Answers
Related Questions
What is x divided by 3?
Answers
Answer:
X can be any number it' a variable
Step-by-step explanation:
Prove that
(a) there exist integers m and n such that 2m + 7n = 1.
(b) there exist integers m and n such that 15m + 12n = 3.
(c) there do not exist integers m and n such that 2m + 4n = 7.
(d) there do not exist integers m and n such that 12m + 15n = 1.
(e) for every integer t, if there exist integers m and n such that 15m + 16n = t, then there exist integers rand s such that 3r + 8s = t.
(f) if there exist integers m and n such that 12m + 15n = 1, then m and n are both positive.
(g) for every odd integer m, if m has the form 4k + 1 for some integer k, then m + 2 has the form 4j - 1 for some integer j. (h) for every integer m, if m is odd, then m2 = 8k + 1 for some integer k.
(i) for all odd integers m and n, if mn = 4k - 1 for some integer k, then m or n is of the form 4} - 1 for some integer j.
Answers
LStep-by-step explanation:
(a) To proof this statement choose m = 4 and n = -1, from here we have 2(4) + 7(-1) = 1 as required. Hence th statement is true.
(b) To proof this statement choose m = 1 and n = -1, from here we have 15(1) + 12(-1) = 3 as required. Hence the statement is true.
(c) To proof this statement, suppose m and n are integers, since integers are closed under addition and multiplication then 2m, 4n and 2m + 4n are all integers. Obviously 2m and 4n are even integers, therefore their sum is also an even integer. This contradicts the equation 2m + 4m = 7, hence there do not exist integers m and n that satisfy the statement.
(d) To proof this statement, suppose m and n are integers, then 12m, 15n and 12m + 15n are all integers, since integers are closed under addition and multiplication. Factoring out 3 from the sum, we have: 3(4m + 5n). Therefore 3(4m + 5n) = 1 is a contradiction, because it will give 4m + 5n = 1/3 and addition of two integers can never give a fraction.
(e) To proof this statement, suppose m and n are integers, then 15m + 16n = t can be rewritten as 3(5m) + 8(2n) = t. Since integers are closed under multiplication, then 5m and 2n are integers. Let 5m = r and 2n = s, then we have: 3r + 8s = t as required.
(f) To proof this statement, suppose that m and n are both negative integers, we see that 12m + 15n = 1 is clearly impossible because the sum would be less than 0. Therefore, if there exist integers m and n such that 12m + 15n = 1, then they must be positive.
(g) To proof this statement, suppose m is an integer and has the form 4k + 1 for some integer k, then m + 2 = 4k + 1 + 2 = 4k + 3 = 4k + 4 - 1 = 4(k + 1) - 1. Since k is an integer then k + 1 is an integer because integers are closed under addition. Therefore, put j = k + 1. Hence we have 4j - 1.
(h) suppose that m is odd, then there is an n such that m = 2n + 1, therefore m² = (2n + 1)² = 4n² + 4n + 1 = 4(n² + n) + 1. Here, we need a lemma that says: suppose k is an integer, k(k + 1) is an even integer. This can be proven intuitively, when k is odd, the term in the bracket becomes even, and the whole expression is even. If k is even, then automatically the whole expression becomes even. Hence, our lemma is proven intuitively. This implies that n² + n is an even integer and can be replaced by 2k for some k that is an integer. Therefore, we have 4(2k) + 1 = 8k + 1 as required.
(i) suppose that m and n are odd integers such that mn = 4k - 1 for some k that is an integer. If we assume that neither m nor is in the for 4j - 1, then:
mn = (4a + 1)(4b + 1) for some a and b that are integers. Expanding that we have mn = 4(4ab + a + b) + 1 which is not in the form 4k - 1 for some k that is an integer as assumed. Therefore, if m and n are odd integers such that mn is in the form 4k - 1 for some k that is an integer, then m and n are in the form 4j - 1 for some j that is an integer.
Point R(x, 4) and point T (5, 13) are points that lie on a line that had a slope of 3/2. What is the value of x?
Answers
Answer:
Step-by-step explanation:
Nxjxhxnddjndzjzjzjzjzjzj
Which statement is true about the value of the expression below? (-2^3)^-2
. It is between -1 and 0
.it is less than -1
.it is between 0 and 1
. It is greater than 1
Answers
Answer:
it is between 0 and 1
Step-by-step explanation:
Triple the sum of x and five amounts to the product of two and x.
Answers
Answer: 15
Step-by-step explanation:
3(x+5)=2x
3x+15=2x
15=x
the other one is 27
Answers
12. Dominic drives a taxi. He charges a $2 flat fee plus $1.50 per mile.
The table represents f(x), a function that can be used to predict the
total cost of any trip in Dominic's taxi.
