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Ann [662]
2 years ago
6

Explain how you might use the properties of multiplication to solve 5 × 120 × 6.232 mentally. Then solve.

Mathematics
1 answer:
zysi [14]2 years ago
6 0

Answer:

Follows are the solution to this question:

Step-by-step explanation:

In this question, we apply the associative property that calculates the given  value, which can be defined as follows:  

Rule:

\bold{\to (A\times B)\times C=  A \times (B\times C)}

Let,

A= 5\\B=120\\C=6.232

put the value in the above rule:

Solve L.H.S part:

\to (5\times 120)\times 6.232\\\\\to (600)\times 6.232\\\\\to 3,739.2

Solve R.H.S part:

\to 5 \times (120 \times 6.232)\\\\\to 5 \times 747.84\\\\\to 3,739.2

So, L.H.S=R.H.S

You might be interested in
WRITE AN ALGEBRAIC EXPRESSION TO MODEL THE GIVEN CONTEXT. GIVE YOUR ANSWER IN SIMPLEST FORM. The original price  of an item le
quester [9]

Answer:

The original price of an item less a discount of 20% is 0.8p where p is the original price

Step-by-step explanation:

Here, we want to write an algebraic expression that represents the original price of an item less a discount of 20%

Let the original price of the item be p

The meaning of the ‘less’ is that we are subtracting 20% of the price from the original price ;

So 20% of the price will be 20/100 * p = 20p/100 = p/5 = 0.2p

So let’s take this away from the original price p

That will be;

p - 0.2p = p(1-0.2) = 0.8p

6 0
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
For each of the following vector fields
olga nikolaevna [1]

(A)

\dfrac{\partial f}{\partial x}=-16x+2y

\implies f(x,y)=-8x^2+2xy+g(y)

\implies\dfrac{\partial f}{\partial y}=2x+\dfrac{\mathrm dg}{\mathrm dy}=2x+10y

\implies\dfrac{\mathrm dg}{\mathrm dy}=10y

\implies g(y)=5y^2+C

\implies f(x,y)=\boxed{-8x^2+2xy+5y^2+C}

(B)

\dfrac{\partial f}{\partial x}=-8y

\implies f(x,y)=-8xy+g(y)

\implies\dfrac{\partial f}{\partial y}=-8x+\dfrac{\mathrm dg}{\mathrm dy}=-7x

\implies \dfrac{\mathrm dg}{\mathrm dy}=x

But we assume g(y) is a function of y alone, so there is not potential function here.

(C)

\dfrac{\partial f}{\partial x}=-8\sin y

\implies f(x,y)=-8x\sin y+g(x,y)

\implies\dfrac{\partial f}{\partial y}=-8x\cos y+\dfrac{\mathrm dg}{\mathrm dy}=4y-8x\cos y

\implies\dfrac{\mathrm dg}{\mathrm dy}=4y

\implies g(y)=2y^2+C

\implies f(x,y)=\boxed{-8x\sin y+2y^2+C}

For (A) and (C), we have f(0,0)=0, which makes C=0 for both.

4 0
3 years ago
If 5 friends wanted to share 1.25 of a pizza evenly how much each person get
Debora [2.8K]

0.25 = \frac{1}{4}

1.25 = 1 \frac{1}{4} = \frac{5}{4}

there are 5 quarters thus each person woud get one quarter


6 0
3 years ago
Read 2 more answers
If you are selecting courses for next semester and you have 4 options to fill your science requirement, 2 options to fill your d
schepotkina [342]

Answer: 160

Step-by-step explanation:

Given : The options to fill science requirement =4

The options to fill diversity requirement =2

The options to fill English requirement =5

The options to fill math requirement = 4

The Fundamental Counting Principle say that the number of total outcomes is equal to the product of the number of ways of all the events occur in the problem.

Using Fundamental Counting Principle, we have the total number of possible outcomes for the given situation :-

4\times2\times5\times4=160

Hence, the total number of possible outcomes = 160

5 0
3 years ago
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