Answer:
720 mm²
Step-by-step explanation:
The area of a parallelogram is given by the formula ...
A = bh
For the given base and height, the area is ...
A = (40 mm)(18 mm) = 720 mm²
3. Find the value of x in this figure
answer:
120°
Step-by-step explanation:
∠OPM=∠ONM=90°
X°＝360°-60°-90°*2＝120°
g A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. At α = 0.05, in a left-tailed test (assuming equal variances) the test statistic is: Group of answer choices
Answer:
0.236
Step-by-step explanation:
Given :
x1 = 667 ; n1 = 10 s1 = 20
x2 = 679 ; n2 = 14 s2 = 15
Test statistic :
(x1 - x2) / √[Sp² (1/n1 + 1/n2)]
The pooled Variance, Sp² :
Sp² = [(n1 - 1)s1² + (n2 - 1)s2²] / (n1 + n2 - 2)
Sp² = [(9*20²) + (13*15²)] / (10+14-2)
Sp² = 6525 / 22 = 296.59
T = (667 - 679) / √(296.59*(1/10 + 1/14)
T = -12 / 50.844
T = 0.236
Test statistic = 0.236
A rectangle has a perimeter equal to 24 if we consider its width x how could we talk about its length y in terms of x what are the possible values of x what aree the possible values of y
2x + 2y must equal 24. 24 - 2x = 2y and 24 - 2y = 2x. Therefore, 12 - y = x. x could be able to add with y to get 12.
example: x = 4, y = 8. (4 + 4 + 8 + 8 = 16 + 8 = 24)
x = 9, y = 3. (9 + 9 + 3 + 3 = 24)
x = 5, y = 7. (5 + 5 + 7 + 7 = 24)
Researchers wanting to assess skin irritation associated with a new sunscreen developed for those with photosensitivity. They randomly sample 240 men with a history of photosensitivity and 240 men without a history of photosensitivity and ask them to apply the cream and report the level of skin irritation they experience after spending 20 minutes in the sun using a scale of 0-10. The average skin irritation score for the group with a history photosensitivity was 1.2 and the average skin irritation score for the group without a history of photosensitivity was 1.4. The Levene's test for equality of variances had a p value of 0.08. You know this means:
A. The researchers should report the t test results assuming equal variances. Select The researchers should report the t test results NOT assuming equal variances. as your answer
B. The researchers should report the t test results NOT assuming equal variances.
C. The researchers should reject the null hypothesis and report there is a difference in the average skin irritation score.
D. The researchers should fail to reject the null hypothesis and conclude there is NOT a difference in the average skin irritation score.
Answer:
Blablabka
Step-by-step explanation:
Blablabla
The answer to this question please.
Answer:
Part A) y=1,100x + 4,500
Part B) 14,400
Step-by-step explanation:
Part A)
There is a base fee of $4,500, meaning that the line begins at y=4500 (i.e. The y-intercept is [0,4500], so 'b' in y=mx+b is 4,500). There is a $1,100 hourly rate, which is proportional to the value of x, the amount of hours filmed. Therefore, 'm' in y=mx+b is $1,100.
Thus, the final equation looks like:
y= 1,100x + 4,500
Part B)
x=9
y=1,100x+4,500
y=1,100(9)+4,500
y=9,900+4,500
y=14,400
We are again studying the times required to solve two elementary math problems. Suppose we ask four students to attempt both Problem A and Problem B. Assume the students are independent and all results are normally distributed, but note that a particular student's times on the two questions are likely to be positively correlated. The results are presented below (in seconds).
student Problem A Problem B
1 20 35 2 30 40 2 3 15 20 4 40 50
Again find a two-sided 95% CI for the difference in the means of A and B.
Answer:
(-16.494 ; -3.506)
Step-by-step explanation:
student Prob A Prob B difference, d (A-B)
1 20 35____ - 15
2 30 40 ___ - 10
3 15 20 ___ - 5
4 40 50 __ - 10
Difference, d = -15, -10, -5, -10
Xd = Σd/ n = - 40 / 4 = - 10
Standard deviation of d ; Sd = 4.082
The confidence interval for the difference is given as :
Xd ± Tcritical*(Sd/√n)
Tcritical at 95%; df = n - 1 ; 4 - 1 = 3
Tcritical(0.05, 3)). = 3.182
C.I = -10 ± 3.182(4.082/√4)
C.I = -10 ± 6.494462
C. I = (-16.494 ; -3.506)
Name the three digit number. My ones digit is an even number which is three times as much as my tens digit. My tens digit is the same as my hundreds digit. The sum of all my digits is 10. What number am i?
