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
Elanso [62]
3 years ago
9

A fair die is rolled twice. What is the probability that: a. The die shows a different number on each toss. e.g. (2,5) b. The su

m of the dots showing is greater than or equal to 10. List the outcomes in this set. Then calculate the probability. c. The total score is less than 4. List the outcomes in this set. Then calculate the probability.
Mathematics
1 answer:
Eduardwww [97]3 years ago
6 0

Answer:

a) \frac{5}{6}

b) \frac{1}{6}

c) \frac{1}{9}

Step-by-step explanation:

Total possible outcomes when a dice is rolled twice

(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)

here total number of possible outcomes is 36

now,

P (Event ) = \frac{\textup{Number of favorable outcomes of an Event}}{\textup{Total possible outcomes}}  

a) P( die shows a different number on each toss )

Favorable outcomes = (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,1) , (2,3) , (2,4) , (2,5) , (2,6), (3,1) , (3,2) ,  (3,4) , (3,5) , (3,6) , (4,1) , (4,2) , (4,3) ,  (4,5) , (4,6) , (5,1) , (5,2) , (5,3) , (5,4) ,  (5,6) , (6,1) , (6,2) , (6,3) , (6,4) , (6,5)

number of Favorable outcomes = 30

thus,

P( die shows a different number on each toss ) = \frac{30}{36}=\frac{5}{6}

b) P( The sum of the dots showing is greater than or equal to 10 )

Favorable outcomes = (4,6) , (5,5) , (5,6) , (6,4) , (6,5) , (6,6)

number of Favorable outcomes = 6

P( The sum of the dots showing is greater than or equal to 10 )

= \frac{6}{36}=\frac{1}{6}

c) P(  total score is less than 4 )

Favorable outcomes = (1,1) , (1,2) , (1,3) , (2,1)

number of Favorable outcomes = 4

P(  total score is less than 4 ) = \frac{4}{36}=\frac{1}{9}

You might be interested in
Volume and surface area are often compared by manufacturers in order to maximize how much of something can go inside of a packag
notka56 [123]
We have no dimensions to work with. I'll pick some and try and comply with the conditions of the problem. 

Suppose you have an object that is 14 by 22 by 27 cm. These three numbers have no common factor so they cannot be reduced any further, which is helpful for this problem.

Find the Volume
Volume

l = 27 cm
w = 14 cm
h = 22 cm

V = 27 *14 * 22
V = 8316 cm^3

Find the surface area
SA = 2*l*w + 2*l*h  + 2*w*h
SA = 2*27*14  +  2*27*22   +  2*14*22
SA = 756 + 1188 + 616
SA = 2558

Just looking at these numbers The surface area is about 1/3 of the volume. I don't think this is always true.


 \frac{SA}{V} =  \frac{2*L*W  + 2*L*H + 2*W*H}{L*W*H} 

Another way to do this is to consider a cube which might give you a more useful result. 

s = L = W = H all three dimensions are equal in a cube.
The volume of a cube is s*s*s = s^3
The surface area of a cube is 2*s*s + 2*s*s + 2s*s = 6s^2

\frac{SA_cube}{V_cube} =  \frac{6s*s}{s*s*s}
\frac{SA}{V} =  \frac{6}{s}

That means whatever the side length, the Surface Area to volume = 6/the side length which is kind of an interesting result.


4 0
3 years ago
What is the volume of a sphere with surface area of 25 pi yd squared?
kherson [118]

\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=25\pi \end{cases}\implies 25\pi =4\pi r^2 \\\\\\ \cfrac{25\pi }{4\pi }=r^2\implies \cfrac{25}{4}=r^2\implies \sqrt{\cfrac{25}{4}}=r\implies \cfrac{\sqrt{25}}{\sqrt{4}}=r\implies \cfrac{5}{2}=r \\\\[-0.35em] ~\dotfill

\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \frac{5}{2} \right)^3}{3}\implies V=\cfrac{4\pi \cdot \frac{125}{8}}{3}\implies V=\cfrac{\frac{500\pi }{8}}{~~\frac{3}{1}~~} \\\\\\ V=\cfrac{500\pi }{8}\cdot \cfrac{1}{3}\implies V=\cfrac{500\pi }{24}\implies V=\cfrac{125\pi }{6}\implies V\approx 65.45

7 0
3 years ago
How do you solve a problem involving squeeze theorem?
nadezda [96]

Answer:

Step-by-step explanation:

if two functions are squeezed together at a particular point , then any function trapped between them will get squeezed to that point. the squeeze theorem deals with limit value , rather than function value. the squeeze theorem sometimes called Pinch Theorem.

3 0
3 years ago
What is the eighth term in the arithmetic sequence defined by the explicit formula
RideAnS [48]

Answer:

Find out the what is the eighth term in the arithmetic sequence defined by the explicit formula.

a_{n} = 2n + 7

To prove

As given the explicit formula for the arithmetic sequence .

a_{n} = 2n + 7

Put n = 8

a_{8} = 2\times 8 + 7

a_{8} = 16 + 7

a_{8} = 23

Therefore the eighth term in the arithmetic sequence is 23 .




5 0
3 years ago
Read 2 more answers
CAN SOMEONE JUST PLEASE ANSWER THIS ASAP FOR BRAINLIEST!!
aksik [14]

Answer:

F= 3x^2

Step-by-step explanation:

1) Multiplying exponents causes them to add, for instance if you were to multiply x^3 * x^4 the final product would be x^7. If you were to divide exponents then they would subtract.

2) Similarly in this problem  you would determine the missing factor by dividing the product from -10x^3

3)  Using the steps above, begin dividing.

-30x^5 / -10x^3

4) -30 divided by -10 is 3 and as mentioned in step number one, you subtract exponents whenever they are divided by each other.  5-3=2

5) Due to all of the steps mentioned above, The answer is 3x^2

6 0
3 years ago
Read 2 more answers
Other questions:
  • A couple that already has two daughters wants to have another child. the couple is hoping for a son. what is the probability tha
    5·1 answer
  • Gcf of 147x^7,-21^8,3x^9
    6·1 answer
  • There are 30 senators and 60 members of the house of representatives in the Arizona Legislature.Suppose 20 senators and 25 repre
    10·1 answer
  • Problem 3.2.14a<br><br> Show that 2^2x+1 +1 is divisible by 3.
    12·1 answer
  • So If Mr. Cohen drives 84 2/10 miles on Tuesday,84 6/10 miles on Wednesday,85 miles on Thursday how many miles would He drive on
    12·2 answers
  • Solve the system by elimination <br><br> 4x+3y=-5<br><br> -x+3y=-10
    8·1 answer
  • Which point represents the x-intercept of this exponential function?
    9·1 answer
  • Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 25 and, in a separat
    14·2 answers
  • for the following problems do at least one problem using unit form and at least one problem using fraction form 3.2 x 1.4=
    5·1 answer
  • 9. Which is a solution of the equation 5(x – 8) = -55 ?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!