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That's wrong you do 6/7 x 1/2

3/7 of his savings was left

keep in mind that 1 gallon = 4 quarts and 1 quart = 4 cups

So the recipe has 12 cups of punch. 1 1/2 cups of it is pineapple, 1/4 cups of it is orange, and 12 - 1 1/2 - 1/4 = 10 1/4 cups of lemon-lime soda. 

9 gallons of punch is equivilent to 36 quarts of punch, or 12 times the amount of the recipe. so, she needs:

1 1/2$\cdot$12=$\boxed{18 \ cups}$ of pinaple juice

1/4$\cdot$ 12 = $\boxed{3 \ cups}$ of orange juice

10 1/4 $cdot$ 12 = $\boxed{123 \ cups}$ of lemon lime soda.

4F  + 4V   =  240     divide  through  by   4   ⇒   F + V  =  60   ⇒    F =  60  - V    (1)

3F +  5V  =   234      (2)

Sub  (1)  into (2)  for F

3 ( 60 - V)  +  5V   =  234

180  -  3V +  5V  =  234

2V  =  234  -  180

2V  =  54

V =  54 /  2   =   27  (dollars)

 no problemo

:D :D :D

3)  Let DC =  x     and  BD  =  8  -   x

Since  AD  is  an angle  bisector, we  have  the following relationship

AB/ BD =  AC / DC

6/ (8 - x)  =  10 / x               cross-multiply

6x  =  10  (8- x)

6x  =  80   - 10x

6x + 10x  =  80

16x  =  80

x = 80 / 16   =   5  =   DC

The  area  of  triangle   ADC  =  (1/2) (AB) (DC)  = (1/2)(6)(5)  = 15

Happy bday bro hope you enjoy it :)

2)  Let  the side  of  the  square  =  S.....so [ ABCD ]  =  S^2

The  heght of  the  equilateral  triangle =  Ssqrt (2)

The  side  of  the equilateral  triangle  =  Ssqrt (2) * 2 / sqrt (3) =  (2/3)sqrt  (6)  S

Area  of  the  equilateral  trinagle = (1/2)  ( (2/3) sqrt (6 S))^2 sqrt (3)  / 2    =  (2sqrt(3) / 3 *  S^2

Ratio  of      area  of    square  to  area  of  equilateral triangle =   S^2  /   [ 2sqrt (3)  / 3 * S^2  ]   =

3 / [2 sqrt (3) ]   =   sqrt (3)  / 2

1)  The  toal area  of  boh squares = 4^2  + 5^2  =  16 +  25  = 41

We  have three squares outside  the  shaded  region

One is a  right triangle with  legs  of  1  and  5.....its area  =  (1/2) 5 * 1 =  5/2  =  2.5

Another  is a triangle  ith a height of  5 and a  base of  9.....its  area  = (1/2)(9) (5)  = 45/2  = 22.5

The last  triangle is also a right triangle with legs of  4...its area = (1/2) (4) (4)  = 16/ 2  =  8

Shaded  region  =   41   -  [ 2.5  + 22.5  + 8]  =    8  (units)^2

12.4

Total: $62
20%=2/10

62/10*2= $12.4

The amount of the tip is $12.4

To figure out the answer, you need to find 20% of 62. This is the same as multiplying it by 0.20.

Therefore, the answer is 0.20 * 62

or

12.4 dollars.

There are 9 possible numbers (1,2,3,4,5,6,7,8,9) that can be placed in 5 places.

N= 9^5 = 59049

1/59049 = 0.00169350878084%

Oops. 

Nice job for catching the mistakes. :))

=^._.^=

The first step to solving this problem is to figure out how many types of books there are, and how many books are in each type.

Here, I've listed each book type as a variable, so it will be easier to add them all up in the end.

x = 16.21    (15 of these)

y = 25.10    (14 of these)

z = 20.70    (16 of these)

r = 38.59    (variable number of these)

We know that there are 75 books in total, so once you subtract the number of each type of book from 75, you get:

75 - 15 - 14 - 16 = 30

This means that there are 30 of r books.