A. 424
B. 028
C. 226
D. 622
find the sum of the given infinite geometric series. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW
Answer:
320/3
Step-by-step explanation:
First find the common ratio
20/80 = 1/4
The sum of an infinite geometric series
sum = a1/ (1-r) where a1 is the first term and r is the common ratio
=80/ ( 1-1/4)
= 80/(3/4)
= 80 *4/3
= 320/3
Joey's strategy for his first marathon (26.2 miles)was to run 2 miles, walk 1 mile, run 2 miles, walk 1 mile, and continue this pattern until he completed the race. Joey's average running pace is 8 minutes per mile, and his average walking pace is 16 minutes per mile. How many minutes will it take Joey to complete the marathon
========================================================
Explanation:
We have this sequence
(2+1)+(2+1)+(2+1)...
Effectively, we're repeating "2+1" over and over.
We can see that
2+1 = 3(2+1)+(2+1) = 3+3 = 6(2+1)+(2+1)+(2+1) = 3+3+3 = 9Each time we add on another copy of (2+1), we're adding on 3
Dividing 26.2 over 3 gets us (26.2)/3 = 8.733 approximately
If we had 8 copies of (2+1) added together, then we would get
8*(2+1) = 8*3 = 24
This is 26.2-24 = 2.2 miles short of his goal.
He'll need to run 2 more miles, plus walk another 0.2 of a mile
----------------------------------------------------
In summary so far, Joey will run 8+1 = 9 sections (two miles each) and walk 8 sections that are 1 mile each. At the very end, he'll walk 0.2 miles to finish the race. Each running and walking section is alternated of course.
Since he runs 9 sections, each 2 miles, that accounts for 9*2 = 18 miles.
His running pace is 8 minutes per mile, so this means he has run for 8*18 = 144 minutes. This is just the running part and not the walking part.
Let A = 144 so we can use it later.
----------------------------------------------------
He walks 8 sections of 1 mile each. His walking pace is 16 minutes per mile. This must mean he spends 8*16 = 128 minutes on this walking portion.
Then for the last 0.2 mile section he walks, we can solve the proportion below
(1 mile)/(16 min) = (0.2 miles)/(x min)
1/16 = 0.2/x
1*x = 16*0.2
x = 3.2
He spends 3.2 minutes walking the remaining 0.2 of a mile at the end.
So his total walking time is 128+3.2 = 131.2 minutes.
Let B = 131.2
-----------------------------------------------------
To wrap things up, we'll add up the results of each of the previous two sections.
A = total running time = 144 min
B = total walking time = 131.2 min
C = total marathon time
C = A+B
C = 144+131.2
C = 275.2 minutes
This converts to 275 min, 12 sec.
This is also equivalent to 4 hrs, 35 min, 12 sec.
Carlos owns a small business. There was a profit of $9 on Saturday and a loss of $6 on Sunday. Find the total profit or loss for the weekend. $15 profit $3 loss $3 profit $15 loss
Answer:
$3 profit
Step-by-step explanation:
Since you got a profit of $9 on Saturday and a loss of $6 on Sunday, you have to subtract 9 and 6, which is 3.
Temperatures in northern Canada ranged as high as 37°F one summer. That same year the lowest temperature was −28°F. What was the range of temperatures for the year?
Answer:
65 degrees
Step-by-step explanation:
Find the range of temperatures by finding the difference between the lowest and highest temperatures:
37 - (-28)
37 + 28
= 65
So, the range of temperatures was 65 degrees
WILL MARK BRAINLYST!!! Enter the correct answer in the box. Write your answer in the form y=mx+ b, using the appropriate inequality symbol in place of the equal sign.
What inequality is shown in the graph?
Answer:
The inequality shown in the graphic is [tex]y > 4x + 1[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line is given by:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept(value of y when x = 0).