Answers
Answer:
The y-intercept represents the flat fee.
Step-by-step explanation:
The y-intercept on the graph would be the point at which the line cuts across or intercepts the y-axis. At this point, the value of x (miles travelled) would be 0. The y-intercept in this case, would be the flat fee which is given as $2.
At x = 0, f(0) = 2.
The y-intercept represents the flat fee on the graph of f(x).
Solve for y: 3x < 2y - 6
Answers
Answer: y>6
Step-by-step explanation:
y>3x+6
y>3(0)+6
y>6
Select ALL of the perfect squares
6
100
25
5
Answers
Answer:
100 and 25 are the perfect squares
Our answers are 100 and 25.
Some insight:
6 = [tex]\sqrt{6}*\sqrt{6}[/tex] -- We cannot simplify the square root of 6 to integers, so no.
100 = [tex]\sqrt{100}* \sqrt{100}[/tex] = 10*10 -- This is a perfect square
25 = [tex]\sqrt{25}* \sqrt{25}[/tex] = 5*5 -- This is a perfect square
5 = [tex]\sqrt{5}* \sqrt{5}[/tex] -- No.
Rewrite the following in logarithmic form:
e^x=16
Answers
Answer:
[tex]log_e16=x[/tex]
Step-by-step explanation:
Exponential to Logarithmic: [tex]b^m=x[/tex] → [tex]log_bx=m[/tex]
Step 1: Define
eˣ = 16
b = e
x = 16
m = x
Step 2: Rewrite
[tex]log_bx=m[/tex]
[tex]log_e16=x[/tex]
A storm door is made using two sheets of aluminum with a layer of
insulation between them. Each sheet of aluminum is 1/16 in. thick. The
insulation layer is 3/4 in. thick. How thick is the door?
Answers
Hey! Hope your having a amazing day! Can you please help me and answer this questions? I need this fast! Thanks! ;( (Integers!)
Answers
Answer:
19
Step-by-step explanation:
Simple, just add 34 and -15 and you should get the net (average) gain. :)
what is a positive - negative
Answers
Answer:
Numbers can either be positive or negative. ... Adding and multiplying combinations of positive and negative numbers can cause confusion and so care must be taken. Addition and Subtraction. Two 'pluses' make a plus, two 'minuses' make a plus. A plus and a minus make a minus.
Harvey worked 36 hours this week. He earns $28.46 an hour. How much did he earn this week
Answers
Answer:
$1,024.56
Step-by-step explanation:
Simple math, So what you would do to find this answer would be taking the amount of money hes earning an hour and times that by how many hours he worked that week. so $28.46 x 36 = $1,024.56
Answer:
1024.56
Step-by-step explanation:
28.46
x 36
___________
17076
+ 85380
____________
1024.56
how was y'alls day? :)
Answers
answer-good how was yours
Pls help me with this
Answers
Answer:22. Plug in all the options and see if they are equal
Step-by-step explanation:
Step-by-step explanation:
Numeber 22 is D or -10
Explication
If (44)^x = 4^32, what is the value of x?
Answers
Answer:4.611*10^19
Step-by-step explanation:4^32= 1.84 *10^19/4 = 4.611*10^19
The auxiliary bookstore in the student center has one checkout counter where one employee operates the cash register. Customers arrive at a rate of 24 per hour following a Poisson distribution and service times are exponentially distributed, with a mean rate of 30 customers per hour. The average purchase per customer is $48. The bookstore considers adding another employee to assist the present operator. There are several options to utilize this additional staff. One is to enable more customers to be served in less time, thus increasing the service rate from 30 customers per hour to 40 customers per hour. Alternatively, the bookstore could redesign to add a second cash register, one has its own line. Assume existing customers split evenly between the two cash registers and each has her/his own line, just like most grocery stores. Finally, the bookstore can use this additional staff as a second register but unlike option 2, there is only one combined line shared by these two registers (like most of the bank tellers). Assume the hourly rate for each employee is $20, regardless what job do they perform. Assume that each customer is only waiting for up to 1 minute to be served, or would renege (i.e., leave the store unpurchased). Which option should the bookstore adopt to minimize the total cost?
Answers
Answer and explanation:
Find attached
Both customers' arrival and service times follow exponential distribution. We have calculated the essential operating characteristics of this queuing system
Write the phrase 'The quotient of 8 and a number p" as an expression
Answers
Answer:
8 divided by p
Step-by-step explanation:
What is the reciprocal of
2/7?
Answers
Answer:
7/2
Step-by-step explanation:
To find the reciprocal of a fraction we just flip it
2/7 =7/2
The reciprocal of 2/7 is 7/2, and it plays a significant role in various mathematical operations involving fractions.
