All categories

3 years ago

The speed of sound in dry air at 20° C (68° F) is 1.236 × 103 km/h. What is the speed of sound written as an ordinary number?

Mathematics

1 answer:

defon3 years ago

7 0

Step-by-step explanation:

The speed of sound has nothing to do with "sea level" and sound pressure and without the medium air there is no speed of sound. In SI units with dry air at 20°C (68°F), the speed of sound c is 343 meters per second (m/s). This also equates to 1235 km/h, 767 mph, 1125 feet per second (ft/s), or 666 knots.

You might be interested in

What is the interest earned on $20,000 for five years, at an interest rate of 3% compounded daily?

SSSSS [86.1K]

Answer:

The final balance is $23,232.33.

The total compound interest is $3,232.33.

6 0

2 years ago

Find the mean, variance &a standard deviation of the binomial distribution with the given values of n and p.

MrMuchimi

A random variable following a binomial distribution over $n$ trials with success probability $p$ has PMF

$f_X(x)=\dbinom nxp^x(1-p)^{n-x}$

Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.

$\displaystyle\sum_xf_X(x)=\sum_{x=0}^n\binom nxp^x(1-p)^{n-x}=1$

The mean is given by the expected value of the distribution,

$\mathbb E(X)=\displaystyle\sum_xf_X(x)=\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^nx\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^n\frac{n!}{(x-1)!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!}p^{x-1}(1-p)^{(n-1)-(x-1)}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\frac{(n-1)!}{x!((n-1)-x)!}p^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\binom{n-1}xp^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^{n-1}\binom{n-1}xp^x(1-p)^{(n-1)-x}$

The remaining sum has a summand which is the PMF of yet another binomial distribution with $n-1$ trials and the same success probability, so the sum is 1 and you're left with

$\mathbb E(x)=np=126\times0.27=34.02$

You can similarly derive the variance by computing $\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2$ , but I'll leave that as an exercise for you. You would find that $\mathbb V(X)=np(1-p)$ , so the variance here would be

$\mathbb V(X)=125\times0.27\times0.73=24.8346$

The standard deviation is just the square root of the variance, which is

$\sqrt{\mathbb V(X)}=\sqrt{24.3846}\approx4.9834$

7 0

3 years ago

Due rn!!! please help

Alex Ar [27]

Answer: The answer is A.

Step-by-step explanation:

4 0

2 years ago

4 x 1 + 1 x 1/100 + 9 x 1/1000 in standard form

uysha [10]

Answer:

4.1

Step-by-step explanation:

5 0

3 years ago

I NEED THIS ASAP 5/8 of 48 is equal to 8/15 of some number. What is this number?

murzikaleks [220]

(5/8) × 48 = (8/15) × n

Multiply by the inverse of the coefficient of n. That inverse is 15/8.

n = (15/8)×(5/8)×48 = (75/64)×48 = 225/4 = 56 1/4

5/8 of 48 is equal to 8/15 of 56 1/4

5 0

2 years ago