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schepotkina [342]
3 years ago
11

Determine whether p ∧ (p → q) and p ∧ q are logically equivalent.

Mathematics
1 answer:
Andrej [43]3 years ago
7 0

Answer:

Yes they are logically equivalent

p∧(p→q)≡p∧q

Step-by-step explanation:

The statements are logically equivalent if they have the same truth tables. So let´s use truth tables in order to determine if they are logically equivalent or not:

The picture that I attached you shows the truth table for each case. As you can see, p∧(p→q) has exactly the same truth values as p∧q. So we can conclude that they are logically equivalent.

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Consider a population with population proportion p, and a sample from the population with sample proportion pˆ. Which of the fol
Deffense [45]

According to CollegeBoard.org:

<u>Answer</u>: "To estimate the probability of observing a value as extreme as  pˆ  given  p."

<u>Explanation</u>: "The test statistic for a one-sample z-test is the distance, in units of standard deviations, between the statistic and the given parameter. From that distance, probabilities (a p-value) can be calculated and a claim can be assessed."

3 0
3 years ago
sal works for a computer repair shop. he has determines that customers pay on average $150 for each computer they bring in. He p
Effectus [21]

Answer:

The answer is :

sal must repair 320 computers in a year to break even.

Step-by-step explanation:

The break even point in a business is the point at which the total costs and the total revenue in a business are equal.

In order to calculate sal's break even point, we will first of all calculate the total costs incurred during the business year, then using the selling price (repairing price), we will calculate how many computers will be repaired to reach the incurred cost. This is done as follows:

Rent per month = $2,000

∴ Rent for a year (12 months) = 2,000 × 12 = $2,400

Cost incurred in fixing each computer = $75

Priced charged for fixing each computer = $150

Next, since we know that sal requires $75 in parts and labor to fix a computer, we will calculate the net price charged for each computer fixed as follows:

Net price charged = Priced charged for fixing each computer - Cost incurred in fixing each computer

Net price charged = 150 - 75 = $75

Finally to calculate the break even point, we know the net income (net price charged) for each computer and the costs of rent for each year, therefore, we will divide the cost incurred by the net price charged, as follows:

break even point = cost of rent for one year ÷ net price charged

break even point = 24,000 ÷ 75 = 320 computers.

Therefore, by the time sal repairs 320 computers during the year, he must have covered the costs incurred in operations, every additional repair, becomes a profit.

3 0
3 years ago
Determine the standard form of the equation of the line that passes through ( -5,0 ) ( 0 ,-9)
insens350 [35]

The general form for a line through two points (a,b) and (c,d) is

(c-a)(y-b)=(d-b)(x-a)

This is better than the slope forms because it works in the no slope case, as does the standard form.

If you haven't seen it before, it works because when (x,y)=(a,b) we get (c-a)(b-b)=(d-b)(a-a), both sides zero, and when (x,y)=(c,d) we get (c-a)(d-b)=(d-b)(c-a), clearly equal sides.

Here we have

(0 - -5)(y - 0) = (-9 - 0)(x - - 5)

5y = -9(x+5)

5y = -9x - 45

9x + 5y = -45

Ironically there are two standards for standard form; one with the constant alone on the right and one with the whole thing equal to zero.  I like the constant alone.

Answer: 9x + 5y = -45

Check:

We check each point is on the line

(-5,0)

9(-5) + 5(0) = -45, good

(0, -9)

9(0) + 5(-9) = -45, good again


5 0
3 years ago
Read 2 more answers
a recipe calls for 2 2/3 cups of flour every 1/6 cup of cinnamon.If Richard has 1 cup of cinnamon already in the recipe, how man
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Step-by-step explanation:

2 2/3

=><em>If</em> 8/3 = 1/6

x =1

1/6x = 8/3 ( Divide both sides by <em>1</em><em>/</em><em>6</em><em> </em>)

___ ___

1/6 1/6

(By cross-multiplying the numerators and denominators)

=> 1×6 8×6

___ x = ___

6×1 3×1

Cancelling out , we have

x = 8×2

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1 × 1

<em>The</em><em> </em><em>final</em><em> </em><em>answer</em><em> </em><em>becomes</em><em> </em><em>1</em><em>6</em>

<em>Hope</em><em> </em><em>it</em><em> </em><em>helps</em><em>.</em>

6 0
3 years ago
Solve for x.<br> x-8=-20
NeX [460]

Answer:

Step-by-step explanation:

To solve:

x - 8 = -20

Simply add +8 to both sides of the equation.

It becomes :

x - 8 +8 = -20 + 8

Note that, -8 + 8 will cancel out, and results to zero.

Therefore the equation becomes :

x = -20 + 8

x = -12.

Hope this helped!

8 0
3 years ago
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