1. Find y, A. and B.

28 to 42 means 28/42

We now reduce 28/42 to lowest terms.

28 ÷ 7 = 4

42 ÷ 7 = 6

We now have 4/6.

We now reduce 4/6.

4 ÷ 2 = 2

6 ÷ 2 = 3

Final answer: 2/3

Answer:

• = { (4,1) , (3,2) , (2,3) , (1,4) }

Step-by-step explanation:

Let's start writing the sample space for this experiment :

{ (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) }

Let's also define the event ⇒

: '' The sum of the two dice is 5 ''

We can describe the event by listing all the favorables cases from ⇒

= { (4,1) , (3,2) , (2,3) , (1,4) }

In order to calculate we are going to divide all the cases favorables to over the total cases from . We can do this because all 36 of these possible outcomes from are equally likely. ⇒

⇒

Finally we are going to define the event ⇒

: '' The number of the first die is exactly 1 more than the number on the second die ''

⇒

= { (2,1) , (3,2) , (4,3) , (5,4) , (6,5) }

Now given two events A and B ⇒

P ( A ∩ B ) =

We define the conditional probability as

with

We need to find therefore we can apply the conditional probability equation :

  (I)

We calculate at the beginning of the question. We only need .

Looking at the sets and we find that (3,2) is the unique result which is in both sets. Therefore is 1 result over the 36 possible results. ⇒

Replacing both probabilities calculated in (I) :

We find out that

Final answer:

When rolling two dice, there are 4 combinations that sum to 5. Hence, probability P(E) is 1/9. If considering the event F where the roll on the first die is 1 more than on the second die, it has 5 possible outcomes. So P(F) is 5/36. However, if event E has already happened, P(F|E) is 1/4.

Explanation:

The subject of this question is probability, which is part of Mathematics, specifically, it is a high school-level question. The event E described here is the scenario in which the sum of the numbers rolled on the two dice equals 5. There are 4 possibilities for this event: (1,4), (2,3), (3,2), and (4,1). As there are 36 possible outcomes when rolling two dice, the probability P(E) is 4/36 = 1/9.

Now considering event F where the number on the first die is exactly 1 more than the number on the second die, we have five possible pairs: (2,1), (3,2), (4,3), (5,4), (6,5). So the P(F) is 5/36. However, we're asked to find P(F|E), the probability of event F given that event E has occurred. Looking at the pairs that fit both conditions, we see that there is only one pair: (3,2). Therefore, P(F|E) is 1/4.

Learn more about Probability here:

brainly.com/question/22962752

#SPJ3

Answer:

x = -16

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

10(1/2x + 2) - 5 = 3(x - 6) + 1

Step 2: Solve for x

1. Distribute:                                   5x + 20 - 5 = 3x - 18 + 1
2. Combine like terms:                   5x + 15 = 3x - 17
3. Subtract 3x on both sides:         2x + 15 = -17
4. Subtract 15 on both sides:         2x = -32
5. Divide 2 on both sides:              x = -16

Step 3: Check

Plug in x into the original equation to verify it's a solution.

1. Substitute in x:                     10(1/2(-16) + 2) - 5 = 3(-16 - 6) + 1
2. Multiply:                                10(-8 + 2) - 5 = 3(-16 - 6) + 1
3. Add/Subtract:                       10(-6) - 5 = 3(-22) + 1
4. Multiply:                                -60 - 5 = -66 + 1
5. Subtract/Add:                       -65 = -65

Here we see that -65 does indeed equal -65.

∴ x = -16 is the solution of the equation.

To create a Venn diagram for this data, we need to represent the number of people who like chocolate ice cream, vanilla ice cream, and both.

Let's start by drawing two overlapping circles. The left circle represents chocolate ice cream, the right circle represents vanilla ice cream, and the overlapping region represents people who like both.

To find the number of people who like only chocolate ice cream (a), we subtract the number of people who like both from the total number of people who like chocolate ice cream. So, 60 - 20 = 40 people like only chocolate ice cream.

To find the number of people who like only vanilla ice cream (b), we subtract the number of people who like both from the total number of people who like vanilla ice cream. So, 25 - 20 = 5 people like only vanilla ice cream.

To find the number of people who don't like either chocolate or vanilla ice cream (c), we subtract the total number of people who like chocolate or vanilla ice cream from the total number of people surveyed. So, 125 - (60 + 25 - 20) = 60 people don't like either flavor.

To find the number of people who like either chocolate ice cream or vanilla ice cream or both (d), we add the number of people who like only chocolate ice cream, the number of people who like only vanilla ice cream, and the number of people who like both. So, 40 + 5 + 20 = 65 people like either chocolate ice cream or vanilla ice cream or both.

In summary:

a) 40 people like only chocolate ice cream.

b) 5 people like only vanilla ice cream.

c) 60 people don't like either chocolate or vanilla ice cream.

d) 65 people like either chocolate ice cream or vanilla ice cream or both.

Answer:

Factoring the term we get

Step-by-step explanation:

We need to factor the term:

Factoring:

Taking (y+4) common

It cannot be further factored.

So, Factoring the term we get