# Questions on Algebra: Real numbers, Irrational numbers, etc answered by real tutors!

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Question 994704: I just need my work checked please. Also sorry if this is the wrong place for the problem.
Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water.
Part A: Write an equation in one variable that can be used to find the total number of liters of lemon juice and water in the bottle. Define the variable used in the equation.
Part B: How many liters of lemon juice are present in the bottle? Show your work.
Here's my work:
0.60*1/0.40 = x
0.60/0.40 = x
1.5 = x

Found 2 solutions by MathTherapy, Fombitz:
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I just need my work checked please. Also sorry if this is the wrong place for the problem.
Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water.
Part A: Write an equation in one variable that can be used to find the total number of liters of lemon juice and water in the bottle. Define the variable used in the equation.
Part B: How many liters of lemon juice are present in the bottle? Show your work.
Here's my work:
0.60*1/0.40 = x
0.60/0.40 = x
1.5 = x
The equation you set up and the amount you got are for the amount of lemon juice in the bottle, but you need an equation for the total amount of lemon juice and water.
This is done as follows:
40% or .4 represents the amount of water in the bottle. Since that amount is 1 L, and with amount of lemon juice and water being T, we get:

-------- Cross-multiplying

You actually have the answer to Part B, as there is indeed 1.5 L of lemon juice in the bottle



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If it's a 1 liter bottle, how can 1.5 liters be lemon juice?
.
.
The bottle is a total of 1 liter.
Lemon juice is 60% of the liter.
Water is 40% of the liter.

Question 994707: Evaluate: 10-2[2-(5-4)+8+4*2]
You can put this solution on YOUR website!
Using our PEMDAS rules,
10-2[2-(5-4)+8+4*2] =
10-2[2-1+8+16] =
10-2[25] =
10 - 50 =
-40

Question 994576: Write the expression in the form of a + bi, where a and b are real numbers
(1-sqrt-36)(7-sqrt-4)

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Write the expression in the form of a + bi, where a and b are real numbers
(1-sqrt-36)(7-sqrt-4) = (1-6i)(7-2i) = (7-12)-42i-2i = -5-44i
----------------------------
Cheers,
Stan H.
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Question 994517: The formula for the perimeter of a rectangle is P=2l,+ 2w, where l is the length and w is the width. A rectangle has a perimeter of 24 inches. Find its dimensions of it length is 3 inches greater than its width.
Found 2 solutions by macston, josgarithmetic:
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.
W=width; L=length=W+3in
.
P=2L+2W
P=2(L+W)
24in=2(L+W)
12in=L+W
12in=(W+3in)+W
12in=2W+3in
9in=2W
4.5in=W
ANSWER 1: The width is 4.5 inches.
.
L=W+3in=4.5in+3in=7.5in
ANSWER 2: The length is 7.5 inches.
.
CHECK:
P=2L+2W
24in=2(7.5in)+2(4.5in)
24in=15in+9in
24in=24in

You can put this solution on YOUR website!
Your perimeter formula looks like "P is twenty-one plus two w".

Use a better variable.

Description and question give you this:

and just a couple of substitutions will give you a way to first solve for w.

STEPS

, the width

Question 993888: Hi,
I don't know if this is the right category, but while gkimming through a question paper i found one question:
a+b+c=10, find the maximum value possible for (a*b*c)+(a*b)+(b*c)+(a*c).
Please help me solve this, as this is not just one of it's type in the question paper, there are 5 or 6 such ones.

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a+b+c=10, find the maximum value possible for (a*b*c)+(a*b)+(b*c)+(a*c).
==================
Using Excel, I confirmed my suspicion that the max is at a = b = c
Max = 69967/999
= 31*61/27
=====================
27 is obviously 3*3*3, but I don't know the significance of 31 or 61.
I don't yet have a proof, either.

Question 993806: What set does 27/3 belong to
You can put this solution on YOUR website!
.
= 9.

It belongs to whole numbers; natural numbers, integer numbers; rational numbers; real numbers; complex numbers.

So, the selection is up to you!

Question 993727: the set Z under multiplication
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What about the set Z under multiplication? Re-post following ALL of the instructions for posting, please.

John

My calculator said it, I believe it, that settles it

Question 993683: All real numbers that are less than -4 or greater than 1

Question 992991: (16)-3/3
You can put this solution on YOUR website!
Is that written the way you are given?

Question 992807: What are the subsets for the following questions , 12/18 . -5 , pi , square root of 2, square root of 13, - 4/3 , and square root of 61
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.
What are the subsets for the following questions, 12/18, -5, pi, square root of 2, square root of 13, - 4/3, and square root of 61.
------------------------------------------------------------------------

1.   = .   Do you know it?

2.  Your set is   { , -5, , , , , }.

It has  7  elements,  in total.

The number of all subsets is   = 128.

It is  toooooo  many to list them here.

You can do it yourself,  or,  it is better to say,  you can understand how to do it,  if you recall what a subset is.

This question is not to ask others.

It is for you to think about.

