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2 months ago

Guest #2392696

2 months ago

Given that the equation of the revenue is R=2x2+55x+10 and the equation of the cost is C=2x2 – 15x – 40, you will get the profit by subtracting the revenue from the cost: R-C=P. Therefore, P=(2x2+55x+10)-(2x2 – 15x – 40). You will get P=70x+50 where x is is the number of cellphones sold. If 240 cellphones are sold, then the profit is 16850 dollars.

Guest #2392697

2 months ago

**Answer:**

**70x + 50; $16, 850**

Question

Find the errors in each of the following statements: (a) The probabilities that an automobile salesperson
will sell 0, 1, 2, or 3 cars on any given day in February
are, respectively, 0.19, 0.38, 0.29, and 0.15.
(b) The probability that it will rain tomorrow is 0.40,
and the probability that it will not rain tomorrow
is 0.52.
(c) The probabilities that a printer will make 0, 1, 2,
3, or 4 or more mistakes in setting a document are,
respectively, 0.19, 0.34,−0.25, 0.43, and 0.29.
(d) On a single draw from a deck of playing cards, the
probability of selecting a heart is 1/4, the probability
of selecting a black card is 1/2, and the probability
of selecting both a heart and a black card is
1/8.

Solution 1

The **error **in the given options are the sum of probability given **greater **than 1, the **negative value **of the probability and the wrong value given in (d).

**Probability **is the branch of Mathematics that deals with the measurement of the chance of occurrence of a** random event**.

The probability of any event always lie in the **close interval** of 0 and 1 [0,1].

The given **options **can be examined one by one as follows.

(a) The sum of the probabilities is given as,

⇒ 0.19 + 0.38 + 0.29 + 0.15 = 1.01

Since, the sum of the probabilities cannot be greater than 1.

The given statement is incorrect.

(b) The probability of complementary event is the difference of 1 and the

probability of that event.

It implies P(rain) = 1 - P(not rain)

Here, P(rain) = 0.40 and P(not rain) = 0.52 which do not form the **complementary pair**.

Thus, the given statement is incorrect.

(c) The probability of an event cannot be **negative**.

Thus, the given statement is incorrect.

(d) The given probabilities are calculated as,

P(heart) = Number of hearts ÷ Total cards

⇒ 4/52 = 1/13

Which is given 1/4 in the given option.

Thus, the given statement is incorrect.

Hence, the error in the given **statements **are found by using the **properties **of probability.

To know more about **probability **click on,

#SPJ2

Solution 2

**Answer:**

fff

**Step-by-step explanation:**

f4r

Question

Toms of Maine sells toothpaste in a tube advertised to contain 8 ounces. In their continuous production process, the amount of toothpaste put in a tube is normally distributed with a mean of 8.21 ounces and a standard deviation of 0.09 ounces. If the actual capacity of the tubes used is 8.45 ounces, what proportion of the tubes will be filled beyond capacity?

Solution 1

**Answer:**

And we can find this probability using the z table or excel:

**Step-by-step explanation:**

**Previous concepts **

**Normal distribution**, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The **Z-score** is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

**Solution to the problem **

Let X the random variable that represent the amount of toothpasye of a population, and for this case we know the distribution for X is given by:

Where and

The capacity is 8.45 ounces and we are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the z table or excel:

Question

Two additional jurors are needed to complete a jury for a criminal trial. There are six prospective jurors, two women and four men. Two jurors are randomly selected from the six available.a Define the experiment and describe one sample point. Assume that you need describe only the two jurors chosen and not the order in which they were selected.b List the sample space associated with this experiment.c What is the probability that both of the jurors selected are women?

Solution 1

**Answer:**

We need to select two people from the 6 choices available. Let us denote the women by W1, W2 and denote men by M1, M2, M3 and M4.

The experiment is to choose two people among the 6. It is given that the order of selection does not matter. Therefore, M1 M2 is the same as M2 M1.

One sample point is M1, M2. Its description is that when choosing two people from 6 available, we choose Man 1 and Man 2 to be the part of the jury.

**Step-by-step explanation:**

Question

Suppose that a worker in Caninia can produce either 2 blankets or 8 meals per day, and a worker in Felinia can produce either 5 blankets or 1 meal per day. Each nation has 10 workers. For many years, the two countries traded, each completely specializing according to their respective comparative advantages. Now war has broken out between them and all trade has stopped. Without trade, Caninia produces and consumes 10 blankets and 40 meals per day and Felinia produces and consumes 25 blankets and 5 meals per day. The war has caused the combined daily output of the two countries to decline by

Solution 1

**Answer:**

The answer to the question is

The war has caused the combined daily output of the two countries to decline by 50%

**Step-by-step explanation:**

To solve this we have

a worker at Caninia produce Blankets = 2 and Meals = 8

a worker at Felinia produce Blankets = 5 and Meals = 1

Each country has 10 workers, therefore, total production rate for each of the two countries is

Caninia produce Blankets = 20 and Meals = 80

Felinia produce Blankets = 50 and Meals = 10

Total production = Blankets = 70 and Meals = 90

Without trade between the two countries we have

Caninia produce Blankets = 10 and Meals = 40

Felinia produce Blankets = 25 and Meals = 5

Total production = Blankets = 35 and Meals = 45

Therefore the war has caused the combined daily output of the two countries to decrease by

Initial total production = Blankets = 70 and Meals = 90

Present total production = Blankets = 35 and Meals = 45

Difference in production= Blankets = 35 and Meals = 45

(Decline in production)/(Initial production)×100

For blankets → (35/70)×100 = 50 % decrease

For Meals → (45/90)×100 = 50 % decrease

Total decrease in daily output for the two countries = 50 %

Question

Use the four-step procedure to solve the following problem.A mixture of 30 lbs. of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90¢ a pound. How many pounds of each kind were used to make the mixture?

