You pay $3.00 to play. The dealer deals you one card. If it is a spade, you get $10. If it is anything else,you lose your money. Is this game fair?

Answers

Answer 1

Answer:

The game is fair in the sense that the expected value is not negative.

What is expected value?

The expected value serves as a gauge for a random variable's typical value. It is determined by multiplying each of the variables' potential outcomes by its corresponding probability, then adding the resulting products. In order to comprehend the typical outcome of a random process and determine if a given course of action is likely to be lucrative or not, the expected value is a valuable tool in decision-making.

The probability of getting a spade is 13/52 or 1/4.

The probability of getting anything else is 3/4.

he expected value of playing the game can be calculated as:

Expected value = (probability of winning x amount won) - (probability of losing x amount lost)

Expected value = (1/4 x $10) - (3/4 x $3)

Expected value = $2.50 - $2.25

Expected value = $0.25

Since the expected value is positive, this means that on average, you can expect to win $0.25 for every time you play the game.

Hence, game is fair in the sense that the expected value is not negative.

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If m > n, which inequalities must be true? Check all that apply. m + 2.1 > n + 2.1 m - (-4) > n -(-4) m + 3 > n-3 16.5 + m > 16.5 + n 1 m > n + 2 9 + m > 6 + 1

Answers

Let's begin by listing out the information given to us:

m > n

We will proceed to solve the inequalities given as shown below:

$\begin{gathered} If\colon m>n \n \n m+2.1>n+2.1 \n \text{Subtract ''2.1'' from both sides, we have:} \n m>n \n m+2.1>n+2.1\Rightarrow m>n \n \therefore m+2.1>n+2.1(TRUE) \n \n m-(-4)>n-\mleft(-4\mright) \n \Rightarrow m+4>n+4 \n \text{Subtract ''4'' from both sides, we have:} \n m>n \n m+4>n+4\Rightarrow m>n \n \therefore m+4>n+4(TRUE) \n \n m+3>n-3 \n \text{Subtract '3'' from both sides, we have:} \n m>n-3-3\Rightarrow m>n-6 \n m>n-6\ne m>n \n \therefore m+3>n-3(FALSE) \n \n \end{gathered}$

The last three choices are below:

$\begin{gathered} 16.5+m>16.5+n \n \text{Subtract ''16.5'' from both sides, we have:} \n m>n \n 16.5+m>16.5+n\Rightarrow m>n \n \therefore16.5+m>16.5+n(TRUE) \n \n m>n+2 \n m>n+2\ne m>n \n \therefore m>n+2(FALSE) \n \n \n \end{gathered}$

The inequalities marked as TRUE are the inequalities that apply

|m + 3| = 12 – 2m (please show work)

Answers

Answer:

31-12=-2m -m

19=m

m=19

Step-by-step explanation:

Which of the following expressions would give the number of ways to choose a group of 7 from a group of 15?

Answers

The formula is ¹⁵C₇. Then the number of ways to choose a group of 7 from a group of 15 will be 6435.

What are permutation and combination?

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

Then the number of ways to choose a group of 7 from a group of 15 will be given by the combination formula.

Then we have

Number of ways = ¹⁵C₇

Number of ways = 6435

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You didn't supply any expressions, but it'd be one of these (assuming it's unique combinations, rather than the duplicate permitting permutations):
(15!)/(7!(15-7)!)
or
(15!)/(7!8!)
or
(15•14•13•12•11•10•9)/(7!)
or
(15•14•13•12•11•10•9)/(7•6•5•4•3•2)
or
32432400/5040
or
6435

depending on what it has as possible answers.

A person springs off a 12-foot high diving board with an initial velocity of 10 feet per second. How many seconds does it take the person to hit the water?

Answers

Answer:

1.2 seconds

Step-by-step explanation:

The height of the diving board above water is 12 feet.

The person dives with an initial velocity of 10 feet per second.

The time taken is gotten by dividing the height jumped by the velocity at which the person dived.

That is:

t = d / s

where d = height jumped = 12 ft

s = velocity = 10 ft/s

Therefore:

t = 12 / 10 = 1.2 seconds

It took the person 1.2 seconds to hit the water.

In a group of 31 students, 7 study both Art and Biology.14 study Biology but not Art.
7 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?

Answers

Answer:

7/10 or 0.7 or 70%

Step-by-step explanation:

I would use a venn diagram, and fill it in! Then there are 7 do A &B and 3 who just do A. That as a probaility, your answer!

A team gets3 points for each match it wins
1 point for each match it draws
and 0 points for each match it loses
Jill's team has played 40 matches.
Jill's team has drawn 16 matches.
Jill's team has got a total of 55 points.
How many matches has Jill's team lost?

Answers

Answer:

Jill's team lost 11 matches.

Step-by-step explanation:

Jill's team drawn matches = 16

Points earned for the matches drawn = 16

Total points earned = 55

Therefore, points earned by winning the matches = 55 - 16 = 39

Total matches won by Jill's team = $\frac{\text{Points earned by winning the matches}}{\text{Points earned by winning one match}}$

= $(39)/(3)$

= 13

Total matches won + matches drawn = 16 + 13 = 29

Matches lost by the team = 40 - 29 = 11

Therefore, Jill's team lost 11 matches.

Final answer:

Jill's team has lost 11 matches. This was calculated by subtracting the matches drawn and matches won from the total matches played.

Explanation:

To answer this mathematics question, we first need to know how many points Jill's team has earned from the matches they've drawn. Since each draw earns 1 point and Jill's team has drawn 16 matches, they've earned 16 points from draws. They have a total of 55 points, and if we subtract the 16 from draws, that leaves us 39 points earned from wins. Since a win is worth 3 points, we can calculate the number of matches won by dividing 39 by 3, giving us 13 matches won. As the team has played a total of 40 matches (16 drawn + 13 won), the team has lost the remainder. So, subtract the 29 matches won or drawn from the total 40 to get 11. Therefore, Jill's team has lost 11 matches.

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