1

3

7

13

21

Find an expression, in terms of n for the nth term of this quadratic sequence.

Answer:

9514 1404 393

**Answer:**

n² -n +1

**Step-by-step explanation:**

First differences of the terms of the sequence are ...

3-1 = 2

7-3 = 4

13-7 = 6

21-13 = 8

Second differences are ...

4-2 = 2

6-4 = 2

8-6 = 2

In a quadratic sequence the coefficient of the squared term is half of the second difference value. Here, that means the squared term will be (2/2)n² = n².

__

We can find the other terms of the quadratic expression by considering the differences between n² and the actual sequence.

The sequence of n² terms is ...

1, 4, 9, 16, 25

When we subtract these from the actual sequence, we get ...

1-1 = 0

3-4 = -1

7-9 = -2

13-16 = -3

21-25 = -4

That is, the amount subtracted from n² is one less than the term number.

The expression for the n-th term is ...

** an = n² -n +1**

A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 5%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that a) None of the LED light bulbs are defective? b) Exactly one of the LED light bulbs is defective? c) Two or fewer of the LED light bulbs are defective? d) Three or more of the LED light bulbs are not defective?

A given binomial distribution has 10 trials and probability of success p=1/3. Compute the standard deviation and explain your solution

both cylinders are emptied, and water is poured into the narrow cylinder up to the 11th mark. how high would this water rise if it were poured into the empty wide cylinder

How big is the home field advantage in the National Football League (NFL)? To investigate, we select a sample of 80 games from the 2011 regular season1 and find the home team scored an average of 25.16 points with a standard deviation 10.14 points. In a separate sample of 80 different games, the away team scored an average of 21.75 points with a standard deviation of 10.33 points. Use this summary information to find a 90%c onfidence interval for the mean home field advantage, µH- µA, in points scored.The 90% confidence interval is______ to________ .

To make a specific shade of green paint, Timia mixes 2 cups of blue paint with 10 cups of yellow point. How many cups of yellow paint should she mix with one cup of blue paint to make the same shade of green.

A given binomial distribution has 10 trials and probability of success p=1/3. Compute the standard deviation and explain your solution

both cylinders are emptied, and water is poured into the narrow cylinder up to the 11th mark. how high would this water rise if it were poured into the empty wide cylinder

How big is the home field advantage in the National Football League (NFL)? To investigate, we select a sample of 80 games from the 2011 regular season1 and find the home team scored an average of 25.16 points with a standard deviation 10.14 points. In a separate sample of 80 different games, the away team scored an average of 21.75 points with a standard deviation of 10.33 points. Use this summary information to find a 90%c onfidence interval for the mean home field advantage, µH- µA, in points scored.The 90% confidence interval is______ to________ .

To make a specific shade of green paint, Timia mixes 2 cups of blue paint with 10 cups of yellow point. How many cups of yellow paint should she mix with one cup of blue paint to make the same shade of green.

**Answer:**

12,280

**Step-by-step explanation:**

just do 1456×5 :))

The proportion of production that is defective and from plant A is

... 0.35·0.25 = 0.0875

The proportion of production that is defective and from plant B is

... 0.15·0.05 = 0.0075

The proportion of production that is defective and from plant C is

... 0.50·0.15 = 0.075

Thus, the proportion of defective product that is from plant C is

... 0.075/(0.0875 +0.0075 +0.075) = 75/170 = **15/34 ≈ 44.12%**

_____

P(C | defective) = P(C&defective)/P(defective)

The question required the use of Bayes' theorem to determine the probability of a defective product coming from plant c. Given the probabilities of defectiveness for each plant, the calculation indicated that there is approximately a 54.55% chance that a defective product came from plant c.

The problem described can be solved using **Bayes' theorem**, which is a principle in Probability that is used when we need to revise/or update the probabilities of events given new data. Since a defective product is received, and we need to determine the probability of it coming from plant c, we apply Bayes' theorem for the probability of events a, b, and c (representative of the products from the respective plants).

The Bayesian formula we will use, given the probabilities of a, b and c respectively and the probability of receiving a nondefective product from these plants, is: P(c|defective) = [P(defective|c) * P(c)] / [P(defective|a) * P(a) + P(defective|b) * P(b) + P(defective|c) * P(c)].

First, calculate the probability of a defective product from each plant (1 minus the probability of a nondefective product): these are 0.25 for plant a, 0.05 for plant b, and 0.15 for plant c.

Then substitute the values: P(c|defective) = [0.15 * 0.50] / [(0.25 * 0.35) + (0.05 * 0.15) + (0.15 * 0.5)] = 0.075 / 0.1375 = 0.5454545.

So, given a defective product, there is approximately a **54.55%** chance that it was produced by plant c.

#SPJ11

**Answer:**

[2,∞)

**Step-by-step explanation:**

The range is the y intercept and the function starts at 2 and continues going up causing the range of the function to be [2,∞)

**Answer:**

b

**Step-by-step explanation:**

Let ∠ ADC = 2β

Ac and BD are perpendicular bisectors of each other ⇒⇒ (Given information)

∴ BD bisects the angle ADC

∴ ∠ADE = 0.5 ∠ADC = β

And in ΔADE:

∵∠DEA = 90° ⇒⇒⇒ from the given information

∴∠DAE = 90° - β

And AC bisects ∠DAB ⇒⇒⇒ from the given information

∴∠EAB = ∠DAE = 90° - β

Ac and BD are perpendicular bisectors of each other ⇒⇒ (Given information)

∴ BD bisects the angle ADC

∴ ∠ADE = 0.5 ∠ADC = β

And in ΔADE:

∵∠DEA = 90° ⇒⇒⇒ from the given information

∴∠DAE = 90° - β

And AC bisects ∠DAB ⇒⇒⇒ from the given information

∴∠EAB = ∠DAE = 90° - β

<EAB = 180 - 90 - (0.5*<ADC)

**Answer:**

3/10

**Step-by-step explanation:**

3/5 se puede convertir en 6/10

(3x2)/(5x2).

9/10 - 6/10 = 3/10

le falta 3/10 para llegar a 9/10.