Answer:
(a)
L is not reflexive, L is anti-reflexive
L is not symmetric.
L is not anti-symmetric
L is transitive.
(b)
D is reflexive
D is not symmetric.
D is anti-symmetric
D is transitive.
Step-by-step explanation:
a)
Given that;
domain of the given relation L is the set of all real numbers
For x , y ∈ R , xLy if x less than y.
relation L, where xLy if x less than y, For x, y ∈ R
so For every x ∈ R, it is then false that x less than x.
That is (x, x) does not belongs to L.
∴ L is not reflexive, L is anti-reflexive.
For every x,y ∈ R, if (x,y) ∈ L (i.e. x < y), then (y, x) does not belongs to L, since it is false that y < x.
∴ L is not symmetric.
For every x ∈ R, we can say its false that x less than x. That is (x, x) does not belongs to L.
∴ L is not anti-symmetric.
For every x,y,z ∈ R, if (x, y) ∈ L(i.e. x < y) and (y, z) ∈ L(i.e. y < z), then (x, z) ∈ L, since it is true that x<z when x<y and y<z.
∴ L is transitive.
b)
Also lets consider a relation D, where xDy if there is an integer n such that y = xn, For x, y ∈ Z.
Now
For every x ∈ Z, it is true that x = x × 1. That is (x, x) belongs to D.
∴ D is reflexive,
For every x,y ∈ Z, if (x,y) ∈ P (i.e. y=x × n), then (y, x).
if (x,y) ∈ D, then there exist an integer n such that y=x × n.
Then x = y × (1/n).
Thus, (y,x) does not belongs to D, since 1/n is not an integer, but it is a real number.
∴ D is not symmetric.
For every x,y ∈ Z, if (x,y) ∈ D (i.e. y=x × n), then (y, x) also belongs to D only when x=y. where n=1.
∴ D is anti-symmetric.
For every x,y,z ∈ Z, if (x,y) ∈ D (i.e. x × n1= y), and (y,z) ∈ D (i.e. y × n2 = z), then (x,z)∈ D.
if (x,y) ∈ D, then there exist an integer n1 such that y=x × n1.
if (y,z) ∈ D, then there exist an integer n2 such that z=y × n2.
Thenz = (x × n1) × n2 ⇒ z=x × (n1 × n2).
where (n1 × n2) is an integer. Thus (x,z) ∈ Z
∴ D is transitive.
An envelope contains an assortment of photos of the same size. The photos are of children, of pets, or of adults. Billy randomly took a photo from
the envelope, recorded what type of picture it was, and then replaced the photo in the envelope. He did this a total of 10 times. The table shows the
outcomes.
Children Pets Adults
5 3 2
Based on these results, what is the probability the next photo taken from the envelope will be a photo of pets?
Answer:
0.3
Step-by-step explanation:
From the question given above, the following data were obtained:
Children (C) = 5
Pet (P) = 3
Adult (T) = 2
Probability of obtaining a photo of pet, P(P) =?
Next, we shall determine the total outcome i.e the sample space (S).
This is illustrated below:
Sample space (S) = nC + nP + nA
Sample space (S) = 5 + 3 + 2
Sample space (S) = 10
Finally, we shall determine the probability of a photo of pet.
This can be obtained as follow:
Event of obtaining Pet, nP = 3
Sample space (S) = 10
Probability of obtaining a phone of pet, P(P) =?
P(P) = nP/nS
P(P) = 3/10
P(P) = 0.3
Therefore, the probability of obtaining a photo of pet is 0.3
For the number 360.048, round to the nearest whole number.
Answer:
360
Step-by-step explanation:
.0 is less than .5 so round down
Answer:
360
Step-by-step explanation:
[tex]360.048 = 360[/tex]
0 to 4 = 0(round down)
5 to 9 =1 (round up)
Whats the prime factorization of 42
Answer:
3,7,2
Step-by-step explanation:
42 = 21*2
42 = 3*7*2
Ta da!
Hope this helps! :)
(pls mark brainliest)
Answer: The prime factorization is 46 = 2 times 3 times 7.
