This question refers to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions and intersections can be calculated as for any subsets. Given two relations R and S from a set A to a set B, R ∪ S = {(x, y) ∈ A ✕ B | (x, y) ∈ R or (x, y) ∈ S} R ∩ S = {(x, y) ∈ A ✕ B | (x, y) ∈ R and (x, y) ∈ S}. Let A = {−4, 4, 7, 9} and B = {4, 7}, and define relations R and S from A to B as follows. For every (x, y) ∈ A ✕ B, x R y ⇔ |x| = |y| and x S y ⇔ x − y is even. Which ordered pairs are in A ✕ B, R, S, R ∪ S, and R ∩ S? (Use set-roster notation to enter your answers.) A ✕ B = R = S = R ∪ S = R ∩ S =
The ordered pairs in each set are:
A ✕ B = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 4), (7, 7), (9, 4), (9, 7)}
R = {(-4, 4), (4, 4), (7, 7), (9, 9)}
S = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 7), (7, 4), (9, 9), (9, 7)}
R ∪ S = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 7), (7, 4), (9, 9), (9, 7)}
R ∩ S = {(-4, 4), (4, 4), (7, 7), (9, 9)}
We have,
A ✕ B:
The concept of Cartesian product was used to generate all possible ordered pairs by pairing each element from set A with each element from set B.
R:
The concept of the absolute value was used to determine the condition for an ordered pair (x, y) to be in relation R, which is that the absolute value of x is equal to the absolute value of y.
S:
The concept of even numbers was used to determine the condition for an ordered pair (x, y) to be in relation S, which is that the difference between x and y is an even number.
R ∪ S:
The concept of a union was used to combine the ordered pairs that are in either relation R or relation S.
R ∩ S:
The concept of intersection was used to find the ordered pairs that are common to both relation R and relation S.
Thus,
The ordered pairs in each set are:
A ✕ B = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 4), (7, 7), (9, 4), (9, 7)}
R = {(-4, 4), (4, 4), (7, 7), (9, 9)}
S = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 7), (7, 4), (9, 9), (9, 7)}
R ∪ S = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 7), (7, 4), (9, 9), (9, 7)}
R ∩ S = {(-4, 4), (4, 4), (7, 7), (9, 9)}
Learn more about sets here:
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I need to know 1 help me with the area
ASAP
Answer:
Hello! question 1: area for question is 547.1136 round if your teacher wants you to. circumference for this question: 82.896 round if teacher wants you to.
On a biology test, a student got 25 questions correct but did not pass. On a second attempt, the student got 33 questions correct. What was the percent increase?
Answer: 32%
Step-by-step explanation:
The percentage increase will be gotten by using the formula:
= Increase in score / Former score × 100
= (33 - 25) / 25 × 100
= 8/25 × 100
= 8 × 4
= 32%
The percentage increase is 32%.
Find the volume of the three dimensional figure in terms of x
Answer:
[tex]V=6x^3+3x^2[/tex]
Step-by-step explanation:
The given figure shows a cuboid whose length is (2x+1) breadth is x and height is 3x.
We need to find the volume of the three dimensional figure.
The volume of a cuboid is given by :
V = lbh
Substitute all the values,
[tex]V=(2x+1)\times x\times 3x\\\\V=(2x+1)\times 3x^2\\\\= 3x^2(2x)+3x^2\\\\V=6x^3+3x^2[/tex]
So, the volume of the figure is equal to [tex]6x^3+3x^2[/tex].
If angle B measures 25°, what is the approximate perimeter of the triangle below?
Hello!
I had this problem in a test, and there is an image of a right triangle in the test
We have been given an image of a right triangle and are asked to find the perimeter of our given triangle.
The answer is 10.3 units, Option A
What is the mean of this data? 13, 16, 3, 27, 32.
Answer:18.2
Step-by-step explanation: you add them up and and divide them
HELPPPPPPPPP ME I WILL GIVE BRAINLIEST
Answer:
1. C
3. D
5. B
Don't know the others sorry!
Step-by-step explanation:
Answer:
4. [tex]g(x)=-x^{2}-10x-15[/tex]
6.[tex](2, -11)[/tex]
In the diagram above z1 =2x+20 and z2 =3x+10. Find the measure of z1.
Answer:
40
Step-by-step explanation:
Angle 1 and 2 are alternate angles
Then they are equal
2x+20=3x+10
Solve for x
X=10
Then 2 (10)+20 =40
Which statements are true about the rectangular pyramid below? Select three options.
A rectangular pyramid. The rectangular base has a length of 6 centimeters and width of 4 centimeters. 2 triangular sides have a base of 6 centimeters and height of 6 centimeters. 2 triangular sides have a base of 4 centimeters and height of 4.6 centimeters.
The area of the base is 24 cm2.
There are four lateral faces.
All the lateral faces are congruent.
The total surface area of the figure is 66.4 cm2.
At least one of the lateral faces has an area equal to 24 cm2.
