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Zielflug [23.3K]
3 years ago
5

Write 2.5896 * 10^-4 in standard form

Mathematics
1 answer:
7nadin3 [17]3 years ago
4 0

Answer: use a standard form calculator

Step-by-step explanation: it helps alot :)

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(a) A parachutist lands at a point on the line between the points A and B, and the target is an operation at A. The operation fa
mr Goodwill [35]

Answer:

a) \frac{B-\frac{A+5B}{6}}{B-A}= \frac{6B -A-5B}{6(B-A)}=\frac{B-A}{6(B-A)}=\frac{1}{6}

b) P(X>1) = 1-P(X\leq 1)=1-\int_{0}^1 \frac{1^{2} x^{2-1} e^{- x}}{\gamma(2)}=0.736

Step-by-step explanation:

Part a

We assume that the parachutist lands at random point in the interval (x=A,y=B) we have a continuous random variable X. And the distribution of X would be uniform Y\sim Unif(A,B). And the density function would be given by:

f(x) =\frac{1}{B-A} , A

And 0 for other case.

The operation fails, if parachutist's distance to A is more than five times as much as her distance to B.

So the point P in the interval (A,B) at which the distance to A is exactly 5 times the distance to B is given by:

P= A + \frac{5}{6} (B-A)= \frac{6A +5B -5A}{6}=\frac{A+5B}{6}

And we can find the probability desired like this:

P(d(P,A) \geq 5 d(P,B))= P(\frac{A+5B}{6} < X< B)

And from the cumulative distribution function of X ficen by F(X)\frac{X-A}{B-A} we got:

\frac{B-\frac{A+5B}{6}}{B-A}= \frac{6B -A-5B}{6(B-A)}=\frac{B-A}{6(B-A)}=\frac{1}{6}

Part b

For this case we assume that X\sim Gamma (2,1)

On this case we assume that \alpha=2, \beta= 1

The density function for the Gamma distribution is given by:

P(X)= \frac{\beta^{\alpha} x^{\alpha-1} e^{-\beta x}}{\gamma(\alpha)}

And on this case we can find the probability using the complement rule like this:

P(X>1) = 1-P(X\leq 1)=0.736

We can solve this problem with the following excel code:

"=1-GAMMA.DIST(1;2;1;TRUE)"

And if we do it by hand we need to do this:

P(X>1) = 1-P(X\leq 1)=1-\int_{0}^1 \frac{1^{2} x^{2-1} e^{- x}}{\gamma(2)}=0.736

6 0
3 years ago
Which statements are true? Check all that apply
MAXImum [283]
The first and third bubble are the answers.
I hope I helped!
6 0
3 years ago
Read 2 more answers
Complete the equation describing how x and y are related
noname [10]

Answer:

.5

Step-by-step explanation:

4+.5=4.5 and 4.5+.5=5

5 0
3 years ago
What is the solution to 3(x + 8) &gt; 2 (2x + 10)?<br> 4<br> O<br> 0<br> (-4, 6)<br> (-5, 4)
Deffense [45]

Answer:

x<4

Step-by-step explanation:

For this inequation:

3(x + 8) > 2 (2x + 10)

or 3x +24 > 4x +20

-4x+ 3x + 24> -4x +4x +20

and we have -x +24> 20

or -x +24 -24 > 20-24

-x >-4 and finally x < 4 ( multiple -1 for both sides, > change into <)

All real number x so that x< 4 is solution.

Have a good day.

4 0
3 years ago
What is the wquation of a circle with center (-2.3) and radius 4
yanalaym [24]
The equation of any circle is

(x - a)^2 + (y - b)^2 = radius^2 where our center is (a, b)

Therefore, our equation is as follows.

(x + 2)^2 + (y - 3)^2 = 16
5 0
3 years ago
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