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Alekssandra [29.7K]
3 years ago
12

The frequency table was made using a box containing slips of paper. Each slip of paper was numbered 0, 1, 2, 3, or 4

Mathematics
1 answer:
Rom4ik [11]3 years ago
4 0
What's the question???
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Solve the following absolute value equation. ​
cestrela7 [59]

Answer:

x= 8

x= -8

Step-by-step explanation:

|x+1| /3 = 3

|x+1| = 9

|x| + |1| = 9

|x| = 8

x= 8

x= -8

4 0
2 years ago
All of the following have the same unit price except _____.
Aliun [14]
2 1/2 for $6.25 is the answer
5 0
3 years ago
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Juan bought 4 pounds of chocolate
Andru [333]

Answer:

Step-by-step explanation:

This is a system of equations.  The 2 equations are:

4c + 2p = 16

2c + 3p = 12

Let's get rid of the p's first.  Do this by multiplying the first equation by -3 and the second equation by 2 to get a new system that looks like this:

-12x - 6p = -48

 4c + 6p =  24

Now add to get

-8c = -24 and

c = 3

That means that chocolate is $3 per pound.  Now sub that back in to either one of the original equations to get the price for peanuts:

4(3) + 2p = 16 and

12 + 2p = 16 and

2p = 4 so

p = 2

The price for peanuts is $2 per pound.

6 0
3 years ago
4 / 7 + −1 / 3 <br> HELP PLAESEEEEE
sasho [114]

Answer:

are those fractions or division signs

Step-by-step explanation:

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6 0
3 years ago
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Determine whether the sequences converge.
Alik [6]
a_n=\sqrt{\dfrac{(2n-1)!}{(2n+1)!}}

Notice that

\dfrac{(2n-1)!}{(2n+1)!}=\dfrac{(2n-1)!}{(2n+1)(2n)(2n-1)!}=\dfrac1{2n(2n+1)}

So as n\to\infty you have a_n\to0. Clearly a_n must converge.

The second sequence requires a bit more work.

\begin{cases}a_1=\sqrt2\\a_n=\sqrt{2a_{n-1}}&\text{for }n\ge2\end{cases}

The monotone convergence theorem will help here; if we can show that the sequence is monotonic and bounded, then a_n will converge.

Monotonicity is often easier to establish IMO. You can do so by induction. When n=2, you have

a_2=\sqrt{2a_1}=\sqrt{2\sqrt2}=2^{3/4}>2^{1/2}=a_1

Assume a_k\ge a_{k-1}, i.e. that a_k=\sqrt{2a_{k-1}}\ge a_{k-1}. Then for n=k+1, you have

a_{k+1}=\sqrt{2a_k}=\sqrt{2\sqrt{2a_{k-1}}\ge\sqrt{2a_{k-1}}=a_k

which suggests that for all n, you have a_n\ge a_{n-1}, so the sequence is increasing monotonically.

Next, based on the fact that both a_1=\sqrt2=2^{1/2} and a_2=2^{3/4}, a reasonable guess for an upper bound may be 2. Let's convince ourselves that this is the case first by example, then by proof.

We have

a_3=\sqrt{2\times2^{3/4}}=\sqrt{2^{7/4}}=2^{7/8}
a_4=\sqrt{2\times2^{7/8}}=\sqrt{2^{15/8}}=2^{15/16}

and so on. We're getting an inkling that the explicit closed form for the sequence may be a_n=2^{(2^n-1)/2^n}, but that's not what's asked for here. At any rate, it appears reasonable that the exponent will steadily approach 1. Let's prove this.

Clearly, a_1=2^{1/2}. Let's assume this is the case for n=k, i.e. that a_k. Now for n=k+1, we have

a_{k+1}=\sqrt{2a_k}

and so by induction, it follows that a_n for all n\ge1.

Therefore the second sequence must also converge (to 2).
4 0
3 years ago
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