Assuming you want to do a cartesian product, then you basically form items (x,y) such that x is in set A, and y is in set A
More generally, A * B will consist of items of the form (x,y) such that x is in A and y is in B. However, we have B = A.
So,
A * A = {
(a,a), (a,b), (a,c)
(b,a), (b,b), (b,c)
(c,a), (c,b), (c,c)
}
I broke things up into separate rows to show that we can form a 3x3 table. Each row is a different x value from the set {a,b,c}. Each column is a different y value from the set {a,b,c}
In my opinion, this helps organize things much better than rather have it all on one single line like this
A * A = { (a,a), (a,b), (a,c), (b,a), (b,b), (b,c), (c,a), (c,b), (c,c) }
which in all honesty looks like a bit of a cluttered mess.
Answer:
Step-by-step explanation:
A={a,b,c}
A×A={a×a,a×b,a×c,b×a,b×b,b×c,c×a,c×b,c×c}
help me with the picture please
=====================================================
Explanation:
Refer to the diagram below. I've drawn diagonal that slopes upward. This diagonal cuts the quadrilateral into two triangles: One is equilateral and the other is isosceles.
The equilateral triangle marked in blue has all three angles 60 degrees each.
Note that the 60 and y angles combined to form 130, so,
60+y = 130
y = 130-60
y = 70
Then focus on the isosceles triangle (angles y, w and w). These three interior angles must add to 180
y+w+w = 180
70+2w = 180
2w = 180-70
2w = 110
w = 110/2
w = 55
This adds onto its adjacent neighbor of 60 to get w+60 = 55+60 = 115 degrees which is the value of x.
The ratio of the measures of the acute angles of a right triangle is $8:1$. In degrees, what is the measure of the largest angle of the triangle?
Answer:
The angles in the triangle and 10, 80 and 90
Step-by-step explanation:
The two angles that are left in a right triangle add to 90 degrees
8:1 means that there total is 9
8x+1x = 9x
9x = 90
Divide by 9
9x/9 = 90/9
x = 10
8*10 = 80
1*10 = 10
The angles are 80 and 10
The angles in the triangle and 10, 80 and 90
find a number such that when 3/4 of it is added to 3½the sum is the same as when 2/3 of it is subtracted from 6½. PLEASE HELP
Answer:
- 120
Step-by-step explanation:
call x is the number you want to find
(3/4 )x + 3[tex]\frac{1}{2}[/tex] = (2/3)x - 6[tex]\frac{1}{2}[/tex](3/4)x + (7/2) = (2/3)x - (13/2)(3/4)x - (2/3)x = - (13 /2) - (7/2)(1/12)x = -10x = -10 / (1/12) = -120A team of 5people to be selected from 7women & 6men. Find the number of different teams that could be selected if there must be more women than men in the team
Answer:i would say 2 differentt teams where there is more then women than men in the team
Step-by-step explanation:
well how i came to this answer is that the team is limited to only 5 people giving the only team where there is more women over men is this first team would be 4 women and 1 men , second team would be 3 women and 2 men anything lower then 3 make its where the team has more men than women so the only options would be 2 team where either they go with 4 women or 3 women and you can't go with more then 4 because then there would be no men in the team which is what the question asks for please go with 2 teams
if this helps please make me brainlist ?!
help me with math pls;(
Answer:
as it is cbe the volume of cube is l*l*l
Step-by-step explanation:
the answercis 5*5*5= 125
Will mark brainlest helppppppp
Answer:
6
Step-by-step explanation:
again ?
7 = (3x - 4)/2
14 = 3x - 4
18 = 3x
x = 6
Find the missing value in each figure below. What does “y” equal?
Answer:
Step-by-step explanation:
The perpendicular is equal to 6. That's because the left triangle's missing angle is 180 - 45 -90 = 45
The angle in the right triangle is given as 52.
The cos(52) = adjacent side (which we just found to be 6) / y
Multiply both sides by y
y cos(52) = 6
cos(52) = 0.6157
Divide by sides by cos(52)
y = 6 / cos(52)
y = 6 / 0.6157
y = 9.76
I suck at math ik but i need anyones help please
Answer:
f(2)= 1
f-¹(1)= 2
f-¹(f(2))= 2
I hope I helped you^_^
Jeanette ice cream shop sold 10 sundaes with nuts and 7 sundaes without nuts to the total number of sundaes
Math models helpppp plss if you know about math models answer this pls
Answer:
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences and engineering disciplines, as well as in non-physical systems such as the social sciences.
A sample is generated from a population of 20 items. Each of the 20 items are given a label, and a 20-sided die is rolled 3 times to determine which 3 items are in the sample. This is an example of a __________.
A. systematic sample
B. random sample
C. convenience sample
D. self-selecting sample
Answer:
Option B, random sample
it should be the answer
The given information is an example of a random sample. The correct option is B.
What is a random sample?In statistics, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a method of choosing a sample at random.
It is given that A sample is generated from a population of 20 items. Each of the 20 items is given a label, and a 20-sided die is rolled 3 times to determine which 3 items are in the sample.
