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3 years ago

A recent survey found that 80% of jeans have back pockets, 65% have front pockets, and 48% have both back and

Mathematics

1 answer:

OlgaM077 [116]3 years ago

5 0

Answer:

.52

Step-by-step explanation:

its only a little bit over a 50% chance to get a front pocketed jean, then to also have back pockets is under 50% chance so when you even those it comes to .52

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2 years ago

Select all that apply.

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Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions

monitta

I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take $z=y'$ , so that $z'=y''$ and we're left with the ODE linear in $z$ :

$y''-y'=0\implies z'-z=0\implies z=C_1e^x\implies y=C_1e^x+C_2$

Now suppose $y$ has a power series expansion

$y=\displaystyle\sum_{n\ge0}a_nx^n$
$\implies y'=\displaystyle\sum_{n\ge1}na_nx^{n-1}$
$\implies y''=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}$

Then the ODE can be written as

$\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge1}na_nx^{n-1}=0$

$\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge2}(n-1)a_{n-1}x^{n-2}=0$

$\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0$

All the coefficients of the series vanish, and setting $x=0$ in the power series forms for $y$ and $y'$ tell us that $y(0)=a_0$ and $y'(0)=a_1$ , so we get the recurrence

$\begin{cases}a_0=a_0\\\\a_1=a_1\\\\a_n=\dfrac{a_{n-1}}n&\text{for }n\ge2\end{cases}$

We can solve explicitly for $a_n$ quite easily:

$a_n=\dfrac{a_{n-1}}n\implies a_{n-1}=\dfrac{a_{n-2}}{n-1}\implies a_n=\dfrac{a_{n-2}}{n(n-1)}$

and so on. Continuing in this way we end up with

$a_n=\dfrac{a_1}{n!}$

so that the solution to the ODE is

$y(x)=\displaystyle\sum_{n\ge0}\dfrac{a_1}{n!}x^n=a_1+a_1x+\dfrac{a_1}2x^2+\cdots=a_1e^x$

We also require the solution to satisfy $y(0)=a_0$ , which we can do easily by adding and subtracting a constant as needed:

$y(x)=a_0-a_1+a_1+\displaystyle\sum_{n\ge1}\dfrac{a_1}{n!}x^n=\underbrace{a_0-a_1}_{C_2}+\underbrace{a_1}_{C_1}\displaystyle\sum_{n\ge0}\frac{x^n}{n!}$

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2 years ago

The Westside Bakery uses 310 pounds of flour to make 1,000 loaves of bread. Each loaf

DanielleElmas [232]

Answer:

310 / 1000 = 0.31 pounds

Step-by-step explanation:

When dividing by a number that is 1 less 0 than how many digits the number has, we can move the decimal point the number of times zero is repeated at the end of the number.

1000 has 3 zeroes, so we move the decimal point 3 moves to the left.

So, we do this:

After 0 moves: 310

After 1 move: 31.0

After 2 moves: 3.10

After 3 moves = 0.310

0.310 is the same as 0.31

Therefore, 0.31 pounds of flour are in each loaf.

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2 years ago

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Answer: 0,13/3

Step-by-step explanation: Hope this helps - Lily ^_^

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