1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aliya0001 [1]
3 years ago
8

Three aluminum cans can be recycled to make a new can. How many new cans can eventually be made from 243 aluminum cans? (Remembe

r that the first new cans that are made can then be recycled into even newer cans!) Do not include the original 243 cans in your count.
Mathematics
1 answer:
DENIUS [597]3 years ago
7 0

Answer:

121 new cans can eventually be made from 243 aluminum cans

Step-by-step explanation:

Unit rate defined as the rates are expressed as a quantity 1 such as 2 miles per second or 5 kilometer per hour.

As per the statement:

Three aluminum cans can be recycled to make a new can.

Unit rate per aluminium can = \frac{1}{3} new can

We have to find the new cans can eventually be made from 243 aluminum cans.

By definition of unit rate;

\text{Number of new cans made from 243 cans} = \text{Unit rate per aluminium can} \times 243

Substitute the given values we have;

\text{Number of new cans made from 243 cans} = \frac{1}{3} \times 243 = 81

Again do the same process:

Number of new can made from 81 can  is \frac{1}{3} \cdot 81 = 27

Similarly,

Number of new cans made from 27 can = \frac{1}{3} \cdot 27 = 9

Number of new cans made from 9 can =\frac{1}{3} \cdot 9 = 3

Number of new cans made from 3 can =  \frac{1}{3} \cdot 3 = 1

Now, No further new can made.

Therefore, total new can made from 243 is 81+27+9+3+ 1 =121 cans

You might be interested in
Robert's dog is 4 years older than Karen's cat. In 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. How
mylen [45]

Answer:

5.5 years old.

Step-by-step explanation:

Let D represent present age of Robert's dog and C represent present age of Karen's cat.

We have been given that Robert's dog is 4 years older than Karen's cat. We can represent this information in an equation as:

D=C+4...(1)

We are also told that in 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. After 3 years age of dog and cat would be D+3 and C+3 respectively.

We can represent this information in an equation as:

D+3+C+3=13...(2)

From equation (1), we will get:

C=D-4

Upon substituting this value in equation (2), we will get:

D+3+D-4+3=13

Combine like terms:

2D+2=13

2D+2-2=13-2

2D=11

\frac{2D}{2}=\frac{11}{2}

D=5.5

Therefore, Robert's dog is 5.5 years old right now.

3 0
3 years ago
ZX is perpendicular bisector of WY if WY=24 what is WX
bixtya [17]

Answer:

12

Step-by-step explanation:

6 0
3 years ago
The harbormaster wants to place buoys where the river bottom is 20 feet below the surface of the water. Complete the absolute va
Natalija [7]

Answer:

The answer is below

Step-by-step explanation:

The bottom of a river makes a V-shape that can be modeled with the absolute value function, d(h) = ⅕ ⎜h − 240⎟ − 48, where d is the depth of the river bottom (in feet) and h is the horizontal distance to the left-hand shore (in feet). A ship risks running aground if the bottom of its keel (its lowest point under the water) reaches down to the river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 20 feet below the surface. Complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed

Answer:

To solve the problem, the depth of the water would be equated to the position of the river bottom.

d(h)=river \ bottom\\\\The \ river \ bottom=-20\ feet(below)\\\\d(h) = -20\\\\\frac{1}{5}|h-240|-48=-20\\ \\\frac{1}{5}|h-240|=-20+48\\\\\frac{1}{5}|h-240|=28\\\\|h-240|=28*5\\\\|h-240|=140\\\\h-240=140\ or\ h-240=-140\\\\h=140+240\ or\ h=-140+240\\\\h=380\ or\ h=100\\\\The\ buoys\ should\ be\ placed\ at\ 100\ feet\ and\ 380\ feet\ from\ left-hand\ shore

4 0
3 years ago
<img src="https://tex.z-dn.net/?f=4%20%5Cdiv%20%20%5Cfrac%7B1%7D%7B2%7D%20" id="TexFormula1" title="4 \div \frac{1}{2} " alt="4
IRINA_888 [86]

Answer:

8

Step-by-step explanation:

4 ÷ 1/2

~Turn the 4 into a fraction

4/1 ÷ 1/2

~Copy Dopt Flip

4/1 * 2/1

~Multiply

8/1

~Simplify

8

Best of Luck!

8 0
2 years ago
Read 2 more answers
Perform a first derivative test on the function ​f(x)equals2 x cubed plus 3 x squared minus 120 x plus 6​; ​[minus5​,8​]. Bold
maria [59]

Answer:

a) Critical points

x = 4 and x = -5

b) x = 4 corresponds to a minimum point for the function f(x)

x = - 5 corresponds to a maximum point for the function f(x)

c) The minimum value of f(x) in the interval = -298

The maximum value of f(x) in the interval = 431;

Step-by-step explanation:

f(x) = 2x³ + 3x² - 120x + 6 in the interval [-5, 8]

a) To obtain the critical points, we need to obtain the first derivative of the function with respect to x. Because at critical points of a function, f(x), (df/dx) = 0

f'(x) = (df/dx) = 6x² + 6x - 120 = 0

6x² + 6x - 120 = 0

Solving the quadratic equation,

x = 4 or x = -5

The two critical points, x = 4 and x = -5 are in the interval given [-5, 8] (the interval includes -5 and 8, because it's a closed interval)

b) To investigate the nature of the critical points, we obtain f"(x)

Because f'(x) changes sign at the critical points

If f"(x) > 0, then it's a minimum point and if f"(x) < 0 at c, then it's a maximum point.

f"(x) = (d²f/dx²) = 12x + 6

at critical point x = 4

f"(x) = 12x + 6 = 12(4) + 6 = 54 > 0, hence, x = 4 corresponds to a minimum point.

at critical point x = -5

f"(x) = 12x + 4 = 12(-5) + 4 = -56 < 0, hence, x = -5 corresponds to a maximum point.

c) At x = 4,

f(x) = 2x³ + 3x² - 120x + 6 = 2(4)³ + 3(4)² - 120(4) + 6 = -298

At x = - 5

f(x) = 2x³ + 3x² - 120x + 6 = 2(-5)³ + 3(-5)² - 120(-5) + 6 = 431

7 0
2 years ago
Other questions:
  • Oliver can read 28 1/2 pages in 1 1/6 hours. how long does it take him to read one page
    15·1 answer
  • 108=-12 - 4 (-5n+7)I need help
    6·1 answer
  • Simplify (4x+7)-(-3x-9)+9x-28
    13·1 answer
  • You received a discount on each book you buy . The original price of each book is x dollars You buy 5 books for a total of (5x -
    14·1 answer
  • The speed of light is about 6.71x10 squared (8) miles per hour. write that number in standared form?
    11·1 answer
  • Marlene's taxable income is $95,000. Use this tax schedule to calculate the total amount she owes in taxes. A. 12,88.75 B. 17,90
    9·1 answer
  • Matilda and Lorraine work in the mail room of a large company sorting letters. Matilda has already sorted 50 letters and continu
    9·1 answer
  • 2
    11·1 answer
  • If f(x) = 12 – 2 and g(x) = x + 3, find all values of x, to the nearest tenth, for
    9·1 answer
  • What is the difference between 7 million and 7 ten thousand
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!