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Anni [7]
3 years ago
5

Prof. Dumbledore is concerned that Harry, Ron and a few other students are still having some difficulties with significant figur

es. Hermione seems to have gotten it though. Why don’t we try to review them. How many significant figures does the result of the following expression have? (6.635-1.321)*(1747.4)*(3.54-2.6).
Mathematics
1 answer:
pochemuha3 years ago
6 0

Answer: The expression has 6 significant figures.

Step-by-step explanation:

First =, we need to understand what significant figure is.

Here's the definition: each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first non-zero digit.

For example: 3.56 has 3 significant numbers

23.51 has 4 significant figures

3.450 has 4 significant figures, because even if the 0 after the 5 is there, we can remove it and the number remains the same.

4.09 has 3 significant figures, because the 0 after the comma makes a difference.

To know how many significant figures the expression has we need to solve it first, so:

(6.635-1.321)*(1747.4)*(3.54-2.6) =

5.314*1747.4*0.94 = 8728.54

8728.54 has 6 significant figures.

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United Flight 15 from New York's JFK airport to San Francisco uses a Boeing 757-200 with 182 seats. Because some people with res
Tcecarenko [31]

Answer:

There is a 29.27% probability that the flight is overbooked. This is not an unusually low probability. So it does seem too high so that changes must be made to make it lower.

Step-by-step explanation:

For each passenger, there are only two outcomes possible. Either they show up for the flight, or they do not show up. This means that we can solve this problem using binomial distribution probability concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And \pi is the probability of X happening.

A probability is said to be unusually low if it is lower than 5%.

For this problem, we have that:

There are 200 reservations, so n = 200.

A passenger consists in a passenger not showing up. There is a .0995 probability that a passenger with a reservation will not show up for the flight. So \pi = 0.0995.

Find the probability that when 200 reservations are accepted for United Flight 15, there are more passengers showing up than there are seats available.

X is the number of passengers that do not show up. It needs to be at least 18 for the flight not being overbooked. So we want to find P(X < 18), with \pi = 0.0995, n = 200. We can use a binomial probability calculator, and we find that:

P(X < 18) = 0.2927.

There is a 29.27% probability that the flight is overbooked. This is not an unusually low probability. So it does seem too high so that changes must be made to make it lower.

5 0
3 years ago
Let f(x)=(x-2)^3+8 Find the inverse of f(x). Please show steps in written form would be gladly appreciated
Tatiana [17]

Hello from MrBillDoesMath!

Answer:

(x-8)^(1/3) +2

Discussion:

To find the inverse of a function swap the values of x and y in the original equation y = (x-2)^3 +8  and solve for y.

y = (x-2)^3 +8          =>  original function. swap x and y values

x = (y-2)^3 + 8        =>  subtract 8 from both sides

x - 8  = (y -2)^3        =>  take cube root of both sides

(x-8)^(1/3) = y - 2     => add 2 to both sides

(x-8)^(1/3) +2 = y      => y is the inverse



Thank you,

MrB

4 0
3 years ago
You buy the same number of brushes, rollers, and paint cans. Write an expression in simplest form that represents the total amou
Soloha48 [4]

If you buy ' N ' of each item, then you'll pay  3.99N  for brushes,
21.79N  for cans of paint, and  6.89N  for rollers.

The question assures us that you bought the same number of
each item.  So your total bill at the hardware store checkout is

                      3.99N + 21.79N + 6.89N

                 =  N (3.99 + 21.79 + 6.89)

                 =        32.67 N .
 

3 0
3 years ago
Sample annual salaries (in thousands of dollars) for employees at a company are listed. 42 36 48 51 39 39 42 36 48 33 39 42 45 (
Sonja [21]

Answer:

a) Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45

\bar X = 41.538

s = 5.317

b) 44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25

\bar X = 43.615

s= 5.583

c) 3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75

\bar X= 3.462

s = 0.443

d) As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3.462).

And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.

And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.

Step-by-step explanation:

For this case we can use the following formulas for the mean and standard deviation:

\bar X = \frac{\sum_{i=1}^n X_i}{n}

s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

Part a

Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45

And if we calculate the mean we got:

\bar X = 41.538

s = 5.317

Part b

For this case we know that each value present a 5% of rise so we just need to multiply each value bu 1.05 and we have this new dataset:

44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25

And if we calculate the new mean and deviation we got:

\bar X = 43.615

s= 5.583

Part c

The new dataset would be each value divided by 12 so we have:

3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75

And the new mean and deviation would be:

\bar X= 3.462

s = 0.443

Part d

As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3,462).

And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.

And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.

5 0
3 years ago
A small box measures 4 in.by 3in. by 3/4 in. high. Find the volume of the box
GalinKa [24]

Answer:

V=e^3

Step-by-step explanation:

4 0
3 years ago
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