answers
Explanation
Lets first find the slope:
[tex]m=\frac{2-(-5)}{-2-(-6)}=\frac{2+5}{-2+6}=\frac{7}{4}[/tex]Now let's use the point-slope formula:
[tex]\begin{gathered} y-2=\frac{7}{4}(x-(-2)) \\ y-2=\frac{7}{4}(x+2) \\ y-2=\frac{7}{4}x+\frac{7}{2} \\ y=\frac{7}{4}x+\frac{7}{2}+2 \\ y=\frac{7}{4}x+\frac{7}{2}+\frac{4}{2} \\ y=\frac{7}{4}x+\frac{11}{2} \end{gathered}[/tex]Answer
[tex]y=\frac{7}{4}x+\frac{11}{2}[/tex]is 3 13/28 bigger than 3 17/20
Answers
Answer: 3 17/20 is bigger than 3 13/28
Step-by-step explanation:
2 ways:
1) Turn the fractions into decimal form.
13/28 = 0.464
0.464 + 3 = 3.464
17/20 = 0.85
0.85 + 3 = 3.85
2) Check which one is bigger
3.85 is bigger than 3.464 because the tenth place is bigger than the second number.
Second way:
1) Remove the 3s.
Both equations have three, so you could remove both sides three
3 13/28 ? 3 17/20
13/28 ? 17/20
2) Multiply both bottom expressions by itself.
(The numbers that its multiplying equals to 1. When multiplying a number by 1, it stays the same.)
13/28 * 20/20 = 260/560
17/20 * 28/28 = 476/560
3) Compare the fractions
260/560 ? 476/560
260/560 < 476/560
The number in the fraction is bigger
Answer:
No, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.
Step-by-step explanation:
Convert both mixed numbers into improper fractions:
[tex]\implies 3 \frac{13}{28}=\dfrac{3 \times 28+13}{28}=\dfrac{97}{28}[/tex]
[tex]\implies 3 \frac{17}{20}=\dfrac{3 \times 20+17}{20}=\dfrac{77}{20}[/tex]
The lowest common multiple of 28 and 20 is 140.
Therefore, multiply the numerator and denominator of each improper fraction by the same number to make both denominators 140:
[tex]\implies \dfrac{97 \times 5}{28 \times 5}=\dfrac{485}{140}[/tex]
[tex]\implies \dfrac{77 \times 7}{20 \times 7}=\dfrac{539}{140}[/tex]
Therefore, as 539 > 485:
[tex]\implies \dfrac{539}{140} > \dfrac{485}{140}[/tex]
[tex]\implies \dfrac{77}{20} > \dfrac{97}{28}[/tex]
[tex]\implies 3 \frac{17}{20} > 3 \frac{13}{28}[/tex]
Therefore, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.
Complete the table and find the value of each vehicle at the end of the indicated year.Car ACar BCar Value at the Endof the Indicated Year1st2nd3rd4th 5th
Answers
Let's look at car A first.
As already solved, just after it is purchased its value decreases 20%.
Purchased at $30000, its value inmediatly decreases to $24000 ($30000 -
0.2*$30000 = $24000).
We know the yearly depreciation for car A os $2000.
Then, at the end of the first year, its value will decrease from $24000 to $24000 - $2000 = $22000.
Every year its value decreases $2000. Followint the same logic, at the end of the second year its value will decrease from $22000 to $22000 - $2000 = $20000 and so on. Now, we can build the table:
End of first year: $24000 - $2000 = $22000
End of second year: $22000 - $2000 = $20000
End of third year: $20000 - $2000 = $18000
End of fourth year: $18000 - $2000 = $16000
End of fifth year: $16000 - $2000 = $14000
The distance an object travels is determined by how fast it goes and for how long it moves. If an object's speed
remains constant, the formula is d=rt, where d is the distance, r is the speed, and t is the time.
If you drive at 50 miles per hour for 5 hours, how far will you have traveled?
a. 200 miles
b. 10 miles
c. 250 miles
d.300 miles
Answers
Answer:
c. 250 miles
Step-by-step explanation:
[tex]d=(50)(5)=250[/tex]
11. The perimeter of rectangle DOGS is 408 cm. The ratio of the length to width is 5:7. What is thewidth of the rectangle?
Answers
The width of the rectangle DOGS is 119cm
To solve this, since is a ratio problem, we know that the two ratios must add to the total. This is, for a ratio of 5:7, 5 + 7 = 12 is the total "divisions" for the ratio.