Step-by-step explanation:
So we have the number 42.
First, break 42 up into 2 and 21.
Then split those two numbers further into 3 and 7 from 21 (because they are the factors of 21).
Since you can't break it down any further, take the prime numbers from there and multiply them against each other. This is why it is called prime factorization.
Don't simplify any further and don't multiply them together. Just keep it as 46 = 2 times 3 times 7. There you go!
Eight committee members are meeting in a room that has twelve chairs. In how many ways can they sit in the chairs
Answer:
495 different waysStep-by-step explanation:
We will use the combination rule to solve this questions since it bothers selection. Combination has to do with selection.
If r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
If there are Eight committee members meeting in a room that has twelve chairs, the number of ways they can sit in the chair can be done in 12C8 number of ways.
12C8 = 12!/(12-8)!8!
12C8 = 12!/4!8!
12C8 = 12*11*10*9*8!/4*3*2*8!
12C8 = 12*11*10*9/4*3*2
12C8 = 11*10*9/2
12C8 = 11*5*9
12C8 = 495
Hence the committee can sit in the chairs in 495 different ways
1
What function family does f(x)=3* belong to.
Answer:
Constant family
The ratio of money in Brian's wallet to Colin's wallet one day was 7:2. Brian spent £39 that day. Brian now had £4 less than Colin. How much did Brian initially have?
Answer:
Step-by-step explanation:
Collin initially have 14
Step-by-step explanation:
Let
x------> money that Brian had initially
y------> money that Collin had initially
we know that
x/y=7/2
solve for x
x=7/2y -------> equation A
y-39=y-4 ------> equation B
substitute equation A in equation B
7/2y-39=y-4
7/2y-y=39-4
5/2y=35
y=14
Answer:
£49.
Step-by-step explanation:
Let the ratio of brain's money to Colin's is 7x : 2x.
From the given info:
7x - 39 = 2x - 4
5x = -4 + 39 = 35
x = 7
So initially Brian had 7*7 = £49.
Colin had £14.
As x goes to positive infinity, y (the function) goes to...
Write an equation in slope-intercept form of the line that satisfies the given conditions.
Slope 5; y-intercept (0,-9)
Answer:
y = 5x + -9
Step-by-step explanation:
y = mb + b
m = 5
b = -9
Answer:
y = 5x -9
Step-by-step explanation:
The slope intercept form of an equation is
y = mx+b where m is the slope and b is the y intercept
y = 5x -9
town A has 95364 children out of which 43336 are girls. Town b has 100005 children out of which 53495 are boys find the number of boys in town A and number of girls in town B which town has more number of girls? please solve this
Answer:
1. Number of boys in A is 52028.
2. Number of girls in B is 46510.
3. Town B has more number of girls.
Step-by-step explanation:
1. [tex]95364 - 43336 = 52028[/tex]
2. [tex]100005-53495=46510[/tex]
3. [tex]43336<46510[/tex] (A < B)
The combined (verbal + quantitative reasoning) score on the GRE (Graduate Record Exam) is normally distributed with mean 1049 and standard deviation 189. Suppose n = 16 randomly selected students take the GRE on the same day.
a. What is the probability that one randomly selected student scores above 1100 on the GRE?
b. Describe the sampling distribution of the sample mean for the 16 students (description should include mean, standard deviation and shape).
c. What is the probability that a random sample of 16 students has a mean GRE score that is less than 1100?
d. What is the probability that a random sample of 16 students has a mean score that is more than 1100?
e. If the sample size in (d) above was increased to 64, what affect would it have on the probability (more, less, the same, can't tell) and why?
Answer:
Kindly check explanation
Step-by-step explanation:
Given The following :
Assume score is normally distributed with;
Mean (m) = 1049
Standard deviation (sd) = 189
Numbw rof observations (n) = 16
A) What is the probability that one randomly selected student scores above 1100 on the GRE?
