Answer:
x = 1/3
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define Equation</u>
8x - 3 = 2(x - 1/2)
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distributive 2: 8x - 3 = 2x - 1
- Subtract 2x on both sides: 6x - 3 = -1
- Add 3 to both sides: 6x = 2
- Divide 6 on both sides: x = 1/3
Let p be: John goes to the beach
Let q be: He will go surfing.
Then in symbolic form, the argument becomes:
p ⇒ q
p
---------------------
∴ q
An argument is valid if the conjuction of the premises implies the conclusion.
p | q | p ⇒ q | (p ⇒ q) ∧ p | [(p ⇒ q) ∧ p] ⇒ q
---------------------------------------------------------------------\
F | F | T | F | T
F | T | T | F | T
T | F | F | F | T
T | T | T | T | T
The table above shows that the argument is a tautology.
Hence, the argument is valid
A) We can first start with the how: our equation is 2x+y=3. First, subtract 2x from each side. We get y=-2x+3. Our Y variable is isolated.
B) Now we can describe which points our equation goes through. One of them is obvious in our form, and that is (0,3) or our y-intercept. Another 2 would be branching off that line, such as (1,1) or (-1,5)
C) To make our system inconsistent, we can easily make another equation, with same slope, but the y-intercept has to be different. Our equation can be y=-2x+2, y=-2x+4, or even y=-2x+3.00000001.
Hope this helps you.
Answer: 0.3125.
Step-by-step explanation:
- The chance of having a boy is 0.5,
- the chance of having a girl is also 0.5.
<u>Outcome 1: all boys</u>
boy boy boy boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
<u>Outcome 2: first child is a girl, all others are boys</u>
girl boy boy boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
<u>Outcome 3: second child is a girl, all others are boys</u>
boy girl boy boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
<u>Outcome 4: third child is a girl, all others are boys</u>
boy boy girl boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
<u>Outcome 5: fourth child is a girl, all others are boys</u>
boy boy boy girl
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
Therefore,
0.0625 + 0.0625 + 0.0625 + 0.0625 + 0.0625 = 0.0625 * 5 = 0.3125
