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klemol [59]
3 years ago
12

A council of three people is to be chosen from a group of 4 lawyers, one artist, and 3 teachers

Mathematics
1 answer:
padilas [110]3 years ago
4 0

Answer: 0.2857

<u>Step-by-step explanation:</u>

At least one teacher means exactly 1 or exactly 2 or exactly 3 teachers. Find the probability of each and add them up.

\text{One teacher}:\dfrac{3\ teachers}{8\ total\ people}\times\dfrac{5\ others}{7\ people}\times \dfrac{4\ others}{6\ people}=\dfrac{5}{28}=0.1786\\\\\\\text{Two teachers}:\dfrac{3\ teachers}{8\ total\ people}\times\dfrac{2\ teachers}{7\ people}\times\dfrac{5\ others}{6\ people}=\dfrac{5}{56}=0.0893\\\\\\\text{Three teachers}:\dfrac{3\ teachers}{8\ total\ people}\times\dfrac{2\ teachers}{7\ people}\times\dfrac{1\ teacher}{6\ people}=\dfrac{1}{56}=0.0179

One teacher + Two teachers + Three teachers = 0.2857

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Solve |5 - 8x| - 7 &lt; 8<br><br>​
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5
−
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5
−
8
x
|
<
15
|
5
-
8
x
|
<
15
Remove the absolute value term. This creates a
±
±
on the right side of the inequality because
|
x
|
=
±
x
|
x
|
=
±
x
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5
−
8
x
<
±
15
5
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x
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±
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−
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x
<
15
5
-
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x
<
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>
−
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4
x
>
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4
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8
x
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−
15
5
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x
>
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x
x
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x
<
5
2
x
<
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2
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−
5
4
x
>
-
5
4
and
x
<
5
2
x
<
5
2
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−
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4
<
x
<
5
2
-
5
4
<
x
<
5
2
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Inequality Form:
−
5
4
<
x
<
5
2
-
5
4
<
x
<
5
2
Interval Notation:
(
−
5
4
,
5
2
)
(
-
5
4
,
5
2
)

6 0
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Read 2 more answers
Consider f (x) = StartRoot x squared minus 1 EndRoot and g (x) = StartRoot x squared + 1 EndRoot. What value(s) of x would make
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Any value of x

<em></em>

Step-by-step explanation:

Given

f(x) = \sqrt{x^2 - 1}

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Required

What value of x is  f(g(x)) = g(f(x))

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f(x) = \sqrt{x^2 - 1}

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Solve the inner square

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f(g(x)) = x

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g(x) = \sqrt{x^2 + 1}

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g(f(x)) = \sqrt{x^2 - 1 + 1}

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g(f(x)) = x

Equate f(g(x)) and g(f(x))

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x = x

<em>This implies that </em>f(g(x)) = g(f(x))<em> at any value of x</em>

8 0
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