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2 years ago

1. -5(x - 2) - (x + 2) = 50

Mathematics

2 answers:

Serjik [45]2 years ago

4 0

Answer:

x = - 7

Step-by-step explanation:

Given

- 5(x - 2) - (x + 2) = 50 ← distribute parenthesis on left side

- 5x + 10 - x - 2 = 50, that is

- 6x + 8 = 50 ( subtract 8 from both sides )

- 6x = 42 ( divide both sides by - 6 )

x = - 7

Nat2105 [25]2 years ago

4 0

Answer:

(-5x - 10) - 2x = 50

-7x - 10 = 50

+10 +10

-7x = 60

-7x/7 = 60/7

x=8.57142857143 or 60/7

Step-by-step explanation:

You first distribute the -5 to X and 2 then add x and 2. Then add 10 on both sides. Next divided each side by POSITIVE 7 and decimal or fraction is ur final answer

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The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of si

OverLord2011 [107]

Answer:

a) P(x=3)=0.089

b) P(x≥3)=0.938

c) 1.5 arrivals

Step-by-step explanation:

Let t be the time (in hours), then random variable X is the number of people arriving for treatment at an emergency room.

The variable X is modeled by a Poisson process with a rate parameter of λ=6.

The probability of exactly k arrivals in a particular hour can be written as:

$P(x=k)=\lambda^{k} \cdot e^{-\lambda}/k!\\\\P(x=k)=6^k\cdot e^{-6}/k!$

a) The probability that exactly 3 arrivals occur during a particular hour is:

$P(x=3)=6^{3} \cdot e^{-6}/3!=216*0.0025/6=0.089\\\\$

b) The probability that <em>at least</em> 3 people arrive during a particular hour is:

$P(x\geq3)=1-[P(x=0)+P(x=1)+P(x=2)]\\\\\\P(0)=6^{0} \cdot e^{-6}/0!=1*0.0025/1=0.002\\\\P(1)=6^{1} \cdot e^{-6}/1!=6*0.0025/1=0.015\\\\P(2)=6^{2} \cdot e^{-6}/2!=36*0.0025/2=0.045\\\\\\P(x\geq3)=1-[0.002+0.015+0.045]=1-0.062=0.938$

c) In this case, t=0.25, so we recalculate the parameter as:

$\lambda =r\cdot t=6\;h^{-1}\cdot 0.25 h=1.5$

The expected value for a Poisson distribution is equal to its parameter λ, so in this case we expect 1.5 arrivals in a period of 15 minutes.

$E(x)=\lambda=1.5$

3 0

3 years ago

Suppose that in a senior college class of 500 students itis found that 210 smoke, 258 drink alcoholic beverages, 216 eatbetween

Katarina [22]

Answer:

a)Smoke but doesn't drink alcoholic beverages

P=0.176 or 17.6%

b)eats between meals and drinks alcoholic beverages but doesn't smoke

P=0.062 or 6.2%

c.) neither smokes nor eats between meals

P=0.342 or 34.2%

Step-by-step explanation:

Using a Venn diagram with three circles, one for each bad health habit. Let us $a$ for the students that only smoke, $b$ for only drink alcoholic beverages, and $c$ for only eat between meals. Following this logic, $d$ represents smoke and drink alcoholic beverages but not eat between meals, $e$ drink alcoholic beverages and eat between meals but not smoke, $f$ eat between meals and smoke but not drink alcoholic beverages. Finally $g$ for having all the three, this means $g=52$ .

To find $f$ , subtract 52 (the three problems) from 97 because this last number represents all the students that smoke and eat between meals, including the students that have the three bad habits. The same goes for 'd' and 'e'.

$f=97-52=45$

$e=83-52=31$

$d=122-52=70$

To find $a$ , subtract $e$ , $f$ , and $g$ from the total of smokers. This is because $e$ , $f$ , and $g$ represent smoke and at least another bad habit and $a$ represents only smoking.

$a=210-d-f-g=210-70-45-52=43$