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3 years ago

A school survey found that 7 out of 30 students walk to

Mathematics

1 answer:

nika2105 [10]3 years ago

5 0

Answer: 7/145

Step-by-step explanation:

The probability that the first student walks to school will be: = 7/30.

The probability of selecting the second student that walks to school will be: = 6/29.

Then we multiply both together and this will be:

= 7/30 × 6/29

= 7/145

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Show that a = −1 + √3i and b = 2 satisfy 1/a+b=1/a + 1/b

Zarrin [17]

Answer:

LHS = $\frac{1 - \sqrt3i}{4}$ = RHS = $\frac{1 - \sqrt3i}{4}$

Step-by-step explanation:

Data provided in the question:

a = −1 + √3i and b = 2

to prove:

$\frac{1}{a+b}=\frac{1}{a} + \frac{1}{b}$

Considering the LHS

⇒ $\frac{1}{a+b}$

substituting the value of a and b, we get

⇒ $\frac{1}{−1 + \sqrt3i+2}$

⇒ $\frac{1}{1 + \sqrt3i}$

on multiplying and dividing by conjugate ( 1 - √3i )

we get

$\frac{1}{1 + \sqrt3i}\times\frac{1 - \sqrt3i}{1 - \sqrt3i}$

$\frac{1 - \sqrt3i}{(1^2 - (\sqrt3i)^2}$

$\frac{1 - \sqrt3i}{1 + 3}$ (as (√i)² = -1 )

$\frac{1 - \sqrt3i}{4}$

Now,

considering the RHS

$\frac{1}{a} + \frac{1}{b}$

substituting the value of a and b, we get

⇒ $\frac{1}{-1 + \sqrt3i} + \frac{1}{2}$

⇒ $\frac{2\times1 + ( -1 + \sqrt3i)\times1}{(-1 + \sqrt3i)\times2}$

⇒ $\frac{2 + ( -1 + \sqrt3i)}{(-1 + \sqrt3i)\times2}$

⇒ $\frac{1 + \sqrt3i}{(-1 + \sqrt3i)\times2}$

now,

on multiplying and dividing by conjugate ( -1 - √3i )

we get

$\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1 - \sqrt3i}{-1 - \sqrt3i}$

$\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1( 1 + \sqrt3i)}{-1 - \sqrt3i}$

$\frac{(1 + \sqrt3i}^2\times(-1){((-1)^2 - (\sqrt3i)^2)\times2}$

$\frac{(1^2 + (\sqrt3i)^2+2(1)(\sqrt3i)\times(-1)}{(1 + 3)\times2}$

$\frac{(1 - 3 + 2\sqrt3i)\times(-1)}{(4)\times2}$

$\frac{(-2 + 2\sqrt3i)\times(-1)}{(4)\times2}$

$\frac{-2( 1 - 2\sqrt3i)\times(-1)}{(4)\times2}$

$\frac{( 1 - 2\sqrt3i)}{(4)}$

Since, LHS = RHS

hence satisfied

3 0

3 years ago

Find the difference 7,299.04subtract 238.40

nalin [4]

I think it is 7060.54 it was all mental sorry

5 0

4 years ago

A large water bottle holds 32 fluid ounces, which is 0.946353 liters. Round this decimal to the nearest thousandth.

Tatiana [17]

Answer:

0.946 liters

Step-by-step explanation:

since the fourth decimal place is below 5, you would not round up the thousandths. also, the thousandths is the third decimal place (tenths, hundredths, thousandths).

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3 years ago

Use the drop-down menus to complete each equation so the statement about its solution is true.

disa [49]

Answer:

Step-by-step explanation:

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3 years ago

There were 125 females and 100 males present at the high school pep rally. Find the ratio of males to the total number of people

riadik2000 [5.3K]

Total number of people = 125 + 100 = 225

Number of males = 100

Set as ratio

100:225

Simplify to 4:9 (can not simplify further without having decimals but you can’t have half a person)

5 0

3 years ago