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
denis-greek [22]
3 years ago
5

The only contents of a container are 10 disks that are each numbered with a different positive integer from 1 through 10, inclus

ive. if 4 disks are to be selected one after the other, with each disk selected at random and without replacement, what is the probability that the range of the numbers on the disks selected is 7
Mathematics
1 answer:
allsm [11]3 years ago
6 0

First we calculate for the total number of possibilities (permutation) to select 4 disks from the container:

Total number of possibilities = 10 * 9 * 8 * 7

Total number of possibilities = 5040

<span>
Now let us find the 4 disks that will result in a range of 7. </span>

Range = highest number – lowest number

The pair of highest and lowest number that will result in range of 7 is: (1 & 8), (2 & 9), (3 & 10)

 

As a basis of calculation, let us use the pair 1 & 8.

There are four possible ways to select 1 and three for 8.

Arrangements of maximum and minimum pair = 4 * 3

Arrangements of maximum and minimum pair=12

Now we need to calculate for the remaining 2 disk. There are 6 numbers between 1 & 8. The total possibilities for selecting 2 disk from the remaining 6 is:

Possibilities of selecting 2 disk from remaining 6 = 6 * 5

Possibilities of selecting 2 disk from remaining 6 = 30

Therefore, the total possibility to get a range of 7 from a pair of 1 & 8 is:

Total possibility for a pair = 12 * 30

Total possibility for a pair = 360

 

Since there are a total of three pairs (1 & 8), (2 & 9), (3 & 10):

Total possibilities of the 3 pairs = 360 * 3

Total possibilities of the 3 pairs = 1080

 

Therefore:

Probability = Total possibilities of the 3 pairs / Total number of possibilities

<span>Probability = 1080 / 5040 = 3 / 14                      (FINAL ANSWER)</span>

You might be interested in
3 3/4 divide 2 1/12<br><br><br> sssss
dybincka [34]
3 3/4 divide 2 1/12 = 1.8


8 0
3 years ago
What is the arc measure of AEB in degrees
jasenka [17]

Answer:

305 degree

Step-by-step explanation:

As AD and CE are the diameters of circle P, so that they intersect each other at point P.

=> So that ∡CPA and ∡DPE are two vertical angles.

=> ∡CPA = ∡DPE = 93 degree

As we can see, ∡CPA = ∡CPB + ∡BPA =38 + ∡BPA

=> ∡BPA = ∡CPA - 38 = 93 - 38 = 55 degree

As P is the centre of the circle, so that ∡BPA is equal to the measure of the arc AB, equal to 55 degree.

In the circle P, the total measure of arc AEB and arc AB are 360 degree

=> arc AEB + arc AB = 360

=> arc AEB = 360 - arc AB = 360 - 55 = 305

So that the measure of arc AEB is 305 degree

7 0
2 years ago
Pls help me guys!<br> Thanks =P
hichkok12 [17]
I would just try to identify the pattern. First, for the cups column, if the amount increases by 5 each time, then the missing box must be 5 less than 10 or 5

The, for the servings column, you can test to find the pattern. If you were to guess the pattern is 3, when you check, you would see that the boxes are 6 and 9 because then it increases by 3 each time

Hope this helps
8 0
2 years ago
Read 2 more answers
Write the fraction is simplest form.<br> 4) 7/28 <br> 5) 12/20
KATRIN_1 [288]

Answer:

1/4 and 3/5

Step-by-step explanation:

4. 7/28 5. 12/20

1/4 6/10

3/5

8 0
3 years ago
Read 2 more answers
ASAP<br>Find all solutions to the equation.<br><br><br>7 sin^2 x - 14 sin x + 2 = -5
matrenka [14]

Answer:

{-π/2, π/2}

Step-by-step explanation:

Rewrite this as:

7sin^2 x - 14sin x + 7 = 0.  Reduce this result by dividing all terms by 7:

sin^2 x - 2sin x + 1

Temporarily replace "sin x" with y:

y^2 - 2y + 1 = 0

Solve this through factoring:  (y - 1)^2 = 0, or y - 1 = ± 0, or y = ±1

Recalling that y = sin x, we write

sin x = ±1, whose solutions are sin x = 1 and sin x = -1

The solution of sin x = 1 is π/2 and that of sin x = -1 is -π/2

and so the solution set is {-π/2, π/2}

3 0
2 years ago
Other questions:
  • A school cafeteria sold 1,280 slices of pizza the first week,640 the second week,and 320 the third week.if this pattern continue
    12·1 answer
  • How many terms are in the algebraic expression 11;; +3 ?
    8·1 answer
  • I'm confused on this
    8·1 answer
  • when Miguel was six years old his little sister leila was half of his age if Miguel is 40 years old today how old is leila
    14·1 answer
  • What is the volume of the following rectangular prism????help fast pleasee
    14·1 answer
  • Determine the slope of the following graph.
    9·1 answer
  • a fish tank has a height of 30 inches, length of 20 inches, and a width of w 25 inches. how many cubic inches will the tank hold
    8·1 answer
  • Which values of a, b, and c correctly represent the answer in simplest form? 3 =a O a=38.0= 14.0=1 a=1.0= 14.C = 38 O a= 1.5=7.C
    10·1 answer
  • Five pairs of socks are in a drawer. Three pairs
    8·1 answer
  • Solve the equation. x2 + 18x + 81 = 25
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!