All categories

3 years ago

What is the sum of all the terms in the 10th row of Pascal's Triangle

Mathematics

1 answer:

pantera1 [17]3 years ago

3 0

Look up an image of the triangle, and you can see the sum of 2048.

You might be interested in

Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a

lara31 [8.8K]

Answer:

A) 0.0009765625

B) 0.0060466176

C) 2.7756 x 10^(-17)

Step-by-step explanation:

A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10

If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5

Now the definition of binomial probability is given by;

P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)

Now, we want the definition of this probability at k = 10.

Thus;

P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)

P(x = 10) = 0.0009765625

B) here we are given that p = 0.6 while n remains 10 and k = 10

Thus;

P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)

P(x=10) = 0.0060466176

C) we are given that;

P((x_i) = 1) = 1/(2^(i))

Where i = 1,2,3.....,n

Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;

P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)

This gives;

P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]

This gives;

P(x = 10) = [1/(2^(55))]

P(x = 10) = 2.7756 x 10^(-17)

3 0

3 years ago

The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. Th

e-lub [12.9K]

Answer:

95% of monthly food expenditures are between $110 and $190.

Step-by-step explanation:

Given : The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20.

To find : Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts?

Solution :

At 95% of the data is between two standard deviation to left and right of the mean is given by,

To the left side, $\bar{x}-2\sigma$

To the right side, $\bar{x}+2\sigma$

We have given,

The sample mean $\bar{x}=\$150$

The standard deviation $\sigma=\$20$

Substitute in the formula,

$\bar{x}-2\sigma$

$=150-2(20)$

$=150-40$

$=110$

$\bar{x}+2\sigma$

$=150+2(20)$

$=150+40$

$=190$

Therefore, 95% of monthly food expenditures are between $110 and $190.

6 0

3 years ago

Simplify the expression (2^3)^-2

snow_lady [41]

1/64

2^3 = 8

8^-2 = 1/64

5 0

3 years ago

Read 2 more answers

If all guitar players are musicians, then all musicians are guitar players.

IrinaVladis [17]

Answer:

This does not make sense.

Step-by-step explanation:

Just because you are a musician does not mean you play the guitar.

You can play the piano and a trumpet, but not be able to play a guitar!

5 0

3 years ago

Read 2 more answers

Two added to three times a number m is the same as 18

Mumz [18]

3*16/3+2=18

16+2=18 i found this on a website hope it helped!

https://www.algebra.com

is the link

8 0

3 years ago