The above information is an example of a random sample. Follow the given definition above.
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what is a possible solution to the inequality?
1/4a +1 > 9
Answer:
a > 32 is one possible solution to the inequality 1/4a +1 > 9.
Step-by-step explanation:
Please help !!!!!!!!!!!
Answer:
98°+62°+6x = 180
160+6x = 180
6x = 180 - 160
6x = 20
x= 20/6
x= 3.33
therefor your answer is 3.33
help please I'm doing some math homework
Answer:
Slope is 5/2
Step-by-step explanation:
[tex]{ \boxed{ \bf{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1}} }}}[/tex]
Substitute the terms:
[tex]{ \tt{slope = \frac{7 - ( - 3)}{4 - 0} }} \\ = \frac{5}{2} [/tex]
find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]
Convert to p/q form[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]
[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]
A computer vauled at $30,000 is depreciated to $0 value over a 6 year period. find the rate of change in the computer's value per year.
Answer:
$5000 per year
Step-by-step explanation:
Given data
initial value of the computer= $30000
Final value = $0
Duration= 6years
Hence the rate of change in the value per year is
=30000/6
=$5000 per year
find the missing side. Round it to the nearest tenth.
Answer:
14.3
Step-by-step explanation:
sin73 = opposite/hypotenuse = x/15
x = 15sin73 = 14.344571 = 14.3
Samia created the following tables of values for a linear system. She concluded that there is no
solution to the system
Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.
How many solutions do a system of linear lines have?A system of equations, involving two linear lines has solutions as follows:
Unique Solution: When the lines intersect, the point of intersection is the solution.No Solution: When the lines are parallel, no solution exists.Infinite Solution: When the lines coincide, then all points on the line become solutions, giving an infinite number of solutions.How to solve the question?In the question, we are informed that Samia created the given tables for a linear system, and concluded that no solution exists for the system.
We are asked to comment on her conclusion.
To check for her conclusion, we calculate the slopes of both the lines to check whether the relations are parallel or not, as, for parallel relations, the slopes are equal.
Slope can be calculated using the formula, m = (y₂ - y₁)/(x₂ - x₁), when (x₁, y₁), and (x₂, y₂) are the points on the line.
Thus, the slope for:-
Relation 1, is m₁ = (22 - 8)/(4 - (-3)) = 14/7 = 2.
Relation 2, is m₂ = (12 - (-2))/(4 - (-3)) = 14/7 = 2.
Since the slope of the two relations is equal, that is, m₁ = m₂, and they are not coinciding with each other, we can say that the two relations are parallel to each other.
Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.
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if the radius of a sphere is7 cm find its volume
Answer:
1437.33 cm square
Step-by-step explanation:
Now we will use the frmula to et the volume of a sphere
volume of sphere is
4÷3pi r cube
where r is the radius of the sphere
Nina is making pink candles to use as decorations on Valentine's Day. She melts red and white wax together and pours them into a heart-shaped mould. Then, she melts double the amount of red wax and double the amount of white wax together and pours them into a flower-shaped mould. Which candle is a lighter shade of pink?
Answer:
answer is neither, they are both the same shade.
Step-by-step explanation:
if she doubled the colors exactly then it wouldn't be any different. Also IXL told me I'm right :)
Answer:
Neither.
Step-by-step explanation:
Originally, she used the same amount. For the second one, she used double the same amount, but it was still the amount of red wax as of white wax. So, they both had the same amount, which means it is neither.
It is known that seventy percent (70%) of married couples paid for their honeymoon themselves. You randomly select 9 independent married couples and ask each if they paid for their honeymoon themselves. Let our random variable be X = the number of married couples that paid for their honeymoon themselves. What is the probability that all married coupled asked stated they paid for their honeymoon themselves? (Round your answer to four decimal places).
Answer:
0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.
Step-by-step explanation:
For each couple, there are only two possible outcomes. Either they paid for their honeymoon, or they did not. The probability of a couple having paid for their honeymoon is independent of any other couple, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
It is known that seventy percent (70%) of married couples paid for their honeymoon themselves.
This means that [tex]p = 0.7[/tex]
You randomly select 9 independent married couples.
This means that [tex]n = 9[/tex]
What is the probability that all married coupled asked stated they paid for their honeymoon themselves?
This is P(X = 9). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{9,9}.(0.7)^{9}.(0.3)^{0} = 0.0404[/tex]
0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.
Write the equation in slope-intercept form. y = 6(x + 2) + 5x
Answer:
y=11x+12
Step-by-step explanation:
y = 6(x + 2) + 5x
y=6x+12+5x
y=11x+12
in slope interception form= y=mx+c
y=11x+12
To wash a window that is 4 meters off the ground, Rafi leans a 5-meter ladder against the side of the building. To reach the window, how far away from the building should Rafi place the base of the ladder?
Answer:
Base of the ladder is 3 meters away from the building.
Step-by-step explanation:
Let's use Pythagoras theorem to solve.
Pythagoras theorem says,
[tex]a^{2} +b^{2} =c^{2}[/tex]
Here let horizontal distance is "a''
Vertical distance of window is 4 m
So, b=4
The Rafi leans 5 m ladder against the wall. So, c=5.
