Answer:
-$13.5
Step-by-step explanation:
Let x be a random variable of a count of player gain.
- We are told that if the die shows 3, the player wins $45.
- there is a charge of $9 to play the game
If he wins, he gains; 45 - 9 = $36
If he looses, he has a net gain which is a loss = -$9
Thus, the x-values are; (36, -9)
Probability of getting a 3 which is a win is P(X) = 1/6 since there are 6 numbers on the dice and probability of getting any other number is P(X) = 5/6
Thus;
E(X) = Σ(x•P(X)) = (1/6)(36) + (5/6)(-9)
E(X) = (1/6)(36 - (5 × 9))
E(X) = (1/6)(36 - 45)
E(X) = -9/6 = -3/2
E(X) = -3/2
This represents -3/2 of $9 = -(3/2) × 9 = - 27/2 = -$13.5
Point B is has a square so it’s a 90° angle.
Answer:
b. -84
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<u /><u />
<u />
<u>Step 2: Solve for </u><em><u>a</u></em>
- Addition Property of Equality:
- [Simplify] Add:
- Multiplication Property of Equality:
- [Simplify] Multiply:
<u>Step 3: Check</u>
<em>Plug in a into the original equation to verify it's a solution.</em>
- Substitute in <em>a</em>:
- [Frac] Divide:
- Subtract:
Here we see that 5 does indeed equal 5.
∴ a = -84 is the solution to the equation.
Answer:
You can denote the width of the rectangle as x,
than the length of the rectangle will be 2x
and the perimeter of the rectangle will be two length plus two width and it should be equal to 54 in
and the equation will look 2(2x)+2x=54
solving the equation 6x=54, x=9in
So the width of the rectangle is 9in and the length is 9*2=18in
and the area of the rectangle is 9*18=162 sq in.
Answer:
See answer below
Step-by-step explanation:
This is a separable equation, so we solve it like this:
Then for any constant k (this is the general solution). This solution is defined in (-∞,∞) (there are no singularities) and when x tends to infinity, no terms of the solution vanish, hence there are no transient terms.