Mark this and return
there are four lateral faces
Answer:
1
2
4
Step-by-step explanation:
A study is done to find the 95% confidence interval for the difference in means between the ACT scores between two schools in a given city. One school had a random sample of 39 students had a sample mean of 25.90 with a sample standard deviation of 3.49. The second school had a random sample of 37 students had a sample mean 27.70 with a sample standard deviation of 2.47. What is the lower bound of the 95% confidence interval for the difference in means
Solution :
95% confidence interval for the difference between the means of ACT scores between two schools, is given by :
[tex]$[(\overline X_1 - \overline X_2)-ME, (\overline X_1 - \overline X_2)+ME]$[/tex]
[tex]$\overline X_1 = 25.90 , \ \ \ \overline X_2 = 27.70$[/tex]
[tex]$S_1=3.49, \ \ \ S_2 = 2.47$[/tex]
[tex]$n_1=39, \ \ n_2=37$[/tex]
M.E. , Margin of error,
[tex]$=t_{n_1+n_2-2,0.025} \times \left( s \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$[/tex]
[tex]$s^2 = \frac{(n_1-1)S_1^2+(n_2-1)S^2_2}{n_1+n_2-2}$[/tex]
[tex]$=\frac{38(3.49)^2+36(2.47)^2}{39+37-2}$[/tex]
= 9.222
s = 3.03
[tex]$t_{74,0.05} = 1.99$[/tex]
[tex]$M.E. = 1.99 \times 3.03 \times \sqrt{\frac{1}{39}+\frac{1}{37}}$[/tex]
= 1.4
Therefore, 95% CI = [(25.90-27.70) - 1.4 , (25.90-27.70) + 1.4]
= [-3.2, -0.4]
Therefore, the lower bound is -3.2
Average rate change to the nearest hundredth can be which answer ?
Answer:
0.47
Step-by-step explanation:
f(x) = (x - 2)^(1/3)
average rate of change from x = -2 to x = 4 is [f(4) - f(-2)]/[4 - (-2)]
f(-2) = (-4)^(1/3) = -1.587401
f(4) = 2^(1/3) = 1.25992
[f(4) - f(-2)]/[4 - (-2)] = [1.25992 - (-1.587401)]/[4 - (-2)] = 0.47
A empty bowl has a mass of 600 grams. Sue puts 8 cans of equal mass into bowl. She weighs the filled bowl. It has a mass of 7 kilograms. What is the mass of each can in grams?
Answer:
6400/8 = 800gm
because 7000-600= 6400
and 6400/8 is our answer = 800grams
Step-by-step explanation:
1) First we can convert kg into grams
2) Then we deduct 600grams from the mass to show the weight of the mass without the weight of the bowl = - 600grams
1) 7kg = 7000gm
2) 7000-600 = 6400
6400/8 = 800 grams
Answer:
Option B (800))
Step-by-step explanation:
We know that the mass of the empty container is 600 gr
And when they put 8 cans of equal mass then the final weight of the container is 7 kilograms or 7000 grams
If we call x the weight of the cans then this situation can be represented.
Now we solve the equation for the variable x.
Composite scores on the ACT are normally distributed with a mean of 21 and a standard deviation of 5. find the Z score for a student that gets a 31
Answer:
[tex]Z = 2[/tex]
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 21 and a standard deviation of 5.
This means that [tex]\mu = 21, \sigma = 5[/tex]
Find the Z score for a student that gets a 31
This is Z when X = 31. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{31 - 21}{5}[/tex]
[tex]Z = 2[/tex]
helpppppppppppppppppppppppppppppppppppppppppp
Answer:
x ≈ 5
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
Given
[tex]log_{10}[/tex] x ≈ 0.701 , then
x = [tex]10^{0.701}[/tex] ≈ 5
Help me
Brandee wants to add new wallpaper to her wall around the window. The inner light blue rectangle represents the window and the outer orange rectangle represents the wall around the window. What is the area of the wall around the window, or the orange rectangle around the blue rectangle? Select the correct number from the drop down menu to show the area of the wall around the window.
A= Choose... ft2
Answer:
What are the answer choices?
What is the solution to the equation?
Answer:
3/4
Step-by-step explanation:
2/3a=1/3+1/6
2/3a=3/6
a=1/2x3/2
a=3/4
Answer:
[tex]a = \frac{3}{4} [/tex]Step-by-step explanation:
[tex] \frac{2}{3} a - \frac{1}{6} + \frac{1}{3} [/tex][tex] \frac{2}{3} a = \frac{1}{3} + \frac{1}{6} [/tex][tex] \frac{2}{3} a = \frac{3}{6} [/tex][tex]a = \frac{3}{2} \times \frac{1}{2} [/tex][tex]a = \frac{3}{4} [/tex]Hope it is helpful....Suppose a school survey showed that 5 out of 38 students had tried vaping. What percent of these students have tried vaping? Round your answer to the nearest whole percent.
Answer:
13.157894736842% or 13.2% or 13%
Step-by-step explanation:
me with math: (┬┬﹏┬┬)
What is the probability that a student is in 11th grade and plays football?
