A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? We would assign a probability of to the design 1 outcome, to design 2, to design 3, to design 4, and to design 5. In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Design Number of Times Preferred 1 10 2 5 3 30 4 40 5 15 Do the data confirm the belief that one design is just as likely to be selected as another? Explain. Yes, the sum of the assigned probabilities is 1. No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely. Yes, the average of the assigned probabilities is 0.20. No, a probability of about 0.50 would be assigned using the relative frequency method if selection is equally likely.

Answers

Answer 1

Answer:

Answer:

Correct option: "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."

Step-by-step explanation:

The assumption made is that all the 5 different packages are equally likely, i.e. the probability of selecting a package is $(1)/(5)=0.20$ .

The probability distribution is shown below.

According to the probability distribution:

The probability of a person preferring design 1 is,

$P(X=1)=0.10$

The probability of a person preferring design 2 is,

$P(X=2)=0.05$

The probability of a person preferring design 3 is,

$P(X=3)=0.30$

The probability of a person preferring design 4 is,

$P(X=4)=0.40$

The probability of a person preferring design 1 is,

$P(X=5)=0.15$

So it can be seen that the probability of preferring any of the 5 designs are not same.

Thus, the designs are not equally likely.

The correct option is "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."

Answer 2

Answer:

The selection Probability determined using the relative frequency method do not match the assigned probabilities, suggesting that the data do not confirm the belief that one design is as likely to be selected as another.

The given data can be used to calculate the relative frequencies of each package design selected by the consumers.

To determine the selection probabilities using the relative frequency method, divide the number of times a design was preferred by the total number of consumers.

For example, for design 1, the selection probability would be 10/100 = 0.1.

Similarly, for design 2, the selection probability would be 5/100 = 0.05.

The selection probabilities for designs 3, 4, and 5 would be 0.3, 0.4, and 0.15 respectively.

Comparing these probabilities to the assigned probabilities, it can be observed that the assigned probabilities do not match the observed relative frequencies, indicating that the data do not confirm the belief that one design is just as likely to be selected as another.

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Which expression is the simplest form -(4x^3+x^2)+2(x^3-3x^2)

Answers

The simplest form of the given expression $(4x^(3) +x^(2) )+2 (x^(3) -3x^(2) )$ is,

$6x^(3) - 5x^(2)$ .

Here, given expression is,

$(4x^(3) +x^(2) )+2 (x^(3) -3x^(2) )$

What is simplest form of equation?

The simplest form is the smallest possible equivalent fraction of the number.

Now,

Simplest form of expression,

$(4x^(3) +x^(2) )+2 (x^(3) -3x^(2) )\n4x^(3) +x^(2) +2 x^(3) -6x^(2) \n6x^(3) - 5x^(2)$

Hence, The simplest form of the given expression $(4x^(3) +x^(2) )+2 (x^(3) -3x^(2) )$ is, $6x^(3) - 5x^(2)$ .

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Answer:

6x^3-5x^2

Step-by-step explanation:

(4x^3+x^2)+2(x^3-3x^2)

4x^3+x^2+2x^3-6x^2

4x^3+2x^3+x^2-6x^2

6x^3+x^2-6x^2

6x^3-5x^2

An elementary school is offering 3 language classes: one in Spanish, one inFrench, and one in German. The classes are open to any of the 100 students inthe school. There are 28 students in the Spanish class, 26 in the French class,and 16 in the German class. There are 12 students that are in both Spanish andFrench, 4 that are in both Spanish and German, and 6 that are in both Frenchand German. In addition, there are 2 students taking all 3 classes.(a) If a student is chosen randomly, what is the probability that he or she isnot in any of the language classes

Answers

Answer:

0.5 = 50% probability that he or she is not in any of the language classes.

Step-by-step explanation:

We treat the number of students in each class as Venn sets.

I am going to say that:

Set A: Spanish class

Set B: French class

Set C: German class

We start building these sets from the intersection of the three.

In addition, there are 2 students taking all 3 classes.

This means that:

$(A \cap B \cap C) = 2$

6 that are in both French and German

This means that:

$(B \cap C) + (A \cap B \cap C) = 6$

$(B \cap C) = 4$

4 French and German, but not Spanish.

4 that are in both Spanish and German

This means that:

$(A \cap C) + (A \cap B \cap C) = 4$

$(A \cap C) = 2$

2 Spanish and German, but not French

12 students that are in both Spanish and French

This means that:

$(A \cap B) + (A \cap B \cap C) = 12$

$(A \cap B) = 10$

10 Spanish and French, but not German

16 in the German class.

This means that:

$(C - B - A) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 16$

$(C - B - A) + 2 + 4 + 2 = 16$

$(C - B - A) = 8$

8 in only German.

26 in the French class

$(B - C - A) + (A \cap B) + (B \cap C) + (A \cap B \cap C) = 26$

$(B - C - A) + 10 + 4 + 2 = 26$

$(B - C - A) = 10$

10 only French

28 students in the Spanish class

$(A - B - C) + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 16$

$(A - B - C) + 10 + 2 + 2 = 28$

$(A - B - C) = 14$

14 only Spanish

At least one of them:

The sum of all the above values. So

$(A \cup B \cup B) = 14 + 10 + 8 + 10 + 2 + 4 + 2 = 50$

None of them:

100 total students, so:

$100 - (A \cup B \cup B) = 100 - 50 = 50$

(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?

50 out of 100. So

50/100 = 0.5 = 50% probability that he or she is not in any of the language classes.

A bookshelf is 3 feet long. Each book on the shelf is 3/4 inches wide. How many books will fit on the shelf? (Remember, there are 12 inches in a foot.)

Answers

Answer:

Step-by-step explanation:

3 feet is 36 inches. 3/4 of an inch is .75 inches. So you have a very simple equation of 36/.75=48

Perform the operation. (10x2 – 10x – 6) + (x+6)

Answers

Answer:

10x² - 9x

Step-by-step explanation:

(10x² - 10x - 6) + (x + 6)

10x² - 10x - 6 + x + 6

10x² - 9x - 6 + 6

10x² - 9x

What is the lateral surface area of this cylinder? r = 7ft h = 16ft Answers:

702.96 sq ft
703.36 sq ft
703.96 sq ft
704.36 sq ft

Answers

Answer:

703.36 sq ft

Step-by-step explanation:

The lateral area is the product of the circumference and the height.

LA = 2π·r·h = 2·3.14·(7 ft)(16 ft) = 703.36 ft²

_____

Comment on the answer choices

Please note this is not the actual area, which rounds to 703.72 ft². The above value is obtained only by using an inappropriate value for π. The 5-significant-digit answer is not supported by a 3-significant-digit value for π. More appropriate would be π≈3.1416.

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