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2 years ago

The average of 10 numbers is -5. A new number is added to the list making the average -6. What is the new number?

Mathematics

1 answer:

Shtirlitz [24]2 years ago

4 0

Answer:

- 16

Step-by-step explanation:

Average is calculated as

average = $\frac{total}{count}$

Thus for the given 10 numbers we have

$\frac{total}{10}$ = - 5 ( multiply both sides by 10 )

total = - 50

let the number added be x, then

$\frac{total+x}{11}$ = - 6 ( multiply both sides by 11 )

total + x = - 66, that is

- 50 + x = - 66 ( add 50 to both sides )

x = - 16

The new number is - 16

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Solve the system of inequalities: y + 2x > 3 and y 3.5x − 5 The first inequality, y + 2x > 3, is in slope-intercept form.

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The Community Relief Fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 s

asambeis [7]

The question is incomplete:

The Community Relief Fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 sweaters, $5 books. They want to buy 200 items and send them to schools in earthquake-hit areas. They must order as many books as school bags and sweaters combined. How many of each item should they order?

Answer:

They must order 40 bags, 60 sweaters and 100 books.

Step-by-step explanation:

From the information provided, you can write the following equations:

x+y+z=200 (1)

20x+25y+5z=2800 (2)

z=x+y (3), where:

x=amount of bags

y=amount of sweaters

z=amount of books

Now, you can replace (3) in (1) and (2):

x+y+x+y=200

2x+2y=200 (4)

20x+25y+5(x+y)=2800

20x+25y+5x+5y=2800

25x+30y=2800 (5)

Then, you will have 2 equations:

2x+2y=200 (4)

25x+30y=2800 (5)

You can isolate x in (4):

2x=200-2y

x=100-y (6)

After this, you can replace (6) in (5):

25(100-y)+30y=2800

2500-25y+30y=2800

5y=2800-2500

y=300/5

y=60

Next, you can replace the value of y in (6) to find the value of x:

x=100-60

x=40

Finally, you can replace the value of x and y in (3) to find the value of z:

z=40+60

z=100

According to this, the answer is that they must order 40 bags, 60 sweaters and 100 books.

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2 years ago

Paco's cell phone carrier charges him $0.20 for each text message he sends or receives, $0.15 per minute for calls, and a $15 mo

Katarina [22]

Given:

Paco's cell phone carrier charges him $0.20 for each text message he sends or receives, $0.15 per minute for calls, and a $15 monthly service fee. Paco is trying to keep his bill for the month below $30.

To Find:

The number of texts 't' Paco can send/receive in a month.

Answer:

$0\leq t$

best describes the number of texts he can send or receive to keep his bill less than $30 in a month.

Step-by-step explanation:

Paco wants to keep is monthly bill below $30.

We see that he has to pay a foxed monthly service fee of $15. This means he is only left with a limit of $30 - $15 = $15 for his monthly calls and texts.

That is, the amount he has to pay for texting and calling has to be less than $15.

For texts, the cell phone carrier charges $0.20 for sending/receiving texts.

For calls, he is charged $0.15 per minute.

Let the number of text messages Paco can send or receive in a month be denoted by 't'.

Let the number of minutes Paco can call in a month be denoted by 'c'.

Then, the total cost of text messages he can send or receive per month would be 0.20t and the total cost of the minutes he spends on calls would be 0.15c. Together, the sum of these has to be less than $15 if his monthly bill has to be kept less than $30 (accounting for the monthly service fee).

So,

$0.20t+0.15c$

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So, putting c = 0, the aboce equation can be written as

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