Inequality:
Values greater than the dashed line, dashed so the line is not part of the inequality, thus, the inequality is:
[tex]y > mx + b[/tex]
Dashed line:
The dashed line goes through (0,1) and (1,5).
Point (0,1) means that when [tex]x = 0, y = 1[/tex], so [tex]b = 1[/tex], and:
[tex]y > mx + 1[/tex]
Finding the slope:
When we have two points, the slope is given by the change in y divided by the change in x. In this question, we have point (0,1) and (1,5), so:
Change in y: 5 - 1 = 4
Change in x: 1 - 0 = 1
Slope: [tex]m = \frac{4}{1} = 4[/tex]
What inequality is shown in the graph?
[tex]y > 4x + 1[/tex]
help with 1 b please. using ln.
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Differentiation
DerivativesDerivative NotationImplicit DifferentiationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
*Note:
You can simply just use the Quotient and Chain Rule to find the derivative instead of using ln.
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{\frac{x}{2 - x}}[/tex]
Step 2: Rewrite
[Function] Exponential Rule [Root Rewrite]: [tex]\displaystyle y = \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}}[/tex][Equality Property] ln both sides: [tex]\displaystyle lny = ln \bigg[ \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg)[/tex]Step 3: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[lny] = \frac{dy}{dx} \bigg[ \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg) \bigg][/tex]Logarithmic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \frac{dy}{dx} \bigg[ \frac{x}{2 - x} \bigg][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \bigg[ \frac{2}{(x - 2)^2} \bigg][/tex]Simplify: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{-1}{x(x - 2)}[/tex]Isolate [tex]\displaystyle \frac{dy}{dx}[/tex]: [tex]\displaystyle \frac{dy}{dx} = \frac{-y}{x(x - 2)}[/tex]Substitute in y [Derivative]: [tex]\displaystyle \frac{dy}{dx} = \frac{-\sqrt{\frac{x}{2 - x}}}{x(x - 2)}[/tex]Rationalize: [tex]\displaystyle \frac{dy}{dx} = \frac{-\frac{x}{2 - x}}{x(x - 2)\sqrt{\frac{x}{2 - x}}}[/tex]Rewrite: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{x(x - 2)(2 - x)\sqrt{\frac{x}{2 - x}}}[/tex]Factor: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{-x(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
z/3 - 4(z-1) = 5(z-2)+1
What is the value of z?
Answer: [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
First, we need to open the brackets on either side of the equation.
[tex]\frac{z}3}[/tex] - 4z+4 = 5z-10+1
After opening the brackets, we need to separate the variables from the constants.
[tex]\frac{z}{3}[/tex] -4z-5z = -10+1-4
Then we need to convert the variable fraction into a normal variable by multiplying the variable fraction and also all other terms in the equation.
3([tex]\frac{z}{3}[/tex]) 3(-4z) 3(-5z) = 3(-10) + 3(1) + 3(-4)
z -12z -15z = -30+3-12
Now, we can simplify the equation !
-26z = -39
z = -39÷-26
= [tex]\frac{3}{2}[/tex]
60kg of rice must be put into three equal bags. what weight of rice must be put into each bag?
Answer:
20kg of rice in each bag
Step-by-step explanation:
we have 60kg of rice and 3 bags. we know that we need to have an eqal amount of rice in each bag so we can divide the 60kgs of rice by 3.
60÷3=20
Checking our Answer:
we can check our work by doing the opposite of division which is multiplication. to check our work we'd have to multiply the dividend (in our case 3) and our quotient (in our case 20) to see if we get the larger dividend (in our case 60) as our answer.
3×20=60
PLEASE I NEED HELP RIGHT NOW
Select the graph that correctly translates ƒ(x) = |x| 4 units in the negative x-direction and 3 units in the positive y-direction.
answers are the pictures
Answer:
The third graph
Step-by-step explanation:
What the translation is saying is that for each value of f(x) = |x|, the graph is translated 4 units in the negative x direction and 3 units for the positive y direction. Another way to say this is that for each f(x), we can add (-4) (or subtract 4) to its x value and add 3 to its y value.
One way to find which graph works is to take a point, figure out where it should be, and work from there.
