A fruit company delivers its fruit in two types of boxes : large and small. A delivery of 6 large boxes and 5 small boxes has a total weight of 190 kilograms. A delivery of 2 large boxes and 3 small boxes has a total of 84 kilograms. How much does each type of boxes weigh ?

Answers

Answer 1

Answer: 4 large and 8 small weigh 113kg
so
2 large and 4 small weigh 56.5 kg
but
2 large and 3 small weigh 50 kg
so taking the difference
1 small weighs 56.5 - 50 = 6.5 kg.

Substitute :
2 large and 3 small weight 50 kg
2 large weigh 50 - 3*6.5 = 50 - 19.5 = 30.5 kg
1 large weighs 15.25 kg

Answer 2

Answer:

We have this system

6L + 5S = 190 (1)

2L + 3S = 84 multiply through by -3 ⇒ -6L - 9S = -252 (2)

Add (1) and (2) and we get that

-4S = -62

S = -62 / -4 = 15.5 kilos for a small box

And

2L + 3S = 84

2L + 3 (15.5) = 84

2L = 46.5 = 84

2L = 84 - 46.5

2L = 37.5

L = 37.5 /2 = 18.75 kilos for a large box

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Lucy needs to hire a host. host a is offering his services for an initial $75 in addition to $13.75 per hour. hostess b is offering her services for an initial $80 in addition to $12.25 per hour. when will the two hosts charge the same amount of money? if necessary, round your answer to the nearest tenth.

Answers

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I need help PLEASE.

Answers

Notes:
The notation ">=" without quotes means "greater than or equal to"
The upper case "U" means "set union"
Instead of using the intersection symbol, I will use a lower case 'n'

-------------------------------

Problem 1

A = {x | x < 1} which is the set of x values smaller than 1
B = {x | x >= 5} is the set of x values that are equal to 5 or larger
A U B = set of values that are from set A OR they are from set B (or both)
A U B = {x | x < 1 or x >= 5}
we simply connect the two inequalities mentioned with an "or"

note: how there is no overlap between the two regions. The "U" means "set union" which is like a sort of glue to tie the two sets together with an "or".

Answer: {x| x < 1 or x >= 5}
-------------------------------
Problem 2

A = {x | x < 1}
C = {x | x = 5} which is the set of one value only: 5 (x cannot equal any other value)
A U C = {x| x < 1 or x = 5}

So if a number is in set A U C, then this number is either less than 1, OR it is equal to 5

Answer: {x|x < 1 or x = 5}
-------------------------------
Problem 3

B U C = {x | x >= 5} because set C already has the "or equal to" part in there.

Set C is a subset of set B. If an item is in set C, then it is also in set B.

Answer: {x| x >= 5}
-------------------------------
Problem 4

Again recall that I'm using an 'n' to indicate "set intersection" instead of the upside down "U" symbol

A n B is the set of items that are in BOTH sets A and B at the same time. From problem 1, I mentioned there's a gap. There is no x value that is both less than 1 AND greater than or equal to 5. So this means that

A n B = empty set

which we use the "O" with a slash through it. This is a special symbol to indicate "empty set"

Another way to write "empty set" is to use curly braces with nothing inside like so { }

Answer: The "O" with a slash through it
-------------------------------
Problem 5

B n C is the same as {x| x = 5}

Why? Because if an item is in B n C, then it has to be in BOTH set B and set C at the same time. The only way this happens is if x = 5. If x is any other value, then it won't be in set C

Answer: {x| x = 5}

What is 14/20 as a percent

Answers

Remember 'bout :

Percent is /100

So :

14 ×5 70

-------- = ----- -

20×5 100

70 %

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Answers

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Answers

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