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zzz [600]
3 years ago
15

On one map of a town , the scale from the town to the map is 12mi to 3 cm. the school is 2.5cm from the grocery store on this ma

p. on a different map of the same town ,the scale from the town to the map is 12mi to 2cm .the school is 1.5cm from the library on that map. is the grocery store or library closer to the school?
Mathematics
1 answer:
AleksandrR [38]3 years ago
3 0

Answer:

Step-by-step explanation:

Grocery Store

12 mi / 3 cm = x / 2.5 cm            Cross multiply

12 * 2.5 = 3 * x                             Multiply

30 = 3x                                        Divide by 3

30/3 = x

x = 10 miles

Library

12 mi / 2 cm = x / 1.5                  Cross multiply

12 * 1.5 = 2x

18 = 2x                                        Divide by 2

18/2 = x

9 miles

The library is closer than the grocery store.

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A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?
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Answer:

The probability that the month starts with the letter J or the letter M is 41.66%.

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Given that a month of the year is chosen at random, to determine what is the probability that the month starts with the letter J or the letter M, the following calculation must be performed:

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Which of the following is an asymptote of y = sec(x)?
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4) limit of sec(x) = lim of 1 / cos(x).

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Answer:

a) The support of X is {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

b) The mean of X is 7.5

c) The variance of X is 10

Step-by-step explanation:

a) Since you can toss up to 20 coins, and from that you can obtain any number of heads from 0 to 20, then the support of X {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

b) To compute the mean of X, we need to see how is the <em>behavior</em> of X. Since 3 dices will gives 10 coins to toss and the other 3 will give us 20, then there is a probability of 1/2 that we tossed 10 coins and a probability of 1/2 that we tossed 20.

The random variable X, conditioned to the event 'The dice is 1,2 or 3' (or equivalently, 10 coins are tossed), will have a binomial distribution with paramenters n = 10, p = 1/2. The mean of X in this case is np = 5. If X is conditioned to the event 'The dice is 4,5 or 6', then X will have also binomial distribution, but this time with paramenters n = 20, p = 1/2. The mean of X in this case is 20*1/2 = 10.

Since each event we conditioned in had probability 1/2 to occur, then E(X) = 1/2 * 5 + 1/2 * 10 = 7.5.

c) Remember that V(X) = E(X²)- E(X)². Since we alredy know the mean of X, we just need to compute the mean of X squared.

The variance of a binomial distribution Z with paramenters n and p is

V(Z) = np(1-p)

since V(Z) = E(Z²)- E(Z)² = E(Z²)- n²p², then

E(Z²) = V(Z) + E(Z)² = np(1-p) + n²p² = p²(n²-n) + np

Therefore

E(X²) = E(X² | 10 coins are tossed) * 1/2 + E(X² | 20 coins are tossed) * 1/2 =

1/2*(0.5²(10²-10) + 5) + 1/2*(0.5²(20²-20) + 10) = 13.75 + 52.5 = 66.25

As a consecuence

V(X) = 66.25 - 7.5² = 10

The variance of X is 10.

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