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2 years ago

There are 30 students in Ava’s class. Nine of them belong to the Pep Club. What fraction of the class are Pep Club members?

Mathematics

1 answer:

Alex Ar [27]2 years ago

7 0

Answer:

total no. of students=30

pep club students =9

:=9/30 divide by 3

;=3/10

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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

Find the value of x and y that make the quadrilateral

vitfil [10]

The quadrilateral have equal opposite sides, for example:

Then, (4x + 6) must be equal to (7x - 3), and (4y - 3) is equal to (3y + 1), therefore

$4x+6=7x-3$

We can solve that equation for x

$\begin{gathered} 4x+6=7x-3 \\ \\ 3x=9 \\ \\ x=\frac{9}{3}=3 \end{gathered}$

Hence, x = 3. Now let's solve the other equation

$\begin{gathered} 4y-3=3y+1 \\ \\ y=4 \end{gathered}$

Then the value of y is 4.

Final answers:

x = 3

y = 4

4 0

1 year ago

Name a point on this line. y - 8 = -7(x + 1) (-1,8) (1, -8) (8,-1) (-8,1)

Ksju [112]

Answer:

Step-by-step explanation:

You should approach this problem by plugging the answer choices into the equation, since there are only four that you need to do. A works because 8-8 = -7(-1+1) which are both equal to 0

8 0

3 years ago

50 people sponsor paula and she raises a total of £180 for charity. what is the mean average amount sponsored

mylen [45]

The mean is the average so 180/50 = 3.6 therefor the mean of each donation from each sponsor is £3.60

4 0

3 years ago

Read 2 more answers

X^3 = 64 Solve it pls

AnnyKZ [126]

Answer:

x=4