One example of this is (-1,1). If x=-1, |x| is 1, so in the original graph, our point is (-1, 1). In our translated graph, we need to subtract 4 from the x component (the first number, which is -1 in this case) and add 3 to the y component (the second number, or 1 in this case). Our new point comes to
(-1-4 , 1+3)
= (-5, 4)
Therefore, one point on the resulting graph is (-5, 4). We can look through each graph and see if it has the point.
Looking at each graph, it is clear that the graph in the bottom left, or the third graph, contains the point.
The equation of the translated function will be f(x) = |x + 4| + 3. Then the correct option is C.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x – h | + k
The function is given below.
f(x) = |x|
Then the function is translated 4 units in the negative x-direction and 3 units in the positive y-direction. Then the vertex will be at (-4, 3). Then the equation of the function will be
f(x) = |x + 4| + 3
Then the graph is given below.
Then the correct option is C.
More about the absolute function link is given below.
https://brainly.com/question/10664936
#SPJ2
Cho hai tập hợp A={1;2;3;4},B={2;4;6;8} . Tập hợp nào sau đây bằng tập hợp A ∩B ?
Answer:
A∩B ={2;4}
Step-by-step explanation:
Chúc bạn học tốt
Would a scatter plot of the data described below be likely to show a positive relationship, negative relationship, or no relationship.
The number of letters in a person's first name and their heigh
There would likely be no relationship between first name and height of a person in a random sample.
Hope this helps :)
Answer: it’s B. I answered it right now and it said it was correct.
Step-by-step explanation:
McDonald’s fry’s are better than jack in the box’s fry’s.
help asap pleaseeee asap
Find the midpoint of the segment between the points (17, 1) and (-2,8)
a. (15, 9)
b. (-15,-9)
c. (19/2, -7/2)
d. (15/2, 9/2)
Answer:
Option d
Step-by-step explanation:
(17+(-2))/2 , (8+1)/2
which is,
15/2, 9/2
Answered by GAUTHMATH
write the expression as a trinomial (5c+2)(2c-1)
Answer:
10c^2-c-2
Step-by-step explanation:
FOIL method
or just multiply all of the numbers by each other, if you get 4 numbers you did it right then simplify;
(5c+2)(2c-1) 5c*2c; 2*-1; -1*5c; 2*2c = 10c^2, -2, -5c, 4c, simplify, 10c^2 -c -2. Hope this helps :)
Answer:
10c² - c - 2
Step-by-step explanation:
(5c+2)(2c-1)
10c² - 5c + 4c - 2
10c² - c - 2
Find the perimeter of the figure below, in inches
Answer:the perimeter is 200.4
Step-by-step explanation: I got this answer by separating the shape into multiple pieces then I added it all together.
How much does college tuition cost? That depends, of course, on where you go to college. Construct a weighted average. Using the data from "College Affordable for Most," estimate midpoints for the cost intervals. Say 46% of tuitions cost about $4,500; 21% cost about $7,500; 7% cost about $12,000; 8% cost about $18,000; 9% cost about $24,000; and 9% cost about $31,000. Compute the weighted average of college tuition charged at all colleges.
Answer:
0.127
Step-by-step explanation:
The weight of potato chip bags filled by a machine at a packaging plant is normally distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. What is the probability that a randomly chosen bag will weigh more than 15.6 ounces
Answer:
0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.
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 15.0 ounces and a standard deviation of 0.2 ounces.
This means that [tex]\mu = 15, \sigma = 0.2[/tex]
What is the probability that a randomly chosen bag will weigh more than 15.6 ounces?
This is 1 subtracted by the p-value of Z when X = 15.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.6 - 15}{0.2}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a p-value of 0.9987.
1 - 0.9987 = 0.0013
0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.
I NEED HELP PLEASE!!
sine --> cosecant
csc(x) = 1/sin(x)
cosine --> secant
sec(x) = 1/cos(x)
tangent --> cotangent
cot(x) = 1/tan(x)
Correct Answer: A
Hope this helps!
Using the applet, explore the results for simulating a group of 30 people and noting whether there is a duplicated birthday (whether at least two people have a matching birthday). Run at least 40 trials. What is the relative frequency of trials that had at least two people with the same birthday
Answer:I just need points
Step-by-step explanation:
Hey
Evaluate the expression for n = –8.
