What is the probability of the following.

A leprechaun places a magic penny under a girl's pillow. The next night there are 2 magic pennies under her pillow. Each night

11Alexandr11 [23.1K]

Answer:

tn = 2097152 pennies
tn = 20971.52 dollars.

Step-by-step explanation:

A surprisingly large amount of money.

The question is "Does the amount of money just double or do the previous amounts add to the present amount?"

I think it just doubles. Not only that, but she can't spend any of it until night 22 is reached.

tn = a*2^(n - 1)
a = 1 She starts with 1 penny.
n = 22
tn = 1*2^(22 - 1)
tn = 1*2^21
tn = 2097152 pennies
tn = 20971.52 dollars.

8 0

4 years ago

Find the tangent line approximation for 10+x−−−−−√ near x=0. Do not approximate any of the values in your formula when entering

Svetllana [295]

Answer:

$L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x$

Step-by-step explanation:

We are asked to find the tangent line approximation for $f(x)=\sqrt{10+x}$ near $x=0$ .

We will use linear approximation formula for a tangent line $L(x)$ of a function $f(x)$ at $x=a$ to solve our given problem.

$L(x)=f(a)+f'(a)(x-a)$

Let us find value of function at $x=0$ as:

$f(0)=\sqrt{10+x}=\sqrt{10+0}=\sqrt{10}$

Now, we will find derivative of given function as:

$f(x)=\sqrt{10+x}=(10+x)^{\frac{1}{2}}$

$f'(x)=\frac{d}{dx}((10+x)^{\frac{1}{2}})\cdot \frac{d}{dx}(10+x)$

$f'(x)=\frac{1}{2}(10+x)^{-\frac{1}{2}}\cdot 1$

$f'(x)=\frac{1}{2\sqrt{10+x}}$

Let us find derivative at $x=0$

$f'(0)=\frac{1}{2\sqrt{10+0}}=\frac{1}{2\sqrt{10}}$

Upon substituting our given values in linear approximation formula, we will get:

$L(x)=\sqrt{10}+\frac{1}{2\sqrt{10}}(x-0)$

$L(x)=\sqrt{10}+\frac{1}{2\sqrt{10}}x-0$

$L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x$

Therefore, our required tangent line for approximation would be $L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x$ .

8 0

3 years ago

A merchant has coffee worth $20 a pound that she wishes to mix with 70 pounds of coffee worth $90 a pound to get a mixture that

Dvinal [7]

Let us start with assuming the amount of coffee worth $20 a pound to be "x" pounds.

Now she wants to mix "x" pounds of $20 coffee with 70 pounds of $90 coffee.

So the mixture would be (x + 70) pounds.

And the value of mixture would be = 20·x + (90)·(70) = (20x + 6300) dollars.

She want to sell this mixture at rate of $30 a pound. Her earning would be = 30·(x + 70) = (30x + 2100) dollars.

We know that the value of mixture would be equal to her earnings.

30x + 2100 = 20x + 6300

30x - 20x = 6300 - 2100

10x = 4200

x = 420

So, 420 pounds of $20 coffee would be used.

7 0

3 years ago

Read 2 more answers

A bookstore has 7 shelves of books about animals. There are 30 books on each shelf. How many books about animals does the bookst

Alenkinab [10]

The answer is 210 .. .

7 0

3 years ago

What is (1. 6x 7. 3) (–0. 6x 2) – (7. 8 – 3. 4x), simplified? (1. 6x 7. 3) (–0. 6x 2) – (7. 8 – 3. 4x) 1. 6x 7. 3 – 0. 6x 2 – 7.

bekas [8.4K]

The simplified form of the equation is 4.4x + 1.5.

Given

Equation; (1.6x + 7.3) + (–0.6x + 2) – (7.8 – 3.4x)

<h3>Addition</h3>

The addition is the process of adding things together.

To simplify the equation follow all the steps given below.

First, open the brackets combine like terms, and simplify.

Then,

The equation in simplified form is;

$\rm (1.6x + 7.3) + (-0.6x + 2) - (7.8 -3.4x)\\\\1.6x+7.3-0.6x+2-7.8+3.4x\\\\1.6x-0.6+3.4x+7.3-7.8\\\\4.4x+1.5$

Hence, the simplified form of the equation is 4.4x + 1.5.

To know more about addition click the link given below.

brainly.com/question/15892196

7 0

2 years ago