MATHEMATICS HIGH SCHOOL

A company that translates books between various languages is currently testing a computer-based translation service. The founder of the company expects the computer program to make some errors, but then so do human translators. The computer error rate is supposed to be an average of 2 per 500 words of translation. Suppose the company founder randomly selects a 3,000-word passage. Assume that the Poisson distribution applies and that the computer error rate is actually 2 errors per 500 words. Complete parts a through c.a. Determine the probability that no errors will be found.
The probability is _. Round to four decimal places as needed.)

b. Calculate the probability that more than 30 errors will be found.
The probability is _. (Round to four decimal places as needed.)

c. Find the probability that fewer than 15 errors will be found.
The probability is ___. (Round to four decimal places as needed.)

Answers

Answer 1

Answer:

The probability that noerrors will be found is 0.

The probability of finding more than 30 errors is 0.0001.

The probability of finding fewer than 15 errors is 0.9452.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The number of errors in a 3,000-word passage follows a Poisson distribution with a mean of 12 errors.

i.e

Since 3,000 is six times 500.

The probability that no errors will be found.

P(X = 0) = $e^(-12)$ x $12^0$ / 0!

= 0.000006

Rounded to four decimal places.

= 0.0000.

The probability of finding more than 30 errors.

P(X > 30) = 1 - P(X ≤ 30)

We can use a Poisson table.

P(X ≤ 30) = 0.9999.

P(X > 30) = 1 - 0.9999

= 0.0001

Rounded to four decimal places.

= 0.0001.

The probability of finding fewer than 15 errors.

P(X < 15) = P(X <= 14)

= ∑(k=0 to 14) $e^(-12)$ x $12^k$ / k!

From the Poissontable.

P(X ≤ 14) = 0.9452

P(X < 15) = P(X ≤ 14)

= 0.9452

Rounded to four decimal places.

= 0.9452.

Thus,

The probability that no errors will be found is 0.

The probability of finding more than 30 errors is 0.0001.

The probability of finding fewer than 15 errors is 0.9452.

Learn more about probability here:

brainly.com/question/14099682

#SPJ2

Answer 2

Answer:

Step-by-step explanation:

this is the answer of this question

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the total cost for 8 bracelets; including shipping was $54. the shipping charge was $6. Define your variable and write a. equation that models the cost of each bracelet.

Need answer please

Answers

16.8. dhsjdjdjdjdjdjdjdhd

Answer:

Volume = 16.8

Step-by-step explanation:

v= $\pi$ r²h/3

v= $\pi$ 2²4/3

v= $\pi$ 16/3

v=16.755

8) Kim rolls a white die and a red die. What is the probability that the sum of her two diceis 10?

Answers

Answer:

The probability is really close.

Step-by-step explanation:

10/2 = 5. So both die must land on a 5.

Answer:

there is a 18.75% chance of rolling a sum of 10

Step-by-step explanation:

Question 3 (1 point)Cynthia drove 12 miles in 4.8 minutes. How long would it take her to drive 37 miles? "

Answers

Answer:

14.8 minutes

Step-by-step explanation:

4.8 min/12mi= 0.4 min/1 mile driven

multiply the time by the distance:

37mi*(.4min/1mi), mi cancels and you're left with min

37*0.4=14.8 min

D=RT; 12=R*(.08 hours); R=150mph
Now, 37=150*T; T=37/150=14.8 minutes

The base of a cone can beA. an ellipse
B. a square
C. a triangle
D. a pentagon

Answers

a cone has frequently, though not necessarily, circular base
so i think that the answer is A. an ellipse

the answer is a. an elipse

(x-5) divided by (x^2+3x-40)

Answers

Answer:

1/ x +8

*The 1 over x + 8

Answer:

$(1)/(x+8)$

Step-by-step explanation:

Here is your original equation:

$(x-5)/(x^(2) +3x-40)$

What we need to focus on is simplification, specifically simplifying the denominator. First, let's isolate the denominator (we'll get back to $x-5$ later):

$x^(2) +3x-40$

Next, we take a look at -40. Our goal is to find what factors of 40 create a sum of 3 so we can separate the equation for polynomial division.

Let's begin building our expressions. We know that $x^(2)$ has an exponent of 2. When variables are multiplied, the exponents are added, meaning that $x*x=x^(2)$ . (Or $x^(1) + x^(1) =x^(2)$ , the 1s just don't show)

We can also see that -40 is a negative number. A negative multiplied by a positive makes a negative product, so we can also include one positive and one negative in each expression.

$x^(2) +3x-40 = (x+)(x-)$

Next, let's look at the factors of 40:

1 and 40 2 and 20 4 and 10 5 and 8

Which of these factors can make a sum of 3? Remember that one number has to be positive and the other has to be negative!

$8-5=3$

In this instance, our positive number is 8 and our negative number is 5. They create the sum of 3 that we're splitting in $3x$ . Therefore, $8(-5)=-40$ .

$x^(2) +3x-40 = (x+8)(x-5)$

Now let's go back to our original equation and substitute our old expression with the new one:

$(x-5)/((x+8)(x-5))$

Do you notice that the numerator and part of the denominator are equal? This means that they can cancel each other out! Think of it as a $(1)/(1)$ .

$(x-5)/((x+8)(x-5))$ = $(1)/(x+8)$

Therefore, your simplified answer is $(1)/(x+8)$ !

Here's the whole process:

$(x-5)/(x^(2) +3x-40) \n\n(x+?)(x-?)\n\n40:\n1, 40\n2, 20\n4, 10\n5, 8\n\n8-5=3 \n(8x-5x=3x)\n\n(x+8)(x-5)\n\n(x-5)/((x+8)(x-5))=(1)/(x+8) \n\n(1)/(x+8)$

To check your answer, confirm your expressions using the box method attached.

I hope this helps! If you have any more questions or concerns about the answer or the process, let me know!

The probability that Emma has heart disease is 0.6. She decides to take a test for the disease that is 80% accurate. What is the probability that Emma has heart disease and the test predicts heart disease?

Answers

Answer:

The probability that Emma has heart disease and the test predicts heart disease is:

48%

Step-by-step explanation:

Let A denote the event that Emma has a heart disease.

and B denote the event that the test predicts accurate.

Hence, A∩B denote the event that Emma has heart disease and the test predicts heart disease.

From the given equation we have:

P(A)=0.6

and P(B)=80%=0.8

As we know that event A and event B are independent.

Hence, we have:

P(A∩B)=P(A)×P(B)

⇒ P(A∩B)=0.6×0.8

⇒ P(A∩B)=0.48=48%

Hence, the probability is:

48%

0.6 x 0.8 = 12/25 The probability that Emma has heart disease and the test predicts it is 48%

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