Now, we can multiply each of the costs by the number of books.

15x = 16.21*15

14y = 25.10*14

16z = 20.70*16

30r = 38.59*30

From this, we get:

x_cost = 243.15

y_cost = 351.40

z_cost = 331.20

r_cost = 1157.70

Now, we can add all of the numbers together to get:

243.15+351.4+331.2+1157.70 = 2083.45

(Hopefully this is correct!) 

THNX!!!! 

A: 

FRACTION: 1/3
DECIMAL: 0.333...

RATIO: 2:4

PERCENT: 33$\frac13$%

WORDS: one out of three

b: 

FRACTION: 0
DECIMAL: 0

RATIO: 0

PERCENT: 0

WORDS: no chance

C: 

FRACTION: 1/8
DECIMAL: 0.125

RATIO: 2:14

PERCENT: 12.5%

WORDS: one out of eight

D: 

FRACTION: 1/1
DECIMAL: 1.00

RATIO: 1:1

PERCENT: 100%

WORDS: 1 out of 1 

By the way, I'm guessing you need to use common sense to figure out B and D.

 a) Roll a 3 or 5 on a die labeled 1 to 6.

b) January immediately follows June.

c) Pick an orange out of a basket that contains 2 oranges, 6 apples, and 8 peaches.

d) The sun will set tomorrow.

A: 

FRACTION: 1/3
DECIMAL: 0.33333....

RATIO: 1 to 3

PERCENT: 33.333%

WORDS: One-third

B: 

FRACTION: 0/1 (or 0/x, x being any number, is fine)
DECIMAL: 0.0

RATIO: 0 to 1 (or 0 to x, x being any number, is fine)

PERCENT: 0%

WORDS: No chance at all.

C: 

FRACTION: 1/8
DECIMAL: 0.125

RATIO: 1 to 8

PERCENT: 12.5%

WORDS: One-eighth of a chance

D: 

FRACTION: 1/1 (or x/x, x being any number, is fine)
DECIMAL: 1

RATIO: 1 to 1

PERCENT: 100%

WORDS: A full chance, or a one-hundred percent chance.

That is asking for the area of APE, and he/she is asking for AP.

triangle PQC is a 45-45-90, so QC=x

triangle PQB is a 30-60-90 triangle, so BQ = x$\sqrt3$

QC+BQ=4=x+x$\sqrt3$

x($\sqrt3$+1)=4

x=$\dfrac4{\sqrt3+1}$

we can multiply top and bottom of the fraction by $\sqrt3-1$:

x=$\dfrac{4\sqrt3-4}{3-1}=2\sqrt3-2$

PC=x$\sqrt2=2\sqrt6-2\sqrt2$

AP=AC-PC=$4\sqrt2-2\sqrt6+2\sqrt2=\boxed{6\sqrt2-2\sqrt6}$

By "How many nails does Isaac use to build the shelves", you could mean the total amount or the amount for each type fo shelve, so I'll try and answer both.

The total nails are not too hard to figure out, it's just simple addition, so: 282 + 315 = 597 total nails

Now, for the harder question, how many nails does Isaac need to build each shelve type? We can figure this out by using simple algebra.

4 small shelves and 3 large shelves use 282 nails.

5 small shelves and 3 large shelves use 315 nails.

4x + 3y = 282

5x + 3y = 315

Using a simple system of equations tactic, you can figure out that the answer needed is:

33 nails for small shelves

and

50 nails for large shelves.

To prove that this is correct, we can input the answers into the system, getting:

4 (33) + 3 (50) = 282    (Correct)

and

5 (33) + 3 (50) = 315    (Correct)

So, Isaac needs 33 nails for small shelves and 50 nails for large shelves.

y = 3x + 42

2x + 49 = 3x + 42

-x + 49 = 42

-x = -7

x = 7
 

y = 2x + 49

y = 2(7) + 49

y = 14 + 49

y = 63

Josh would pay $63 either way for 7 additional days.