Zscore = (x - m) / sd
X = 1100
Zscore = (1100 - 1049) / 189
Zscore = 51 / 189 = 0.27
From z-table ; 0.27 correspond to 0.6064
P(X > 1100) = 1 - P(X < 1100) = 1 - 0.6064 = 0.3936
2) sample mean will be equal to population mean = 1049
Sample Standard deviation : (population standard deviation / sqrt (n))
= 189 / sqrt(16) = 189/4 = 47.25
Shape of distribution is approximately normal
3)
P(Z < 1100)
X = 1100
Zscore = (x - m) / standard error
Standard Error = population standard deviation / sqrt (n)
= 189 / 4 = 47.25
Zscore = (1100 - 1049) / 47.25
Zscore = 51 / 47.25 = 1.0793650 = 1.08
From z-table :
P(Z < 1100) = 0.8599
4)
D.)
P(Z > 1100)
X = 1100
Zscore = (x - m) / SE
Zscore = (1100 - 1049) / 47.25
Zscore = 51 / 47.25 = 1.0793650 = 1.08
From z-table :
P(X > 1100) = 1 - P(X < 1100) = (1 - 0.8599) = 0.140
E)
With a sample size of 64
Standard Error becomes:
189 / sqrt(64) = 189/ 8 = 23.63
Zscore = (1100 - 1049) / 23.63
Zscore = 51 / 23.63 = 2.16
P(Z > 2.16) = 1 - P(Z < 2.16) = 1 - 0.9846 = 0.0154
Probability is less due to increase in sample size
If a fraction has
____ in the denominator, it is undefined.
Answer:
Zero
Step-by-step explanation:
Zero
Answer
To fill in the blank, it would be zero
Step-by-step explanation:
the table below shows the amount that must be repaid, y, when x dollars are borrowed.
Answer:
see below
Step-by-step explanation:
You can try the answer choices to see which one works. Since the amount repaid is greater than the amount borrowed, you can be pretty sure that the multiplier of x will not be 4/5 (a value less than 1).
You can see right away that
y = 5/4x
does not work for x=100, because it gives y=(5/4)(100) = 125, and the table value is 135. Note that 135 is 10 more than 125, so we expect that ...
y = 5/4x +10
will be correct. Trying that function on the other table values shows it fits exactly:
5/4(200) +10 = 250 +10 = 260
5/4(500) +10 = 625 +10 = 635
5/4(800) +10 = 1000 +10 = 1010
_____
You can also use the table values to create the relation equation. One possible method uses the 2-point form of the equation for a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (260 -135)/(200 -100)(x -100) +135
y = 125/100(x -100) +135 . . . . simplify a bit
y = 5/4x -125 +135 . . . . . . . . . simplify more
y = 5/4x +10 . . . . . . . . . . . . . . simpler yet; matches 3rd choice
Please help me out!!!
Answer:
[tex]= 2^2^8 \times 3^-^2^0\times 9^4[/tex]
Step-by-step explanation:
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\times\:b\right)^n=a^nb^n\\\left(2^7\times\:3^{-5}\times\:9\right)^4=\left(2^7\right)^4\times\left(3^{-5}\right)^4\times\:9^4\\=\left(2^7\right)^4\cdot \left(3^{-5}\right)^4\cdot \:9^4\\\\= 2^2^8 \times 3^-^2^0\times 9^4[/tex]
Answer:
[tex] {2}^{28}. {3}^{ - 20}. {9}^{4} [/tex]Multiply the exponent 4 by each of the exponents inside the parentheses.
Hope this helps..
Good Luck!Josh and his brother earn points when they do house chores. The ratio of Josh's points to his brother's points is 4:3. Together, they have 420 points. How many points does each boy have?