This means that if 12 of 12 parts add to the perimeter (408cm):
[tex]\frac{5}{12}+\frac{7}{12}=\frac{12}{12}[/tex]12/12 represents the perimeter 408cm.
The, we can divide the perimeter by 12 and get:
[tex]\frac{408}{12}=34[/tex]Since the width is 7/12 of the perimeter:
[tex]34\cdot7=238[/tex]But, we are taking the perimeter of a rectangle, which is twice the width plus twice the length, thus we need to divide this number by 2:
[tex]\frac{238}{2}=119[/tex]And we get the final answer of 119cm
How many different committees can be formed from 11 teachers and 36 students if the committee consists of 2 teachers and 2 students?
Answers
The number of different committees that can be formed is 34,650.
How many different committees can be formed?First, we know that there are 11 teachers and the committee needs to have two teachers, so let's find the number of combinations here.
Remember that if we have a set of N elements and we need to select K of these, the number of different selections is given by:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case we would have N = 11 and K = 2, so we get:
[tex]C(11, 2) = \frac{11!}{(11 - 2)!*2!} = \frac{11*10}{2} = 11*5 = 55[/tex]
There are 55 combinations.
For the students we do the same thing, here we have 36 students and we need to select two, so:
[tex]C(36, 2) = \frac{36!}{(36 - 2)!*2!} = \frac{36*35}{2} = 630[/tex]
So we have 55 combinations for the teachers and 630 for the students, then the total number of different committees is:
C = 630*55 = 34,650
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Nolan is dividing 2 by 11. If he continues the process, what will keep repeating in the quotient?\
Answers
If Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...
Here Nolan is dividing 2 by 11.
Division is one of the basic arithmetic operation. Division is operation of splitting a specific number into equal parts
The quotient is the result from dividing a number from another number.
Divide the given terms and the result will be
2/11 = 0.1818...
The result will be a repeating quotient . Here the pattern is repeating endlessly
Hence, if Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...
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solve thw variable 6/18=×/36
Answers
6/18=×/36
solve for x
x=(6/18)36
x=6(36/18)
x=6(2)
x=12
Ms. Lantz recently participated in the Rocket Run 5k. The distribution of finishing time for females is approximately normal with a mean of 57 minutes with a standard deviation of 8 minutes. According to the Houston Chronicle, a healthy female person should be able to run a 5K in less than 50 minutes.
Part C: Ms. Lantz’s finishing time was 0.85 standard deviations below the mean. What was her finishing time?
Answer:____ minutes
Answers
Ms. Lantz would need to finish in 50.28 minutes to be eligible for the Houston Marathon.
How to find her finishing time?The relationship between a score and the mean over a set of scores is simply quantified by a Z-Score, which is a measurable statistic.
A Z-score can explain to a trader why a value is unusual or average for a given set of data.
A Z-score below 1.8 suggests that a company is on the verge of bankruptcy, while a score closer to 3 shows that the company is doing well financially.
Solution:
The z-score is calculated using the formula:
z = (x - μ)/σ
μ = Sample's average
σ = Sample's standard deviation
The values are as follows:
μ equals 57 minutes.
σ = 8 minutes
Probability equals 20%, or 0.20.
Determine the z-score for 0.20 using the negative z-table.
Z score is -0.84.
To find x, enter the values into the z formula.
z = (x - μ)/σ
-0.84 = (x - 57)/8
Simplifying;
x = -6.72 + 57
x = 50.28 minutes
Thus, Ms. Lantz would need to complete the Rocket Run 5k in 50.28 minutes in order to be eligible for the Houston Marathon.
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John pizza sells one 18-inch or two 12 inch pizza for $10.99. Determine which size gives more pizza
Answers
Using the formula for the area of a circle calculate the area for both deals.
for the 18-inch pizza
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot18in^2 \\ A=324\pi\approx1017.88in^2 \end{gathered}[/tex]for the two 12-inch pizza
[tex]\begin{gathered} A=2\cdot\pi\cdot r^2 \\ A=2\cdot\pi\cdot12^2 \\ A=288\pi\approx904.78in^2 \end{gathered}[/tex]Part 1Simplifyeach fraction. Some fractions can be simplified more than once A 110/390
Answers
Given the fraction below
[tex]\frac{110}{390}[/tex]To simplify the above fraction, we will divide both the numerato
MODELING REAL LIFE A football player punts a football from a height of 2 feet. The ball reaches a maximum height of
50 feet after traveling 56 feet horizontally, and is caught 111 feet from where the ball was kicked. The path of the ball can
be modeled by a parabola, where y is the height (in feet) and x is the horizontal distance traveled (in feet). At what height
is the ball caught? Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
please help!!!! Worth 80 points!
