MATHEMATICS COLLEGE

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__ .

Answers

Answer 1

Answer:

0.74 to 6.06

Step-by-step explanation:

The groups are independnet,

SE(xh bar-xa bar)=sqrt [sh^2/nh+sa^2/na]=sqrt [10.1^2/80+10.3^2/80]=1.61

At df=157, the t critical is 1.65

90%c.i=(xh bar-xa bar)+-tcritical SE(xh bar-xa bar)

=(25.2-21.8)+-1.65*1.61

=0.74 to 6.06

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After writing a $800 check to pay a bill, a student had a balance of $350 in his account. How muchdid he have in the account before he wrote the check?
a) Let X = his balance before writing the check. Write the equation you would use to solve this
problem.

Answers

The equation to solve the problem is X - $800 = $350. And the amount in his account before he wrote the check is $1150.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that after writing an $800 check to pay a bill, a student had a balance of $350in his account.

We need to find out how much did he have in the account before he wrote the check.

The amount of the check = $800

The amount the student has in balance = $350

The amount the student had before he wrote the check.

Let X be the amount the student had before the check.

Now,

X - $800 = $350

X - 800 = 350 is our equation to find the amount the student has before the check.

The value of X can be written as,

We have,

X - $800 = $350

Add $800 on both sides

X = $350 + $800

X = $1150

Hence, the equation to solve the problem is X - $800 = $350. And the amount in his account before he wrote the check is $1150

Learn more about Equation here:

brainly.com/question/14686792

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Answer:

x=800+350

Step-by-step explanation:

The money spent plus the money he has left would equal the money he had in the first place.

A small regional carrier accepted 19 reservations for a particular flight with 17 seats. 14 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 52% chance, independently of each other. (Report answers accurate to 4 decimal places.)1. Find the probability that overbooking occurs.
2. Find the probability that the flight has empty seats.

Answers

Answer:

(a) The probability of overbooking is 0.2135.

(b) The probability that the flight has empty seats is 0.4625.

Step-by-step explanation:

Let the random variable X represent the number of passengers showing up for the flight.

It is provided that a small regional carrier accepted 19 reservations for a particular flight with 17 seats.

Of the 17 seats, 14 reservations went to regular customers who will arrive for the flight.

Number of reservations = 19

Regular customers = 14

Seats available = 17 - 14 = 3

Remaining reservations, n = 19 - 14 = 5

P (A remaining passenger will arrive), p = 0.52

The random variable X thus follows a Binomial distribution with parameters n = 5 and p = 0.52.

(1)

Compute the probability of overbooking as follows:

P (Overbooking occurs) = P(More than 3 shows up for the flight)

$=P(X>3)\n\n={5\choose 4}(0.52)^(4)(1-0.52)^(5-4)+{5\choose 5}(0.52)^(5)(1-0.52)^(5-5)\n\n=0.175478784+0.0380204032\n\n=0.2134991872\n\n\approx 0.2135$

Thus, the probability of overbooking is 0.2135.

(2)

Compute the probability that the flight has empty seats as follows:

P (The flight has empty seats) = P (Less than 3 shows up for the flight)

$=P(X<3)\n\n1-P(X\geq 3)\n\n=1-[{5\choose 3}(0.52)^(3)(1-0.52)^(5-3)+{5\choose 4}(0.52)^(4)(1-0.52)^(5-4)+{5\choose 5}(0.52)^(5)(1-0.52)^(5-5)]\n\n=1-[0.323960832+0.175478784+0.0380204032]\n\n=0.4625399808\n\n\approx 0.4625$

Thus, the probability that the flight has empty seats is 0.4625.

Rewrite each fraction with a denominator of 121212.
\dfrac{3}{4} =

Answers

Answer:

9/12

Step-by-step explanation:

First you multiply 3x12 which equal 36 then you divide 36 by 4 which equal 9 so your answer is 9/12

The graph of f(x) = x2 was transformed to create the graph of g(x) = (x − 7.5)2. Which of these describes this transformation?A.
A horizontal shift to the right 7.5 units

B.
A horizontal shift to the left 7.5 units

C.
A vertical shift down 56.25 units

D.
A vertical shift up 56.25 units

Answers

Answer:

A. A horizontal shift to the right 7.5 units

Step-by-step explanation:

Replacing x with x-7.5 shifts the graph 7.5 units to the right.

In general, g(x) = f(x-h)+k will shift h units right and k units up. In this problem there is no vertical shift.

A large operator of timeshare complexes requires anyone interested in making a purchase to first visit the site of interest. Historical data indicates that 20% of all potential purchasers select a day visit, 50% choose a one-night visit, and 30% opt for a two-night visit. In addition, 10% of day visitors ultimately make a purchase, 30% of onenight visitors buy a unit, and 20% of those visiting for two nights decide to buy. Suppose a visitor is randomly selected and is found to have made a purchase. How likely is it that this person made a day visit? A one-night visit? A two-night visit?

Answers

Answer:

0.087 = 8.7% probability that this person made a day visit.

0.652 = 65.2% probability that this person made a one-night visit.

0.261 = 26.1% probability that this person made a two-night visit.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = (P(A \cap B))/(P(A))$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Made a purchase.

Probability of making a purchase:

10% of 20%(day visit)

30% of 50%(one night)

20% of 30%(two night).

$p = 0.1*0.2 + 0.3*0.5 + 0.2*0.3 = 0.23$

How likely is it that this person made a day visit?

Here event B is a day visit.

10% of 20% is the percentage of purchases and day visit. So

$P(A \cap B) = 0.1*0.2 = 0.02$

$P(B|A) = (P(A \cap B))/(P(A)) = (0.02)/(0.23) = 0.087$

0.087 = 8.7% probability that this person made a day visit.

A one-night visit?

Event B is a one night visit.

The percentage of both(one night visit and purchase) is 30% of 50%. So

$P(A \cap B) = 0.3*0.5 = 0.15$

$P(B|A) = (P(A \cap B))/(P(A)) = (0.15)/(0.23) = 0.652$

0.652 = 65.2% probability that this person made a one-night visit.

A two-night visit?

Event B is a two night visit.

The percentage of both(two night visit and purchase) is 20% of 30%. So

$P(A \cap B) = 0.2*0.3 = 0.06$

Then

$P(B|A) = (P(A \cap B))/(P(A)) = (0.06)/(0.23) = 0.261$

0.261 = 26.1% probability that this person made a two-night visit.

Need help asap
Graph f(x) = 3x + 4 and h(x) = f(x) +1

Answers

The coordinatepoints to plot on the graph are (0, 5) and (1, 8). The graph for the given functions are plotted below.

The given functions are f(x) = 3x + 4 and h(x) = f(x) +1.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, h(x)=3x+5

The graph of f(x) = 3x + 4 is as follows:

Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept: (0, 4)

The coordinatepoints to plot on the graph are (0, 4) and (1, 7)

The graph of h(x)=3x+5 is as follows:

Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept: (0, 5)

The coordinate points to plot on the graph are (0, 5) and (1, 8)

The coordinatepoints to plot on the graph are (0, 5) and (1, 8). The graph for the given functions are plotted below.