An ordinary (falr) dle is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a dle is rolled twice in succession
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 8.
Event B: The sum is divisible by 5.
Write your answers as fractions.
(a) P(X) =

(b) P(B) =

Answers

Answer 1

By finding the number of outcomes that meet each criteria, we will see that the probabilities are:

A) P = 0.25B) P = 7/36 = 0.194

How to find the probability?

We know that the fair die has 6 outcomes, so if we roll it twice, there are a total of:

6*6 = 36 outcomes.

To find the probability of getting a given event, we need to find the number of outcomes that make the event true.

A) The sum is greater than 8.

The outcomes that make this true are:

first roll    second roll     sum

 4                   5                 9

 4                   6                 10

5                     5                10

5                    6                 11

6                     3                 9

6                    4                 10

6                     5                11

6                     6                  12

3                     6                   9

So there are 9 outcomes whose sum is greater than 8, so the probability to getting this event is:

P = 9/36 = 0.25

B) The sum is divisible by 5.

The sum must be 5 or 10, the outcomes that give that are:

first roll    second roll     sum

   1                   4                 5

   2                  3                 5

   3                  2                 5

   1                   4                 5

   4                   6                10

  5                    5                10

   6                   4                 10

There are 7 outcomes, so the probability is:

P = 7/36 = 0.194

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Related Questions

Which inequality represents all the solutions of -2(3x + 6) = 4(x + 7)?
ОА.
X2-4
ОВ.
XS-4
O c. 28
OD.
xs 8

Answers

The answer is x=-4

I’ve attached my work explaining why below :)

x≤-4 is the inequality represents all the solutions of -2(3x + 6) = 4(x + 7)

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given equation is -2(3x + 6) = 4(x + 7

We need to find the inequality which represents the solutions of the equation.

Let us solve for x

-2(3x + 6) = 4(x + 7)

Apply distributive property

-6x-12=4x+28

Take the variable terms on one side.

-6x-4x=28+12

-10x=40

Divide both sides by 10

x=-4

Hence, x≤-4 is the inequality represents all the solutions of -2(3x + 6) = 4(x + 7)

To learn more on Equation:

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Tina buys three 7/8 yards of material at the fabric store she uses to make a skirt Afterward she has one and 3/8 of the fabric left over how many yards of material did Tina use

Answers

Answer:

1 and 2/8 yards of material used

Step-by-step explanation:

Write the equation of the circle that has a center of (-7, 17) with
a radius of V19.

Answers

I think your question seems to be :-

Write the equation of the circle that has a center of (-7, 17) with a radius of √19

So , as we know that the equation of circle with centre at (h,k) and radius r is given by [tex]{\bf{(x-h)^{2}+(y-k)^{2}=r^{2}}}[/tex] . Now , using same concept in this question ;

[tex]{:\implies \quad \sf \{x-(-7)\}^{2}+(y-17)^{2}=(\sqrt{19})^{2}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{(x+7)^{2}+(y-17)^{2}=19}}}[/tex]

This is the required equation of Circle

Urgent need help pls answer with the correct explanation

Answers

with two semi-circles on both sides, it forms a full circle.

area of circle:

π * radius²

π * 2²

4π in²

area of rectangle:

length * width

20 * 4

80 in²

total area:

4π in² + 80 in²

93 in²

area of triangular prism:

( base length * perpendicular height * length ) ÷ 2

( 12.6 * 1.6 * 10.75 ) ÷ 2

216.72 ÷ 2

108.36 mm³

Determine the area of the triangle.
12 cm
24 cm
The area is
(Type an integer or a decimal.)

Answers

Answer: 144 square centimeters

Step-by-step explanation:

An area of a triangle is determined by this formula: Area = Length * Height/2. Since 12 x 24 = 288, divide 288 by 2 and you will have 144

Conclusion:

it's 144 square centimeters

[tex]6+\sqrt[5]{249-2x} =7[/tex]

Answers

Answer: 124

Step-by-step explanation:

First, subtract 6 on both sides to get:

[tex]\sqrt[5]{249-2x} =1[/tex]

Take both sides to the 5th power. The radical will cancel, and the right side will be unchanged:

[tex]249-2x=1[/tex]

Subtract 249 on both sides:

[tex]-2x=-248[/tex]

[tex]2x=248[/tex]

[tex]x=124[/tex]

Answer:

x=124

Step-by-step explanation:

[tex]6+\sqrt[5]{249-2x} =7\\\sqrt[5]{249-2x} =7-6=1\\249-2x=1^5=1\\249-1=2x\\2x=248\\x=\frac{248}{2} =124[/tex]

A shipping container is in the form of a right rectangular prism, with dimensions of
20 ft by 8 ft by 9 ft 9 in. If the container holds 359 cubic feet of shipped goods, what
percent is full? Round your answer to the nearest whole number if necessary.

Answers

Answer:

23%

Step-by-step explanation:

1) Find the area of the container. (20*8*9.9)

2) Divide 359 by 1584 (the area) to find the percent

3) Round up the percent and you get 23%.

What is the sum of the squared distances from the mean?

Answers

Answer:

The sum of squares is the sum of the square of variation, where variation is defined as the spread between each individual value and the mean. To determine the sum of squares, the distance between each data point and the line of best fit is squared and then summed up. The line of best fit will minimize this value.

Emily says that a square is always a rectangle. Jenna says a rectangle is always a square. Who is correct and why are they correct?​

Answers

Answer:

Jenna is right

Step-by-step explanation:

Jenna is right because what makes up a square is its four sides. When calculating the area of a rectangle you use the same formula as you would for a square. A rectangle is just an elongated square.

Please help me need ASAP

Answers

Answer:

B

Step-by-step explanation:

Because you will divide U in X the give you correct answer.

solve the following inequality |2x-6|<10

Answers

Answer:

Absolute Value Inequality entered :      |2x-6|<10 

Step by step solution :STEP 1:Rearrange this Absolute Value InequalityAbsolute value inequalitiy entered      |2x-6| < 10 STEP 2:Clear the

Absolute Value BarsClear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x-6| For the Negative case we'll use -(2x-6) For the Positive case we'll use (2x-6) STEP 3:Solve the Negative Case      -(2x-6) < 10      Multiply      -2x+6 < 10      Rearrange and Add up      -2x < 4      Divide both sides by 2       -x < 2      Multiply both sides by (-1)      Remember to flip the inequality sign       x > -2    
  Which is the solution for the Negative Case

STEP 4:Solve the Positive Case      (2x-6) < 10      Rearrange and Add up      2x < 16      Divide both sides by 2       x < 8      Which is the solution for the Positive Case

STEP 5:Wrap up the solution    -2 < x < 8 Solution in Interval Notation    (-2,8) Solution on the Number Line

One solution was found :    -2 < x < 8

Step-by-step explanation:

mark me brainliest!!

10) Consider the function f(x) = x2 shown, which describes the graph of the function? A) increasing B) decreasing C) increasing then decreasing D) decreasing the increasing​

Answers

The function f(x) = x^2 is a quadratic function

The graph is (D) decreasing the increasing​

How to describe the function?

The function is given as:

f(x) = x^2


From the graph of the function, we can see that the function values decreases then increases.

Hence, the statement that describes the graph is (D) decreasing the increasing​

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the area of a square is 80cm find the diagonal line​

Answers

Answer:

d~~12.65

Step-by-step explanation:

Which pairs of angles are alternate interior angles? Select all that apply.
3
20
N
517
618
co

Answers

Answers: Choice A and Choice C

Explanation:

Think of the vertical lines as train tracks (the metal rails).

Stuff between the rails are interior angles.

Angles 3 and 6 are one pair of alternate interior angles because they are on alternating sides of the transversal line. The other pair of alternate interior angles are angles 4 and 5.

Alternate interior angles are congruent when we have parallel lines like this.

3x4^2=144 determin if true

Answers

Answer:

False

Step-by-step explanation:

By order of operations, in this case, we first have to solve exponents and THEN multiply by 3.

[tex]3*4^2=144[/tex] [tex]3*16=144[/tex] [tex]48\neq 144[/tex]

Therefore, this equation is false.

Answer:

False

Step-by-step explanation:

4^2=16

4^2=163x16=48

4^2=163x16=4848=144

4^2=163x16=4848=144The numbers dont match.

4^2=163x16=4848=144The numbers dont match.Hence the equation is false.

how do you graph y = 3x + 2

Answers

Here’s a desmos photo: but if you’re curious how to do it on paper. Just look for x and t intercepts.

X int where y=0 (-2/3,0)
Y int where x=0 (0,2)

30 percent off entire purchase the gloves cost $35 before the discount

Answers

30% off 35.00 is 24.50
The difference is 10.50

3. Higher Order Thinking The
lengths of the pencils are
given at the right.
Write and solve a two-step
problem about the pencils.
6 cm
8 cm
10 cm

Answers

The lengths of the three pencils form a right-triangle, and the two-step problem is:

6^2 + 8^2 = 10^2100 = 100

How to write the two-step problem

The lengths of the pencils are given as:

6cm, 8cm and 10cm

Using the Pythagoras theorem, we have:

6^2 + 8^2 = 10^2

Evaluate the exponents

100 = 100

Hence, the lengths of the three pencils form a right-triangle

Read more about two-step problem at:

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please answer this question​

Answers

We have the given indefinite integral ;

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{x+1}{x(xe^{x}+2)}dx}[/tex]

We will use substitution hence to solving this integral

Now , put ;

[tex]{:\implies \quad \sf e^{x}=u}[/tex]

So that :

[tex]{:\implies \quad \sf dx=\dfrac{du}{u}\quad and\quad log(u)=x}[/tex]

Now , putting the values in the integral , it can be written as ;

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{log(u)+1}{log(u)\{ulog(u)+2\}}\times \dfrac{du}{u}}[/tex]

Now , we will again use substitution method for making the integral easy. So put ;

[tex]{:\implies \quad \displaystyle \sf ulog(u)+2=v}[/tex]

So that ;

[tex]{:\implies \quad \displaystyle \sf du=\dfrac{dv}{log(u)+1}\quad and\quad ulog(u)=v-2}[/tex]

Now , we have ;

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{\cancel{\{log(u)+1\}}}{log(u)v}\times \dfrac{dv}{\cancel{\{log(u)+1\}}u}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dv}{v\{ulog(u)\}}}[/tex]

Now , putting the value of ulog(u) = v - 2

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dv}{v(v-2)}}[/tex]

Now , using partial fraction decomposition , ths given integral can be further written as ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\int \left(\dfrac{1}{v-2}-\dfrac{1}{v}\right)dv}[/tex]

Now ,as integrals follow distributive property. So ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\left(\int \dfrac{1}{v-2}dv-\int \dfrac{1}{v}dv\right)}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}(log|v-2|-log|v|)+C}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{v-2}{v}\bigg| +C}[/tex]

Putting value of v ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{ulog(u)+2-2}{ulog(u)+2}\bigg| +C}[/tex]

Now, putting value of u ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{e^{x}log(e^{x})}{e^{x}log(e^{x})+2}\bigg| +C}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{xe^{x}}{xe^{x}+2}\bigg| +C}[/tex]

[tex]{:\implies \quad \therefore \displaystyle \underline{\underline{\int \bf \dfrac{x+1}{x(xe^{x}+2)}dx=\dfrac{1}{2}log\bigg|\dfrac{xe^{x}}{xe^{x}+2}\bigg| +C}}}[/tex]

Used Concepts :-

[tex]{\boxed{\displaystyle \bf \int \dfrac{1}{x}dx=log|x|+C}}[/tex]

[tex]{\boxed{\displaystyle \bf \dfrac{d}{dx}(u\cdot v)=v\dfrac{du}{dx}+u\dfrac{dv}{dx}}}[/tex]

[tex]{\boxed{\displaystyle \bf log(a)-log(b)=log\left(\dfrac{a}{b}\right)}}[/tex]

[tex]{\boxed{\displaystyle \bf log(a^b)=blog(a)}}[/tex]

[tex]{\boxed{\displaystyle \bf \dfrac{d}{dx}\{log(x)\}=\dfrac{1}{x}}}[/tex]

[tex]{\boxed{\displaystyle \bf \dfrac{d}{dx}(e^x)=e^{x}}}[/tex]

y + 8.63 = 11.001

Help, what does y equal to?!??!

50 points to whoever answers this question!!!!!

Answers

Answer:

2.371

Step-by-step explanation:

subtract 8.63 to 11.001

The contents of each box of books weighs 18 pounds. There are 24 books in each box. How much does each book weigh?

Answers

18 divided by 24 will give you .75 pounds
each

Fill in the blank
y / 5
(y + 5) / 5
(y + 6) / 6
y / 2
y / 6

Answers

Step-by-step explanation:

[tex] \frac{x + 3}{3} = \frac{y + 2}{2} [/tex]

[tex]2(x + 3) = 3(y + 2)[/tex]

[tex]2x + 6 = 3y + 6[/tex]

[tex]2x = 3y[/tex]

[tex] \frac{x}{3} = \frac{y}{2} [/tex]

1
If 3 dogs equally share pound of dog
food what share will each dog get?
2

Answers

Answer:

.333 pounds hope this helps

For what values of θ, 0° ≤ θ ≤ 360°, will y = cos (θ) equal 0?

I. 0° II. 90° III. 180° IV. 270° V. 360°

Answers

Answer:

D) I, III, and V

Step-by-step explanation:

Edge

it costs $50 to join a gym plus $28 per month define the variable

Answers

Answer:

28

Step-by-step explanation:

because it's value increases by 28 every month

Jace and Lianna each baked a loaf of bread. jace cut his loaf into halves and lianna cut her loaf into thirds. Jace says they can use their loaves of bread to show the 1/2 is less than 1/3. lianna says they cant. who is correct explain why or why not

Answers

Answer:

Jace is correct they can use their loaves of bread to show 1/2 is less than 1/3. Because they have 2 loaves of bread

Which of the following describes the transformation?
A. Reflection over the X axis
B. Reflection over the Y axis
C. Rotation 90° clockwise about the origin
D. Rotation 180° clockwise about the origin

Answers

Answer:

D

Step-by-step explanation:

I hope this helps!

Answer:

B

Step-by-step explanation:

Imagine a mirror at the Y-axis, the two triangles will be mirror-image of each other.  So the CORRECT answer is B. Reflection over the Y axis

Does (5, 7) make the equation y = x true?

Answers

Answer:

x = y the answer is this...

Consider the following functions.
f(x) = x^2 + 1
g(x) = f(x - 5)
h(x) = f(x+3)

Please help set the table up!

Answers

The table of values for the functions f(x) = x^2 + 1, g(x) = f(x - 5) and h(x) = f(x+3) is:

[tex]\left[\begin{array}{cccccc}x&f(x)&x&g(x)&x&h(x)\\-2&5&-2&50&-2&2\\-1&2&-1&37&-1&5&0&1&0&26&0&10&1&2&1&17&1&17&2&5&2&10&2&26\end{array}\right][/tex]

How to set up the table

The equations of the functions are given as:

[tex]f(x) = x^2 + 1[/tex]

[tex]g(x) = f(x - 5)[/tex]

[tex]h(x) = f(x+3)[/tex]

For function f(x), we have:

f(-2) = (-2)^2 + 1 = 5

f(-1) = (-1)^2 + 1 = 2

f(0) = (0)^2 + 1 = 1

f(1) = (1)^2 + 1 = 2

f(2) = (2)^2 + 1 = 5

For function g(x), we have:

g(-2) = f(-2 - 5) = f(-7) =  (-7)^2 + 1 = 50

g(-1) = f(-1 - 5) = f(-6) =  (-6)^2 + 1 = 37

g(0) = f(0 - 5) = f(-5) =  (-5)^2 + 1 = 26

g(1) = f(1 - 5) = f(-4) =  (-4)^2 + 1 = 17

g(2) = f(2 - 5) = f(-3) =  (-3)^2 + 1 = 10

For function h(x), we have:

h(-2) = f(-2 + 3) = f(1) =  (1)^2 + 1 = 2

h(-1) = f(-1 + 3) = f(2) =  (2)^2 + 1 = 5

h(0) = f(0 + 3) = f(3) =  (3)^2 + 1 = 10

h(1) = f(1 + 3) = f(4) =  (4)^2 + 1 = 17

h(2) = f(2 + 3) = f(5) =  (5)^2 + 1 = 26

Substitute the above values in the blank table.

So, we have:

[tex]\left[\begin{array}{cccccc}x&f(x)&x&g(x)&x&h(x)\\-2&5&-2&50&-2&2\\-1&2&-1&37&-1&5&0&1&0&26&0&10&1&2&1&17&1&17&2&5&2&10&2&26\end{array}\right][/tex]

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A large plastic bucket is in the shape of a right, circular cylinder with dimensions shown below. If there are volume of this cylinder? 1000 cubic centimeters in a liter and 3.785 liters in a gallon, then which of the following is true about the volume of this cylinder?

Answers

The volume of the cylinder is between 5 and 6 gallons.

What is the volume of the cylinder?

A cylinder is a three-dimensional shape that is made up of a prism with a circular base.

Volume of a cylinder = nr^2h

Where:

h = heightn = 22/7r = radius

22/7 x 28 x (15^2) = 19,800 cubic centimeters

First convert the volume to liters = 19,800 / 1000 = 19.8

Now convert to gallons =  19.8 / 3.785 = 5.23 gallons

Please find attached the complete question. To learn more about to determine the volume of a cylinder, check: https://brainly.com/question/9624219

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