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Another important point is!
Is it possible to fill a Glass with water 100% I think not! because water droplets are larger than air pockets,that Glass contains! so the answer must always be Only 99.99999....% possible!
But everyone knows 99.99999...% = 100%
Problem # 5 answer = 1and 5/7hr
Nedra and latonya Dominguez are 12 miles apart hiking toward each other. How long will it take them to meet if Nedra walks at 3 mph and Latonya walks at 1 mph faster?
Nedra walks 3 mph and Latonya walks 4 mph. When they meet the sum of the distances they walked is 12 miles and they are approaching each other at a rate of 7 mph. So at a speed of 7mph, it takes 1 and 5/7 hour to cover 12 miles (12/7 = 1 5/7)
Another way to look at it:
Let T equal the time it takes to meet. Nedra will walk 3T in that time and Latonya will walk 4T. Together the distance they cover is 12 miles. 3T + 4T = 12; 7T = 12; T = 1 5/7
Problem # 4 answer = 4500
If $3000 is invested at 6% annual simple interest, how much should be invested at 9% annual simple interest so that the total yearly income from both investments is $585?
The $3000 you invested at 6% will earn you $180. You need to earn $585 - 180 = $405 from you other investment. If X is the amount you invest in the 2nd company at 9%
(.09)X = $405
X= $4500
Problem #3 answer = 400 0unces How much of an alloy that is 20% copper should be mixed with 200 ounces of an alloy that is 50% copper in order to get an alloy that is 30% copper?
Let X be the amount in ounces of the 20% copper you are adding. The total weight of the 30% alloy would then be 200 + x.
(.20)X + (.50)200 = (.30)(200 + X)
.2X + 100 = 60 + .3X
40 = .1X
X=400
Problem #2 answer = 30,000@8%;24,000@10%
How can $54,000 be invested, part at 8% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts will be equal?
Let P = the amount invested in the first company. The 54000 - P is the amount invested in the second company. The profits of the 2 companies are .08P and .10(54000-P). The profits are equal:
.08P = .10(54000)-P
.08P = 5400 - .1P
.18P = 5400
P = 30000
30000 was invested in the company that earned 8% for a profit of 2400.
24000 was invested in the company that earned 10% for a profit of 2400.
Problem 1:
Let P = the amount that he invested in the profitable company
Then 10000-P = the amount that he invested in the other company
The profit (or loss) would be .11P for the profitable company and -.04(10000-P) for the other. The sum of these is 650
.11P + -.04(10000-P) = 650
.11P - 400 + .04P = 650
.15P = 1050
P=7000
He invested in the 7000 in the profitable company ($770 profit) and 3000 in the other company ($120 loss).
There are 4 lines that make up this rectangle/parallelogram. The lines and their slopes are:
(0,3) to (2,0) with a slope of (3-0) / (0-2) = -3/2
(2,0) to (-1,-2) with a slope of (0-(-2)) / (2-(-1)) = 2/3
(-1,-2) to (-3,1) with a slope of (-2-1) / (-1-(-3) = -3/2
(-3,1) to (0,3) with a slope of (1-3) / (-3-0) = 2/3
The lines with equal slopes are parallel to each other. For this figure to be a rectangle, the lines that intersect must be perpendicular to each other which implies that they have slopes which are the negative inverses of each other. The negative inverse of -3/2 is 2/3. So it is a rectangle.
You're on the right track. And to prove to yourself that it's right, plug your new point of (1,3) into your equation. Your equation should be y = 5x - 2 rather than y= 5x - (-2). Plug in 1 for x and 3 for y:
3 = 5(1) - 2
3=3
Success.
To graph, first plot the point (0,4). The slope is -2. The slope is "rise over run" so the denominator is the change in x and the numerator is the change in y. A slope of -2 is the same as -2 / 1. If x changes by 1 (the denominator), y changes by -2 (the numerator).
Let's find another point on this line by increasing X by 1. That gives us 1 (0+1). Everytime X increases by 1, y decrease by 2 (slope is -2). So the y value would be 2 (4-2). Plot the point (1,2) and draw a line through (0,4) and (1,2) and you're done.
Lines which are parallel have the same slope. If you have two points (x1, y1) and (x2, y2), the slope is calculated as (y2 - y1) / (x2 - x1). So the slope of the line going through (2,3) and (11, 6) is (6-3) / (11-2) = 1/3. The slope of the line going through (-3,18) and (8,21) is (21-18) / (8 -(-3)) = 3/11. The slopes aren't the same, so they are not parallel.
If 2 lines are perpendicular, the slope of one will be the negative inverse of the other. For example if the slope of one line is 1/5, the slope of the line perpendicular will be the the inverse of 1/5 (which is 5) multiplied by -1. The slope would be therefore be -5.
We already know the slope of the line going through (2,3) and (11,6) is 1/3. The slope of the line between (2,3) and (-3,18) is (18-3) / (-3-2) = -3. So the slopes are 1/3 and -3. They are negative inverses of each other, so they are perpendicular to each other.
