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ryzh [129]
2 years ago
9

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
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Ksju [112]

Answer:

A

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

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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
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X^3 = 64<br> Solve it pls
AnnyKZ [126]

Answer:

x=4

Step-by-step explanation:

8 0
3 years ago
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