Question 992785: What's the prime factorization of 68 is
2. The prime factorization of 90 is
3.8x÷52
4.28x÷70x
5.12x2÷28x

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.
1. What's the prime factorization of 68 is?  68 = *.

2. The prime factorization of 90 is          90 = ...

3. 8x÷52                                      = .

4. 28x÷70x                                    = .

5. 12x2÷28x                                   = .


Question 992554: Show that if x^2 is odd, x is odd. Use proof by contradiction.
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.
Show that if x^2 is odd, x is odd. Use proof by contradiction.
----------------------------------------------------------------

We are given that    is odd.
We need to prove that  x  is odd.

Let us assume that  x  is not odd.  Then  x  is even.  In other words,  x  is divisible by  2.  Hence,  x = 2n,  where  n  is integer.

Then   = =  is even.

This contradicts to the fact that    is odd,  which is given.

The source of the contradiction is the assumption that  x  is not odd.

Hence,  x  is odd.

The proof is completed.

Question 991733: Find the probablity of not rolling multiples of 3 on pair of dice
Answer by Edwin McCravy(13211)   (Show Source):
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Here are all 36 ways a pair of dice can fall:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Add each pair and we get these numbers:

2   3   4   5   6   7

3   4   5   6   7   8

4   5   6   7   8   9

5   6   7   8   9  10

6   7   8   9  10  11

7   8   9  10  11  12

The multiples of 3 are 3,6,9, and 12.

We take those out, and we have:

2       4   5       7

4   5       7   8

4   5       7   8

5       7   8      10

7   8      10  11

7   8      10  11

Count those.  There are 24 of them.

So the probability is 24 out of 36.

Or 24/36 which reduces to 2/3.

Edwin

Question 991510: Two hikers start walking in opposite directions from a camp at the same time. The average rate of the northwood hiker is 3 mi/hr faster than the rate of the southwood hiker. If they are 22 miles apart after two hours, what is the rate of each hiker?
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If they are going in opposite directions, then their combined rate of separation is the sum of their speeds,

Solve for

John

My calculator said it, I believe it, that settles it

Question 991505: Give an example for non zero real numbers is not closed under subtraction r
You can put this solution on YOUR website!
by definition, if the operation produces even one element outside of the set, the operation is closed
set of natural numbers is closed under subtraction
example: let and , then => is element of
is subset of the set of real numbers
note:
Real Numbers include:
Whole Numbers (like , , , , , etc)
Rational Numbers (like , , ..., , etc )
Irrational Numbers (like , sqrt(3), etc )
One subset of Real Numbers is counting (or natural) numbers. This subset includes all the numbers we count with starting with "" to infinity. The subset would look like this:
{ , ,, , ...}
Another subset is whole numbers. This subset is exactly like the subset of counting numbers, with the addition of one extra number. This extra number is "". The subset would look like this:
{ , , ,, , ...}
so, your answer is set or you can choose set of whole numbers

Question 989975: name all the subsets of the real numbers to which the number (-2)power of 4 belongs?
You can put this solution on YOUR website!

Integers
Rationals

Question 991005: What is the rule that tells you which values of x satisfy the inequality x>the square root of x?
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x has to be greater than 1,

Question 990665: Hi,
I'm having trouble understanding this particular question about sets. Was wondering if someone could explain to me what it means.
{x|x is represented by a digit in the decimal expansion of 178/185}
I don't know what is being asked.
Thanks

You can put this solution on YOUR website!
.
Hello,

do not be scared !   This phrase

{x|x is represented by a digit in the decimal expansion of 178/185} "

means

"the set of those digits that participate in the decimal expansion of   ".

The number    is rational,  SO its decimal expansion is either finite or periodic decimal fraction.  Are you familiar with it?

Next,  I performed long division of  178  by  185  for you.

It is the decimal fraction  0.9(621).

The three digits in parentheses are periodic part of the decimal expansion.

So,  the digits that participate in this decimal expansion of the number    are  1,  2  6  and  9.

Therefore,  our set is the set consisting of four digits  1,  2  6  and  9.

Thus

{x|x is represented by a digit in the decimal expansion of 178/185} = {1, 2, 6, 9}.

THAT IS ALL.

Question 990228: All real numbers that are less than -3 or greater than or equal to 5
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{x | -3 > x ≥ 5}

Question 990023: 27/3

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27/3 = 9
Cheers,
Stan H.
-------

Question 989854: In a biology class, three-fourths of the students received a passing grade. If there are 24 students in the class, how many students received failing grades ?
You can put this solution on YOUR website!
24*0.25=6
------------
24*1/4=24/4=6

Question 989840: If the price of a cell phone, 10 years ago, was 4 times (300%) higher
than it is now, can we say that the same cell phone is 300% cheaper
now?

You can put this solution on YOUR website!
If the price of a cell phone, 10 years ago, was 4 times (300%) higher
than it is now, can we say that the same cell phone is 300% cheaper
now?
-----------------
4 times higher is 400% higher, not 300%.
1 time higher is a 100% increase
2 times higher is a 200% increase
3 times higher is a 300% increase
etc
---
Nothing can be 300% cheaper. If it's 100% cheaper, the price is zero (0).