The correct answer is Josh has 240 points and his brother has 180 points
Explanation:
The ratio 4:3 means for every four points Josh has, his brother has three points. Now, to find how many points each boy has if there are 420 points, follow this process:
1. Use the ratio to write the equivalent fraction
4 : 3 = [tex]\frac{4}{3}[/tex]
2. Find the total number of parts
4 + 3 = 7
3. Divide the total number into the parts
420 ÷ 7 = 60 (each of the part is equivalent to 60)
4. Multiply the value of each part by each section of the ratio
4 × 60 = 240 - This represents the number of points Josh has if there are 420 points
3 × 60 = 180 - This represents the points Josh's brother has
This means Josh has 240 points and his brother has 180 points
Answer:
Josh has 240 points and his brother has 180 points\
I hope this helps. Have a nice day :D
A plane is 2 dimensional. Group of answer choices True False
Answer:
Step-by-step explanation:
False
The number, N, of napkins used in a restaurant is N =f(C) = 2C, where C is the number of customers.
What is the dependent variable? The independent variable?
Answer:
The dependent variable is N; Number of Napkins
The independent variable is C; Number of Customers
Step-by-step explanation:
Given
[tex]N = f(c) = 2c[/tex]
Required
Determine the dependent and independent variable
Dependent variables are variables that standalone and are not influenced by other variables;
In the given parameters
The customers, C is the independent variable
Independent variables are the opposite of the dependent variables; They depend on other variables for their own values.
In the given parameters
The number of Napkin, N is the dependent variable
Solve the equation for x.
(x=21)= 103
X =
Answer:
Step-by-step explanation:
I don't know if you made a mistake when typing but I am guessing you meant x - 21 = 103
(x-21) = 103 Add 21 to each side
x - 21 + 21 = 103 + 21
x = 124
$31,600
$26,070
None of These
$32,864
$27,112.80
Answer:
33 x 15.80
521.40 x 50= 26,070
B 26,070
Hope this helps! （づ￣3￣）づ╭❤～
1. What concepts of functions can you associate with the pictures?
Step-by-step explanation:
what concepts of functions can you associate with the picture
The concepts of functions that can be associated with the pictures are :
Money AccountRevenueSavingsattached below is the missing diagram.
A concept is general idea about a Thing which can be represented in different forms. It can be visual or non-visual. therefore some of the concept of function represented in the pictures includes ; money, Financial Accounts, savings. e.t.c.
Hence from the pictures attached below the concepts that are represented in them includes ; Money, Account, Revenue and Savings.
learn more : https://brainly.com/question/1103669
3y+2=2y+4
multi-step equations
Answer:
y = 2
Step-by-step explanation:
This equation can be solved three steps, classifying it as a multi-step equation.
To solve, you need to get the constants on one side and the variables on the other and then isolate the variable. These steps are illustrated below.
3y + 2 = 2y + 4 Subtract 2y from both sides of the equation.
y + 2 = 4 Subtract 2 from both sides of the equation.
y = 2
I have no idea how to do this im trying to learn on 3 hours of sleep rn ^-^;
Answer:
[tex]x=7,y=16[/tex]
Step-by-step explanation:
The tick marks you see on the sides denote congruence. If they have the same number of tick marks, then their side length are congruent.
And, recall that congruent side lengths have the same measure.
So, look at the sides with 2 tick marks. They are congruent. Therefore:
[tex]2x+5=x+12[/tex]
Subtract x from both sides:
[tex]x+5=12[/tex]
Subtract 5 from both sides:
[tex]x=7[/tex]
So, x is 7.
Now, look at the sides with only 1 tick mark. Again, they are congruent. Thus:
[tex]y-4=x+5[/tex]
We already know x is 7. So:
[tex]y-4=(7)+5[/tex]
Add:
[tex]y-4=12[/tex]
Add 4 to both sides:
[tex]y=16[/tex]
So, y is 16.
solve
3(8-169)-5(4-36)
I am a number whose prime factors are all of the prime numbers between 6 and 15. No factor is repeated. What number am I?
Answer:
Question Answer
I am a number whose prime factors are all the prime numbers between 6 and 15 no factor is repeated what number am i? 1001
The number is 1001 if a number whose prime factors are all of the prime numbers between 6 and 15.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
We have:
I am a number whose prime factors are all of the prime numbers between 6 and 15.
The prime number between 6 and 15:
As we know, the prime number is the number that is divisible by 1 and itself.
