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3 years ago

Wich is a better deal, a bag of sand witch is 60 pounds for $5 or B a bag of sand witch is $12 for 150 pounds?

Mathematics

1 answer:

kodGreya [7K]3 years ago

5 0

1) find unit rate of both bags

60/5 = 12pound per dollar

150/12 = 12.5pounds per dollar

2) Comparing

12 (A) < 12.5 (B)

Therefore, B is a better deal

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Describe the rule for the sequence 2, 1, 2/3, 1/2, 2/5, 1/3, 1/7,...

Triss [41]

Multiply 2 by 1/2 to get 1.

Multiply 1 by 2/3 to get 2/3.

Multiply 2/3 by 3/4 to get 6/12 = 1/2.

Multiply 1/2 by 4/5 to get 4/10 = 2/5.

Multiply 2/5 by 5/6 to get 10/30 = 1/3.

Multiply 1/3 by 6/7 to get 6/21 = 2/7. (I suspect there's a typo in the question.)

And so on, so that the nth term in the sequence is multiplied by n/(n + 1) to get the (n + 1)th term.

Recursively, the sequence is given by

$\begin{cases}a_1=2\\a_n=\dfrac{n-1}na_{n-1}&\text{for }n>1\end{cases}$

We can solve this exactly by iterating:

$a_n=\dfrac{n-1}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}{n-1}\dfrac{n-3}{n-2}a_{n-3}=\cdots$

and so on down to

$a_n=\dfrac{(n-1)\cdot(n-2)\cdot(n-3)\cdot\cdots\cdot3\cdot2\cdot1}{n\cdot(n-1)\cdot(n-2)\cdot\cdots\cdot4\cdot3\cdot2}a_1$

$a_n=\dfrac{(n-1)!}{n!}a_1$

and with lots of cancellation, we end up with

$a_n=\dfrac{a_1}n=\boxed{\dfrac2n}$

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Step-by-step explanation:

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Aleksandr-060686 [28]

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Step-by-step explanation:

The rest of the question is the attached figure

According to the graph, we will check which option is true.

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Because: h intersects line f at B only.

b. Line h is the intersection of planes R and T (Wrong)

Because: g is the intersection of planes R and T

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and the points of h on the plane R

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above sea level its positive

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