Write a fraction less than 1 with a denominator of 6 that is greater than 3/4

An airplane can travel 365mph in still air. If it travels 2716 miles with the wind in the same length of time it travels 2394 mi

Anestetic [448]

Answer: the speed of the wind is 365 mph

Step-by-step explanation:

Let x represent the speed of the wind.

An airplane can travel 365mph in still air. If it travels 2716 miles with the wind, it means that its total speed while flying with the wind is (365 + x) mph.

Time = distance/speed

Time spent in flying with the wind is

2716/(365 + x)

In the same length of time, it travels 2394 miles against the wind. it means that its total speed while flying against the wind is (365 - x) mph.

Time spent in flying against the wind is

2394/(365 - x)

Since the time is the same, it means that

2716/(365 + x) = 2394/(365 - x)

Cross multiplying, it becomes

2716(365 - x) = 2394(365 + x)

991340 - 2716x = 873810 + 2394x

2394x + 2716x = 991340 - 873810

5110x = 1865150

x = 1865150/5110

x = 365 mph

5 0

4 years ago

Which of the following statements about Pascal's Triangle are true?

Anarel [89]

Answer:

1. It is symmetric

2. The second diagonal is the counting numbers

3. Any number in the triangle is the sum of the two numbers directly above it

Step-by-step explanation:

1. The first diagonal shows the counting numbers.

2. The sums of the rows give the powers of 2.

3. Each row gives the digits of the powers of 11

6 0

3 years ago

Stephanie has $4,500 in her saving account.

AfilCa [17]

so whats the question

7 0

3 years ago

Hellloooooooooooooooooooo

barxatty [35]

Answer:

D

Step-by-step explanation:

3 0

3 years ago

If we sample from a small finite population without replacement, the binomial distribution should not be used because the event

seropon [69]

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

<em>As we see, the situation is exactly the same,</em> but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

6 0

3 years ago