Answers
All the identifiers that are included when identifying significant digits are-
All non zero digits are significantZeros between two other significant digits are significantZeros to the left of the first nonzero digits in a decimal are not significantZeros at the end of a number to the right of a decimal point are significantZeros at the end of a number without a decimal point are assumed to be not significant.What is defined as the significant digits?Each of the digits of a number starting with the digit farthest to a left that is not zero as well as ending with the digit farthest to a right that is neither zero or is a zero but is considered exact.
For the given options.
Except option 1 every option is correct.
All non zero digits are significantZeros between two other significant digits are significantZeros to the left of the first nonzero digits in a decimal are not significantZeros at the end of a number to the right of a decimal point are significantZeros at the end of a number without a decimal point are assumed to be not significant.To know more about significant digits, here
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x^2=49 which numbers are solutions to the equation
Answers
So we need to solve the following equation for x:
[tex]x^2=49[/tex]We can apply a square root to both sides but it is important to remember the following property. For any given number a we have:
[tex]\sqrt[]{a^2}=\lvert a\rvert[/tex]Which means that:
[tex]\sqrt[]{a^2}=a\text{ and }\sqrt[]{a^2}=-a[/tex]So for our case we have:
[tex]\begin{gathered} \sqrt[]{x^2}=\sqrt{49} \\ \lvert x\rvert=7 \\ x=7\text{ and }x=-7 \end{gathered}[/tex]Then the solutions are 7 and -7.
Simplify (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² - 5x + 3y).
Answers
The simplified form for (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y) is (5x² + 0y² - 10x + 4y - 2xy).
At least one squared term must be present because a quadratic is a second-degree polynomial equation. It is also known as quadratic equations. The answers to the issue are the values of the x that satisfy the quadratic equation. These solutions are called the roots or zeros of the quadratic equations. The solutions to the given equation are any polynomial's roots. A polynomial equation with a maximum degree of two is known as a quadratic equation, or simply quadratics.
How is an equation made simpler?The equation can be made simpler by adding up all of the coefficients for the specified correspondent term through constructive addition or subtraction of terms, as suggested in the question.
Given, the equation is (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y)
Removing brackets and the adding we get,
3x² + 2x² + 2y² - 2y² + (- 5x) + (- 5x) + y + 3y + (- 2xy) = (5x² + 0y² - 10x + 4y - 2xy)
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What is the range of this quadratic function
Answers
The range of the equation of the function given as y = x^2 + 4x + 7 is y >= 3
How to determine the range?The equation of the function is given as
y = x^2 + 4x + 7
Differentiate the function with respect to x
So, we have
y' = 2x + 4
Set the differentiated function to 0
So, we have
2x + 4 = 0
This gives
2x = -4
Divide by 2
x = -2
Substitute x = -2 in the equation y = x^2 + 4x + 7
So, we have
y = (-2)^2 - 4 x 2 + 7
Evaluate
y = 3
The leading coefficient is positive
This means that the vertex is a minimum
So, we have the range to be
y >= 3
Hence, the range is y >= 3
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find the probability not rolling factors of 3 on a die
Answers
Answer:
1/6 chance
Step-by-step explanation:
An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%.
What is a possible reading on the scale if you put 500 kilograms of iron ore on it?
(Would enjoy an explanation!)
Answers
If An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. Its possible reading on the scale if you put 500 kilograms of iron ore on it is :495, 505.
Percent errorPercent error = 1%
Kilogram of iron ore = 500 kilograms
First step is to find the 1% of 500 kilograms
= .01 × 500 kilograms
= 5
Second step is to find the possible reading
Possible reading :
500 - 5
=495
500 + 5
= 505
Therefore we can conclude that based on the above analysis the possible reading can be between 495 and 505.
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2 5/8 divided by 2 1/4
Answers
Answer:
Step-by-step explanation:
[tex]2\frac{5}{8} =\frac{2 \times 8+5}{8} =\frac{21}{8} \\2\frac{1}{4} =\frac{2 \times 4+1}{4} =\frac{9}{4} \\2\frac{5}{8} / 2\frac{1}{4} \\=\frac{21}{8} /\frac{9}{4} \\=\frac{21}{8} \times \frac{4}{9} \\=\frac{7}{6} \\=1\frac{1}{6}[/tex]