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3 years ago

Bob did chores for his neighbor. The first day he earned $8. Then he earned $10 a day for

Mathematics

1 answer:

Bumek [7]3 years ago

3 0

Answer: $128

Step-by-step explanation: So first Bob earned 8 dollars. Then he started earning 10 dollars a day every week for 2 weeks. that would have been 148 dollars (plus the 8 dollars he earned in the beginning), but he took a break once a week, subtracting 20 dollars from his pay, giving him 128 dollars in total.

Let me know if this was helpful! :D

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6) Supplementary Exercise 5.51

tresset_1 [31]

Answer:

$P(X \le 4) = 0.7373$

$P(x \le 15) = 0.0173$

$P(x > 20) = 0.4207$

$P(20\ge x \le 24)= 0.6129$

$P(x = 24) = 0.0236$

$P(x = 15) = 1.18\%$

Step-by-step explanation:

Given

$p = 80\% = 0.8$

The question illustrates binomial distribution and will be solved using:

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

Solving (a):

Given

$n =5$

Required

$P(X\ge 4)$

This is calculated using

$P(X \le 4) = P(x = 4) +P(x=5)$

This gives:

$P(X \le 4) = ^5C_4 * (0.8)^4*(1 - 0.8)^{5-4} + ^5C_5*0.8^5*(1 - 0.8)^{5-5}$

$P(X \le 4) = 5 * (0.8)^4*(0.2)^1 + 1*0.8^5*(0.2)^0$

$P(X \le 4) = 0.4096 + 0.32768$

$P(X \le 4) = 0.73728$

$P(X \le 4) = 0.7373$ --- approximated

Solving (b):

Given

$n =25$

Required

$P(X\le 15)$

This is calculated as:

$P(X\le 15) = 1 - P(x>15)$ --- Complement rule

$P(x>15) = P(x=16) + P(x=17) + P(x =18) + P(x = 19) + P(x = 20) + P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)$

$P(x > 15) = {25}^C_{16} * p^{16}*(1-p)^{25-16} +{25}^C_{17} * p^{17}*(1-p)^{25-17} +{25}^C_{18} * p^{18}*(1-p)^{25-18} +{25}^C_{19} * p^{19}*(1-p)^{25-19} +{25}^C_{20} * p^{20}*(1-p)^{25-20} +{25}^C_{21} * p^{21}*(1-p)^{25-21} +{25}^C_{22} * p^{22}*(1-p)^{25-22} +{25}^C_{23} * p^{23}*(1-p)^{25-23} +{25}^C_{24} * p^{24}*(1-p)^{25-24} +{25}^C_{25} * p^{25}*(1-p)^{25-25}$

$P(x > 15) = 2042975 * 0.8^{16}*0.2^9 +1081575* 0.8^{17}*0.2^8 +480700 * 0.8^{18}*0.2^7 +177100 * 0.8^{19}*0.2^6 +53130 * 0.8^{20}*0.2^5 +12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1 +1 * 0.8^{25}*0.2^0$

$P(x > 15) = 0.98266813045$

So:

$P(X\le 15) = 1 - P(x>15)$

$P(x \le 15) = 1 - 0.98266813045$

$P(x \le 15) = 0.01733186955$

$P(x \le 15) = 0.0173$

ii)

$P(x>20)$

This is calculated as:

$P(x>20) = P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)$

$P(x > 20) = 12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1 +1 * 0.8^{25}*0.2^0$

$P(x > 20) = 0.42067430925$

$P(x > 20) = 0.4207$

iii)

$P(20\ge x \le 24)$

This is calculated as:

$P(20\ge x \le 24) = P(x = 20) + P(x = 21) + P(x = 22) + P(x =23) + P(x = 24)$

$P(20\ge x \le 24)= 53130 * 0.8^{20}*0.2^5 +12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1$

$P(20\ge x \le 24)= 0.61291151859$

$P(20\ge x \le 24)= 0.6129$

iv)

$P(x = 24)$

This is calculated as:

$P(x = 24) = 25* 0.8^{24}*0.2^1$

$P(x = 24) = 0.0236$

Solving (c):

$P(x = 15)$

This is calculated as:

$P(x = 15) = {25}^C_{15} * 0.8^{15} * 0.2^{10}$

$P(x = 15) = 3268760 * 0.8^{15} * 0.2^{10}$

$P(x = 15) = 0.01177694905$

$P(x = 15) = 0.0118$

Express as percentage

$P(x = 15) = 1.18\%$

The calculated probability (1.18%) is way less than the advocate's claim.

Hence, we do not believe the claim.

5 0

2 years ago

Check answer asap now

Lelechka [254]

Answer: It's correct because it is the only one with an angle more than 180°

Step-by-step explanation:

D is a right angle, A is an acute angle, as well as B. So not only is C the only one with an obtuse angle and it also has the biggest angle out of the other two angles on the triangle, you can use process of elimination to figure it out as well. Hope this helps, have a good day! :-)

3 0

2 years ago

Diego’s dog weighs more than 8 kilograms and less than 12 kilograms. Select all the inequalities that MUST be true if w is the w

masha68 [24]

Answer:

4 less kilgrams than previous weight

Step-by-step explanation:

7 0

2 years ago

The label on Lulu’s new roll of tape shows that the roll has 7 meters of tape.

Anton [14]

Answer:

4 meters

Step-by-step explanation:

7-3=4 m

8 0

3 years ago

Read 2 more answers

Kerry has a new phone plan. It works by charging $20 per month and then $0.10 for each minute over 200 minutes.

REY [17]

Answer:

(40-20)/.10

Step-by-step explanation:

40-20 is 20, 20 divided by .10 is 200, she used 200 extra minutes.

3 0

2 years ago