create write an expression that simplifies to 2a + 14 using the distributive property

Probabilities are used to determine how likely it is for an event to happen.

(1) A roll of two dice

Let the dice be A and B. The sample space of each is:

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

To get the sample space (S) of the sum of the dice, we simply add up the individual element of both dice. So, we have:

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

This gives

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

The complete sample space is:

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

[tex]n(S) = 36[/tex] --- the total outcomes

The probability of rolling a sum of 7 is:

[tex]P(7) = \frac{n(7)}{n(S)}[/tex]

Where

[tex]n(7) = 6[/tex] ---- number of 7's in the sample space

So, we have:

[tex]P(7) = \frac 6{36}[/tex]

[tex]P(7) = 0.167[/tex]

The probability of rolling a sum of 7 is 0.167

(2) Restaurant

We have:

[tex]Soup = \{A,B,C,D\}[/tex]

[tex]Salads = \{1,2,3\}[/tex]

To get the sample space (S), we simply pick the individual elements of the above data. So, we have:

[tex]S = \{A1, A2, A3,B1, B2, B3,C1, C2, C3,D1, D2, D3\}[/tex]

(3) Disjoint events

Events are said to be disjointed if they cannot happen at the same time. 3 examples are:

(4) Bob and Sarah

Let

[tex]A \to[/tex] Bob gets to work on time

[tex]B \to[/tex] Sarah gets to work on time

[tex]P(A) = 80\% \\ P(B) = 90\%\\P(A\ n\ B) = 72\%[/tex]

The probability that Bob OR Sarah is late for work is represented as:

[tex]P(A'\ or\ B')[/tex]

This is calculated using:

[tex]P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')[/tex]

Where:

[tex]P(A') = 1 - P(A) = 1 - 80\% = 20\%[/tex]

[tex]P(B') = 1 -P(B) = 1 - 90\% =10\%[/tex]

[tex]P(A\ n\ B') = P(A) \times P(B') = 20\% \times 10\% = 2\%[/tex]

So, we have:

[tex]P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')[/tex]

[tex]P(A'\ or\ B') = 20\% + 10\% - 2\%[/tex]

[tex]P(A'\ or\ B') = 28\%[/tex]

[tex]P(A'\ or\ B') = 0.28[/tex]

The probability that Bob OR Sarah is late for work is 0.28

(5) Jake's Pizza

Let

[tex]A \to[/tex] The proportion of time they deliver on time

[tex]B \to[/tex] You get your pizza for free

So:

[tex]P(A) = 92\%[/tex]

You get your pizza for free if they didn't deliver within 30 minutes.

This means that:

[tex]P(B) = 1 - P(A)[/tex] --- Complement rule

So, we have:

[tex]P(B) = 1 - 92\%[/tex]

[tex]P(B) = 0.08[/tex]

The probability that you get your pizza for free is 0.08.

(6) Students and Soccer

Let:

[tex]A \to[/tex] Probability that a student likes soccer

So:

[tex]P(A) = 54\%[/tex]

If all 3 selected students like soccer, the probability is calculated as:

[tex]Pr = P(A) \times P(A) \times P(A)[/tex]

[tex]Pr = P(A)^3[/tex]

[tex]Pr = 54\%^3[/tex]

[tex]Pr = 0.157[/tex]

The probability that all 3 selected students like soccer is 0.157

(7) Students and Soccer

Let:

[tex]A \to[/tex] Probability that a student likes soccer

[tex]B \to[/tex] Probability that a student does not like soccer

So:

[tex]P(A) = 54\%[/tex]

[tex]P(B)= 1 - P(A)= 1 - 54\% = 46\%[/tex] ---- Complement rule

If all 4 selected students do not like soccer, the probability is calculated as:

[tex]Pr = P(B) \times P(B) \times P(B) \times P(B)[/tex]

[tex]Pr = P(B)^4[/tex]

[tex]Pr = 46\%^4[/tex]

[tex]Pr = 0.045[/tex]

The probability that all 4 selected students do not like soccer is 0.045

(8) Marbles

[tex]Blue = 6 \\ Green = 4 \\ Red = 5[/tex]

When the green marble is selected, we are left with

[tex]Blue = 6 \\ Green = 3 \\ Red = 5[/tex]

The probability of selecting a red marble at this point is:

[tex]P(Red) = \frac{Red}{Blue + Green + Red}[/tex]

[tex]P(Red) = \frac{5}{6+3+5}[/tex]

[tex]P(Red) = \frac{5}{14}[/tex]

[tex]P(Red) = 0.357[/tex]

The probability that the next marble you draw is red is 0.357

(9) Studying for test

Let

[tex]A \to[/tex] Students got an A

[tex]B \to[/tex] Students studied for test

So:

[tex]P(A\ n\ B) = 60\% \\ P(B) = 75\%[/tex]

The probability that a student got an A given that they studied for the test is  represented as:

[tex]P(A | B)[/tex]

So, we have:

[tex]P(A | B) = \frac{P(A\ n\ B)}{P(B)}[/tex]

[tex]P(A | B) = \frac{60\%}{75\%}[/tex]

[tex]P(A | B) = 0.80[/tex]

The probability that a student got an A given that they studied for the test is  0.80

Read more about probabilities at:

https://brainly.com/question/16693319

Answer:51.33ft/s

Step-by-step explanation:Just look at how many seconds are in a hour and divide by that

Answer:

To find area of the quadrilateral ABCD, now we have take the vertices A(x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4) of the quadrilateral ABCD in order (counter clockwise direction) and write them column-wise as shown below. Add the diagonal products x1y2, x2y3, x3y4 and x4y1 are shown in the dark arrows.

Step-by-step explanation:

Answer:

mike spent 6 dollars, each pen cost 2$

Answer:

it's say download FPD SORRY I CAN'T SLOVE IT

6 to 12 months so the answer is 12

Answer:

m∠8 = 49°

Step-by-step explanation:

∠7 and ∠8 are same-side interior angles.

Remember, same-side interior angles are supplementary. This means that the sum of the angles is 180°.

Let's use the variable 'x' to represent the unknown measure of angle ∠8.

[tex]131 +x=180[/tex]

[tex]131-131=0[/tex] (cancels itself out)

[tex]180-131=49[/tex]

[tex]x=49[/tex]

Therefore, the measure of ∠8 is 49°.

Answer:

no solution

Step-by-step explanation:

x + 6 cannot be x so there is no solution. hope this helps

Answer:

No solution

Step-by-step explanation:

[tex]x + 6 = x \\ x - x = 6 \\ 0 = 6[/tex]

Answer:

the present age of the father be x and the present age of the son be y.

It is given that man is 24 years older than his son that is:

x=y+24

x−y=24..........(1)

Also, 12 years ago, he was five times as old as his son that is:

(x−12)=5(y−12)

x−12=5y−60

x−5y=−60+12

x−5y=−48..........(2)

Now subtract equation 1 from equation 2 to eliminate x, because the coefficients of x are same. So, we get

(x−x)+(−5y+y)=−24−48

i.e. −4y=−72

i.e. y=18

Substituting this value of y in (1), we get

x−18=24

i.e. x=24+18=42

Hence, the present age of the father is 42 years and the present age of the son is 18 years.

Step-by-step explanation:

Answer:

Haha great question, Maybe because people will not understand the difference between the fruit and the color.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

x = 256

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\\frac{x}{32} = 8 \\----------\\\rightarrow (\frac{x}{32})32 = 8 * 32\\\\\rightarrow \boxed{x = 256}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

h = 22  for Rachel

Step-by-step explanation:

20 + h = 42

h = 42 - 20

h = 22

Answer:

Yeah you can mark them brainlist but just saying you can always use math-ways i guess.

Bye have a nice day

Answer:

450+120w

will be the expression

Equation: 450+120w = x

Interpreting the inequality, it is found that the correct option is given by F.

------------------

In standard form, the equation of the line is:

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

[tex]2y = 6 - x[/tex]

[tex]y = -0.5x + 2[/tex]

Thus it is a decreasing line, which removes options J.

------------------

[tex]3x^2 + 3y^2 = 12[/tex]

[tex]3(x^2 + y^2) = 12[/tex]

[tex]x^2 + y^2 = 4[/tex]

[tex]d = \sqrt{\frac{|ax + by + c|}{a^2 + b^2}}[/tex]

[tex]d = \sqrt{\frac{|1(0) + 2(0) - 6|}{1^2 + 2^2}} = \sqrt{\frac{6}{5}} = 1.1[/tex]

A similar problem is given at https://brainly.com/question/16505684

Answer:

10,010,011,001

Step-by-step explanation:

Converting the number 10010011001 into a number with commas gives us 10,010,011,001.

Given that,

The number is 10010011001.

Used the concpet of number system which states that,

A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.

Here, the number is 10010011001.

So, it can be written as,

10010011001 = 10,010,011,001

Therefore, the number 10010011001 with commas would be 10,010,011,001.

To learn more about the Number system visit:

https://brainly.com/question/17200227

#SPJ6

Answer: h=-42

Step-by-step explanation:

8=7x2/7 + -h/7

8=7x2-h/7

8=14-h/7

8=-h+14/7

7x8=7(-h+14/7)

7x8=-h+14

56=-h+14

56-14=-h+14-14

42=-h

42/-1=-h/-1

h=-42

hope you found it helpful.

