Consider a problem where we are rolling 2 dices where each dice has 6 faces numbered from 1 to 6.Answer the following questions:(1) What is the sample space?(2) If the event we are interested in is the sum being 10, what would be the probability of observingsuch an event?(3) If the event we are interested in is the sum being 6, what would be the probability of observingsuch an event?

Answers

Answer 1

Answer:

1. See Explanation for Sample Space

2. [tex]P(10) = \frac{1}{12}[/tex]

3. [tex]P(6) = \frac{5}{36}[/tex]

Step-by-step explanation:

Given

Roll of Two die

Solving (1): The Sample Space

Represent the first dice with S1 and the second with S2

[tex]S_1 = \{1,2,3,4,5,6\}[/tex]

[tex]S_2 = \{1,2,3,4,5,6\}[/tex]

The sample space of both die is:

[tex]S = (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)[/tex][tex](4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(55,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}\}[/tex]

Solving (2): Probability of Sum being 10

First, we need to add the outcome of each roll in (1) above:

[tex]S = \{2,3,4,5,6,7, 3,4,5,6,7,8, 4,5,6,7,8,9, 5,6,7,8,9,10, 6,7,8,9,10,11 7,8,9,10,11,12\}[/tex][tex]n(S) = 36[/tex]

[tex]n(10) = 3[/tex]

The required probability is:

[tex]P(10)= \frac{3}{36}[/tex]

[tex]P(10) = \frac{1}{12}[/tex]

Solving (3): Probability of Sum being 6

[tex]n(S) = 36[/tex]

[tex]n(6) = 5[/tex]

The required probability is:

[tex]P(6) = \frac{5}{36}[/tex]


Related Questions

Solve for k.
k/4 + 8 = 12 ​

Answers

Answer:

k = 16

Step-by-step explanation:

To solve this we must isolate k.  Let's first simplify this equation by subtracting   8 from both sides:

k/4 = 4

Next, remove the fraction by multiplying both sides by 4:

k = 16

Answer the following questions using the table below.
-2
-1
0
-10
-8
-6
-4
1
Is this a linear function?
<
What is the slope?
h
What is the y-intercept?
What is the equation of the linear function?

Answers

Answer:

the - are the x or y

Step-by-step explanation:

Find the value of x for which l is parallel to m. The diagram is not to scale.

Answers

Answer:

x= 41

Step-by-step explanation:

3x-43= 80 is the equation since they are alternate interior angles.

Step 1- Add 43 to both sides.

3x-43= 80

  +43 +43

Step 2- Divide both sides by 3.

3x= 123

3      3

x= 41

The given angles are the alternate interior angles formed by a common

transversal to two parallel lines.

The value of x for which line l is parallel to line m is c. 41°.

Reasons:

When line l is parallel to line line m, we have;

The alternate interior angles will be equal

Therefore;

(3·x - 43)° = 80°

Which gives;

[tex]x = \dfrac{80^{\circ} + 43^{\circ} }{3} =41^{\circ}[/tex]

The value of x is 41°

Learn more here:

https://brainly.com/question/16987641

I don’t get thiss so can someone help me

Answers

Step-by-step explanation:

use algabraic expreshens it will help trust me

Consigna:
Resuelve el siguiente problema:
Para comprar un juego de mesa para divertirnos en familia durante la pandemia. yo aporté un quinto (6)
del total del precio, mi hermana María aportó la sexta parte (') y mi papá aporto el resto que faltaba.
¿Qué parte del costo del del juego aportó mi papá? Si pagamos el total de $90, ¿Cuánto dinero puso
cada uno?
DATOS
GRÁFICOS O DIBUJOS OPERACIONES
RESULTADOS

Answers

Answer:

El padre pago el 63% del valor del juego, es decir, $57.

Step-by-step explanation:

Si el valor total del juego es de $90, y el redactor aportó una quinta parte del total del precio, el total aportado por él es de $18 (90 / 5 = 18). A su vez, su hermana María aportó una sexta parte del valor, es decir $15 (90 / 6 = 15). Por ende, el padre de los niños aportó $57 (90 - 18 - 15 = 57), es decir, el 63% del valor total.


1. Ms. Scott raised $4,763 for the local charity. Find the opposite of this integer.

Answers

Answer:

D

Step-by-step explanation:

Shsgbsbdh

Both of the equations below have the same solution when solved for x. What is the value of t?

Answers

Answer:

-.75x-6

Step-by-step explanation:

Step 1: simplify the first equation

1/4(x-28)=2x, or .25x-7=2x.

Step 2: simplify the second equation so that one side equals 2x

13-5x=-7.5x-t. Add 7x to either side to get 13+2x=-.5x-t. Then, subtract 13 from either side and then you have 2x=-.5x-t-13

Step 3: make both equations into one equation

Since 2x=.25x-7, and 2x=-.5x-t-13, then it's safe to say .25x-7=-.5x-t-13.

