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Mathematics

1 answer:

Dovator [93]3 years ago

5 0

The simplest exact fraction for the decimal number 0.123 is 1231000

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In the diagram of O, m∠JOK = 60° and OJ = 6 in. What is the exact area of the shaded region?

Sophie [7]

Answer: 6π

Step-by-step explanation:

Area of a circle is π r².

Area of a section of a circle is π r² × the section of the circle.

$A=\pi r^2\bigg(\dfrac{\theta}{360^o}\bigg)$

Given: r = 6, Ф = 60°

$A=\pi (6)^2\bigg(\dfrac{60^o}{360^o}\bigg)\\\\\\.\quad =\pi (6)^2\bigg(\dfrac{1}{6}\bigg)\\\\\\.\quad =6\pi$

3 0

3 years ago

Let \[f(x) = \frac{3x - 7}{x + 1}.\]find the range of $f$. give your answer as an interval.

ra1l [238]

Hello :
let : $y= \frac{3x-7}{x+1}$
calculate : x ......x ≠ -1
 $y(x+1) = 3x-7$
$yx+y =3x-7$
$yx-3x = -y-7$
$x(y-3) = -7-y$
$x = \frac{y+7}{3-y}$
the inverse function is : $g(x) = \frac{x+7}{3-x}$
domain of : g is the range of : f
as an interval : ]-∞: 3 [U ]3;+∞[

7 0

4 years ago

In a certain lottery, an urn contains balls numbered 1 to 26. From this urn, 6 balls are chosen randomly, without replacement

expeople1 [14]

Answer:

\frac{1}{230230}

Step-by-step explanation:

Given that in a certain lottery, an urn contains balls numbered 1 to 26

From this urn, 6 balls are chosen randomly, without replacement.

Bet amount 1 dollar and he selects a set of six numbers.

If these match with those chosen from the urn he wins (order does not matter)

Total ways of choosing 6 out of 26 = $26C6 = \frac{26!}{20!6!} \\=230230$