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3 years ago

5

In a New York State daily lottery game, a sequence of five digits (not necessarily different) in the range 0-9 are selected at r

andom. Find the probability that all five are different.

1 answer:

Slav-nsk [51]3 years ago

8 0

Answer: Our required probability is 0.30.

Step-by-step explanation:

Since we have given that

Number we have 0 to 9 = 10

Number of digits = 5

Total number of outcomes = $10^5=10000$

All 5 are different.

So, the number of ways selecting all 5 are different is given by

$^{10}C_5\times 5!=30240$

So, probability that all five are different is given by

$\dfrac{30240}{10000}\\\\=0.30240\\\\\approx 0.30$

Hence, our required probability is 0.30.

You might be interested in

The sum of 6 consecutive integers is 339.

Zigmanuir [339]

Answer:

<u>54, 55, 56, 57, 58, and 59</u> are the numbers

Step-by-step explanation:

Let's pretend that the first number is $n$ .

We know that these numbers are consecutive, meaning each number is one more than the other.

This means that

$n + (n+1)+ (n+2)+ (n+3)+ (n+4)+ (n+5) = 339$ , since each number is consecutive.

We can combine like terms to get $6n + 15 = 339$ .

Now let's solve for n.

$6n + 15 - 15 = 339-15\\\\6n = 324\\\\n = 54$

So $n=54$ . This means the other 5 digits will be one more than the next.

So 54, 55, 56, 57, 58, and 59.

Hope this helped!

4 0

3 years ago

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 44,663 miles, with a standard

expeople1 [14]

Answer:

The probability is $P(| \= X- \mu| < 199 ) = 0.733$

Step-by-step explanation:

From the question we are told that

The mean mileage of a tire is $\mu = 44663$

The standard deviation is $\sigma = 2594$

The sample size is n = 209

Generally the standard error of mean is mathematically represented as

$\sigma_{x} = \frac{\sigma}{\sqrt{n} }$

=> $\sigma_{x} = \frac{2594}{\sqrt{209} }$

=> $\sigma_{x} = 179.4$

Generally the probability that the sample mean would differ from the population mean by less than 199 miles is mathematically represented as

$P(| \= X- \mu| < 199 ) = P(|\frac{\= X - \mu}{ \sigma_{x}}| < \frac{199}{ 179.4})$

$\frac{\= X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \= X )$

=> $P(| \= X- \mu| < 199 ) = P(|Z| < \frac{199}{ 179.4})$

=> $P(| \= X- \mu| < 199 ) = P(|Z|< 1.11)$

=> $P(| \= X- \mu| < 199 ) = P(-1.11 \le Z \le 1.11 )$

=> $P(| \= X- \mu| < 199 ) = P(Z \le 1.11 ) - P( Z \le -1.11 )$

From the z table the area under the normal curve to the left corresponding to 1.11 and -1.11 is

$P(Z \le 1.11 ) = 0.8665$

and

$P(Z \le - 1.11 ) = 0.1335$

So

$P(| \= X- \mu| < 199 ) = 0.8665 - 0.1335$

=> $P(| \= X- \mu| < 199 ) = 0.733$

8 0

3 years ago

Help 5th grade math need help ASAP

Galina-37 [17]

Answer:

A. The 2 groups could be quadrilateral and triangles.

quadrilateral-1,2,,6,7

Triangles-3,4,5,8,9

B.You could also sort them into shapes with 4 sides and shapes with 3 sides.

4 sides-1,2,,6,7

3 sides--3,4,5,8,9

C. They are all polygons becuase they all have 3 or more striaght sides and they all are closed shapes.

Step-by-step explanation:

7 0

3 years ago

Change the equation 2x - 5y + 4 = 0 into an equivalent equation written in the slope-intercept form

mamaluj [8]

Answer: The equation in slope intercept form is

y = 2x/5 + 4/5

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = y intercept

m represents the slope of the line.

The given equation is expressed as

2x - 5y + 4 = 0

Adding 5y to the left hand side and the right hand side of the equation, it becomes,

2x - 5y + 5y + 4 = 5y

5y = 2x + 4

Dividing the left hand side and the right hand side of the equation by 5, it becomes,

5y/5 = 2x/5 + 4/5

y = 2x/5 + 4/5

6 0

3 years ago

Suppose there were “x” students in a class who scored 100 and “y” students who scored 50. write an algebraic expression for the

bezimeni [28]

(100x + 50y) / 2

(I hope that's the answer!)

3 0

3 years ago