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WITCHER [35]
3 years ago
9

How big is the home field advantage in the National Football League (NFL)? To investigate, we select a sample of 80 games from t

he 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________ .
Mathematics
1 answer:
ElenaW [278]3 years ago
5 0

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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y is 1/4 when x is -1 if I did interpret your equation right. Please see that I did.

I believe the equation to be y=2^{2x}.  If you meant y=2^2x, please let me know.

Thanks kindly.

Step-by-step explanation:

If (-1,y) lies on the graph of y=2^{2x}, then by substitution we have:

y=2^{2\cdot -1}.  

We just need to simplify to determine y:

y=2^{2 \cdot -1}  

Multiply the 2 and -1:

y=2^{-2}

Use reciprocal rule for exponents to get rid of the negative:

y=\frac{1}{2^2}

2^2 just means 2(2):

y=\frac{1}{2(2)}

y=\frac{1}{4}.

8 0
2 years ago
A circle of centre M has a radius of 11CM . if CA=16.3cm ,what is AB ? give your answer to the nearest tenth!​
zhenek [66]

Answer:

16.4

Step-by-step explanation:

If it is asking for the tenth it will be the 1st one after the point and you round it to the next one.

6 0
3 years ago
1 + tanx / 1 + cotx =2
Lera25 [3.4K]

Answer:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

Step-by-step explanation:

Solve for x:

1 + cot(x) + tan(x) = 2

Multiply both sides of 1 + cot(x) + tan(x) = 2 by tan(x):

1 + tan(x) + tan^2(x) = 2 tan(x)

Subtract 2 tan(x) from both sides:

1 - tan(x) + tan^2(x) = 0

Subtract 1 from both sides:

tan^2(x) - tan(x) = -1

Add 1/4 to both sides:

1/4 - tan(x) + tan^2(x) = -3/4

Write the left hand side as a square:

(tan(x) - 1/2)^2 = -3/4

Take the square root of both sides:

tan(x) - 1/2 = (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

tan(x) = 1/2 + (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Take the inverse tangent of both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) = 1/2 - (i sqrt(3))/2

Take the inverse tangent of both sides:

Answer:  x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

4 0
3 years ago
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