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Anna11 [10]
3 years ago
5

The amount of money a student spends at the end of year carnival can be represented by the given equation. Graph the equation on

the coordinate plane.

Mathematics
1 answer:
Rom4ik [11]3 years ago
7 0

Answer: See the graph attached.

Step-by-step explanation:

The Slope-intercept form of the equation of the line is:

y=mx+b

Where "m" is the slope and "b" is the intersection of the line with the y-axis.

Given the equation y=\frac{1}{2}x+3, you can identify that:

m=\frac{1}{2}\\\\b=3

The line intercepts the y-axis when x=0, therefore, you can know that the line passes through the point:

(0,3) → Point of intersection with the y-axis.

Now, substitute y=0 and solve for "x" to find the point of intersection with the x-axis:

0=\frac{1}{2}x+3\\\\-3=\frac{1}{2}x\\\\(-3)(2)=x\\\\x=-6

Now, you know that the line also passes through the point:

(-6,0) → Point of intersection with the x-axis.

Draw the a line that passes through these points.

Therefore, you get the graph attached.

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Your friend asks if you would like to play a game of chance that uses a deck of cards and costs $1 to play. They say that if you
gtnhenbr [62]

Answer:

Expected value = 40/26 = 1.54 approximately

The player expects to win on average about $1.54 per game.

The positive expected value means it's a good idea to play the game.

============================================================

Further Explanation:

Let's label the three scenarios like so

  • scenario A: selecting a black card
  • scenario B: selecting a red card that is less than 5
  • scenario C: selecting anything that doesn't fit with the previous scenarios

The probability of scenario A happening is 1/2 because half the cards are black. Or you can notice that there are 26 black cards (13 spade + 13 club) out of 52 total, so 26/52 = 1/2. The net pay off for scenario A is 2-1 = 1 dollar because we have to account for the price to play the game.

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

Now onto scenario B.

The cards that are less than five are: {A, 2, 3, 4}. I'm considering aces to be smaller than 2. There are 2 sets of these values to account for the two red suits (hearts and diamonds), meaning there are 4*2 = 8 such cards out of 52 total. Then note that 8/52 = 2/13. The probability of winning $10 is 2/13. Though the net pay off here is 10-1 = 9 dollars to account for the cost to play the game.

So far the fractions we found for scenarios A and B were: 1/2 and 2/13

Let's get each fraction to the same denominator

  • 1/2 = 13/26
  • 2/13 = 4/26

Then add them up

13/26 + 4/26 = 17/26

Next, subtract the value from 1

1 - (17/26) = 26/26 - 17/26 = 9/26

The fraction 9/26 represents the chances of getting anything other than scenario A or scenario B. The net pay off here is -1 to indicate you lose one dollar.

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

Here's a table to organize everything so far

\begin{array}{|c|c|c|}\cline{1-3}\text{Scenario} & \text{Probability} & \text{Net Payoff}\\ \cline{1-3}\text{A} & 1/2 & 1\\ \cline{1-3}\text{B} & 2/13 & 9\\ \cline{1-3}\text{C} & 9/26 & -1\\ \cline{1-3}\end{array}

What we do from here is multiply each probability with the corresponding net payoff. I'll write the results in the fourth column as shown below

\begin{array}{|c|c|c|c|}\cline{1-4}\text{Scenario} & \text{Probability} & \text{Net Payoff} & \text{Probability * Payoff}\\ \cline{1-4}\text{A} & 1/2 & 1 & 1/2\\ \cline{1-4}\text{B} & 2/13 & 9 & 18/13\\ \cline{1-4}\text{C} & 9/26 & -1 & -9/26\\ \cline{1-4}\end{array}

Then we add up the results of that fourth column to compute the expected value.

(1/2) + (18/13) + (-9/26)

13/26 + 36/26 - 9/26

(13+36-9)/26

40/26

1.538 approximately

This value rounds to 1.54

The expected value for the player is 1.54 which means they expect to win, on average, about $1.54 per game.

Therefore, this game is tilted in favor of the player and it's a good decision to play the game.

If the expected value was negative, then the player would lose money on average and the game wouldn't be a good idea to play (though the card dealer would be happy).

Having an expected value of 0 would indicate a mathematically fair game, as no side gains money nor do they lose money on average.

7 0
2 years ago
What is the slope of the line passing through the points (6,1) and (-3,-4)?​
miskamm [114]

Answer:

5/9

Step-by-step explanation:

y2-y1/x2-x1 = 5/9

5 0
3 years ago
The ratio of the radii of two distinct spheres is 3:4. what is the ratio of their respective surface areas?
Naya [18.7K]

Hey , here is the answer to ur question.....!
Given: Radii is in the ratio 3:4
To find : ratio of Surface area of the two distinct spheres
Solution: Surface area of a sphere =4* pi *r^2
=>(3/4)^2=9/16
Therefore , the ratio of the areas of teh two distinct spheres=9:16
Hope this helps u!!!!!!.........

7 0
3 years ago
How many times does 2/3 go into 3/8?
oksano4ka [1.4K]

Answer:

91/6 times

Step-by-step explanation:

(2/3)(x)=3/8

2x/3=3/8

16x=9

x=9/16

So, 2/3 goes into 3/8, 9/16 times

3 0
3 years ago
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Jamie is playing a card game. Jamie's score changes by -12 points for 8 turns in a row.
Brilliant_brown [7]
Your answer will be negative 96
3 0
2 years ago
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