–2n − 6 =
Answer:
10Step-by-step explanation:
-2n - 6 = ?let n be -8-2 (-8) - 6 = ?= 10[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
What is the equation
Answer:
y=3x+1
Step-by-step explanation:
Determine slope with two coordinates and use it in the formula
find r and s on the triangle
Answer:
r=24
s=21
Step-by-step explanation:
I use proportion of 2 to 3
I multiply 16 and 3/2 to get r
r=24
I multiply 14 and 3/2 to get s
s=21
Mr. Montes is writing a short, three-question, true or false quiz for his Algebra 2 classes. He had planned on using a random answer generator to determine which of true or false would be the correct answer for each quiz question, but his internet is not working. Instead, he writes each possible answer combination on a small slip of paper, folds each paper in half, and then places them in a box. Without looking, he draws one of the slips of paper.
Use what you know about counting methods and set operations to answer the following questions.
After grading the quizzes, Mr. Montes decides that his students could use some additional practice with the concepts tested. He writes a take-home assignment for his students. The assignment starts with two true or false questions and then has 3 multiple choice questions. The multiple choice questions each have 4 answer options, only 1 of which is correct. Luckily, Mr. Montes’ internet is working when he writes the quiz and he is able to use a random answer generator.
After grading the take-home assignments, Mr. Montes randomly selects 5 take-home assignments to analyze. He considers the student’s responses to the three multiple choice questions, which are as shown.
Student 1: Student 2: Student 3: Student 4: Student 5:
{C, A, C} {C, B, B} {C, B, C} {C, B, A} {C, A, A}
Amisha was too tired to work on the take home assignment Mr. Montes gave her, so she randomly selected answers without reading any of the questions. Suppose that you wanted to find the odds that Amisha answered at least 3 of the 5 questions correctly. Do you think you would use a permutation or a combination?
1. The correct responses for the multiple choice questions are, in order, C, B, and A. If Set 1 represents the subset of these students who answered C for number 1, Set 2 represents the subset of these students who answered B for number 2, and Set 3 represents the subset of students who answered A for number 3, find each of the following. Explain what each notation means in context of this scenario.
a. Set 1 ∩ Set 2
b. Set 2 ∪ Set 3
c. The complement of Set 1
2. Amisha was too tired to work on the take home assignment Mr. Montes gave her, so she randomly selected answers without reading any of the questions. Suppose that you wanted to find the odds that Amisha answered at least 3 of the 5 questions correctly. Do you think you would use a permutation or a combination?
Answer:
There are 4 questions to answer here and the answers are given below:
1. COMBINATION
2. SET 2
3. {S2, S3, S4, S5}
4. { } OR ∅
Step-by-step explanation:
The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.
The assignment has 5 questions in all. The options for each question are listed below and separated by commas:
1. True, False
2. True, False
3. A, B, C, D
4. A, B, C, D
5. A, B, C, D
Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.
QUESTION 1
If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?
ANSWER TO QUESTION 1
You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only two possible answers (also known as options) while questions 3, 4 and 5 have four possible answers/options to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.
QUESTION 2
Find "Set 1 ∩ Set 2" and explain the notation in the sentence.
ANSWER TO QUESTION 2
First list out relevant information:
- The correct answers to questions 3, 4 and 5 are respectively C, B, A
- The universal set consists of five students: S1, S2, S3, S4, S5 hence
Ц = {S1, S2, S3, S4, S5}
Next, enlist the elements of each defined set
Set 1: {S1, S2, S3, S4, S5} Set 2: {S2, S3, S4} Set 3: {S4, S5}
Note: Set 1 is equal to the universal set.
Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.
In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.
If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:
The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.
So the answer to question 2 is
Set 1 ∩ Set 2 = Set 2
QUESTION 3
Find "Set 2 ∪ Set 3" and explain the notation in the sentence.
ANSWER TO QUESTION 3
The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.
So, Set 2 union Set 3 = {S2, S3, S4, S5}
As earlier stated, Student 4 isn't appearing twice in the new set.
QUESTION 4
Find the ' of Set 1 and explain the notation in this sentence.
ANSWER TO QUESTION 4
The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.
Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!
Set 1 ' Ц = { } or ∅
where the empty bracket symbol and the slashed zero symbol represent null set.
Kudos!
