Mark's football team has scored about 24 points each game. They played 12 games this season.What is the best estimate for the total number of points they scored in the season?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

well you could add 24+12 which equals 36

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consider a sequence of independent tosses of a biased coin at times k=0,1,2,…,n. On each toss, the probability of Heads is p, and the probability of Tails is 1−p.A reward of one unit is given at time k, for k∈{1,2,…,n}, if the toss at time k resulted in Tails and the toss at time k−1 resulted in Heads. Otherwise, no reward is given at time k.Let R be the sum of the rewards collected at times 1,2,…,n.We will find E[R] and var(R) by carrying out a sequence of steps. Express your answers below in terms of p and/or n using standard notation. Remember to write '*' for all multiplications and to include parentheses where necessary.We first work towards finding E[R].1. Let Ik denote the reward (possibly 0) given at time k, for k∈{1,2,…,n}. Find E[Ik].E[Ik]=2. Using the answer to part 1, find E[R].E[R]=The variance calculation is more involved because the random variables I1,I2,…,In are not independent. We begin by computing the following values.3. If k∈{1,2,…,n}, thenE[I2k]=4. If k∈{1,2,…,n−1}, thenE[IkIk+1]=5. If k≥1, ℓ≥2, and k+ℓ≤n, thenE[IkIk+ℓ]=6. Using the results above, calculate the numerical value of var(R) assuming that p=3/4, n=10.var(R)=

Answers

Answer:

1. p*(1-p)

2. n*p*(1-p)

3. p*(1-p)

4. 0

5. p^2*(1-p)^2

6. 57/64

Step-by-step explanation:

1. Let Ik denote the reward (possibly 0) given at time k, for k∈{1,2,…,n}. Find E[Ik].

E[Ik]= p*(1-p)

2. Using the answer to part 1, find E[R].

E[R]= n*p*(1-p)

The variance calculation is more involved because the random variables I1,I2,…,In are not independent. We begin by computing the following values.

3. If k∈{1,2,…,n}, then

E[I2k]= p*(1-p)

4. If k∈{1,2,…,n−1}, then

E[IkIk+1]= 0

5. If k≥1, ℓ≥2, and k+ℓ≤n, then

E[IkIk+ℓ]= p^2*(1-p)^2

6. Using the results above, calculate the numerical value of var(R) assuming that p=3/4, n=10.

var(R)= 57/64

Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480. Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days.

Part B: Write the equation obtained in Part A using function notation.

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Answers

First find the slope using the two points (2,225) and (5,480)
(480-225)/(5-2) = 85
Then find b.
225 = 85*2 + b
225 = 170 + b
55 = b
y = 85x + 55 OR f(x) = 85x + 55 This is the answer to PART B.
Standard form PART A is 85x - y = 55
PART C Plot the y intercept, 55. From the y intercept count the slope 85 up right 1 and plot a point, draw a line through the points
The x axis is the number of days so it would be in intervals of 1.
The y axis is money, I would do intervals of $5

Which of the following best describes a three-dimensional solid made fromtwo parallel and congruent discs not in the same plane and all the points
between them?
A. Cylinder
B. Cone
C. Cube
D. Prism

Answers

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The correct option is A.

What is a cylinder?

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

The solid is described as a three-dimensional solid made from

two parallel and congruent discs, not in the same plane, and all the points

between them is a Cylinder.

Hence, the correct option is A.

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Find the indicated probability. a bag contains four chips of different colors, including red, blue, green, and yellow. a chip is selected at random from the bag and then replaced in the bag. a second chip is then selected at random. make a list of the possible outcomes (for example rb represents the outcome red chip followed by blue chip) and use your list to determine the probability that the two chips selected are the same color. (hint: there are 16 possible outcomes.)

Answers

Answer:

0.25

Step-by-step explanation:

Let

r = red

b = blue

g = green

y = yellow

If the first chip is r, the second can be r, b, g or y. The 4 possibilities are rr, rb, rg, ry.
If the first chip is b, the second can be r, b, g or y. The 4 possibilities are br, bb, bg, by.

If the first chip is g, the second can be r, b, g or y. The 4 possibilities are gr, gb, gg, gy.

If the first chip is y, the second can be r, b, g or y. The 4 possibilities are yr, yb, yg, yy.

From the 4 + 4 + 4 + 4 = 16 possible outcomes, there are 4 in which the chips are of the same color (rr, bb, gg, yy). The probability that the two chips selected are the same color is

4/16 = 0.25 = 25%

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:

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."

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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What is $45.79 multiplied by .50 equal

Answers

Answer:

$45.79 multiplied by .50 equals 22.895

Answer:

686.85

Step-by-step explanation:

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