What happens when you multiply a positive number by a number greater than 1?

(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

What value for x makes the two ratios equivalent?

Makovka662 [10]

1/15

1/9:5/3 = 3/45:1
3:45 = 1/15

5 0

3 years ago

Read 2 more answers

Which statement is true?

Maslowich

Answer:

A

Step-by-step explanation:

on the left of the equation, (6^4)^-5 = 6^-20

the right side you add the exponents so it would be (-7-3) =-10

so it would be 6^-10, which is greater than 6^-20

5 0

2 years ago

8. Jack is going to paint the ceiling and four

Ugo [173]

Answer:

D

Step-by-step explanation:

7 0

3 years ago

1. Over 3 years, how much more does $3000 in a savings account with an APR of 3.2% compounded

Sedbober [7]

Answer:

$1080

Step-by-step explanation:

$((3000 \times 0.032) \times 2) \times 3 = 576$

convert % to decimal by multiplying 3.2%x100=0.032

then multiply by initial amount 3000x0.032

then multiply by 2 because it's compounding semiannual

then multiply by 3 because it's over a 3 yr period

do the same for the quarterly compound but multiply by 4 because it's quarterly

$((3000 \times 0.03) \times 2) \times3 = 1080$

over a 3 yr period the quarterly compounded amount will earn:

$1080 - 576 = 504$

$504 more than the account compounded semiannual

5 0

3 years ago