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IgorLugansk [536]
3 years ago
11

(very urgent) will gave 20 pts

Mathematics
1 answer:
kakasveta [241]3 years ago
5 0

Answer:

a. 45/1024

b. 1/4

c. 15/128

d. 193/512

e. 9/256

Step-by-step explanation:

Here, each position can be either a 0 or a 1.

So, total number of strings possible = 2^10 = 1024

a) For strings that have exactly two 1's,

it means there must also be exactly eight 0's.

Thus, total number of such strings possible

10!/2!8!=45

Thus, probability is

45/1024

b) Here, we have fixed the 1st and the last positions, and eight positions are available.

Each of these 8 positions can take either a 0 or a 1.

Thus, total number of such strings possible

=2^8=256

Thus, probability is

256/1024 = 1/4

c) For sum of bits to be equal to seven, we must have exactly seven 1's in the string.

Also, it means there must also be exactly three 0's

Thus, total number of such strings possible

10!/7!3!=120

Thus, probability

120/1024 = 15/128

d) Following are the possibilities :

There are six 0's, four 1's :

So, number of strings

10!/6!4!=210

There are seven 0's, three 1's :

So, number of strings

10!/7!3!=120

There are eight 0's, two 1's :

So, number of strings

10!/8!2!=45

There are nine 0's, one 1's :

So, number of strings

10!/9!1!=10

There are ten 0's, zero 1's :

So, number of strings

10!/10!0!=1

Thus, total number of string possible

= 210 + 120 + 45 + 10 + 1

= 386

Thus, probability is

386/1024 = 193/512

e) Here, we have fixed the starting position, so 9 positions remain.

In these 9 positions, there must be exactly two 1's, which means there must also be exactly seven 0's.

Thus, total number of such strings possible

9!/2!7!=36

Thus, probability is

36/1024 = 9/256

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A new gas- and electric-powered hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally di
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Answer:

a) P [ Z > 70 ]  = 0.1075  or 10.75 %

b)  P [ Z < 60 ] = 0.1038   or  10.38 %

c)  P [ 55 ≤ Z ≤ 70 ] =  0.8882   or 88.82 %

Step-by-step explanation:

Normal Distribution  μ = 65    and σ = 4

a) The probability of the car travels more than 70 miles per gallon is:

P [ Z > 70 ]  =  (Z-μ) ÷ σ  ⇒   P [ Z > 70 ] = (70-65) ÷4     P [ Z > 70 ] = 1.25

the point 1.25 corresponds at values, from left tail up to 70 so we must go and look for the area for the point 1.24 which is 0.8925. Then we have the area or probability of all cars traveling up  to 70 miles therefore  we have to subtract 1 -0,8925

P [ Z > 70 ]  = 0.1075  or 10.75 %

b)The probability of the car travels less than 60 miles per gallon is:

P [ Z < 60 ]  = ( 60 - μ ) ÷  σ ⇒  P [ Z < 60 ] = (60-65)÷ 4    P [ Z < 60 ] = -1.25

Again -1.25 corresponds to 60 miles per gallon threfore we move to the left and find for point -1.26  which area is 0.1038 so

P [ Z < 60 ] = 0.1038     10.38 %

c) P [ 55 ≤ Z ≤ 70]

For  point  Z = 70 or 1.25 (case a above)  P [ Z ≤ 70] = (70-65)÷4  

P [ Z ≤ 70] = 1.25

In this case we got the whole area from the left tail up to 1.25

P [ Z ≤ 70]  = 0.8944 (includes the area of the point from the left tail up to the point assocciated to 55 miles and for that reason we have to subtract that area)

P [ Z ≥ 55 ]  = (55-65) ÷ 4     P [ Z ≥ 55 ] = -2.5  and the area is 0.0062

So P [ 55 ≤ Z ≤ 70 ] =  0.8944 - 0.0062  = 0.8882

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3 years ago
HELPPPP PLEASEE. IT IS DUE IN 20 MIN. THANK YOU SO MUCH! :)
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Answer:

A.) 65x + 35X + 50 = 250

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35X = cost of pouring/finishing concrete per cubic yard, X is yd³

50 = delivery cost

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B.) 400 + 15n = 505

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400 = some money in account after n week passed

505 = initial money in bank

C.) 1.1X - 10 = 55

55 = total cost of clothes

1.1X = tax rate where X is the undiscounted clothe cost

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Read 2 more answers
On a measure of artistic abilities the mean for college students in New Zealand is 150 and a standard deviation is 25 give the Z
Digiron [165]

The method for computing a z-score is  \bold{z = \frac{(x-\mu)}{\sigma}}, where x is the crude score, \bold{\mu} is the mean population, and \bold{\sigma} seems to be the <em><u>standard population difference.</u></em>

  • The Z value of x is a number \bold{\frac{(x - \text{mean(series))}}{\text{SD(series)}}} are defined where SD is the standard deviation.
  • Here, we consider series as scores of students of colleges in New Zealand for their artistic abilities.

\bold{\bar{x}=150}\\\\ \bold{\sigma=25}

following are the calculation of the Z scores:

\to \ (a)\  100:\  \text{Z score}=\frac{(100-150)}{25}= \frac{(-50)}{25} = -2\\\\\to \ (b)\  120:\  \text{Z score}=\frac{(120-150)}{25}= \frac{(-30)}{25} = -1.2\\\\\to \ (c)\  140:\  \text{Z score}=\frac{(140-150)}{25}= \frac{(-10)}{25} = -0.4\\\\\to \ (a)\  160:\  \text{Z score}=\frac{(160-150)}{25}= \frac{(10)}{25} = 0.4\\\\

Using formula:

\to \text{Raw score = Mean(series) +Z score} \times \text{SD(series)}

Calculating the Raw scores:

\text{(e) -1: Raw score= 150 +(-1)} \times 25 = 125 \\\\\text{(f) -0.8: Raw score= 150 +(-0.8)} \times 25 = 130\\\\\text{(e) -0.2: Raw score= 150 +(-0.2)} \times 25 = 145\\\\\text{(e) 1.38: Raw score= 150 +(1.38)} \times 25 = 184.5\\\\

Learn more:

brainly.com/question/12865701

3 0
2 years ago
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