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3 years ago

8

Construct a truth table for the statement: (p v q) v (~p ^ q) -> q

1 answer:

Gnom [1K]3 years ago

8 0

Step-by-step explanation:

We have the following statement $(p\lor q)\lor(\lnot p \land q) \rightarrow q$

A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

The simple statements from the statement given are:

$\lnot p$ , $p\lor q$ , $\lnot p \land q$ , and $(p\lor q)\lor(\lnot p \land q)$

This is the truth table.

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Ming works as a quality assurance analyst at a bottling factory. She wants to use a one-sample z interval to estimate what propo

Nastasia [14]

Answer:

Sample size is $n=423$

Step-by-step explanation:

Given that,

Margin of error $=4$ %

Confidence level $=90$ %

Suppose, sample proportion $=0.5$

i.e. $\hat{P}=0.5$

We know that,

Margin of error $=2^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }$

∴ $1.64\sqrt{\frac{0.5(0.5)}{n} } \leq 4\%$

$\Rightarrow 1.64\sqrt{\frac{0.25}{n} } \leq 0.04$

$\Rightarrow \frac{0.5}{\sqrt{n} } \leq \frac{0.04}{1.64}$

$\Rightarrow \frac{0.5}{\sqrt{n} } \leq 0.0243$

$\Rightarrow \sqrt{n}\geq \frac{0.5}{0.0243}$

$\Rightarrow \sqrt{n}\geq 20.57$

squaring on both side,

∴ $n=423.1249$

Hence, the sample size is,

$n=423$

Hence, the correct option is $(b).$

7 0

3 years ago

if a toy rocket is launced vertically upward from ground level with an inital velocity of 128 feet per second, then its high h,

makkiz [27]

The toy rocket hits the ground when h(t) = 0.
So, h(t) = 0 = -9t^2 + 81.

Solving the equation,
-9t^2 = -81
Dividing by -9
t^2 = 9
Taking the square root.
t = 3

The answer is 3 seconds.

7 0

3 years ago

Use complete sentences to describe the possible solution(s) to a system of equations that includes the equation of a circle and

goldfiish [28.3K]

Answer:

A general line can be represented as , y= m x + c

And general equation of circle is , ax²+by²+2 g x +2 f y +c=0

Now there are following possibilities

1. A line and circle have no common point of intersection, that is no solution.

2. A line may be a tangent to a circle, that is one common point, one solution.

3. A line may intersect a circle maximum at two points, that is 2 solution.

Image is depicted below.

3 0

3 years ago

Read 2 more answers

The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:

kotykmax [81]

Answer: Last one is right C = 5 / 9 (F-32)

Step-by-step explanation: Solving C from equation F = (9/5)C + 32 :

1. multiply by 5 you get 5F = 9C + 160 and 5(F-32) = 9C

2. divide by 9 you get (5/9) (F-32) = C

8 0

2 years ago

Why is the answer to this integral's denominator have 1+pi^2

ss7ja [257]

It comes from integrating by parts twice. Let

$I = \displaystyle \int e^n \sin(\pi n) \, dn$

Recall the IBP formula,

$\displaystyle \int u \, dv = uv - \int v \, du$

Let

$u = \sin(\pi n) \implies du = \pi \cos(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Then

$\displaystyle I = e^n \sin(\pi n) - \pi \int e^n \cos(\pi n) \, dn$

Apply IBP once more, with

$u = \cos(\pi n) \implies du = -\pi \sin(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Notice that the ∫ v du term contains the original integral, so that

$\displaystyle I = e^n \sin(\pi n) - \pi \left(e^n \cos(\pi n) + \pi \int e^n \sin(\pi n) \, dn\right)$

$\displaystyle I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n - \pi^2 I$

$\displaystyle (1 + \pi^2) I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n$

$\implies \displaystyle I = \frac{\left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n}{1+\pi^2} + C$

6 0

2 years ago