This info can be used for your other post in figuring out if a shape is a square or a parallelogram. A square has perpedicular lines whereas a parellalgram does not (unless it's also a square since all squares are parallelograms).
The slope is "rise over run". The rise is the change in the Y axis, in this case is 1800 feet. The run is the the change in the x axis, in this case it is 3.25 mile. So the slope is 1800 feet/ 3.25 mile. There's 5280 feet in a mile.
One small correction to Mathsyperson response. The difference between the two populations is 26000, not 16000. So add on another 50 years. 26000/200=130.
Heck, I'll take more than that. Mark me down for a couple of thousand. Put the check in the mail.
You divide -2 by 2 since your expression says -x/2. The price of the product goes down as the number sold goes up. Sort of a volume discount.
Yes, 17 being prime is a big part of it. Because it is prime, people in positions 2-5 will never sit at the same table twice (until you have more than 17 sessions). That's critical because those in position 1 don't move.
So Jim, you can either figure out how to handle eighteen tables or limit it to 17 and turn it into a marketing ploy - "Due to popular demand, seating is unlimited and must be reserved in advance. First come, first served. Get your seat TODAY!"
First of all, I think that should be 3x + 4y = 12. The first pair is (0,3). Plug in 0 for x and 3 for y and see if the equation is true. 3(0) + 4(3) = 12. Yep.
For the second one, plug in 3/4 for Y and solve for X.
3x + 4y = 12
3x + 4(3/4) = 12
3x + 3 = 12
3x = 9
x = 3
So that give you (3, 3/4)
Do something similar for the last one:
3x + 4y = 12
3 (8/3) + 4y = 12
8 + 4y = 12
4y = 4
y = 1
So: (8/3, 1)
I'm not positive this would work but it might.
Each seat is assigned a table letter (A-Q) and table position (1-5). So there are five seats at table A: A1, A2, A3, A4, A5.
Assign every one a seat for the first session. For each subsequent session, each person willl always be seated in the same position at a table as the position they were for the first session. Different table probably, but same position.
People in position 1 at each table stay where they're at. So the person in seat A1 will be there for every session.
The people in position 2 at each table go to the next lettered table and sit in the same position as they were at their first table. The person in A2 would go to B2, then C2 and then D2.
The people in position 3 would skip over a table and go to the next one: A3, C3, E3, F3
The people in position 4 would skip over 2 tables and go to the 3rd table: A4, D4, G4, J4
The people in position 5 would skip over 3 table and go to the 4th table: A5, E5, I5, M5
Consider the tables to be in a circular pattern. If you trying to move past table Q, start over at table A. So the person starting at N5 would go to A5, E5 and then I5.
You need to map this completely out before you implement to make sure it works. I got as far as scheduling half of the people and didn't run into any problems.
E
N
T
and then E, T, T, F, F, S, S, E, N, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, F
And if you wanted you program to round to the nearest hundred, it would look something like this:
x = INT(x/100 + .5) * 100
Test Examples:
If x = 1949
x/100 = 19.49
x/100 + .5 = 19.99
INT (x/100 + .5) = 19
INT(X/100 + .5) * 100 = 1900
If x = 1950
x/100 = 19.5
x/100 + .5 = 20.0
INT(x/100 + .5) = 20
INT(x/100 + .5) * 100 = 2000
If x = 1951
x/100 = 19.51
x/100 + .5 = 20.01
INT(x/100 + .5) = 20
INT(x/100 + .5) * 100 = 2000
7x - 5 + 3x = 6+x - 10
First simplify:
10x - 5 = x - 4
9x - 5 = -4 (subtract 1x from each side)
9x = 1 (add 5 to each side)
x = 1/9 (divide each side by 9)
Check the answer:
7(1/9) - 5 + 3(1/9) = 6 + 1/9 - 10
7/9 - 5 + 3/9 = -3 8/9
-3 8/9 = -3 8/9
The distance between the X coordinates is 7-1=6. 2/3's of that is 4. Your new X coordinate is 1+4=5.
The distance between the Y coordinates is 6-3=3. 2/3's of that is 2. Your new Y coordinate is 3+2=5.
So the answer is (5,5).
IC ==> icy
In the computer languages I've dealt with, the INT function always rounds down to the nearest integer. In other words, it truncates. If you wanted to round up any number with 5 or greater in the tenth's, you would do something like: INT (X+.5). If X was 12.1, X+.5=12.6, and the INT function would still chop it off to 12. If X was 12.6, X+.5 = 13.1 and the INT function would chop it off to 13, effectively rounding up.
You would always round down. And it really makes mores sense if you round down the intermediate steps. Consider the 14 through 18 (inclusive) example. You divide 18 by 4 to find out how many multiples of 4 there are. You get 4 1/2 but you can't really have 1/2 of a multiple of 4. You really should round down to 4 here.
And dividing 13 by 4 gives you 3 1/3. Round it down to 3 and subtract it from 4 to get 1.
Edited: Looks like I'm a minute late on my reply!
An angle plus its complement is always equal to 90. In this case, 3 times the complement is 150 degrees, so the complement is 50 degrees. 50 + A = 90, therefore A = 40.