All categories

3 years ago

Complete equation by showing how you use group size to simplify 5/15:( )=1/3

Mathematics

2 answers:

Flauer [41]3 years ago

6 0

2,416667 i hope it helped

ICE Princess25 [194]3 years ago

3 0

Your missing number should be 1/9

You might be interested in

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

A sporting goods store displays the following sale sign. What percent off is the sale

victus00 [196]

Answer:

The sale is 5% off.

Step-by-step explanation:

$25 regular price.
$18.75 sale price.

You need to find the percentage that deducts $1.25 from the regular price. I start with 5% and work my way up from there until I find the answer.

So, 5% of 25 = ?

5% * 25 = 1.25

You needed $1.25, 5% gives you that.

Therefore, the answer is 5%.

8 0

3 years ago

What ratio form a poportion with 4/15

Sonja [21]

Answer:

4:15 is the ratio formed by the proportion.

6 0

3 years ago

What is the horizontal shift ?

Marizza181 [45]

Answer: 45 degrees

Step-by-step explanation:

5 0

3 years ago

Given f(x)=x2+14x+40. Enter the quadratic function in vertex form in the box.

slega [8]

For this case we have an equation of the form:
$y = ax ^ 2 + bx + c
$
This equation in vertex form is:
$f (x) = a (x - h) ^ 2 + k
$
where (h, k) is the vertex of the parabola.
We have the following function:
$f (x) = x ^ 2 + 14x + 40
$
We look for the vertice.
For this, we derive the equation:
$f '(x) = 2x + 14
$
We equal zero and clear the value of x:
$2x + 14 = 0

2x = -14

x = -14/2

x = -7$
Substitute the value of x = -7 in the function:
$f (-7) = (- 7) ^ 2 + 14 * (- 7) +40

f (-7) = -9$
Then, the vertice is:
$(h, k) = (-7, -9)
$
Substituting values we have:
$f (x) = (x + 7) ^ 2 - 9$
Answer:
The quadratic function in vertex form is:
$f (x) = (x + 7) ^ 2 - 9$

6 0

3 years ago