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4 years ago

2.318181818 repeating as a mix number

1 answer:

4 0

As you can see, 18 is a constantly repeating number in this situation. So take out the 2.3 to get 0.01818..... To make infinitely long rational numbers with repeating digits into a fraction, put it over 99. so 0.1818...... would be 18/99. But since it is 0.0181818...., you have to put 18 over 990. 18/990 is 2/110, which is 1/55. Now you have to add 2.3 to 1/55 which will be 2 7/22

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Match each polynomial to the term that does not change the polynomial's classification when added to it.

zmey [24]

It all depends in what there exponents are

4 0

3 years ago

jeff pizza is cut into 8 equal pieces. he eats 1/2 of it. Samantha says he ate 2/8 of the pizza. how did she get the answer?

Volgvan

How she probably are the answer is by and by her thinking that if you eat 1/2 since half is too she put two and she thought he could only to have the two slices maybe that's how did the error went but to the right as yours actually see so you are correct and she is wrong

6 0

3 years ago

Given the table. find the slope of the line. show all work on separate sheet of paper

Eduardwww [97]

The answer is 1/-0.5 because it is increasing it’s x by 1 and it’s y is decreasing by -0.5

5 0

3 years ago

I can't seem to figure this one out. Could someone show how to do it and the answer? Thanks in advance!

vagabundo [1.1K]

Answer:

$\displaystyle (-\infty, -\frac{1}{6})$

Step-by-Step explanation:

We have the function:

$\displaystyle y=\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt$

And we want to find the interval for which y is concave upwards.

Therefore, we will need to find the second derivative of y, find its inflection points (where y''=0), and test for values.

So, let's take the derivative of both sides with respect to x. So:

$\displaystyle y^\prime=\frac{d}{dx}\Bigg[\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt\Bigg]$

By the Fundamental Theorem of Calculus:

$\displaystyle y^\prime=\frac{1}{3+x+3x^2}$

So, we will take the derivative again. Hence:

$\displaystyle y^\prime^\prime=\frac{d}{dx}\Big[\frac{1}{3+x+3x^2}\Big]=\frac{d}{dx}\Big[(3+x+3x^2)^{-1}\Big]$

We will use the chain rule. Let:

$\displaystyle u=x^{-1}\text{ and } v=3+x+3x^2$

Differentiate:

$\displaystyle y^\prime^\prime=-(3+x+3x^2)^{-2}(1+6x)$

Rewrite:

$\displaystyle y^\prime^\prime=-\frac{6x+1}{(3+x+3x^2)^2}$

So, points of inflection, where the concavity changes, is whenever the second derivative is 0 or undefined.

We can see that the second derivative will never be undefined since the denominator can never equal 0.

So, our only possible inflection points are when it's equal to 0. Hence:

$\displaystyle 0=-\frac{6x+1}{(3+x+3x^2)^2}$

Multiplying both sides by the denominator gives:

$0=-(6x+1)$

Then it follows that:

$\displaystyle x=-\frac{1}{6}$

So, our only possible point of inflection is at x=-1/6.

We will test for values less than and greater than this inflection point.

Testing for x=-1, we see that:

$\displaystyle y^\prime^\prime=-\frac{6(-1)+1}{3+(-1)+3(-1)^2}=1>0$

Since the result is positive, y is concave up for all values less than -1/6.

And testing for x=0, we see that:

$\displaystyle y^\prime^\prime=-\frac{6(0)+1}{3+(0)+3(0)^2}=-\frac{1}{3}$

Since the result is negative, y is concave down for all values greater than -1/6.

Therefore, the interval for which y is concave up is:

$\displaystyle (-\infty, -\frac{1}{6})$

Note that we use parentheses instead of brackets since at exactly x=-1/6, our graph is neither concave up nor concave down.

5 0

3 years ago

Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothes

PolarNik [594]

Answer:

Option A) 2.5

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 46

Sample mean, $\bar{x}$ = 50

Sample size, n = 25

Alpha, α = 0.05

Population standard deviation, σ = 8

First, we design the null and the alternate hypothesis

$H_{0}: \mu \leq 46\\H_A: \mu > 46$

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{50 - 46}{\frac{8}{\sqrt{25}} } =2.5$

Option A) 2.5

6 0

4 years ago