The reciprocal of a fraction is obtained by interchanging the numerator and denominator. For the fraction 2/7, its reciprocal is 7/2. To understand why this is the case, let's break it down.
When we take the reciprocal of a fraction, we essentially flip it upside down. In the case of 2/7, we switch the positions of 2 (numerator) and 7 (denominator) to get 7/2. This reciprocal property holds true for any fraction.
The reciprocal of 2/7 is an essential concept in mathematics, especially when dealing with division of fractions. When you divide a fraction by another fraction, it is equivalent to multiplying the first fraction by the reciprocal of the second fraction. So, dividing by 2/7 is the same as multiplying by 7/2.
In conclusion, the reciprocal of 2/7 is 7/2, and it plays a significant role in various mathematical operations involving fractions.
To know more about reciprocal:
https://brainly.com/question/15590281
#SPJ6
213.9 divided by 9.3
Answers
Answer:
23
Step-by-step explanation:
I used a calculator!!
Solve for x: -3|2x + 61 = -12
Answers
-3|2x + 6| = -12
-6x - 18 = -12
-6x = 6
x = -1
(sorry if I misunderstood your question)
helpp meeeeeee pleasereee
Answers
Answer:
take 6 divide by 11 and one :)
Step-by-step explanation:
yes this anser hope you like :)
Write in words: 970,001
Answers
Answer:
nine hundred, seventy thousand and one
Step-by-step explanation:
Step-by-step explanation:
Nine Hundred,Seventy Thousand and One
Consider the following information about travelers (based partly on a recent Travelocity poll): 40% check work e-mail, 30% use a cell phone to stay connected to work, 25% bring a laptop with them, 23% both check work e-mail and use a cell phone to stay connected, and 51% neither check work e-mail nor use a cell phone to stay connected nor bring a laptop. Finally, 88 out of every 100 who bring a laptop check work e-mail, and 70 out of every 100 who use a cell phone to stay connected also bring a laptop.
(a) What is the probability that a randomly selected traveler who checks work e-mail also uses a cell phone to stay connected?
(b) What is the probability that someone who brings a laptop on vacation also uses a cell phone to stay connected?
(c) If a randomly selected traveler checked work e-mail and brought a laptop, what is the probability that s/he uses a cell phone to stay connected?
Answers
Step-by-step explanation:
I defined the following events:
J = travellers check email
K = they use a cell phone to stay connected
M = they have a laptop alongside
P(J) = 0.40
P(K) = 0.30
P(M) = 0.25
P(J n K) = 0.23
P(J U K U M)' = 0.51
P(J|M) = 0.88
P(M|K) = 0.70
A.
We are to find probability of K|J
P(JnK)/p(J)
= 0.23/0.40
= 0.575
B.
P(K|M)
= P(KnM)/P(m)
= 0.21/0.25
= 0.84
C.
P(J U K U M) = 1 - p(J U K U M)'
= 1-0.51
= 0.49
P(JnM) = p(J|M)p(M)
=0.88x0.25
= 0.22
P(JnKnM) = 0.49-0.40-0.30-0.25+0.23+0.22+0.21
= 0.20
P(K|JnM) = P(JnKnM)/p(JnM)
= 0.20/0.22
= 0.909
We can and should control our thoughts. True False
Answers
Answer:
True
Step-by-step explanation:
Only we can control ourselves, but if something is coming in our head and we want to think of something else we can. It could be hard for some but you can with effort
Hope this helps (:
Answer: True
Step-by-step explanation: Because I got it right on edge
fran drank 19/20 liter of juice how many quarts of juice did she drink (1 L =1.06qt). set up a proportion and solve using means of extremes
Answers
Given :
Fran drank 19/20 liter of juice.
1 L = 1.06 qt.
To Find :
How many quarts of juice did she drink.
Solution :
It is given that :
[tex]1 \ L=1.06\ qt\\\\1=\dfrac{1.06\ qt}{L}[/tex]
Now, amount of water he drink :
[tex]\dfrac{19}{20}\times 1 \ L\\\\\dfrac{19}{20}\times 1.06\ \dfrac{qt}{L}\times L\\\\\dfrac{19}{20}\times 1.6 \ qt\\\\1.52\ qt[/tex]
Hence, this is the required solution.
five ninths and four sixths
Answers
Answer:
5/9 & 4/6Step-by-step explanation:
Hope this helps! <3
You have been saving $4.50 per week for the last several weeks. Today you decide to spend $21 which is 1/6 of your savings. How much money did you have saved?How many weeks have you been saving for?
Answers
Answer:
You have $126 saved and you've been saving for 28 weeks
Step-by-step explanation:
What is an odd number minus an odd number
Answers
Answer:
7-3
Step-by-step explanation:
Answer:
0 i think
Step-by-step explanation:
hope this helps