1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alchen [17]
2 years ago
13

In the Minnesota Northstar Cash Drawing, you pick five different numbers between 1 and 35. What is the probability of picking th

e winning combination (order does not matter)
Mathematics
1 answer:
maw [93]2 years ago
5 0

Answer:

\frac{1}{324632} probability of picking the winning combination

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Since the order is not important, the combinations formula is used to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Desired outcomes:

The correct five numbers from a set of 5. So

D = C_{5,5} = \frac{5!}{5!0!} = 1

Total outcomes:

Five numbers from a set of 35. So

T = C_{35,5} = \frac{35!}{5!30!} = 324632

Probability:

p = \frac{D}{T} = \frac{1}{324632}

\frac{1}{324632} probability of picking the winning combination

You might be interested in
Factor: 100x^2- 81
Alex17521 [72]

Answer:

Choice 'D' (10x + 9) (10x-9) is the correct answer

Step-by-step explanation:

100x^2 - 81

This is a difference of squares...

therefore = (10x + 9) (10x - 9)

7 0
3 years ago
2^x times 3^x<br><br> Work out the value of x
kumpel [21]
6^x is 3×2 is six I hope I've helped you
3 0
3 years ago
13.27 = t - 24.45
Alika [10]

Answer:

=

3

7

.

7

2

Step-by-step explanation:

Add

2

4

.

4

5

24.45

24.45

to both sides of the equation

1

3

.

2

7

=

−

2

4

.

4

5

1

3

.

2

7

+

2

4

.

4

5

=

−

2

4

.

4

5

+

2

4

.

4

5

4 0
2 years ago
Which of the following is NOT equivalent to 22/7?
jasenka [17]

Answer:

the option c is the answer for this question

5 0
2 years ago
Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product o
koban [17]

Answer:  17.6 grams

Step-by-step explanation:

As the problem tells us, the velocity of the reaction is proportional to the product of the quantities of A and B that have not reacted, so from this we get the next equation:

                                                       V = k[A][B]

where [A] represents the remaining amount of A, and [B] represents the remaining amount of B. To solve this equation we have to represent it through a differential equation, which is:

                                              dx/dt = k[α - a(t)][β - b(t)]         (1)

where,

k: velocity constant

a(t): quantity of A consumed in instant t

b(t): quantity of B consumed in instant t

α: initial quantity of A

β: initial quantity of B

Now we need to define the equations for a(t) and b(t), and for this we are going to use the law of conservation of mass by Lavoisier, with which we can say that the quantity of C in a certain instant is equal to the sum of the quantities of A and B that have reacted. Therefore, if we need M grams of A and N grams of B to form a quantity of M+N of C, then we can say that in a certain time, the consumed quantities of A and B are given by the following equations:

                                       a(t) = ( M/M+N) · x(t)

                                       b(t) = (N/M+N) · x(t)

where,

x(t): quantity of C in instant t

So for this problem we have that for 1 gram of B, 2 grams of A are used, therefore the previous equations can be represented as:

                                       a(t) = (2/2+1) · x(t) = 2/3 x(t)

                                       b(t) = (1/2+1) · x(t) = 1/3 x(t)

Now we proceed to resolve the differential equation (1) by substituting values:

                                         dx/dt = k[α - a(t)][β - b(t)]  

                                        dx/dt = k[40 - 2x/3][50 - x/3]

                                         dx/dt = k/9 [120 - 2x][150 - x]

We use the separation of variables method:

                                      dx/[120-2x][150-x] = k/3 · dt

We integrate both sides of the equation:

                                     ∫dx/(120-2x)(150-x) = ∫kdt/9

                                     ∫dx/(15-x)(60-x) = kt/9 + c

Now, to integrate the left side of the equation we need to use the partial fraction decomposition:

                                    ∫[1/90(120-2x) - 1/180(150-x)] = kt/9 + c

                                      1/180 ln(150-x/120-2x) = kt/9 + c

                                           (150-x)/(120-2x) = Ce^{20kt}

Now we resolve by taking into account that x(0) = 0, and x(5) = 10,

for x(0) = 0 ,             (150-0)/(120-0) = Ce^{20k(0)} , C = 1.25

for x(5) = 10 ,           (150-10)/(120-(2·10)) = 1.25e^{20k(5)} , k ≈ 113 · 10^{-5}

Now that we have the values of C and k, we have this equation:

                           (150-x)/(120-2x) = 1.25e^{226·10^{-4}t}

and we have to clear by x, obtaining:

               x(t) = 150 · (1 - e^{226·10^{-4}t} / 1 - 2.5e^{226·10^{-4}t})

Therefore the quantity of C that will be formed in 10 minutes is:

           x(10) = 150 · (1 - e^{226·10^{-4}(10)} / 1 - 2.5e^{226·10^{-4}(10)})

                                            x(10) ≈ 17.6 grams

8 0
3 years ago
Other questions:
  • Is this correct or need more? but still need help
    14·2 answers
  • A rectangle has sides that measure 7 by 13 feet. If the sides are halved what is the new area?
    11·2 answers
  • How to simplify expressions
    12·1 answer
  • The figure in quadrant III it the coordinate plane below is a transformation of the figure in quadrant II. The figure in quadran
    13·2 answers
  • An arc subtends a central angle measuring
    5·1 answer
  • Eighty three million twenty three thousand seven in standard form
    14·2 answers
  • 40. When you translate, (x, y+6) will move
    10·2 answers
  • 2-5=x/1.2<br>(please solve this)​
    8·1 answer
  • Find the slope of the given table
    6·1 answer
  • If $25, 000 is invested into an account paying 4.5% per year, compounded quarterly, how much money can be withdrawn from the acc
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!