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3 years ago

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Peter figures he can build the entire tree house by himself in 20 hours. He figures that each additional friend who helps him wo

uld improve the time by 10%. He created a table using the algebraic expression n – n(0.10), where n is the previous number of hours.
To the nearest tenth of an hour, how long will it take to build the tree house if 4 friends are helping?
It will take
hours.

2 answers:

aleksandr82 [10.1K]3 years ago

7 0

13.1 hours. I did the assignment

andrey2020 [161]3 years ago

3 0

Answer:

the answer is 13.1 i just did the assignment and got it right.

Step-by-step explanation:

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Twenty-three percent of automobiles are not covered by insurance (CNN, February 23,2006). On a particular weekend, 35 automobile

Bingel [31]

Answer:

Step-by-step explanation:

Given that twenty-three percent of automobiles are not covered by insurance (CNN, February 23,2006).

considering the total number of vehicles, probability for a randomly drawn vehicle not covered by insurance = 0.23

Each vehicle can be treated as independent of the other

Hence X no of vehicles not covered by insurance is Binom with n = 35 and p - 0.23

a) the expected number of these automobiles that are not covered by insurance=E(x) =

$np = 35(0.23)\\= 8.05$

b) the variance

= $npq = 8.05(0.77) \\=6.1985$

Std dev = square root of variance = 2.4897

6 0

3 years ago

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that

FromTheMoon [43]

Answer:

The Taylor series is $\ln(x) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{(x-3)^n}{3^n n}$ .

The radius of convergence is $R=3$ .

Step-by-step explanation:

<em>The Taylor expansion.</em>

Recall that as we want the Taylor series centered at $a=3$ its expression is given in powers of $(x-3)$ . With this in mind we need to do some transformations with the goal to obtain the asked Taylor series from the Taylor expansion of $\ln(1+x)$ .

Then,

$\ln(x) = \ln(x-3+3) = \ln(3(\frac{x-3}{3} + 1 )) = \ln 3 + \ln(1 + \frac{x-3}{3}).$

Now, in order to make a more compact notation write $\frac{x-3}{3}=y$ . Thus, the above expression becomes

$\ln(x) = \ln 3 + \ln(1+y).$

Notice that, if x is very close from 3, then y is very close from 0. Then, we can use the Taylor expansion of the logarithm. Hence,

$\ln(x) = \ln 3 + \ln(1+y) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{y^n}{n}.$

Now, substitute $\frac{x-3}{3}=y$ in the previous equality. Thus,

$\ln(x) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{(x-3)^n}{3^n n}.$

<em>Radius of convergence.</em>

We find the radius of convergence with the Cauchy-Hadamard formula:

$R^{-1} = \lim_{n\rightarrow\infty} \sqrt[n]{|a_n|},$

Where $a_n$ stands for the coefficients of the Taylor series and $R$ for the radius of convergence.

In this case the coefficients of the Taylor series are

$a_n = \frac{(-1)^{n+1}}{ n3^n}$

and in consequence $|a_n| = \frac{1}{3^nn}$ . Then,

$\sqrt[n]{|a_n|} = \sqrt[n]{\frac{1}{3^nn}}$

Applying the properties of roots

$\sqrt[n]{|a_n|} = \frac{1}{3\sqrt[n]{n}}.$

Hence,

$R^{-1} = \lim_{n\rightarrow\infty} \frac{1}{3\sqrt[n]{n}} =\frac{1}{3}$

Recall that

$\lim_{n\rightarrow\infty} \sqrt[n]{n}=1.$

So, as $R^{-1}=\frac{1}{3}$ we get that $R=3$ .

8 0

4 years ago

You are performing an experiment in your lab. to compare with other experiments your results must be in moles. during your final

Black_prince [1.1K]

4.6 moles in 187 grams of magnesium oxide (mgo).

<h3>What is mole explain with example?</h3>

One mole is defined as the amount of substance containing as many elementary entities (atoms, molecules, ions, electrons, radicals, etc.) as there are atoms in 12 grams of carbon - 12(6. 023×1023).
The mass of one mole of a substance equals to its relative molecular mass expressed in grams.
The relative formula mass of a compound is calculated by adding together the relative atomic mass values for all the atoms in its formula.
Moles are units used to measure substance amount. Chemistry (Single Science) Atomic structure.

To solve ,

number of moles is equals to the mass in grams divided by RFM

RFM=16+24.3=40.3

=187/40.3

=4.6 moles of MgO

Learn more about relative formula mass brainly.com/question/20664635

#SPJ4

7 0

2 years ago

During a sale, every item in a store is 80% of its regular price. If the regular price of a T-shirt is $10, what is its sale pri

kipiarov [429]

Answer:

Step-by-step explanation:

If the regular price of a T-shirt is 10 USD and the store sells off its wares at 80% of its regular price, then the price at which the store would still the aforementioned T-shirt would be 80% of its 10 USD price.

80% of $10 =

0.8 * 10 = $8

This means that the price at which the T-shirt will go for, due to the ongoing sales will be $8.

Also, being asked to find the 10% and 20% of $10 is just as simple

10% of $10 =

0.1 * 10 = $1

20% of $10 =

0.2 * 10 = $2

Therefore, the 10% and 20% of $10 is $1 and $2 respectively.

3 0

3 years ago

What is the expression for "the sum of 8 times a number and two"?

sweet-ann [11.9K]

The sum= +.

The + of 8 * a number (let number=n) and 2.

8n+2

8 is being multiplied by a number n, and then added to 2.

I hope this helps!
~kaikers

3 0

3 years ago

Read 2 more answers