Sarawong is carrying six pages of math homework and four pages of english homework. a gust of wind blows the pages out of his hands and he is only able to recover seven random pages. what is the probability that he recovers at least five pages of his math homework

Answers

Answer 1

Answer: The sample space of the experiment (i.e. the total number of ways he can pick 7 random pages out of a total of 6 + 4 = 10 pages) is given by:

$^(10)C_7=120$

If he picks at least 5 pages of maths homework, this means that he either picked 5 pages or 6 pages of maths homework.

The number of ways he can pick 5 or 6 maths homework is given by:

$^6C_5+{ ^6C_6}=6*1=6$

Therefore, the probability that he recovers at least 5 pages of his math homework is given by:

$(6)/(120) = (1)/(20)$

Answer 2

Answer:

Final answer:

The probability that Sarawong recovers at least five pages of his math homework is 56.6%, using the combinatory principles of probability.

Explanation:

To solve the problem, we need to calculate the probability that Sarawong recovers at least five pages of his math homework after a gust of wind blows the pages out of his hands. This is a probability problem, which is under the field of mathematics. We first need to understand the total possibilities of the pages he could recover, which is combinations of six math pages and four English pages, that is 10 pages pick 7 pages. We add up the probabilities that he recovers 5, 6, or all 7 math pages. We also need to consider that there is no particular order in which the pages are recovered.

The total number of ways to select 7 pages from 10 can be calculated by 10 choose 7, which is 120.

The number of ways to select 5 math pages out of 6 and 2 English pages out of 4 is 6 choose 5 times 4 choose 2, which equals 60. The probability of this case is 60 / 120 which is 0.5.

The number of ways to select 6 math pages and 1 English page is 6 choose 6 times 4 choose 1, which is also 4. The probability is 4 / 120 which is 0.033.

The number of ways to select all math pages is 6 choose 6 and 4 choose 1, which totals 4. The probability is also 4 / 120 which is 0.033.

Therefore, the total probability that Sarawong recovers at least 5 of his math pages is 0.5 + 0.033 + 0.033 = 0.566, or 56.6%. This is the mathematical solution to the problem.

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Find the prime factorization of
72

Answers

Answer:

72 = {2,2,2,3,3}

Step-by-step explanation:

2433

use the function rule, y=2x +5, to find the values of y when x=1,2,3,and 4. write the answers as ordered pairs that would be used to graph the function please show work

Answers

y = 2x + 5

x = 1

Replace x with 1, and evaluate the right side.

y = 2 * 1 + 5 = 2 + 5 = 7

Ordered pair: (1, 7)

x = 2

Replace x with 2, and evaluate the right side.

y = 2 * 2 + 5 = 4 + 5 = 9

Ordered pair: (2, 9)

x = 3

Replace x with 3, and evaluate the right side.

y = 2 * 3 + 5 = 6 + 5 = 11

Ordered pair: (3, 11)

x = 4

Replace x with 4, and evaluate the right side.

y = 2 * 4 + 5 = 8 + 5 = 13

Ordered pair: (4, 13)

The 4 ordered pairs are: (1, 7), (2, 9), (3, 11), (4, 13)

$y = 2(1) + 5$
y=2+5=7. (1,7)

$2(3) + 5$
y=6+5= 11. (3,11)

$2(2) + 5$
y=4+5=9. (2,9)

$2(4) + 5$
y=8+5=13. (4,13)

3 (w +6 ) = 3w + 18O Distributive Property
O
Commutative Property
O Associative Property
O Transitive Property

Answers

Answer:

Distributive Property (first option)

Step-by-step explanation:

We apply here the distributive property in order to eliminate parenthesis. That is to "distribute" the factor that is outside (3) into the two terms inside the parenthesis, which cannot be combined because they are not like terms.

Divide. Give the quotient and remainder. 41÷8
Quotient:
Remainder:

Answers

Answer:

5 r1

Step-by-step explanation:

Because 40 divided by 8=5 so 8 x 5=40 and 40 but since we need 41 then we still have a remainder of 1 so 5 with a remainder of 1.

Hope it helps have a good afternoon :)

According to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered. (In contrast, only 2% of bikes stolen in New York City are recovered.) Find the probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered. Find the nearest answer.

Answers

Answer:

0.31104

Step-by-step explanation:

Given that according to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered.

If X represents the number of bicyles stolen in Sydney, X is binomial

because each cycle to be stolen is independent of the other.

Also there are two outcomes

n = 6, p = 0.40

Required probability = the probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered

==P(X=2)

= $6C2 (0.4)^2 (0.6)^4\n= 15(0.16)(0.6)^4\n=0.31104$

Answer:

Probability that exactly 2 out of 6 bikes are recovered is 0.31.

Step-by-step explanation:

We are given that according to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered.

Also, there is a sample of 6 randomly selected cases of bicycles stolen in Holland.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^(r) (1-p)^(n-r) ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 6 cases of bicycles

r = number of success = exactly 2

p = probability of success which in our question is % of bicycles

stolen in Holland that are being recovered, i.e; 40%

LET X = Number of bikes recovered

So, it means X ~ $Binom(n=6, p=0.40)$

Now, Probability that exactly 2 out of 6 bikes are recovered is given by = P(X = 2)

P(X = 2) = $\binom{6}{2}0.40^(2) (1-0.40)^(6-2)$

= $15 * 0.40^(2) * 0.60^(4)$

= 0.31

Therefore, Probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered is 0.31.

A certain analytical method for the determination of lead yields masses for lead that are low by 0.5 g. Calculate the percent relative error caused by this deviation for each measured mass of lead. Report the percent relative error with the correct number of significant figures.

Answers

Question Continuation

if the measured weight of lead in the sample is

a.) 764.9g lead

b.)226.3g lead

c.) 53.5g lead

Answer:

Relative Error = 0.065

Relative Error = 0.221

Relative Error = 0.935

Step-by-step explanation:

Given

Absolute Error = 0.5g

Relative error = absolute error/magnitude of measurement.

Relative error % = Relative error * 100

Relative Error = 0.5/764.9 * 100

Relative Error = 50/764.9

Relative Error = 0.065

Relative Error = 0.5/226.3 * 100

Relative Error = 50/226.3

Relative Error = 0.221

Relative Error = 0.5/53.5 * 100

Relative Error = 50/53.5

Relative Error = 0.935

Final answer:

In Chemistry, the percent relative error is calculated by taking the absolute value of the error divided by the original measurement, and then multiplying by 100%. In this case, for a measured value of lead, the percent relative error would be (0.5 g / measured mass) * 100%.

Explanation:

The percent relative error in any measurement is calculated by taking the absolute value of the error divided by the measured value, all multiplied by 100% to get the result in percent forms. In this case, the absolute error is always 0.5 g (which means the values are consistently 0.5 g less than expected). The percent relative error would be calculated as follows:

For a measured value, say M grams, the percent relative error would be (0.5 g / M) * 100%.

Keep in mind, the relative error varies with each measured mass. Therefore, for each different measured mass of lead, you would substitute that value in place of M in the above formula to calculate the respective percent relative error.

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