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2 years ago

A box holds 25 pounds of cans. Each can weighs 8 ounces. How many cans does each box hold?

Mathematics

1 answer:

OverLord2011 [107]2 years ago

6 0

1 pound = 16 ounces.

1 can weighs 8 ounces, so 2 cans weigh 8 +8 = 16 ounces, which is 1 pound.

Multiply total pounds by number of cans per pound:

25 pounds x 2 cans per pound = 50 total cans.

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A cooking magazine shows a photo of a main dish on the front cover of 5 out of the 12 issues it publishes each year. Write and s

Shtirlitz [24]

Ok so the ratio is ... 5/12 (every 5 months out of 12 in on year, the main dish is on the cover)

All you have to do is multiply the top # and bottom # in the fraction by 5.

5*5 = 25
5*12 = 60

In 5 years, there are 60 months. During that time, a main dish will be on the cover 25 times.

5 0

2 years ago

What is the following difference?

Svetllana [295]

Answer:

$-7ab\sqrt[3]{3ab^2}$

Step-by-step explanation:

Remove perfect cubes from under the radical and combine like terms.

$2ab\sqrt[3]{192ab^2}-5\sqrt[3]{81a^4b^5}=2ab\sqrt[3]{4^3\cdot 3ab^2}-5\sqrt[3]{(3ab)^3\cdot 3ab^2}\\\\=(8ab -15ab)\sqrt[3]{3ab^2}=\boxed{-7ab\sqrt[3]{3ab^2} }$

7 0

2 years ago

G identify the solution of the recurrence relation an = 6an − 1 – 8an − 2 for n ≥ 2 together with the initial conditions a0 = 4,

maksim [4K]

Via the generating function method, let

$G(x)=\displaystyle\sum_{n\ge0}a_nx^n$

Then take the recurrence,

$a_n=6a_{n-1}-8a_{n-2}$

multiply everything by $x^n$ and sum over all $n\ge2$ :

$\displaystyle\sum_{n\ge2}a_nx^n=6\sum_{n\ge2}a_{n-1}x^n-8\sum_{n\ge2}a_{n-2}x^n$

Re-index the sums or add/remove terms as needed in order to be able to express them in terms of $G(x)$ :

$\displaystyle\sum_{n\ge2}a_nx^n=\sum_{n\ge0}a_nx^n-(a_0-a_1x)=G(x)-4-10x$

$\displaystyle\sum_{n\ge2}a_{n-1}x^n=\sum_{n\ge1}a_nx^{n+1}=x\sum_{n\ge1}a_nx^n=x\left(G(x)-a_0\right)=x(G(x)-4)$

$\displaystyle\sum_{n\ge2}a_{n-2}x^n=\sum_{n\ge0}a_nx^{n+2}=x^2\sum_{n\ge0}a_nx^n=x^2G(x)$

So the recurrence relation is transformed to

$G(x)-4-10x=6x(G(x)-4)-8x^2G(x)$
$(1-6x+8x^2)G(x)=4-14x$
$G(x)=\dfrac{4-14x}{1-6x+8x^2}=\dfrac{4-14x}{(1-4x)(1-2x)}=\dfrac1{1-4x}+\dfrac3{1-2x}$

For appropriate values of $x$ , we can express the RHS in terms of geometric power series:

$G(x)=\displaystyle\sum_{n\ge0}(4x)^n+3\sum_{n\ge0}(2x)^n=\sum_{n\ge0}\bigg(4^n+3\cdot2^n\bigg)x^n$

which tells us that

$a_n=4^n+3\cdot2^n$

3 0

2 years ago

Emily is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Emily will earn $

Hitman42 [59]

Answer:

(6,2)

Step-by-step explanation:

Variable Definitions:

x= the number of commercials

y= the number of movies

Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:

50x+150y=600

Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.

x=3y

Write System of Equations:

50x+150y=600

x=3y

Solve for y in each equation:

1) 50x+150y=600

150y=−50x+600

y=-1/3x+4

2) x=3y

y=1/3x

The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:

Emily's songs were played on 6 commercials and 2 movies.

4 0

2 years ago

Ben has 400 counters in a bag. He gives 35 of the counters to Sonia 130 of the counters to Phil 75 of the counters to Lance What

aniked [119]

Answer:

2/5

Step-by-step explanation:

subtract 130,35,and 74 from 400 you will have 160/400 left then you find the greatest common and divide! and get 2/5

8 0

2 years ago

Read 2 more answers