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3 years ago

Multiply: (5x − 2)(4x2 − 3x − 2)

Mathematics

2 answers:

Nataliya [291]3 years ago

8 0

Answer:

$20 x^3 - 23 x^2 - 4 x + 4$

Step-by-step explanation:

$(5x-2)(4x^2-3x-2)\\$

Here we use distributive law and distribute 5x and -2 over two brackets

$5x(4x^2-3x-2)-2(4x^2-3x-2)\\$

Now we are goinf to multiply 5x and 2 with each term inside the brackets

$(5x*4x^2-5x*3x-5x*2)-(2*4x^2-2*3x-2*2)$

Simplify

$20x^3-15x^2-10x- (8x^2-6x-4)$

$20x^3-15x^2-10x- 8x^2+6x+4$

bringing terms with same degree together and simplifying we get

$20x^3-15x^2-8x^2-10x+6x+4$

$20x^3-23x^2-4x+4$

Answer

Alex Ar [27]3 years ago

3 0

Hello there!

(5x - 2)(4x² - 3x - 2)

Use the distributive property

=(5x)(4x²) + (5x)(-3x) + (5x)(-2) + (-2)(4x²) + (-2)(-3x)² + (-2)(-2)

= 20x³ - 15x² - 10x - 8x² + 6x + 4

= 20x³ - 23x² -4x + 4

As always, it is my pleasure to help students like you. Let me know if you have any questions.

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3 years ago

The ratio of the number of fiction book is 9:4, the different between the number of fiction and non fiction is 245

Evgesh-ka [11]

Answer:

Step-by-step explanation:

The ratio of the number of fiction books is 9:4

the difference between the number of fiction and nonfictionn is 245

so if the number of fiction books = 9x

then the number of nonfiction books = 4x

then difference = 9x-4x = 5x

the difference is given 245

then 5x= 245

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2 years ago

A data mining routine has been applied to a transaction dataset and has classified 88 records as fraudulent (30 correctly so) an

Firlakuza [10]

Answer:

The classification matrix is attached below

Part a

The classification error rate for the records those are truly fraudulent is 65.91%.

Part b

The classification error rate for records that are truly non-fraudulent is 96.64%

Step-by-step explanation:

The classification matrix is obtained as shown below:

The transaction dataset has 30 fraudulent correctly classified records out of 88 records, that is, 30 records are correctly predicted given that an instance is negative.

Also, there would be 88 - 30 = 58 non-fraudulent incorrectly classified records, that is, 58 records are incorrectly predicted given that an instance is positive.

The transaction dataset has 920 non-fraudulent correctly classified records out of 952 records, that is, 920 records are correctly predicted given that an instance is positive.

Also, there would be 952 - 920 = 32 fraudulent incorrectly classified records, that is, 32 records incorrectly predicted given that an instance is negative.

That is,

Predicted value

Active value Fraudulent Non-fraudulent

Fraudlent 30 58

non-fraudulent 32 920

The classification matrix is obtained by using the information related to the transaction data, which is classified into fraudulent records and non-fraudulent records.

The error rate is obtained as shown below:

The error rate is obtained by taking the ratio of $\left( {b + c} \right)(b+c)$ and the total number of records.

The classification matrix is, shown above

The total number of records is, $30 + 58 + 32 + 920 = 1,040$

The error rate is,

$\begin{array}{c}\\{\rm{Error}}\,{\rm{rate}} = \frac{{b + c}}{{{\rm{Total}}}}\\\\ = \frac{{58 + 32}}{{1,040}}\\\\ = \frac{{90}}{{1,040}}\\\\ = 0.0865\\\end{array}$

The percentage is $0.0865 \times 100 = 8.65$

(a)

The classification error rate for the records those are truly fraudulent is obtained by taking the rate ratio of b and $\left( {a + b} \right)(a+b)$ .

The classification error rate for the records those are truly fraudulent is obtained as shown below:

The classification matrix is, shown above and in the attachment

The error rate for truly fraudulent is,

$\begin{array}{c}\\FP = \frac{b}{{a + b}}\\\\ = \frac{{58}}{{30 + 58}}\\\\ = \frac{{58}}{{88}}\\\\ = 0.6591\\\end{array}$

The percentage is, $0.6591 \times 100 = 65.91$

(b)

The classification error rate for records that are truly non-fraudulent is obtained by taking the ratio of d and $\left( {c + d} \right)(c+d)$ .

The classification error rate for records that are truly non-fraudulent is obtained as shown below:

The classification matrix is, shown in the attachment

The error rate for truly non-fraudulent is,

$\begin{array}{c}\\TP = \frac{d}{{c + d}}\\\\ = \frac{{920}}{{32 + 920}}\\\\ = \frac{{920}}{{952}}\\\\ = 0.9664\\\end{array}$

The percentage is, $0.9664 \times 100 = 96.64$

6 0

3 years ago