6.5%
46.9%
23.3%
23.7%
Answer:
b
Step-by-step explanation:
Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.81 years. Recently, a sample of 10 students had a standard deviation of 2.1 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. Refer to Exhibit 11-1. The test statistic is
Answer:
test statistic = 12.115
Step-by-step explanation:
Given data :
std = 2.1 years
n = 10
( std )^2 = 4.41
determine the test statistic
apply a two-tailed test ( chi squared test for one population variance )
test statistic
λ^2 = [tex]\frac{(n-1)s^2}{3.2761}[/tex] ( Referring to Exhibit 11-1 )
= ( 10 - 1 )*(2.1)^2 / 3.2761
= 12.115
Find the area of rectangle ABCD
Answer: 12
Step-by-step explanation:
You can find the area of a rectangle that forms around it, and then subtract the little extra triangles. You can form a 5 by 5 square around the points. There are 4 extra little triangles. Two of them have a base and height of 2 and 2. Two of them have a base and height of 3 and 3. So you get the total area of those 4 triangles to be: 2+2+4.5+4.5=13. So 25-13=12.
The mean weight of cherry tomatoes on a farm is about 57 grams. The farmer is interested in testing a new type of fertilizer. They use the fertilizer on a particular patch and after the harvest, the mean weight of the tomatoes is 62 grams. They perform a t-test, with the null hypothesis being that the mean of all tomatoes grown with the new fertilizer is equal to 57 grams, and the alternative is that the mean is greater than 57 grams. There is a chance that they will mistakenly conclude the fertilizer improves the size of tomatoes when, in fact, it does not and they just got lucky with this particular crop. They wish to make sure the probability of making this mistake is no more than 8%. Below are four different p-values that they might get from their analysis. For which p-value should they reject the null hypothesis?
a. 0.10
b. 1.00
c. 0.15
d. 0.07
Answer:
The weight of a tomato depends on the variety of tomato. There are cherry, plum, grape, roma, and beef tomatoes of various sizes. The following tables shows different types of tomatoes, along with the average weight (in grams and ounces), the number of tomatoes per kilogram, and the number of tomatoes per pound.
Step-by-step explanation:
Emma have 450000 dollars
Answer:
Is that all to the problem?
Step-by-step explanation:
Answer:
Is there supposed to be more information?
Step-by-step explanation:
Diana can decorate 15 cookies in an hor; Jamie can decorate 15 cookies in two hours. How many hours would it take to decorate 60 cookies if they worked together?
Answer:
2.67 hours
Step-by-step explanation:
Diana: 15 cookies per hour
Jamie: 7.5 cookies per hour
15 + 7.5 = 22.5
22.5 cookies per hour
[tex]\frac{60}{22.5} =\frac{y}{1}[/tex]
22.5 · y = 60 · 1
22.5y = 60
22.5y ÷ 22.5 = 60 ÷ 22.5
[tex]y=2\frac{2}{3}[/tex]
[tex]2\frac{2}{3}[/tex] rounded to the nearest hundredth is 2.67
#1
6
Alie will roll a dice and flip a coin for a
probability experiment. The dice is numbered
one through six and the coin can land on
heads or tails.
If Allie rols the number cube once and flips
the coin once which list contains only the
outcomes in which the number cube lands on a
number less than 3?
B) Heads
D
I Heads
i Tols
Tals
3. Tals
2 Heads
2. Heads
2 Heads
2. Tots
2. Tals
2 Tails
3. Heads
3. Heads
3. Tots
3. Tals
чHeads
4. Tois
5. Heads
5. Tois
6. Heads
6. Tales
A) Heads
C)3 Hoods
Answer:
so it is 20 c because like why not
Please help!!! This really affects my grade! I need a final answer not a guess. Thank you very much. I really appreciate it. Links will be reported!
Answer:
Left skewed
Step-by-step explanation:
Looking at the box and whisker plot attached showing the wait times and the number of times they occur, we can see that as we approach the left, the number of times the wait time occurs increases. The box plot also shows like as if the box was pushed to the right as the center line is closer to the right than left.
Thus, we can say it's left skewed.
Andre has a container that is 10 inches wide 8 inches high and 14 inches deep he wants to fill the container with packages that are 5 inches wide 4 inches high 2 inches deep what is the greatest number of packages that he could put in the container
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
11, 6, 1, ...
Answer:
Step-by-step explanation:
I need help on this!
Study guide for exam
No links
The circle has the same question!
Answer:
60
Step-by-step explanation
20*3 becasuse it equlatrial
find the length indicated. Assume that lines which appear to be tangent are tangent.
9514 1404 393
Answer:
A) 15
Step-by-step explanation:
The angle where the tangent meets the radius is 90°, so the Pythagorean theorem applies to this right triangle.
?² +8² = 17²
?² = 289 -64 = 225
? = √225 = 15
The unknown side length is 15.
Answer:
lenght indicated appear to be tangent
Would you rather
buy...
the twin-pack
sunscreen
or
two separate
sunscreen bottles?
100
100
30
30
SIRIS
ULTISTRERE
$12.49
(Both are two, 6-oz. cans)
buy 1
get 2nd
58 ULTAST SPRTC
50%
$15.49
Answer:
i rath r buy...
the twin-pack
sunscreen
Step-by-step explanation: