A dice is rolled twice. What is the probability of rolling a 3 followed by a 2?

Answers

Answer 1

The two rolls of the number cube are independent events because

the result of 1 roll does not affect the result of the other roll.

To find the probability of two independent events, we first find

the probability of each event, then we multiply the probabilities.

We can find the probability of an event using the following ratio:

number of favorable outcomes/total number of outcomes

Since there is only one way to roll a 3 and there are six

possible outcomes, 1, 2, 3, 4, 5, and 6, the probability of rolling a 3 is 1/6.

Since there is also only one way to roll a 2 and there are

six possible outcomes, the probability of rolling a 2 would be 1/6.

Now we multiply the probabilities.

1/6 x 1/6 is 1/36.

So the probability of rolling a 3 and a 2 is 1/36.

Answer 2

Answer:

1/36

Step-by-step explanation:

Probability of rolling 3 in a dice = 1/6.

Probability of rolling 2 = 1/6

Since, 2 should be followed after 3; we multiply 1/6 and 1/6

1/6 x 1/6 = 1/36.


Related Questions

Please help! Stuck on this question!!

Answers

Answer:

The 2 Gallon Tank is Enough

Step-by-step explanation:

A drink bottler needs to bottle 16 one-pint bottles. He has a 2 gallon tank and a 3 gallon tank.

There are 8 pints in a gallon. This means that 2 gallons would be 16 pints.

[tex]8 * 2 = 16[/tex]

So, the 2 gallon tank has 16 pints, which means that the 2 gallon tank should be enough to bottle all 16 bottles.

Answer:

2 gallon tank

Step-by-step explanation:

16 pints is the same as 2 US gallons

In a school, there are 25% fewer 11th graders than 10th graders, and 20% more 11th graders than 12th graders. The total number of students in 10th, 11th, and 12th grades in the school is 190. How many 10th graders are there at the school?

Answers

Answer:

There are 80 10th graders in the school

Step-by-step explanation:

Let the number of 10th graders be x

There are 25% fewer 11th graders

That mean x - 25% of x

x -0.25x = 0.75x

There are 20% more 11th graders than 12th graders

So if number of 12th graders = y, then

0.75x = y + 20/100 * y = y + 0.2y = 1.2y

Since ;

0.75x = 1.2y

then y = 0.75x/1.2 = 0.625x

So let’s add all to give 190

x + 0.75x + 0.625x = 190

2.375x = 190

x = 190/2.375

x = 80

Find the product of all solutions of the equation (10x + 33) · (11x + 60) = 0

Answers

Answer:

18

Step-by-step explanation:

Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:

10x + 33 = 0 or 11x + 60 = 0

10x = -33 or 11x = -60

x = -33/10 or x = -60/11

Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.

The state of Georgia is divided up into 159 counties. Consider a population of Georgia residents with mutually independent and equally likely home locations. If you have a group of n such residents, what is the probability that two or more people in the group have a home in the same county

Answers

Answer:

[tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]

Step-by-step explanation:

number of counties = 159

n number of people are mutually independent and equally likely home locations

considering the details given in the question

n ≤ 159

The number of ways for people ( n ) will live in the different counties (159) can be determined as [tex](\left \{ {{159} \atop {n}} \right} )[/tex]

since the residents are mutually independent and equally likely home locations hence there are : [tex]159^{n}[/tex] ways for the residents to live in

therefore the probability = [tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]

f(x)=−5x^3−4x^2+8x and g(x)=−4x^2+8, find (f−g)(x) and (f−g)(−2).

Answers

Answer:

see explanation

Step-by-step explanation:

(f - g)(x) = f(x) - g(x) , that is

f(x) - g(x)

= - 5x³ - 4x² + 8x - (- 4x² + 8) ← distribute parenthesis by - 1

= - 5x³ - 4x² + 8x + 4x² - 8 ← collect like terms

= - 5x³ + 8x - 8

Substitute x = - 2 into this expression, thus

(f - g)(- 2)

= - 5(- 2)³ + 8(- 2) - 8

= - 5(- 8) - 16 - 8

= 40 - 16 - 8

= 16

What's the exact value of tan 15°?

Answers

Answer:

The answer is 0.267949192

Step-by-step explanation:

I hope that is enough numbers.

if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=

Answers

Answer:

3

Step-by-step explanation:

f(x)=3x-3

g(x)=-x^2+4,

f(2) = 3(2) -3 = 6-3 =3

g(-2) = -(-2)^2+4 = -4+4 = 0

f(2)-g(-2)= = 3-0 = 3

Pablo rented a truck for one day. There was a base fee of $19.99, and there was an additional charge of 80 cents for each mile driven. Pablo had to pay
$221.59 when he returned the truck. For how many miles did he drive the truck?

Answers

Answer:

252 miles

Step-by-step explanation:

19.99 + .80x = 221.59

,80x = 201.60

x = 252

24. After a vertical reflection across the x-axis, f(x) is

Options:

A. –f(x)
B. f(x – 1)
C. –f(–x)
D. f(–x)

Answers

Answer:

A. –f(x)

Step-by-step explanation:

The transformation of a reflection about the x-axis is

f(x) -> -f(x).

So the answer is

A. –f(x)

Suppose that X; Y have constant joint density on the triangle with corners at (4; 0), (0; 4), and the origin. a) Find P(X < 3; Y < 3). b) Are X and Y independent

Answers

The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is

[tex]f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}[/tex]

where T is the set

[tex]T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}[/tex]

(a) I've attached an image of the integration region.

[tex]P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12[/tex]

(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.

Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:

[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}[/tex]

[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}[/tex]

Clearly, [tex]f_{X,Y}(x,y)\neq f_X(x)f_Y(y)[/tex], so they are not independent.

7. Over the past 50 years, the number of hurricanes that have been reported are as follows: 9 times there were 6 hurricanes, 13 times there were 8 hurricanes, 16 times there were 12 hurricanes, and in the remaining years there were 14 hurricanes. What is the mean number of hurricanes is a year

Answers

Answer:

Step-by-step explanation:

Let us first generate the frequency table from the information given:

Hurricane number(X)       Frequency(f)                f(X)

6                                            9                                   54

8                                            13                                  104

12                                           16                                  192

14                                            12                                168

Total                                     ∑(f) = 50                          ∑f(x) =518

In order to determine the last frequency (the remaining years), we will add the other frequencies and subtract the answer from 50, which is the total frequency (50 years). This is done as follows:

Let the last frequency be f

9 + 3 + 16 + f = 50

38 + f = 50

f = 50 - 38 = 12

Now, calculating mean:

[tex]\bar {X} = \frac{\sum f(x)}{\sum(f)} \\\\\bar {X} = \frac{518}{50} \\\\\bar {X} = 10.36[/tex]

Therefore mean number of hurricanes = 10.4 (to one decimal place)

What is the area of polygon EFGH?

Answers

Answer:

C. 42 square units

Step-by-step explanation:

This is a rectangle and to calculate the area of a rectangle we multiply length and width

The length of this rectangle is 7 units and the width is 6 units

6 × 7 = 42 square units

. line containing ( −3, 4 ) ( −2, 0)

Answers

Answer:

The equation is y= -4x -8

Step-by-step explanation:

The -4 is the slope and the -8 is the y intercept

Answer:

Slope: -4

Line type: Straight and diagonal from left to right going down.

Rate of change: a decrease by 4 for every x vaule

y-intercept is: (0,-8)

x-intercept is: (-2,0)

Step-by-step explanation:

Slope calculations:

y2 - y1 over x2 - x1

0 - 4

-2 - ( -3) or -2 + 3

=

-4/1 =

-4

More slope info on my answer here: https://brainly.com/question/17148844

Hope this helps, and have a good day.

given that f(x)=x^2-4x -3 and g(x)=x+3/4 solve for f(g(x)) when x=9

Answers

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

A train goes at a speed of 70km / h. If it remains constant at that speed, how many km will it travel in 60 minutes?

Answers

Answer:

Total distance travel by train =  70 km

Step-by-step explanation:

Given:

Speed of train = 70 km/h

Total time taken = 60 min = 60 / 60 = 1 hour

Find:

Total distance travel by train

Computation:

Distance = Speed × Time

Total distance travel by train = Speed of train × Total time taken

Total distance travel by train = 70 × 1

Total distance travel by train =  70 km

Brandon is paid 150% of his regular hourly rate for overtime hours. He is paid \$45.00 an hour for overtime hoursWhat is his regular hourly rate?

Answers

Answer:

Regular hourly rate for Brandon is $30

Step-by-step explanation:

Let the payment for regular hours be $x

given that

Brandon is paid 150% of his regular hourly rate for overtime hours

payment for overtime hours = 150% of payment for regular hours

payment for overtime hours = 150/100 * x = 3x/2

Given that He is paid \$45.00 an hour for overtime hours

thus,

3x/2 = 45

=> x = 45*2/3 = 30

Thus,  regular hourly rate for Brandon is $30

area to the right of z=0.72

I don’t have a graphing calculator and I couldn’t find one online. I’m completely clueless on this one.

Answers

Answer:

Desmos could come in handy

Find the first three nonzero terms in the power series expansion for the product f(x)g(x).
f(x) = e^2x = [infinity]∑n=0 1/n! (2x)^n
g(x) = sin 5x = [infinity]∑k=0 (-1)^k/(2k+1)! (5x)^2k+1
The power series approximation of fx)g(x) to three nonzero terms is __________
(Type an expression that includes all terms up to order 3.)

Answers

Answer:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 1 to 3.

= -196.5

Step-by-step explanation:

Given

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to infinity

The expression that includes all terms up to order 3 is:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to 3.

= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)

= -125/2 + 100000/6 - 759375/5040

= -62.5 + 16.67 - 150.67

= - 196.5

Use the definition of continuity and the properties of limits to show that the function f(x)=x sqrtx/(x-6)^2 is continuous at x = 36.

Answers

Answer:

The function is  continuous at  x = 36

Step-by-step explanation:

From the question we are told that

      The  function is [tex]f(x) = x * \sqrt{ \frac{x}{ (x-6) ^2 } }[/tex]  

       The  point at which continuity is tested is  x =  1

Now from the definition  of continuity ,

   At function is continuous at  k if  only  

       [tex]\lim_{x \to k}f(x) = f(k)[/tex]

So

      [tex]\lim_{x \to 36}f(x) = \lim_{n \to 36}[x * \sqrt{ \frac{x}{ (x-6) ^2 } }][/tex]

                            [tex]= 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]

                             [tex]= 7.2[/tex]

Now  

     [tex]f(36) = 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]

     [tex]f(36) = 7.2[/tex]

So  the given function is continuous at  x =  36

because

          [tex]\lim_{x \to 36}f(x) = f(36)[/tex]

An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth rate during those 9 years is approximated by
dh/dt = 1.8t + 3,
where t is the time (in years) and h is the height (in centimeters). The seedlings are 10 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm

Answers

Answer:

(a) After t years, the height is

18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Step-by-step explanation:

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

I really need help please answer!

Answers

Answer:

-2, b, a+c

Step-by-step explanation:

Answer:

-2, b, a+c

Step-by-step explanation:

By looking at where A and C are on the number line, we can tell that A is a negative number close to zero and C is a positive number a little greater than four. This means that if we add the two together, we'll get a positive number a little below four.

By looking at the number line, we can tell that the value of B is a positive number a little below the number three.

Now that we know that B is less than A+C, and we know where -2 is on the number line (two marks to the left of zero) we can decide the least to greatest values.

Since negatives are always less than positives, we know that -2 has the smallest value. Next, we know that B is lower on the number line than A+C. So, in order, from least to greatest, the answer is:

-2, B, A+B

Hope this helps!! <3 :))

Find the domain of the Bessel function of order 0 defined by [infinity]J0(x) = Σ (−1)^nx^2n/ 2^2n(n!)^2 n = 0

Answers

Answer:

Following are the given series for all x:

Step-by-step explanation:

Given equation:

[tex]\bold{J_0(x)=\sum_{n=0}^{\infty}\frac{((-1)^{n}(x^{2n}))}{(2^{2n})(n!)^2}}\\[/tex]

Let   the value a so, the value of [tex]a_n[/tex]  and the value of [tex]a_(n+1)[/tex]is:

[tex]\to a_n=\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}[/tex]

[tex]\to a_{(n+1)}=\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}[/tex]

To calculates its series we divide the above value:

[tex]\left | \frac{a_(n+1)}{a_n}\right |= \frac{\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}}{\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}}\\\\[/tex]

           [tex]= \left | \frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2} \cdot \frac {2^{2n}(n!)^2}{(-1)^2n x^{2n}} \right |[/tex]

           [tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)!^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |[/tex]

           [tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\= \left | \frac{x^{2n}\cdot x^2}{2^{2n} \cdot 2^2(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\[/tex]

           [tex]= \frac{x^2}{2^2(n+1)^2}\longrightarrow 0 <1[/tex]   for all x

The final value of the converges series for all x.

if 280 is to be shared between iyene and nokob in the ratio 2:3. in how many equal part will thE money be shared​

Answers

Answer:

5

Step-by-step explanation:

There will be five equal part because Iyene takes 2 parts and nokob takes 3 parts

Thus, the total parts which have been shared is 2+3=5

Further more, every part is

[tex] \frac{280}{5} = 56[/tex]

Hence, there is 5 parts have been shared and every part is 56 dollars

Answer:

5 equal parts

Because one of the dudes will get 2 and the other one will get 3 parts

3+2 is 5

280/5=56 (1 part)

so iyene will get 56*2=112 and nokob will get 56*3=168

A bag contains 12 blue marbles, 5 red marbles, and 3 green marbles. Jonas selects a marble and then returns it to the bag before selecting a marble again. If Jonas selects a blue marble 4 out of 20 times, what is the experimental probability that the next marble he selects will be blue? A. .02% B. 2% C. 20% D. 200% Please show ALL work! <3

Answers

Answer:

20 %

Step-by-step explanation:

The experimental probability is 4/20 = 1/5 = .2 = 20 %

A line passes through A(3,7) and B(-4,9). Find the value of a if C(a, 1) is on the line.

Answers

Answer:  a=24

Step-by-step explanation:

Lets find the line's  formula (equation of the line).

As known the general formula of any straight line (linear function) is

y=kx+b

Lets find the coefficient k= (Yb-Ya)/(Xb-Xa)=(9-7)/(-4-3)=-2/7

(Xb;Yb)- are the coordinates of point B

(Xa;Ya) are the coordinates of point A

Now lets find the coefficient b.  For this purpose we gonna use the coordinates of any point A or B.

We will use A

7=-2/7*3+b

7=-6/7+b

b=7 6/7

So the line' s  equation is y= -2/7*x+7 6/7

Now we gonna find the value of a usingcoordinates of point C.

Yc=1,  Xc=a

1=-2/7*a+7 6/7

2/7*a= 7 6/7-1

2/7*a=6 6/7

(2/7)*a=48/7

a=48/7: (2/7)

a=24

Answer:

a=24

Step-by-step explanation:

find the slope of the line that passes through the two points (0,1) and (-8, -7)

Answers

Answer:

The slope of the line is 1

Step-by-step explanation:

The slope of a line is found by using the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

where

m is the slope and

(x1 , y1) and ( x2 , y2) are the points

Substituting the above values into the above formula we have

Slope of the line that passes through

(0,1) and (-8, -7) is

[tex]m = \frac{ - 7 - 1}{ - 8 - 0} = \frac{ - 8}{ - 8} = 1[/tex]

The slope of the line is 1

Hope this helps you

At an airport, 76% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that no more than 4 of them were on time.

Answers

Answer:

The probability is  [tex]P( X \le 4 ) = 0.0054[/tex]

Step-by-step explanation:

From the question we are told that

   The percentage that are on time is  p =  0.76

   The  sample size is n =  11

   

Generally the percentage that are not on time is

     [tex]q = 1- p[/tex]

     [tex]q = 1- 0.76[/tex]

     [tex]q = 0.24[/tex]

The  probability that no more than 4 of them were on time is mathematically represented as

        [tex]P( X \le 4 ) = P(1 ) + P(2) + P(3) + P(4)[/tex]

=>     [tex]P( X \le 4 ) = \left n } \atop {}} \right.C_1 p^{1} q^{n- 1} + \left n } \atop {}} \right.C_2p^{2} q^{n- 2} + \left n } \atop {}} \right.C_3 p^{3} q^{n- 3} + \left n } \atop {}} \right.C_4 p^{4} q^{n- 4}[/tex]

[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{11- 1} + \left 11 } \atop {}} \right.C_2p^{2} q^{11- 2} + \left 11 } \atop {}} \right.C_3 p^{3} q^{11- 3} + \left 11 } \atop {}} \right.C_4 p^{4} q^{11- 4}[/tex]

[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{10} + \left 11 } \atop {}} \right.C_2p^{2} q^{9} + \left 11 } \atop {}} \right.C_3 p^{3} q^{8} + \left 11 } \atop {}} \right.C_4 p^{4} q^{7}[/tex]

[tex]= \frac{11! }{ 10! 1!} (0.76)^{1} (0.24)^{10} + \frac{11!}{9! 2!} (0.76)^2 (0.24)^{9} + \frac{11!}{8! 3!} (0.76)^{3} (0.24)^{8} + \frac{11!}{7!4!} (0.76)^{4} (0.24)^{7}[/tex]

[tex]P( X \le 4 ) = 0.0054[/tex]

Nina skated for 2 hours and 14 min she stop at 8:24 pm when did Nina start skating

Answers

Answer:

6:10 pm

Step-by-step explanation:

she skate for 2 h and 14 min so,

8:24- 2:14

=6:10 pm

Circle O has a circumference of 36π cm. Circle O with radius r is shown. What is the length of the radius, r? 6 cm 18 cm 36 cm 72 cm

Answers

Answer:

18 cm.

Step-by-step explanation:

The circumference of a circle is found by calculating 2 * pi * r.

In this case, the circumference is 36 pi cm.

2 * pi * r = 36 * pi

2 * r = 36

r = 36 / 2

r = 18 cm.

Hope this helps!

Answer:

18 centimeters

Step-by-step explanation:

The circumference of a circle can be found using the following formula.

[tex]c=2\pi r[/tex]

We know the circumference is 36π cm, therefore we can substitute 36π in for c.

[tex]36\pi= 2 \pi r[/tex]

We want to find r, the radius. Therefore, we must get r by itself. First, divide both sides of the equation by pi.

[tex]36\pi / \pi = 2 \pi r / \pi\\\\36= 2 \pi r / \pi\\\\36=2r[/tex]

Next, divide both sides of the equation by 2.

[tex]36=2r \\\\36/2=2r/2\\\\36/2=r\\\\18=r\\\\r=18 cm[/tex]

The radius of Circle O is 18 centimeters.

the ration of men to women in a certain factory is 3 to 4. there are 204 men. how many workers are there?

Answers

Answer:

476 workers

Step-by-step explanation:

Men: women : total

3          4           3+4 = 7

We want 204 men

204/3 =68

Multiply each by 68

Men: women : total

3*68    4*68      7*68

204        272      476

Answer:

There are 476 workers

Step-by-step explanation:

Other Questions
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