Step 4: Simplify this final equation

Add .5x to both sides to get .75x-7=-t-13. Then add 13 to both sides to get .75x+6=-t. Then multiply everything by -1 to get -.75x-6=t

Multiply (6x^3+8)(7x^2+8x+7)

Answers

that’s the answer for you
hope this helps if you have any more questions about this let me know!!

Use the given conditions to write an equation in slope-intercept form. passing through (-2, 0) & (0, 2)

Answers

Answer:

Step-by-step explanation:

(2 - 0)/(0 + 2)= 2/2= 1

y - 0 = x + 2

y = x + 2

Does the following number belong to the interval (1.5, 2.4) ?

Square root of 2

Square root of 3

Square root of 5

Square root of 6

Yes or no

Answers

Answer:

Square root of 2: No

Square root of 3: Yes

Square root of 5: Yes

Square root of 6: No

Step-by-step explanation: Verified by RSM

Can anyone help me with my algebra homework ?

Answers

Answer: No, it is not possible

Why not? Because of the phrasing "share an arm AB". If two angles share a common line, segment or ray, then they are considered adjacent angles by definition. You can think of two rooms sharing the same wall. Those rooms are adjacent. So we cannot have nonadjacent angles sharing the same arm AB.


If
3x^2+ 9x + 11
X – 1 =
3x2 + 3x + a + 23
X-1
what is the value of a?

Answers

Answer:

a = -6 - 6x + 3x^2

Step-by-step explanation:

Juan baked 5 dozens of cupcakes which cost her a total of PHP 2675.How much should she sell each cupcake if she wants to get a 25% profit?

Answers

Step-by-step explanation:

5 cupcakes = PHP 2675

25% profit =

25/100 × 2675 = 668.75

Selling price for 25% profit = 2675 + 668.75 = 3343.75

Cost of each cupcake for 25% profit = 3343.75/5

= 668.75

Use linear equation to calculate intercepts. x minus one-half y = negative 4 Complete the table with values for a and b. A 2-column table with 3 rows. Column 1 is labeled x with entries 0, negative 2, b. Column 2 is labeled y with entries a, 4, 0.

Answers

Answer:

Use linear equation to calculate intercepts.

x minus one-half y = negative 4

Complete the table with values for a and b.

A 2-column table with 3 rows. Column 1 is labeled x with entries 0, negative 2, b. Column 2 is labeled y with entries a, 4, 0.

a =  

✔ 8

b =  

✔ –4

Step-by-step explanation:

those are ur correct answers

Answer:

Use linear equation to calculate intercepts.

x minus one-half y = negative 4

Complete the table with values for a and b.

A 2-column table with 3 rows. Column 1 is labeled x with entries 0, negative 2, b. Column 2 is labeled y with entries a, 4, 0.

a =  

✔ 8

b =  

✔ –4

Step-by-step explanation:

What is the prime factorization of 36

Answers

Answer:

[tex]2^{2} x 3^{2}[/tex]

Step-by-step explanation:

Answer:

2^2*3^2

Step-by-step explanation:

You can break down 36 through ways down to its prime factors through multiple ways like a facor tree

                   36

                4       9

             2    2  3   3

Since two and three cannot be broken down anymore, they are prime factors. Also, because you are left with two 2s and two 3s, you would mark that as squared when giving an answer.

Does seth or briana walk faster

Answers

Answer:

PLEASE GIVE BRAINLIST

you need to be more pacific on your question so that can other people can help you.

HOPE THIS HELPED

Which statement is true? Question 7 options: A) |–3| = 3 and –|–4| = –4 B) |–3| = 3 and –|4| = 4 C) –|3| = 3 and |4| = 4 D) |–3| = 3 and |–4| = –4

Answers

Answer:

option A is correct

Step-by-step explanation:

mod's has a simple function -

if |x| is given it simply means that the value of "X" can't be negative

Option A is correct,  |–3| = 3 and –|–4| = –4 is true statement.

What is Number system?

A number system is defined as a system of writing to express numbers.

The absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign.

|-x|=x

For option A

|–3| = 3 and –|–4| = –4 is true

For option B

|–3| = 3 and –|4| = 4 is not true because –|4|  is -4.

For option C

–|3| = 3 and |4| = 4 is not true because –|3| is -3

For option D

|–3| = 3 and |–4| = –4 is not true because |-4| is 4

Hence, option A is correct,  |–3| = 3 and –|–4| = –4 is true statement.

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Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for x=-3 and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ​?

Never mind I got it. mtan=6x+4. Sub in x values, for x=-2, take 6(-2)+4 = -8, and for x=1.5. 6(1.5)+4=13.

Answers

Complete Question

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for [tex] x = 3[/tex] and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ​?

Answer:

The  generally expression for the slope of [tex]y = 2x^2 + 4x[/tex] is  [tex]y' = 4x +4[/tex]

The graph is shown on the first uploaded image

The  generally expression for the slope of [tex]y=2x^2+4[/tex] is   [tex]y' = 4x[/tex]

Step-by-step explanation:

From the question we are told that

  The  equation of the curve is [tex]y = 2x^2 + 4x[/tex]

First we differentiate the equation

So  

     [tex]y' = 4x +4[/tex]

Therefore the generally expression for the slope tangent to the curve [tex]y=2x^2+4x[/tex] is   [tex]y' = 4x +4[/tex]

The  next step is to substitute for x =  3 and  x =  0.5

So  for [tex]x_1 = 3 [/tex]

    [tex]y' = 4(3) +4[/tex]

     [tex]y' =m_1= 16[/tex]

And  for  [tex]x_2 = 0.5[/tex]

      [tex]y' = 4(0.5) +4[/tex]

       [tex]y' =m_2= 6[/tex]

Here m_1  and  m_2 are slops of the curve

Next we obtain the coordinates of the tangent lines

So  at [tex]x_1 = 3 [/tex]

   [tex]y_1 = 2(3)^2 + 4(3)[/tex]

  [tex]y_1 = 21[/tex]

So the coordinate for the first tangent line is  

    [tex](x_1 , y_1 ) = (3 , 21)[/tex]

At  [tex]x_2 = 0.5 [/tex]      

    [tex]y_2 = 2(0.5)^2 + 4(0.5)[/tex]

=>  [tex]y_2 = 2.5[/tex]

So the coordinate for the second  tangent line is  

    [tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex]

Next we obtain the equation for the tangent lines

 So generally the slope is mathematically represented as

        [tex]m = \frac{y - y_1 }{x-x_1}[/tex]

For   [tex](x_1 , y_1 ) = (-3 , 21)[/tex] and  [tex]y' =m_1= 16[/tex]

       [tex] 16 = \frac{y -21 }{x-3)}[/tex]

=>    [tex]y = 16x - 27[/tex]

For  [tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex] and  [tex]y' =m_2= 6[/tex]

       [tex] 6 = \frac{y -2.5 }{x-0.5}[/tex]

       [tex]y = 6x -0.5[/tex]

Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating  y=2x^2+4 as follows

     [tex]y' = 4x[/tex]

     

SOMEONE HELP I NEED THE ANSWERS TO THIS PROBLEM

Answers

Answer:

Step-by-step explanation:

∠6 = 45     {Vertically opposite angles are equal}

∠6 + 5x + 35 = 180  {Co interior angles}

45 + 5x + 35 = 180  {add like terms}

80 + 5x = 180

5x = 180 - 80

5x = 100

x = 100/5

x = 20

5x + 35 =  5*20 + 35 = 100 + 35 = 135

∠8 = 5x + 35   { Corresponding angles}

3) ∠8 = 135

4) ∠ 3 = ∠6    {Alternate interior angles are equal}

3 = 45

5) ∠6 = 45

any help please, asap​

Answers

J = 0 because it is the midpoint of K and P.

Since we know that K is at -5 and P is at 5, KP = 10

Both KP and JQ are equal to 10, therefore, they are equal.

Answer:

14. j=0

15. KP=10

16. yes

Step-by-step explanation:

(The two letters next to each other means that the question is asking for the distance between the points. For example, KP is the distance from K to P, or P to K.)

14.:

If P is the midpoint of J and Q, that means that there is an equal distance between Q and P and J and Q. So, you can see this because

Q-P=5 and 5*2= J

So the distance from J to Q is 10, but to find what J is, subtract the distance from Q, leaving you with 0. So, J=0.

15.:

Since each line represents 5 and the distance from -5 to 5 is 10, KP = 10.

16.:

Since KP = 10 and JQ = 10, then yes, they are the same.

A landscape architect wants to plant a circle of flowers around a triangular garden. She has sketched the triangle on a coordinate grid with vertices at A (0, 0), B (8, 12), and C (18, 0). Explain how the architect can find the center of the circle that will circumscribe triangle ABC. Then find the radius of the circumscribed circle.

Answers

Answer:

The center of the circle is the point (6,3)

Find the base for the following items.
4 is 1% of what number?

Answers

Answer:

400

Step-by-step explanation:

In a particular class of 22 students, 18 are men. What fraction of the students in the class are men

Answers

Answer:

9/11

Step-by-step explanation:

The fraction that are men are

men/total

18/22

Divide the top and bottom by 2

9/11

Barbara’s soccer team selected 15 girls from 75 girls who tried out for the team. What decimal is equivalent to the fraction of girls selected from the group

Answers

Answer:

.2

Step-by-step explanation:

15 /75

Divide the top and bottom by 15

1/5

Changing to decimal form

1/5 * 2/2 = 2/10

.2

Twice the sum of a number and 7 is more than 6 or at most -3. Which compound inequality can represent this relationship

Answers

Answer:

C

Step-by-step explanation:

The inequality 2(x + 7) > 6 and 2(x + 7) ≤ -3 will represents the given situation so option (C) will be correct.

What is inequality?

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

Let's say that number is x

Then,

sum of a number and 7 = x +7

Twice the sum of a number and 7 is more than 6

So,

2(x + 7) > 6

And

Twice the sum of a number and 7 is at most -3, it means it can go up to -3 not more than.

So,

2(x + 7) ≤ -3

Hence "The inequality 2(x + 7) > 6 and 2(x + 7) ≤ -3 will represents the given situation".

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A
Para resolver los siguientes casos, plantea sistemas de
ecuaciones en tu cuaderno y encuentra los valores de las
incógnitas.
1. Horacio quiere poner una hamaca en su jardín. Tiene una cuer-
da que mide 14 metros para amarrar los dos extremos de la
hamaca, por lo que decide cortar la cuerda en dos. Si un pedazo
de cuerda mide 4 metros más que el otro, ¿cuánto miden las
nuevas cuerdas?

2. Imagina que vas a la tienda con un amigo y compras 6 paletas
y 2 gomitas. Tu amigo pide 1 paleta y 10 gomitas. Si tú pagas
$24 y tu amigo $33, ¿cuánto cuestan las gomitas y las paletas?






porfavor ayuda es para una tarea de mañana antes de las 8​

Answers

Answer:

1 La longitud de las nuevas cuerdas = 5 metros y 9 metros

2 El costo de las paletas = $ 3

El costo de las gomitas = $ 3

Step-by-step explanation:

1) Sea la primera mitad de la cuerda representada por = a

Deje que la segunda mitad de la parte superior esté representada por = b

a + b = 14 metros

De la pregunta, se nos dice que ok, la mitad es 4 metros más larga que la otra

a = b + 4

Por lo tanto

b + 4 + b = 14 metros

2b + 4 = 14 metros

2b = 14 - 4

b = 10/2

b = 5 metros

a = b + 4

a = 5+ 4

a = 9 metros

Por lo tanto, la longitud de las nuevas cuerdas = 5 metros y 9 metros

2)

Representemos el costo de las paletas = p

Costo de gomitas = g

De la pregunta 2 se nos dice que:

Tu vas a la tienda con un amigo y compras 6 paletas y 2 gomitas. Si tú pagas $ 24

Por tanto: 6p + 2g = 24 ....... Ecuación 1

Tu amigo pide 1 paleta y 10 gomitas. y tu amigo $ 33

p + 10g = 33 ....... Ecuación 2

p = 33 - 10g

Sustituya p por 33 - 10g en la Ecuación 1

6p + 2g = 24 ....... Ecuación

6 (33-10 g) + 2 g = 24

198 - 60 g + 2 g = 24

-58g = 24-198

-58g = - 174

g = -174 / -58

g = $ 3

Para encontrar p

p = 33 - 10g

p = 33 - 10 × 3

p = 33 - 30

p = $ 3

Por lo tant,

El costo de las paletas = $ 3

El costo de las gomitas = $ 3

please help me fr tho

Answers

Answer: y=2x+1

Step-by-step explanation:

To solve for y, we want to use our algebraic properties to isolate y.

16x+9=9y-2x               [add both sides by 2x]

18x+9=9y                     [divide both sides by 9, divide to each term]

2x+1=y

Now, we know that y=2x+1.

Answer:

no thx and thx for the points

Step-by-step explanation:

Choose the algebraic expression that represents the area of a triangle that has a base 4 inches less than 5 times wider than the height.
a (1/2)(5h)(h – 4)
b (1/2)(5b + 4)(b)
c (1/2)(5h – 4)(h)

Answers

Answer:

c (1/2)(5h – 4)(h)

Step-by-step explanation:

Area of a triangle = 1/2 × base × height

Let

Height of the triangle = h

Base 4 inches less than 5 times wider than the height.

Base of the triangle = 5h - 4

Area of a triangle = 1/2 × base × height

= (1/2)(5h-4)(h)

The algebraic expression that represents the area of a triangle that has a base 4 inches less than 5 times wider than the height is (1/2)(5h-4)(h)

Option C is the correct answer

Answer:

c

Step-by-step explanation:

i had this same question a while ago

helphelphelphelphelphelph ​

Answers

Answer:

first 2 are right and last is right, but 3 is 30 not 66

Step-by-step explanation:

Answer:

you got 1 and 2 and 4 right but 3 is 30

Step-by-step explanation:

3 is 30 because you have to multiply before you add due to pemdas

MATH QUESTION... NEED HELP

Answers

Answer:

C. 7 inches I hope this helps

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