Coordinates of B is [tex](\frac{4}{11} ,\frac{13}{11} )[/tex] that divides AC five-sixths of the way from A to C

Given :

AC with A(4.-7) and C(-4, 11), if point B divides AC five-sixths of

the way from A to C

From the given information , B divides AC internally in the ratio of AB to BC is 5:6

Lets apply section formula to find coordinates of B

[tex](\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]

m:n is the ratio 5:6

A is (x1,y1) that is (4,-7)

B is (x2,y2) that is (-4,11)

Substitute the values inside the formula

[tex](\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )\\(\frac{(5)(-4)+6(4)}{5+6} ,\frac{5(11)+6(-7)}{5+6} )\\(\frac{4}{11} ,\frac{13}{11} )[/tex]

Coordinates of B is [tex](\frac{4}{11} ,\frac{13}{11} )[/tex]

Learn more:  brainly.com/question/22493969

Answer:

-2

Number Line:

                   1   2  3  4  5                                                        

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Answer:

dude it is too easy bro -2 I don't really like math but the answer is -2 so goodluck

Step-by-step explanation:

-7+5=?

count but start from -7 instead like this

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

now we just count from -7  

-7 -6 -5 -4 -3 -2

how much five not subtract add you are going up this time so good luck

here a number line too.

                                              < -10 -9 -8 -7 -6 -5 -4 -3 -2 -1    0    1 2 3 4 5 6 7 8 9 10 >

Answer:

x=8

Step-by-step explanation:

Angle bisector means it cute the big angle into two equal, smaller angles (like cutting a piece of cake in half)

therefore, you can set both smaller angles equal to each other, then solve for x

4x+1=33   Subtract 1 from both sides

4x=32      Divide both sides by 4

x=8

You'll get it, keep studying! :)

Answer:

3/4

Step-by-step explanation:

1/4 + 1/4 + 1/4 =3/4

or

1/4 x 3 = 3/4

Answer:

3/4 feet

Step-by-step explanation:

the common denominator (4) always stays the same.

you add the 3 pieces.

In geometry, transformations are used to move points from one position to another.

The preimage is given as:

[tex]S =(-3,4)[/tex]

[tex]T = (3,4)[/tex]

[tex]U = (-1,0)[/tex]

The image is given as:

[tex]S' = (-2,2)[/tex]

[tex]T' =(4,2)[/tex]

[tex]U' = (0,-2)[/tex]

Using points S and S' as our reference point, we have:

[tex]S =(-3,4)[/tex] and [tex]S' = (-2,2)[/tex]

Calculate transformation

[tex](x,y) \to S -S'[/tex]

[tex](x,y) \to (-2,2)-(-3,4)[/tex]

Rewrite as:

[tex](x,y) \to (-2--3,2-4)[/tex]

[tex](x,y) \to (-2+3,2-4)[/tex]

[tex](x,y) \to (1,-2)[/tex]

So, the transformation from the preimage to image is:

[tex](x,y) \to (x + 1, y-2)[/tex]

Calculate the lengths of the sides of the preimage and the image

Using the following distance formula, we have:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]ST = \sqrt{(-3 - 3)^2 + (4 - 4)^2} = 6[/tex]

[tex]SU = \sqrt{(-3 - -1)^2 + (4 - 0)^2} = \sqrt{20[/tex]

[tex]TU = \sqrt{(3 - -1)^2 + (4 - 0)^2} = \sqrt{32[/tex]

and

[tex]S'T' = \sqrt{(-2 - 4)^2 + (2 - 2)^2} = 6[/tex]

[tex]S'U' = \sqrt{(-2 - 0)^2 + (2 -- 2)^2} = \sqrt{20[/tex]

[tex]T'U' = \sqrt{(4 -0)^2 + (2 -- 2)^2} = \sqrt{32[/tex]

Since

[tex]ST = S'T'= 6[/tex]

[tex]SU = S'U'= \sqrt{20[/tex]

and

[tex]TU = T'U'= \sqrt{32[/tex]

Then, the transformation preserves length

From the graph of [tex]\triangle STU[/tex] and [tex]\triangle S'T'U'[/tex]

Since

[tex]\angle S = \angle S' = 76^o[/tex]

[tex]\angle T = \angle T' = 45^o[/tex]

[tex]\angle U = \angle U' = 59^o[/tex]

Then, the transformation preserves angle measure.

Read more about transformation at:

https://brainly.com/question/12865301

Answer:

2x+7

Step-by-step explanation:

3x +(-x) = 3x - x, so it's 2x

12 + (-5) is the same situation, just being 12 - 5, so it's 7.

putting them together leaves you with 2x+7

Answer:

10

Step-by-step explanation:

10+x+2=-8+3x

12+x =-8+3x

12+8=3x-x

20=2x

X=20/2

X=10

Answer:

1. 9.576

2. 17.442

3. 45.29

4. 79.294

5. 30.736

6. 30.8

7. 31.5

8. 25.85

9. 53.29

10. 49.184

11. 15.18

12. 15.573

13. 17.075

14. 74.06

15. 9.01

Step-by-step explanation:

Use a multiplication method to find the answers. I would put it up here but i dont know how.