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KonstantinChe [14]

3 years ago

5

A set of premises and a conclusion are given. Use the valid argument forms discussed in this chapter to deduce the conclusion fr

om the premises, giving a reason for each step. Assume all variables are statement variables. (a) p ∨ q (b) q → r (c) p ∧ s → t (d) ~r (e) ~q → u ∧ s (f) ∴t Make selections from the ones below to show the first steps of a proof and the reason for the conclusion.

1 answer:

Alex_Xolod [135]3 years ago

4 0

Answer:

See deduction below

Step-by-step explanation:

I will use the known inference rules (modus ponens, etc)

From d) and b),

~r

q → r

Therefore ~q (by Modus Tollens)

From a), and our previous conclusion:

p ∨ q

~q

Therefore p (by disjunctive sillogism)

Until know, we have concluded p and ~q. By e)

~q → u ∧ s

~q

Therefore u∧s. (Modus Ponens)

From p, u∧s, and c)

u∧s

s (simplification)

p (previous conclusion)

p∧s (adjuntion)

p∧s→t (Modus Ponens)

Therefore t, as we wanted to conclude.

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A store down the street is selling a used video game for 25% off the retail price. The game regularly sells for $89.00. What is

Dafna1 [17]

89.00 times .75 (new cost of item is 75% of original) =

66.75

therefor you answer is

D) $66.75

7 0

3 years ago

The law of cosines is used to find the measure of Z.

Shtirlitz [24]

Answer:

C. $Z=51^{\circ}$

Step-by-step explanation:

We have been given a triangle. We are asked to find the measure of angle Z using Law of cosines.

Law of cosines: $c^2=a^2+b^2-2ab\cdot \text{cos}(C)$ , where, a, b and c are sides opposite to angles A, B and C respectively.

Upon substituting our given values in law of cosines, we will get:

$16^2=19^2+18^2-2(19)(18)\cdot \text{cos}(Z)$

$256=361+324-684\cdot \text{cos}(Z)$

$256=685-684\cdot \text{cos}(Z)$

$256-685=685-685-684\cdot \text{cos}(Z)$

$-429=-684\cdot \text{cos}(Z)$

$\frac{-429}{-684}=\frac{-684\cdot \text{cos}(Z)}{-684}$

$0.627192982456=\text{cos}(Z)$

$\text{cos}(Z)=0.627192982456$

Now, we will use inverse cosine or arc-cos to solve for angle Z as:

$Z=\text{cos}^{-1}(0.627192982456)$

$Z=51.1566718^{\circ}$

$Z\approx 51^{\circ}$

Therefore, the measure of angle Z is approximately 51 degrees.

6 0

3 years ago

Read 2 more answers

Population Growth The population P (in thousands) of Oriando,Florida from 1980 through 2009 can be modeled by p = 130e0.0205t,wh

svetoff [14.1K]

Answer: a) 236,000.

b) 2021

Step-by-step explanation:

Given : Population Growth The population P (in thousands) of Oriando,Florida from 1980 through 2009 can be modeled by $p = 130e^{0.0205t}$ (1)

where t = 0 corresponds to 1980.

Then , for 2009

t= 2009-1980=29

a. ⇒The population of Phoenix in 2009 = $p = 130e^{0.0205(29)}$

$p = 130e^{0.5945}$

$p =130(1.81212465608)=235.57620529\approx236$

Hence, the population of Orlando in 2009 was about 236,000.

b) Substitute p= 300 in (1) , we get

$300 = 130e^{0.0205t}$

$2.3077= e^{0.0205t}$ (Divide both sides by 130)

Taking Natural log on both sides,

$\ln(2.3077) = 0.0205t\\\\\Rightarrow\ t=\dfrac{\ln(2.3077)}{0.0205}$

$t=\dfrac{0.836251357528}{0.0205}=40.7927491477\approx41$

Hence, The year Orlando will have a population of 300,000 =1980+41 =2021

6 0

4 years ago

Do you have to get the right answer for your brain to change

Dovator [93]

Answer:

No

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What is the domain of the function f(x) = 2x^2 - 3?

SpyIntel [72]

Domain: Set of all real numbers

If you want to express the domain in set-builder notation, then you'd write something like $\left\{x|x\in\mathbb{R}\right\}$ which is fancy notation to basically say "x is any real number"

If you want to write the domain in interval notation, then you'd write $\left(-\infty, \infty\right)$ which is the interval from negative infinity to positive infinity. In other words, the entire real number line.

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

The domain is the set of all real numbers because we don't have any restrictions to worry about. There are no division by zero errors. There are no cases where we have to worry about taking the square root of a negative number, or anything similar. Any number can replace x to generate an output for y.

4 0

3 years ago