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2 years ago

Find the inverse function of h(x) = - 2/3x + 6.

Mathematics

2 answers:

sergij07 [2.7K]2 years ago

8 0

To find the inverse function, interchange the variables and solve for y.
h^-1 (x) = -9 - 3x/2

alex41 [277]2 years ago

7 0

Answer:

y = $-\frac{3}{2} x - 9$

Step-by-step explanation:

The given function h(x) = $-\frac{2}{3} x + 6$

To find the inverse function, we have to do the following steps:

Step 1: Replace h(x) by "x" and "x" by "y"

x = $-\frac{2}{3} y + 6$

Step 2: Write the function y interms of x.

Subtract 6 from both sides, we get

$x - 6 = -\frac{2}{3} y + 6 - 6$

$x - 6 = -\frac{2}{3} y$

Multiply both sides by the reciprocal of -2/3.

The reciprocal of -2/3 is -3/2.

$-\frac{3}{2} (x - 6) = -\frac{3}{2} *-\frac{2}{3} *y$

y = $-\frac{3}{2} x -\frac{3}{2} *6$

$y = -\frac{3}{2} x - 9$

The inverse function y = $-\frac{3}{2} x - 9$

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A ball is launched into the sky at 54.4 feet per second from a 268.8 meter tall building. The equation for the ball’s height, h,

worty [1.4K]

Answer:

7.41

Step-by-step explanation:

Vertical component:

S = 268.8

U = 0

V =?

A = 9.8

T=?

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3 years ago

Read 2 more answers

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 $\left( {a + b} \right)(a+b)$ .