[tex]a^{2} +4^{2} =5^{2}[/tex]
Simplify it
[tex]a^{2} +16=25[/tex]
Subtract both sides 16
[tex]a^{2} =9[/tex]
Take square root on both sides
a=±3
So, base of the ladder is 3 meters away from the building.
cho tam giác ABC vuông tại A < góc B=a chứng minh: a) 1+[tex]tan^{2}[/tex]a=[tex]\frac{1}{sin^{2}a }[/tex]
làm giúp mình với
[tex]\\ \sf\longmapsto 1+tan^2A[/tex]
[tex]\boxed{\sf tanA=\dfrac{sinA}{cosA}}[/tex]
[tex]\\ \sf\longmapsto 1+\dfrac{sin^2A}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{cos^2A+sin^2A}{cos^2A}[/tex]
[tex]\boxed{\sf cos^2A+sin^2A=1}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1-sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1}-\dfrac{1}{sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{sin^2A}[/tex]
Hence verified
What is the approximate value of x in the diagram below
Answer:
x = 8 cm
Step-by-step explanation:
The first step in solving this problem is to determine which trig function applies. The diagram shows that this triangle is a right triangle, that side x is opposite the 25-degree angle, and that the hypotenuse has a length of 18 cm.
The sine function of an angle Ф is defined as the ratio of the opposite side to the hypotenuse. In this case, sin Ф (or sin 25 degrees) equals x/(18 cm).
We need to determine the value of x. Adapt the above equation to this particular situation: sin 25 degrees = x/(18 cm).
To solve for x, multiply both sides of the most recent equation, above, by (18 cm). The following results: (18 cm)(sin 25 degrees) = x.
Next, use a calculator to find the value of sin 25 degrees: It is 0.4226.
Then the desired value of x is (18 cm)(0.4226), or x = 7.61 cm. This should be rounded off to x = 8 cm to reflect the level of accuracy of the given 18 cm.
A motorist drove from town P to town Q, a distance of 80 km, in 30 minutes . What is his average speed?
Answer:
40km per hour
Step-by-step explanation:
30 minutes × 2 = 60 minutes/1 hour
80 kilometers ÷ 2 = 40 kilometers
40:60
Five consecutive multiples of 7 have a sum of 350. What is the smallest of these numbers?
A. 70
B. 56
C. 77
D. 84
Answer:
B. 56
Step-by-step explanation:
x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350
( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350
5x + 70 = 350
- 70 - 70
_____________
5x = 280
x = 56
Hope this helps!
The smallest number is 56, the correct option is B.
What is Sum?The sum is the output of the mathematical operation, Addition.
Let the first number is x, they are multiples of 7,
As they are multiples of 7, the consecutive numbers will be added by 7 for next term.
The 5 consecutive numbers can be written as x, (x+7), (x+14), (x+21), (x+28).
The equation can be formed for the numbers that are given as,
An equation is a mathematical statement that relates an algebraic expression with other expression by an equal sign.
The sum of the multiples is 350
x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350
Grouping the variables and the constants separately
( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350
5x + 70 = 350
Adding (-70) to both sides of the equation
5x = 280
Dividing both sides by 5
x = 56
The value of the first number of the series is obtained.
The first value is the smallest number of the series.
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A small bird can flap its wings 120 times in 30 s. What is the rate of change of wing flaps?
Answer:
4 Flaps per second
Step-by-step explanation:
M = 120/30
Answer:
4 times per second
Step-by-step explanation:
120 ÷ 30 = 4
30 ÷ 30 = 1
4 flaps per 1 second
so basically 4
A train travels a distance of 60 km at uniform speed. If the speed of the train was reduced by 10 kmh-1, the time taken to travel the 60km will increase by 1/2h. Find the speed of the train at the beginning.
Answer:
Initial speed is 32 m/s
At uniform speed, acceleration is 0, (a = 0).
When speed reduced, (v - u) = 2.78 ms-¹, t = 1800 sec, s = 60 ,000 metres.
From first equation of motion:
[tex]{ \boxed{ \bf{v = u + at}}} \\ { \tt{(v - u) = at}}[/tex]
substitute:
[tex]{ \tt{2.78 = (a \times 1800)}} \\ { \tt{acceleration = 0.0015 \: {ms}^{ - 2} }}[/tex]
from second equation of motion:
[tex]{ \boxed{ \bf{s = ut + \frac{1}{2} a {t}^{2} }}}[/tex]
substitute:
[tex]{ \tt{60000 = 1800u + ( \frac{1}{2} \times 0.0015 \times {1800}^{2}) }} \\ { \tt{1800u = 57570}} \\ { \tt{u = 32 \: m {s}^{ - 1} }}[/tex]
Find the area of triangle ABC.
[PLEASE HELP ME!!]
A.12.16units
B.18.52units
C.31.27units
D.15.14units
Answer:
D
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] × product of 2 sides × sine ( angle between them ) , that is
A = 0.5 × 5.04 × 6.82 × sin61.73° ≈ 15.14 ( to 2 dec. places )
