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3 years ago

A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?

Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

8 0

Answer:

(x-3,y+5)

Step-by-step explanation:

5 units up would be written as: $y + 5$ .

3 units to the left would be $x - 3$ .

The rule that describes the translation of 5 units up and 3 units to the left would be:

$(x,y) \rightarrow (x-3,y+5)$

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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

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

3 years ago

What is the slope for 10,15 and 15,20

makvit [3.9K]

So it will be y1-y2, so 15-20 is -5

Then x1-x2, so 10-15 is -5.

-5/-5 = 1

There’s ya slope : 1

6 0

3 years ago

PLEASE HELP!!!!!!!!!!

erik [133]

Answer: D

Step-by-step explanation:

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3 years ago

Problem type join results unknown

Allisa [31]

Not sure what you are asking for, but,

Here is an example of a JRU (Join Result Unknown) word problem:

There were _____ kids on the playground. ____ more kids came onto the playground. How many kids are on the playground?

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There were ____ kids on the playground. Some more kids came on the playground. Now there are ____ kids on the playground. How many kids came on the playground?

Here is an example of a JSU (Join Start Unknown) word problem:

Some kids were on the playground. ____ kids came on the playground. Now there are ____ kids on the playground. How many kids were on the playground at the beginning?

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3 years ago

In an upcoming race, the top 3 finishers will be recognized with the same award. Ryan is one of 12 people entered in the race.

BARSIC [14]

Since top 3 racers recognized with the same award, answer is 3/12 or 1/4 or .25

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3 years ago

Read 2 more answers