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algol13
2 years ago
11

A battery factory typically produces 12,000 batteries per day and uses 50 boxes for packing the batteries. If the number of boxe

s needed for packing is proportional to the number of batteries produced, how many more boxes would be needed on a day when 18,000 batteries are produced?
Mathematics
1 answer:
weqwewe [10]2 years ago
4 0

Answer:

25 more boxes is needed

Step-by-step explanation:

12000 batteries require 50 boxes. Let's find the unit rate.

That is, how many batteries are in each box??

That's 12,000/50!

12,000/50 = 240 batteries per box

Now, to find how many boxes we would need for 18,000 batteries, we will have to divide the total (18000) by 240(number of batteries per box). That is:

18,000/240 = 75 boxes

We would need 75 boxes to pack 18,000 batteries.

We want "how many MORE boxes needed", so we will the excess:

75 - 50 = 25 more boxes is needed

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Lucy wants to have a fun-filled day without spending too much money. The local zoo charges a $25 entry fee and a parking fee of
ehidna [41]

Answer:

The required system of equations is,

y=25+x

y=20+2x.

Step-by-step explanation:

Let the number of hours spent by Lucy = x

It is given that,

Local zoo charges initial fee $25 and per hour fee $1.

So, the equation representing the cost if Lucy stays 'x' hours is,

y=25+x in dollars.

Also, Local citcus charges initial fee $20 and per hour fee $2.

So, the equation representing the cost if Lucy stays 'x' hours is,

y=20+2x in dollars.

Since, the objective function for the situation is to 'minimize the cost'.

So, upon solving the equations, we will get the minimum value as,

25+x = 20+2x

i.e. x= 5

Thus,

y=25+x implies y=25+5 i.e. y= $30

y=20+2x implies y=20+2\times 5 i.e. y=20+10 i.e. y= $30

Thus, the minimum value is $30.

The required system of equations is,

y=25+x

y=20+2x.

8 0
2 years ago
Which of the following events are equal? (a) A = {1,3}; (b) B = {x | x is a number on a die }; (c) C = {x | x2 −4x +3=0 }; (d) D
rosijanka [135]

Answer:

A and C

Step-by-step explanation:

To determine which events are equal, we explicitly define the elements in each set builder.

For event A

A={1.3}

for event B

B={x|x is a number on a die}

The possible numbers on a die are 1,2,3,4,5 and 6. Hence event B is computed as

B={1,2,3,4,5,6}

for event C

C=[x|x^{2}-4x+3]\\solving  x^{2}-4x+3\\x^{2}-4x+3=0\\x^{2}-3x-x+3=0\\x(x-3)-1(x-3)=0\\x=3 or x=1

Hence the set c is C={1,3}

and for the set D {x| x is the number of heads when six coins re tossed }

In the tossing a six coins it is possible not to have any head and it is possible to have head ranging from 1 to 6

Hence the set D can be expressed as

D={0,1,2,3,4,5,6}

In conclusion, when all the set are compared only set A and set C are equal

5 0
2 years ago
What is the length of segment XY?
Brilliant_brown [7]

Answer:

StartRoot 53 EndRoot units

XY = √53

Step-by-step explanation:

Choose which is point 1 and point 2 so you don't confuse the coordinates.

Point 1 (–4, 0)    x₁ = –4   y₁ = 0

Point 2 (3, 2)      x₂ = 3    y₂ = 2

Use the formula for the distance between two points.

L = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}

XY = \sqrt{(3-(-4))^{2} + (2-0)^{2}}

XY = \sqrt{49 + 4}

XY = \sqrt{53}

Therefore the line of segment XY is √53.

6 0
2 years ago
Read 2 more answers
Find each product.<br> 1) (5n - 5)(4n - 4)
Paraphin [41]

Answer:

20n² - 40n + 20

Step-by-step explanation:

(5n - 5)(4n - 4)

= 5n(4n) + 5n(-4) - 5(4n) - 5(-4)

= 20n² - 20n - 20n + 20

= 20n² - 40n + 20

Another way to do this:

(5n - 5)(4n - 4)

= 5(n - 1) * 4(n - 1)

= 20(n - 1)(n - 1)

= 20(n - 1)²

= 20(n² - 2n + 1)

= 20n² - 40n + 20

6 0
2 years ago
Which of the following does not describe slope?
Sonja [21]
The answer is the first one

I hope that helped
7 0
2 years ago
Read 2 more answers
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