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Romashka-Z-Leto [24]

3 years ago

14

4) Angles 3 and 6 are congruent. What would you use to prove those lines parallel? (pic below)A. Converse of Same-Side Interior

Angles Theorem
B. Alternate Interior Angles Theorem
C. Converse of the Corresponding Angles Postulate
D. Converse of Alternate Interior Angles Theorem

1 answer:

Serjik [45]3 years ago

5 0

Answer:

B?

Step-by-step explanation:

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Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n 2 if heads comes up

Artyom0805 [142]

Answer:

In the long run, ou expect to lose $4 per game

Step-by-step explanation:

Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n^2 if heads comes up first on the nth toss.

Assuming X be the toss on which the first head appears.

then the geometric distribution of X is:

X $\sim$ geom(p = 1/2)

the probability function P can be computed as:

$P (X = n) = p(1-p)^{n-1}$

where

n = 1,2,3 ...

If I agree to pay you $n^2 if heads comes up first on the nth toss.

this implies that , you need to be paid $\sum \limits ^{n}_{i=1} n^2 P(X=n)$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = E(X^2)$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =Var (X) + [E(X)]^2$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+(\dfrac{1}{p})^2$ ∵ X $\sim$ geom(p = 1/2)

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+\dfrac{1}{p^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p+1}{p^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-p}{p^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-\dfrac{1}{2}}{(\dfrac{1}{2})^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{4-1}{2} }{{\dfrac{1}{4}}}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{3}{2} }{{\dfrac{1}{4}}}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ 1.5}{{0.25}}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =6$

Given that during the game play, You pay me $10 , the calculated expected loss = $10 - $6

= $4

∴

In the long run, you expect to lose $4 per game

3 0

4 years ago

How could you use the Pythagorean Theorem in life

ruslelena [56]

Repairing windows when using a ladder and bushes are in the way....viewing the size if a television

3 0

3 years ago

If the temperature outside is 30°C, what is the temperature in F°

emmasim [6.3K]

Answer:

<u>86°F</u>

Step-by-step explanation:

4 0

3 years ago

Please help with this

Free_Kalibri [48]

Answer:

$S_{25}=555$

Step-by-step explanation:

Given that,

In an AP, the 6th term is 39 i.e.

$a_6=a+5d\\\\39=a+5d\ ....(1)$

In the same AP, the 19th term is 7.8 i.e.

$a_{19}=a+18d\\\\7.8=a+18d\ ......(2)$

Subtract equation (1) from (2).

7.8 - 39 = a+18d - (a+5d)

-31.2 = a +18d-a-5d

-31.2 = 13d

d = -2.4

Put the value of d in equation (!).

39 = a+5(-2.4)

39 = a- 12

a = 39+12

a = 51

The sum of n terms of an AP is given by :

$S_n=\dfrac{n}{2}[2a+(n-1)d]$

Put n = 25 and respected values,

$S_{25}=\dfrac{25}{2}[2(51)+24(-2.4)]\\\\=555$

Hence, the sum of first 25 terms of the AP is equal to 555.

6 0

3 years ago

Line AC is 13 units long. Use coordinate algebra to locate a point E on Line AC such that the ratio of AE to EC is equal to the

AnnZ [28]

Refer to the diagram shown below.

The length of AC = 13 (given).

Let the length of AE = x.
Then the length of EC = 13 x.

The ratio of AE to EC is 0.6.
Therefore
$\frac{x}{13-x} =0.6$
Cross multiply.
x = 0.6(13 - x)
x = 7.8 - 0.6x
1.6x = 7.8
x = 4.875

That is,
AC = 4.875
EC = 13 -x = 13 - 4.875 = 8.125

Answer:
E is located on AC such that
AC = 4.875
EC = 8.125

8 0

3 years ago