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Luda [366]
3 years ago
11

During his 2007 MVP season for the New York Yankees, Alex Rodriguez hit 98 singles, 31 doubles, 0 triples, and 54 home runs in a

total of 583 at bats. The following table arranges these data in terms of the number of bases for a hit, counting 0 bases for the times when he did not get a hit and 4 bases for home runs. Number of Bases 0 1 2 3 4 Number of Times 400 98 31 0 54 To the nearest thousandth, what was E(X), the expected number of bases for Alex Rodriguez in a typical at bat in 2007? A. 0.645 B. 0.458 C. 0.314 D. 0.569
Mathematics
2 answers:
Black_prince [1.1K]3 years ago
7 0
I think the answer is 0.458

Pani-rosa [81]3 years ago
3 0
B I think that is the answer. If its not please let me know.
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Calculate the limit values:
Nataliya [291]
A) This particular limit is of the indeterminate form,
\frac{ \infty }{ \infty }
if we plug in infinity directly, though it is not a number just to check.

If a limit is in this form, we apply L'Hopital's Rule.

's
Lim_{x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_ {x \rightarrow \infty } \frac{( ln(x ^{2} + 1 ) ) '}{x ' }
So we take the derivatives and obtain,

Lim_ {x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_{x \rightarrow \infty } \frac{ \frac{2x}{x^{2} + 1} }{1}

Still it is of the same indeterminate form, so we apply the rule again,

Lim_{x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_{x \rightarrow \infty } \frac{ 2 }{2x}

This simplifies to,

Lim_{x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_{x \rightarrow \infty } \frac{ 1 }{x} = 0

b) This limit is also of the indeterminate form,

\frac{0}{0}
we still apply the L'Hopital's Rule,

Lim_ {x \rightarrow0 }\frac{ tanx}{x} = Lim_ {x \rightarrow0 } \frac{ (tanx)'}{x ' }

Lim_ {x \rightarrow0 }\frac{ tanx}{x} = Lim_ {x \rightarrow0 } \frac{ \sec ^{2} (x) }{1 }

When we plug in zero now we obtain,

Lim_ {x \rightarrow0 }\frac{ tanx}{x} = Lim_ {x \rightarrow0 } \frac{ \sec ^{2} (0) }{1 } = \frac{1}{1} = 1
c) This also in the same indeterminate form

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = Lim_ {x \rightarrow0 } \frac{ ({e}^{2x} - 1 - 2x)'}{( {x}^{2} ) ' }

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = Lim_ {x \rightarrow0 } \frac{ (2{e}^{2x} - 2)}{ 2x }

It is still of that indeterminate form so we apply the rule again, to obtain;

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = Lim_ {x \rightarrow0 } \frac{ (4{e}^{2x} )}{ 2 }

Now we have remove the discontinuity, we can evaluate the limit now, plugging in zero to obtain;

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = \frac{ (4{e}^{2(0)} )}{ 2 }

This gives us;

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } =\frac{ (4(1) )}{ 2 }=2

d) Lim_ {x \rightarrow +\infty }\sqrt{x^2+2x}-x

For this kind of question we need to rationalize the radical function, to obtain;

Lim_ {x \rightarrow +\infty }\frac{2x}{\sqrt{x^2+2x}+x}

We now divide both the numerator and denominator by x, to obtain,

Lim_ {x \rightarrow +\infty }\frac{2}{\sqrt{1+\frac{2}{x}}+1}

This simplifies to,

=\frac{2}{\sqrt{1+0}+1}=1
5 0
3 years ago
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 ft.
rosijanka [135]

Answer:

Step-by-step explanation:

for the cylinder

27π = πr²h = πr²(2r) = 2πr³

for the sphere

V = (4/3)πr² = (2/3)(2πr³) = (2/3)27π

7 0
3 years ago
Using the equation F = 1.8C + 32, find the temperature in °C if it is 92°F. Round your answer to the nearest whole number if nec
Andru [333]

Answer:

  33 °C

Step-by-step explanation:

Put 92 where F is in the equation, and solve for C.

  92 = 1.8C +32 . . . . substitute for F

  60 = 1.8C . . . . . . . . subtract 32

  60/1.8 = C ≈ 33.33 ≈ 33 . . . . . divide by the coefficient of C, round the result

The temperature is about 33 °C.

8 0
2 years ago
find the volume of a cylinder whose base has a diemeter of 11 and whose height is 12.5. use 3.14 and round your answer to the ne
atroni [7]
Volume = π (3.14)×22^2×12.5 = 18,997 inches³
3 0
3 years ago
Sally designs web pages. She charges $140 per web page. She also needs to pay
dolphi86 [110]
You will take 140 times 5 since that is the amount she made so you times it buy the price she earns then after you do that subtract it buy 650 since that is what you have to pay
140 x 5 = 700
700 - 650 = 50
so she made a profit of 50
6 0
3 years ago
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