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vlada-n [284]
3 years ago
5

Chen, Lisa, Gabriel, and Artie each take a large piece of paper to

Mathematics
1 answer:
posledela3 years ago
7 0
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Which expression is equivalent to -6x^3 • x • y^2 • y^6?
Georgia [21]

Use the Product Rule: x^ax^b = x^a + b

6x^3 + 1y^2 + 6

Simplify 3 + 1 to 4

6x^4y^2 + 6

Simplify 2 + 6 to 8

<u>= C) 6x^4 y^8</u>

4 0
3 years ago
What is the value of the sum of all the terms of the geometric series 300, 60, 12, …?
ruslelena [56]
<h3>Answer:   375</h3>

=========================================

Work Shown:

a = 300 = first term

r = 60/300 = 0.2 = common ratio

We multiply each term by 0.2, aka 1/5, to get the next term.

Since -1 < r < 1 is true, we can use the infinite geometric sum formula below

S = a/(1-r)

S = 300/(1-0.2)

S = 300/0.8

S = 375

----------

As a sort of "check", we can add up partial sums like so

  • 300+60 = 360
  • 300+60+12 = 360+12 = 372
  • 300+60+12+2.4 = 372+2.4 = 374.4
  • 300+60+12+2.4+0.48 = 374.4+0.48 = 374.88

and so on. The idea is that each time we add on a new term, we should be getting closer and closer to 375. I put "check" in quotation marks because it's probably not the rigorous of checks possible. But it may give a good idea of what's going on.

----------

Side note: If the common ratio r was either r < -1 or r > 1, then the terms we add on would get larger and larger. This would mean we don't approach a single finite value with the infinite sum.

3 0
3 years ago
While drying, apple loses 14% of its weight. How many pounds of fresh apple is needed to get 10 8/25 lbs of dried apple?
aksik [14]

Answer:

12lbs

Step-by-step explanation:

let x be the amount of apples you need, then:

x-0.14x= 10 8/25

0.86x = 10 8/25

(10 8/25) : 86 * 100 = x

x=12

7 0
3 years ago
Read 2 more answers
The table shows the population of a small town over time. The fiction p=10,550(1.1) models the time population x year after the
Salsk061 [2.6K]

Answer:

7 \times (8 + 9) - 6 \times (2000 + 1700) = 19000.02

That is the answer you are looking

6 0
3 years ago
Task Directions: Ms. Chang's class decides to order posters that advertise a walkathon to raise money for
mamaluj [8]

Answer:

a.

Clear Prints = 2p

Sue = 15 + 0.5p

b.  10 posters

c.  See Below

d.  Clear Prints

e. See Below

Step-by-step explanation:

<u>Complete Question:</u>

<em>Ms. Chang’s class decides to order posters that advertise a walkathon to raise money for a local charity. Ichiro obtains quotes from two different companies.Clear Prints charges $2 per poster. Posters by Sue charges $15 plus $.50 per poster.</em>

<em>a. For each company, write an equation Ichiro could use to calculate the cost for any number of posters.</em>

<em>b. For what number of posters is the cost the same for both companies? Explain.</em>

<em>c. Which company do you think the class should buy posters from? Explain your reasoning.</em>

<em>d. If Ms. Chang’s class has an $18 budget for posters, which company do you think the class should buy posters from? </em>

<em>e. If Ms. Chang donates an additional $10 for ordering posters, does it impact the decision made? What factors influenced your decision?</em>

<em />

<u>Solution:</u>

a.

Let the number of posters be "p" so

Clear Print would take 2 * p or "2p"

Sue would take a fixed cost of $15 and 0.5p, so "15 + 0.5p"

b.

We want cost of both to be same. So we can equate:

2p=15 + 0.5p

Now, using algebra, we can solve for "p", the number at which both of the printers will cost same. Lets do this:

2p=15 + 0.5p\\2p-0.5p=15\\1.5p=15\\p=10

So, for 10 posters, the cost of both will be same

c.

It depends.

If the number of posters they order is LESS THAN 10, they should order from Clear Prints. If the number of posters they print is "10", then they can choose any one of the printers since cost would be same. If they print more than 10 posters, then they should choose to go with Sue, as it will cost less.

d.

If the budget is $18, they can get:

Clear Prints = 18/2 = 9 posters made

Sue = 15 already gone as fixed cost, so remaining is 18 - 15 = 3

At 0.5 per poster, 3/0.5 = 6 posters

So, taking Clear Prints would be better.

e.

The budget of 18 is increase by 10, so the budget is:

18 + 10 = $28

From clear prints, you can get:

28/2 = 14 posters

From Sue, you can get:

28 - 15(fixed cost) = 13 left for posters

13/0.5 = 26 posters

Definitely, Sue gives more, so decision made at $18 budget to get Clear Prints would be impacted because they should now go with Sue since it will give them better deal and more posters.

5 0
3 years ago
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