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Nostrana [21]
2 years ago
5

A botany student drew a sketch of a birch tree using a scale of 1 inch:2 meters. Find the

Mathematics
1 answer:
Helga [31]2 years ago
4 0

Answer:

6 meters

Step-by-step explanation:

^_^

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A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A
Zigmanuir [339]

Answer:

The probability that all 4 selected workers will be from the day shift is, = 0.0198

The probability that all 4  selected workers will be from the same shift is = 0.0278

The probability that at least two different shifts will be represented among the selected workers is = 0.9722

The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5256

Step-by-step explanation:

Given that:

A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 4 of these workers for in-depth interviews:

The number of selections result in all 4 workers coming from the day shift is :

(^n _r) = (^{10} _4)

=\dfrac{(10!)}{4!(10-4)!}

= 210

The probability that all 5 selected workers will be from the day shift is,

\begin{array}{c}\\P\left( {{\rm{all \ 4 \  selected   \ workers\  will \  be  \ from  \ the \  day \  shift}}} \right) = \frac{{\left( \begin{array}{l}\\10\\\\4\\\end{array} \right)}}{{\left( \begin{array}{l}\\24\\\\4\\\end{array} \right)}}\\\\ = \frac{{210}}{{10626}}\\\\ = 0.0198\\\end{array}

(b) The probability that all 4 selected workers will be from the same shift is calculated as follows:

P( all 4 selected workers will be) = \dfrac{ (^{10}_4) }{(^{24}_4)}+\dfrac{ (^{8}_4) }{(^{24}_4)} + \dfrac{ (^{6}_4) }{(^{24}_4)}

where;

(^{8}_4) } = \dfrac{8!}{4!(8-4)!} = 70

(^{6}_4) } = \dfrac{6!}{4!(6-4)!} = 15

∴ P( all 4 selected workers is ) =\dfrac{210+70+15}{10626}

The probability that all 4  selected workers will be from the same shift is = 0.0278

(c) What is the probability that at least two different shifts will be represented among the selected workers?

P ( at least two different shifts will be represented among the selected workers)  = 1-\dfrac{ (^{10}_4) }{(^{24}_4)}+\dfrac{ (^{8}_4) }{(^{24}_4)} + \dfrac{ (^{6}_4) }{(^{24}_4)}

=1 - \dfrac{210+70+15}{10626}

= 1 - 0.0278

The probability that at least two different shifts will be represented among the selected workers is = 0.9722

(d)What is the probability that at least one of the shifts will be unrepresented in the sample of workers?

The probability that at least one of the shifts will be unrepresented in the sample of workers is:

P(AUBUC) = \dfrac{(^{6+8}_4)}{(^{24}_4)}+ \dfrac{(^{10+6}_4)}{(^{24}_4)}+ \dfrac{(^{10+8}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0

P(AUBUC) = \dfrac{(^{14}_4)}{(^{24}_4)}+ \dfrac{(^{16}_4)}{(^{24}_4)}+ \dfrac{(^{18}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0

P(AUBUC) = \dfrac{1001}{10626}+ \dfrac{1820}{10626}+ \dfrac{3060}{10626}-\dfrac{15}{10626}-\dfrac{70}{10626}-\dfrac{210}{10626} +0

The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5256

5 0
2 years ago
Find the volume of the cone to the nearest whole number. Radius is 2 and height is 4
KonstantinChe [14]

Volume of the cone is 17 cm³

Step-by-step explanation:

  • Step 1: Volume of a cone = 1/3 πr²h. Find volume of the cone where r = 2 inches and h = 4 cm.

Volume = 1/3 × 3.14 × 2² × 4

             = 16.75 cm³ ≈ 17 cm³ (rounding off to nearest whole number)

6 0
3 years ago
You guys can do at least 2 sentences or 3<br>thank you ​
aalyn [17]
If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if it cannot be written in this form, then it is irrational.
5 0
2 years ago
A RIGHT triangle has three sides: a, b, c such that a=b and LaTeX: a^2\:+\:b^2\:=\:c^2 a 2 + b 2 = c 2 What is the ratio of the
Alex_Xolod [135]

Answer:

c=b\sqrt{2}

Step-by-step explanation:

Refer to the attached image.

A right triangle is considered so when one of its corners are 90°.

If sides a and b are equal in length, then  the corners across from them are equal in size as well.

The only way for this to be possible is if both corners A and B(opposite of sides a and b) are 45°.

Pythagorean theorem

This theorem states that the square of a right triangle's long side is equal to the sum of the squares of the shorter sides.

In this case:

a^{2} +b^{2} =c^{2}

but since:

a=b

the equation can be solved by replacing a with b in the equation:

b^{2} +b^{2} =c^{2} \\2b^{2}=c^{2} \\\sqrt{2b^{2} } = c\\b\sqrt{2} =c

7 0
3 years ago
Multiples of 6 are also multiples of 3
Black_prince [1.1K]

Answer:

(☞゚ヮ゚)☞

Step-by-step explanation:

5 0
3 years ago
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