Prime number = {7, 11, 13}
= 7×11×13
= 1001
Thus, the number is 1001 if a number whose prime factors are all of the prime numbers between 6 and 15.
Learn more about the number here:
brainly.com/question/17429689
#SPJ2
Steve can save 9 dollars every day while Maria can save 12 dollars. What is the least number of days it
will take each person to save the same amount of money?
Answer:
The least number of days it will take each person to save the same amount of money is 36 days.
Step-by-step explanation:
We are given that Steve can save 9 dollars every day while Maria can save 12 dollars.
And we have to find the least number of days it will take each person to save the same amount of money.
Whenever we talk about the least common value, the LCM or Least common multiple comes into account.
Here also; the least number of days it will take each person to save the same amount of money will be the LCM or Least common multiple of 9 and 12.
LCM of 9 and 12 is calculated as;
2 = 9 , 12
2 = 9 , 6
3 = 9 , 3
3 = 3 , 1
1 , 1
Here, the second line means that 12 is divisible by 2 at 6, i.e; 2 [tex]\times[/tex] 6 = 12 and so on.
So, the LCM of 9 and 12 = [tex]2\times 2 \times 3 \times 3[/tex] = 36
Hence, the least number of days it will take each person to save the same amount of money is 36 days.
The price of a share of stock increased $3 each week over a 7-week period. What was the total
change in the price of a share of the stock over this period of time?
Answer:
$21
Step-by-step explanation:
Multiply 7 by 3, since it increased $3 each week for 7 weeks:
7(3)
= $21
So, the total change in the price of a share of stock was $21
Plz help asap
Thanks si much♡︎
Answer:
$1136.88 So she earned more than $1135
Step-by-step explanation:
$8.50 an hour.
31.25 week 1 = 265.625
33.75 week 2 = 286.875
36 week 3 = 306
32.75 week 4 = 278.375
In all - 1136.88 (rounded)
1136.875 (not rounded)
A square has a side length of 9 feet. What is the area of the square
Answer:
81
Step-by-step explanation:
The area of a square is its side length squared so 9^2 is 81
Ari received $100 as a birthday gift and has decided to save this money as well as add $20 of his own money each month. The total money Ari has saved can be estimated using the equation y = 20x + 100, where x is the number of months and y is the total amount of money saved. How much money will Ari have saved after 6 months?
Answer:
$220
Step-by-step explanation:
As per the equation:
y = 20x + 100For x = 6 we get:
y = 20*6 + 100 = 220So Ari will have saved $220 after 6 months
Answer:
14 pennies and 8 nickels
Expla-- Im smart
A) complete the table (use 4 decimal places when applicable)
B) what percent of the people have exactly one sibling ?
Answer:
Step-by-step explanation:
(A).
No' of siblings Frequency Rel. frequency Cumm. frequency
0 51 0.2429 51
1 37 0.1762 51 + 37 = 88
2 34 0.1619 122
3 41 [tex]\frac{41}{169}=0.2426[/tex] 163
4 47 0.2238 210
(B).
Percent of people having exactly one sibling = [tex]\frac{\text{Frequency}}{\text{Total frequency}}\times 100[/tex]
= [tex]\frac{37}{210}\times 100[/tex]
= 17.62%
Write 78 as a product of prime factors
Answer:
13 is a prime number, not divisible by any number greater than 1 or less than 13. So the prime factorisation of 78 is: 78 = 2 ⋅ 3 ⋅ 13 This can also be represented by a factor tree:
Step-by-step explanation:
Answer:
78 = 2 ⋅ 3 ⋅ 13
Step-by-step explanation:
78 ends with an even digit, so is divisible by 2 and we find: 78 = 2 ⋅ 39
39 ends with an odd digit, so is not divisible by 2 .
The digits of 39 add up to a multiple of 3 , namely 3 + 9 = 12 . So we can tell that 39 is divisible by 3 : 39 = 3 ⋅ 13
13 is a prime number, not divisible by any number greater than 1 or less than 13 .
So the prime factorization of
78 is:
78= 2 ⋅ 3 ⋅ 13