1.0*10^-11 + 1.0 x 10^-8

A restaurantis planning to make changes to its menu. In order to decide which potential menu items are most popular with the cit

Alex

Answer:

Simple random sampling survey method

Step-by-step explanation:

A simple random sampling is an unbiased survey technique Hence it will represent all the parts of the city's population.

In statistics, a simple random sample is a subset of individuals (a sample) chosen from a larger set (a population). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process

6 0

3 years ago

D/d{cosec^-1(1+x²/2x)} is equal to

SIZIF [17.4K]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

Let assume that

$\rm :\longmapsto\:y = {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

We know,

$\boxed{\tt{ {cosec}^{ - 1}x = {sin}^{ - 1}\bigg( \dfrac{1}{x} \bigg)}}$

So, using this, we get

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2x}{1 + {x}^{2} } \bigg)$

Now, we use Method of Substitution, So we substitute

$\red{\rm :\longmapsto\:x = tanz \: \rm\implies \:z = {tan}^{ - 1}x}$

So, above expression can be rewritten as

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2tanz}{1 + {tan}^{2} z} \bigg)$

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( sin2z \bigg)$

$\rm\implies \:y = 2z$

$\bf\implies \:y = 2 {tan}^{ - 1}x$

So,

$\bf\implies \: {cosec}^{ - 1}\bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = 2 {tan}^{ - 1}x$

Thus,

$\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

$\rm \: = \: \dfrac{d}{dx}(2 {tan}^{ - 1}x)$

$\rm \: = \: 2 \: \dfrac{d}{dx}( {tan}^{ - 1}x)$

$\rm \: = \: 2 \times \dfrac{1}{1 + {x}^{2} }$

$\rm \: = \: \dfrac{2}{1 + {x}^{2} }$

Hence, 

$\purple{\rm :\longmapsto\:\boxed{\tt{ \dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = \frac{2}{1 + {x}^{2} }}}}$

Hence, Option (d) is correct.

6 0

2 years ago

The average of two numbers is 41. If one of the numbers is 27, what is the other number?

nydimaria [60]

The other number if the average of two numbers is 41 and one is 27 is 55

<h3>How to calculate the average of numbers?</h3>

Average of number is also known as the mean.

Let the unknown number be "x" such that:

x +27/2 = 41

Determine the value of x

x + 27 = 2(41)
x + 27 = 82
x = 82 - 27

x = 55

Hence the other number if the average of two numbers is 41 and one is 27 is 55

Learn more on average here: brainly.com/question/25965491

#SPJ1

4 0

2 years ago

2. What is the minimum value of of the function below

vovangra [49]

What is the minimum value of of the function below y = 2x2 – 8x + 11 O y=-3 O y = 2 O y = 3 O y = 11

4 0

2 years ago

Orville staples is a painter who earns 30,000 a year. he is single and claims 3 allowances

babunello [35]

Using the information in the table given, the Gross pay, deductions and net pay for Orville staples are :

$30,000
$2340
$1860
$600
$450
$34.50
$15.00
$24700.50

Given the tax time table :

Social security tax = 6.2% of $97,500
Medicare = 1.45% of gross income
State tax = 2% of gross pay
Local tax = 1.5% of gross pay
Gross pay = $30,000

1.) Gross pay, total amount earned prior to tax = $30,000

2.) Using the weekly payroll for singles :

Number of weeks in a year = 52

Weekly earning = 30000/52 = 600

The Federal income tax = $25 per week (3 allowances claimed)

Total FIT = $45 × 52 = $2340

3.) Social security tax :

SS tax = 6.2% × $30,000 = $1860

4.) State tax :

2% of gross pay

2% × $30,000 = $600

5.) Local tax :

1.5% × 30,000 = $450

6.) Medical dues = $34.50

7.) Others : = $15.00

8.) Net pay = Gross pay - Total deduction

Net pay = 30000 - $(2340+1860+600+450+34.50+15)

Net pay = 30,000 - 5299.50 = $24700.50

Learn more :brainly.com/question/24919039

8 0

2 years ago