Question 989624: There are 26 carpenters in a crew. On a certain day 29 were present. What is the percentage of the crew was not present

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There are 26 carpenters in a crew. On a certain day 29 were present. What is the percentage of the crew was not present
-------
Sounds like they were all present plus three additional persons.
------
Cheers,
Stan H.
-------------

Question 989613: A student earned a grass of 80% on a math test that had 20 problems. How many problems on the test did the student answer correctly? Round to the nearest whole number.

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A student earned a grade of 80% on a math test that had 20 problems. How many problems on the test did the student answer correctly? Round to the nearest whole number.
------
Ans:: 0.8*20 = 16
----------
Cheers,
Stan H.
---------------

Question 989576: Classify each variable according to the set of numbers that best describes its values.
1-the area of the circle A found by using the formula πr^2

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Classify each variable according to the set of numbers that best describes its values.
1-the area of the circle A found by using the formula πr^2
--------
r:: all Real Numbers greater than zero
-------
I:: all Real Numbers greater than zero
-------------
Cheers,
Stan H.
------------

Question 989164: what is 2.4396 repeating?
Found 2 solutions by MathTherapy, Timnewman:
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what is 2.4396 repeating?
In fractional form, and with 4396 presumably repeating, it's:



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Hi dear,
It is repeating because it is irrational number.
Note that irrational numbers are those numbers that can not expressed as fraction.i.e they do not take the form;where a and are integers and b is not equal to zero.
HOPE THIS HELPS?
::Timnewman::

Question 989192: True or false
1. {Φ} is a subset of the null set Φ.
2. The null set is a subset of itself.
3. The set {x | x is a positive divisor of 15} and the set {15x | x is counting number} are disjoint sets.
4. {1, 2, 3} = {x is a prime number | x divides 6}

You can put this solution on YOUR website!

Number 4 is false. 1 is not a prime number.

John

My calculator said it, I believe it, that settles it

Question 989117: Define complex number
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A complex number is an element of the set

John

My calculator said it, I believe it, that settles it

Question 988998: find 5 irrational number between 4and5
You can put this solution on YOUR website!
find 5 irrational number between 4and5
------------
is one.

Question 988927: What are the solutions of -2<3y-4<14? Graph the solutions
Found 2 solutions by josgarithmetic, algebrahouse.com:
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That is a system of two inequalities combined as AND.

-----------()==============================================()-----------
1                                    6


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-2 < 3y - 4 < 14
2 < 3y < 18 {added 4 to the left, middle, and right}
2/3 < y < 6 {divided the left, middle, and right by 3}

To graph:
- put an open circle (not filled in) on 2/3
- put an open circle (not filled in) on 6
- draw a line between the two circles

For more help from me, visit: www.algebrahouse.com

Question 988579: An irrational number obtained by dividing the circumference of any circle by lenghth of its diameter

Question 988560: What is the difference between a fraction and a rational number?
You can put this solution on YOUR website!
A fraction shows the ratio of two numbers;
A rational number shows the ratio of two INTEGERS.

Question 988159: The difference between 2 numbers is 10. The lesser number is: a. What is the greater number?

Question 988144: A bus traveled on a level road for 3 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 4 hours. Find the average speed on the level road if the entire trip was 188 miles.
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                rate      time    distance
LEVEL           r+20      3
WINDING          r        4
total                             188


Question 987972: (-15)-(2)-(-1)
You can put this solution on YOUR website!
.
(-15) - (2) - (-1) = -15 - 2 + 1 = -16.

It is so simple!

Question 987656: A survey of 400 college students resulted in the following crosstabulation regarding if they smoke or not and whether or not they drink alcohol.

Drink Alcohol
Smoke Yes No Total
Yes 21 13 34
No 318 48 366
Total 339 61 400
a. Of the students surveyed who smoke, what percentage do not drink?
38% or 38.23529 Just want to know if my answer is correct, if not how do you do it?
Thanks

You can put this solution on YOUR website!
.
You are correct.
.

Question 987657: 2. The number of touchdowns scored by the Pittsburgh Steelers during the regular season (not including preseason or postseason) for each of the past 17 years is listed below:
Year Touchdowns Scored
2014 49
2013 41
2012 36
2011 36
2010 41
2009 41
2008 38
2007 46
2006 42
2005 45
2004 41
2003 33
2002 43
2001 38
2000 35
1999 35
1998 26
What is the 60th percentile of this data set?
I am not sure what I am suppose to do to get this or how?
Thanks

You can put this solution on YOUR website!

What you need can be found here:

Regent's Prep Percentiles

John

My calculator said it, I believe it, that settles it

Question 987485: Is 3 a rational or irrational number?
You can put this solution on YOUR website!
A rational number is any number that can be written as a fraction.

3 is a rational number, because it can be written as 3/1.

For more help from me, visit: www.algebrahouse.com

Question 987456: provide an example to show that real numbers are not closed under division,thank u
You can put this solution on YOUR website!
.

Undefined is not a real number.

Question 987455: is a square root of 2 a real number