Solution 1

Answer: 10lbs of the $1.5 a pound chocolate was used in the mixture.

20lbs of the 90¢ a pound chocolate was used in the mixture.

Step-by-step explanation:

Let x represent the number of pounds of the $1.5 a pound chocolate that was used in the mixture.

Let x represent the number of pounds of the 90¢ a pound chocolate that was used in the mixture.

The total number of pounds in the mixture is 30. It means that

x + y = 30

A mixture of 30 lbs. of candy sells for $1.10 a pound. This means that the total cost of 30lbs of the mixture is

30 × 1.1 = $33

This means that

1.5x + 0.9y = 33- - - - - - - - -- - 1

Substituting x = 30 - y into equation 1, it becomes

1.5(30 - y) + 0.9y = 33

45 - 1.5y + 0.9y = 33

- 1.5y + 0.9y = 33 - 45

- 0.6y = - 12

y = - 12/ - 0.6

y = 20

x = 30 - y = 30 - 20

x = 10

Question

A teacher gave a quiz to her class of 30 students. However, she misplaced one of the quizzes. The teacher calculated the mean of the 29 quizzes to be μ = 68 points. At this point, the teacher found the missing quiz. On this quiz, the student scored 98 points. What is the mean for the class of all 30 students?a. 69 b. 83
c. 65.7
d. 68

Solution 1

**Answer:**

B

**Step-by-step explanation:**

Question

A statistics student wants to compare his final exam score to his friend's final exam score from last year; however, the two exams were scored on different scales. Remembering what he learned about the advantages of Z scores, he asks his friend for the mean and standard deviation of her class on the exam, as well as her final exam score. Here is the information:

Solution 1

**Answer:**

So then the correct answer for this case is:

**B) Our student, Z= 1.50; his friend, Z=2.00. **

**Step-by-step explanation:**

Assuming this complete question:

A statistics student wants to compare his final exam score to his friend's final exam score from last year; however, the two exams were scored on different scales. Remembering what he learned about the advantages of Z scores, he asks his friend for the mean and standard deviation of her class on the exam, as well as her final exam score. Here is the information:

Our student: Final exam score = 85; Class: M = 70; SD = 10.

His friend: Final exam score = 45; Class: M = 35; SD = 5.

**The Z score for the student and his friend are: **

**A) Our student, Z= -1.07; his friend, Z= -1.14. **

**B) Our student, Z= 1.50; his friend, Z=2.00. **

**C) Our student, Z= 1.07; his friend, Z= -1.14. **

**D) Our student, Z= 1.07; his friend, Z= 1.50**

**Step-by-step explanation: **

**Previous concepts **

**Normal distribution**, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The **Z-score** is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

**Solution**

Let X the random variable that represent the scores for our student, and for this case we know that:

The z score is given by:

If we use this we got:

Let Y the random variable that represent the scores for his friend, and for this case we know that:

The z score is given by:

If we use this we got:

So then the correct answer for this case is:

**B) Our student, Z= 1.50; his friend, Z=2.00. **

Question

Tiffany makes scarves and sells them at a neighborhoodclothing store. The owner charges her $25 a day for thespace she uses. She sells each scarf for $30. Each scarfcosts her $14 to make. How many scarves must Tiffanysell per day to make a profit of at least $100 per day?Write and solve an inequality.

Solution 1

**Answer:**

8

**Step-by-step explanation:**

100 ≥ (30 - 14)x - 25

100 ≥ 16x - 25

100 + 25 ≥ 16x

125 ≥ 16x

x ≥ 7.81

Since a scarf sale can not be a fraction, she must sell at least 8 scarves daily.

Question

In a study to determine the relationship between self esteem and eating, subjects had been randomly divided into two groups. One group of subjects were individually told something intended to boost their self esteem while in the other group subjects were individually told something intended to lower their self esteem. Each subject was then individually led into a room alone and asked to count the number of chocolate chip cookies in a very large container and told they could eat as many as they liked while conducting their count. Researchers then counted the number of cookies eaten by subjects in each group. Which of the following statements is true regarding this study? Check all that apply.
This study is an observational study.
This study is blind.
This study is an experimental study.
The treatment was the number of cookies eaten.

Solution 1

ANSWER:

The correct answer is

-This study is blind.

-This study is an experimental study.

STEP-BY-STEP EXPLANATION:

This study includes a controlled treatment (in this manner it is an investigation) and subjects didn't have a clue about the idea of the treatment so it is visually impaired.

Question

A researcher is trying to determine the January temperature in regions of the United States using the degrees of latitude. After collecting data, she creates a scatterplot. Given the relationship the researcher is trying to predict, the latitude is the dependent variable and the temperature is the independent variable.True / False.

Solution 1

**Answer:**

False.

Researcher has taken the temperature as independent variable and latitude as the dependent variable which is wrong. Temperature depends on latitude. So it should be taken as dependent variable and the latitude as independent variable.

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