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3 years ago

How can I solve this system of equation with substitution u+6y=32 and u+3y=17

Mathematics

2 answers:

Ne4ueva [31]3 years ago

6 0

U+6y=32 U+3y=17

Solve U+6y=32 for u

Add -6y to both sides

U+6y-6y=32-6y U= -6y+32

Substitute -6y+32 for U in U+3y=17 U+3y=17 -6y+32+3y=17

Simplify both sides of the equation -3y+32=17

Add -32 to both sides -3y+32-32=17-32 -3y=-15

Divide both sides by -3 -3y/-3 = -15/-3 Y=5

Substitute 5 for y in U=-6y+32 U= -6y+32

U= (-6)(5)+32 u= -30 +32 U= 2

Answer : U= 2 and Y=5

I hope that's help and have a great night !

gayaneshka [121]3 years ago

5 0

U= 32 - 6y
u = 17 - 3y

Step 1
32 - 6y = 17 - 3y

Step 2
-6y + 3y = 17 - 32

Step 3
-3y = - 15

Step 4
3y = 15

Step 5
y = 15/3

Step 6
y = 5

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3 years ago

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Assoli18 [71]

Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

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

chubhunter [2.5K]

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, $0.9664 \times 100 = 96.64$

8 0

3 years ago

a piece of land 120 ft by 240 ft contains a circular garden. surrounding the garden, there is a circular fence that is 20 ft in

damaskus [11]

the area of the piece of land that is not part of the garden is $28,486ft^2$ .

<u>Step-by-step explanation:</u>

Here we have , a piece of land 120 ft by 240 ft contains a circular garden. surrounding the garden, there is a circular fence that is 20 ft in diameter. We need to find what is the area of the piece of land that is not part of the garden . Let's find out:

Let's calculate area of land and circular garden , and in order to find the area of the piece of land that is not part of the garden we will subtract area of circular garden from land !

Area of Land:

Area of land is given by

⇒ $length(width)$

⇒ $120(240)$

⇒ $28,880ft^2$

Area of Garden:

Area of circular garden given by

⇒ $\pi r^2$

⇒ $\pi (\frac{D}{2})^2$

⇒ $\pi (\frac{20}{2})^2$

⇒ $\pi (10)^2$

⇒ $100\pi$

⇒ $100(3.14)$

⇒ $314ft^2$

Hence , the area of the piece of land that is not part of the garden is 28,880-314 = 28,486 . Therefore , the area of the piece of land that is not part of the garden is $28,486ft^2$ .

8 0

3 years ago