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victus00 [196]
3 years ago
7

As the number of pages in a photo book increases, the prices of the book also increases. There is an additional shipping charge

a 15%. The price of a book can be modeled by the equation below, where P= the price of the book, 20 is the printing charge, 0.5 is the charge per page, and x= the number of pages:
P=(20+0.5x) + 0.15(20+0.5x)
Jennifer wants to purchase a book but only has $62.10 to spend. What is the maximum number of pages she can have in her book
Mathematics
1 answer:
Brums [2.3K]3 years ago
6 0
Equate P as 62.10 since we are looking for the MAX value for x (then a legitimate one if necessary)

(20 + 0.5x) + (3 + 0.075x) = 62.1
= 0.575x + 23 = 62.1
x = (62.1-23)/0.575
x = 680
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On each round, Ann and Bob each simultaneously toss a fair coin. Let Xn be the number of heads tossed in the 2n flips which occu
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Answer:

P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}

Step-by-step explanation:

In a coin toss the  probability of tossing a head is 0.5 (50% head/50% tails)

If n is the number of rounds and 2n the number of coins tossed (one for each player), the probability of having m heads tossed is:

R=\frac{2n!}{m!*(2n-m)!}

R is the number of cases (combination of coins tossed) that gives a m number of heads. Each case has a probability of P_{case}=0.5^{2n} so:

P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}

<u>For example, to toss 4 heads in 5 rounds: </u>

  • n=5
  • 2n=10
  • m=4

P=\frac{10!}{4!*(10-4)!}*0.5^{10}

P=\frac{10*9*8*7*6!}{4!*6!}*0.5^{10}

P=\frac{10*9*8*7}{4!}*0.5^{10}

P=\frac{10*9*8*7}{4!}*0.5^{10}=0.205

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3 years ago
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3 years ago
The travel time on a section of a Long Island Expressway (LIE) is normally distributed with a mean of 80 seconds and a standard
user100 [1]

Answer:

The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 80 seconds and a standard deviation of 6 seconds.

This means that \mu = 80, \sigma = 6

What travel time separates the top 2.5% of the travel times from the rest?

This is the 100 - 2.5 = 97.5th percentile, which is X when Z has a p-value of 0.975, so X when Z = 1.96.

Z = \frac{X - \mu}{\sigma}

1.96 = \frac{X - 80}{6}

X - 80 = 6*1.96

X = 91.76

The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.

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2 years ago
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