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marta [7]
2 years ago
11

A single die is rolled twice. the set of 36 equally likely outcomes is {(1, 1), (1, 2), (1,3), (1,4), (1,5), (1,6), (2,1), (2, 2

), (2, 3), (2, 4), (2,5), (2,6), (3, 1), (3, 2), (3, 3), (3, 4), (3,5), (3,6), (4,1),(4,2), (4,3), (4,4),(4,5),(4.6), (5,1), (5,2), (5,3), (5, 4), (5,5), (5,6), (6, 1), (6,2), (6,3), (6,4), (6,5), (6, 6)). a. find the probability of getting two numbers whose sum is greater than 9.(3 points) b. find the probability of getting two numbers whose sum is less than 13. (3 points) c. find the probability of getting two numbers whose sum is greater than 9 and less than 13. (3 points)
Mathematics
1 answer:
Nana76 [90]2 years ago
4 0

Answer:

Step-by-step explanation:








.

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Find two positive numbers satisfying the given requirements. The product is 432 and the sum of the first plus three times the se
kogti [31]

Answer:

<h3>36 and 12</h3>

Step-by-step explanation:

Let the two positive integers be x and y.

If their product is 432, then

xy = 432 ......... 1

Also if the sum of the first plus three times the second is a minimum, then;

p(x) = x + 3y

From 1;

y = 432/x ..... 3

Substitute 3 into 2;

p(x) = x+3y

p(x)= x + 3(432/x)

p(x) = x + 1296/x

Since the expression is at minimum when dp(x)/dx = 0

dp/dx = 1 + (-1296)/x²

dp/dx = 1  -1296/x²

0 =  1  -1296/x²

0 = (x²-1296)/x²

cross multiply

0 = x²-1296

x² = 1296

x = √1296

x = 36

Since xy = 432

36y = 432

y = 432/36

y = 12

Hence the two positive numbers are 36 and 12

4 0
3 years ago
In which geometry is there no line parallel to a given line through a point not on the line?
tangare [24]

Answer:

Given a line and a point not on it, no lines parallel to the given line can be drawn through the point. you get an elliptic geometry.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
3.which lines are parallel<br> 4. what wouldbyou use to prove these lines parallel
uysha [10]
3)the line G & H are parallel
4) Parallel line theorem is what I do believe it's called (do you have choices for this one?)
6 0
3 years ago
Suppose the system of linear equations has infinitely many solutions. What is the value of y for the second equation?
Otrada [13]
I believe it would be 4

This is because when divided by 3, 3x+12y=3 turns into x+4y=3
6 0
3 years ago
Read 2 more answers
1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING
iogann1982 [59]

If

y=\displaystyle\sum_{n=0}^\infty a_nx^n

then

y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n

The ODE in terms of these series is

\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0

\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0

\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}

We can solve the recurrence exactly by substitution:

a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0

\implies a_n=\dfrac{(-2)^n}{n!}a_0

So the ODE has solution

y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}

which you may recognize as the power series of the exponential function. Then

\boxed{y(x)=a_0e^{-2x}}

7 0
3 years ago
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