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2 years ago

What’s the difference quotient simplified

Mathematics

1 answer:

mihalych1998 [28]2 years ago

7 0

$\text{Use}\ (a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\f(x+h)\to\text{exchange x to x + h}\\\\f(x)=x^3+3x\\\\f(x+h)=(x+h)^3+3(x+h)\\\\f(x+h)=x^3+3x^2h+3xh^2+h^3+3x+3h\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{x^3+3x^2h+3xh^2+h^3+3x+3h-(x^3-3x)}{h}\\\\=\dfrac{x^3+3x^2h+3xh^2+h^3+3x+3h-x^3-3x}{h}\\\\=\dfrac{(x^3-x^3)+3x^2h+3xh^2+h^3+(3x-3x)+3h}{h}\\\\=\dfrac{3x^2h+3xh^2+h^3+3h}{h}\\\\=\dfrac{h(3x^2+3xh+h^2+3)}{h}\\\\=\boxed{3x^2+3xh+h^2+3}$

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I found a place that will give me 20% discount if i spend over $50.My nill $75.How much money will i save?

Morgarella [4.7K]

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2 years ago

Which could be a conditional relative frequency table? A 4-column table with 3 rows. The first column has no label with entries

kotykmax [81]

Answer:

<u>II. Second table</u>

A B Total

C 0.25 0.75 1.00

D 0.35 0.65 1.00

Total 0.30 0.70 1.00

Explanation:

<h2>Tables</h2>

<u>I. First table </u>

A B Total

C 0.25 0.25 0.50

D 0.25 0.25 0.50

Total 0.50 0.25 1.00

<u>II. Second table</u>

A B Total

C 0.25 0.75 1.00

D 0.35 0.65 1.00

Total 0.30 0.70 1.00

<u>III. Third table</u>

<u></u>

A B Total

C 0.75 0.25 0.50

D 0.25 0.75 0.50

Total 0.50 0.50 1.00

<u>IV. Fourth table</u>

A B Total

C 0.65 0.35 1.00

D 0.35 0.65 1.00

Total 1.00 1.00 1.00

<h2>Solution</h2>

A <em>conditional relative frequency table</em> shows the relative frequencies determined upon a row or column.

There are two types of relative conditional frequency table: 1) row conditional relative frequency, and 2) column conditional relative frequency.

When you divide the joint frequency by the marginal frequency of the column total you have the row conditional frequency table. When you dividethe joint frequency by the row total you have the colum conditional frequency table.

In a row conditional relative frequency each total of the right hand column equals 1. This is the case of the second table.

In a column conditional relative frequency each total of the bottom row equals 1. This is not happening with any of the shown tables.

Hence, only the second table could be a conditional relative frequency table.

5 0

2 years ago

Read 2 more answers

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blsea [12.9K]

Answer:

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Step-by-step explanation:

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$P(X=x)=\lambda e^{-\lambda x}, x>0$