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3 years ago

Determine the truth value of the statement when p is T, q is F, and r is F

Mathematics

1 answer:

gayaneshka [121]3 years ago

4 0

Given P is T, q is F and r is F.

Let us find p ↔ q first.

↔ is called bi-conditional operator and is true when p and q both are matched.

Since here p is T and q is F, p↔q is F. ( Since p and q are not matching)

~p v r = ~T v F = F v F = F

Hence (p↔q)→(~pvr) = F → F = T (Since conditional operator → is false if and if first proposition is T and second proposition is F, for all other values it is T)

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A certain city's population is 120,000 and decreases 1.4% per year for 15 years.

mart [117]

Answer:

Decay Problem.

Decay rate, r = 0.014
Initial Amount =120,000

$P(t)=120000(0.986)^t$
P(10)=104,220

Step-by-step explanation:

The exponential function for growth/decay is given as:

$P(t)=P_0(1 \pm r)^t, where:\\P_0$ is the Initial Population\\r is the growth/decay rate\\t is time$

In this problem:

The city's initial population is 120,000 and it decreases by 1.4% per year.

Since the population decreases, it is a Decay Problem.

Decay rate, r=1.4% =0.014
Initial Amount =120,000

Therefore, the function is:

$P(t)=120000(1 - 0.014)^t\\P(t)=120000(0.986)^t$

When t=10 years

$P(10)=120000(0.986)^10\\=104219.8\\\approx 104220 $ (to the nearest whole number)$

8 0

3 years ago

explain how you could use a number line to show that -4 + 3 and 3 + (-4) have the same value. Which property of addition states

brilliants [131]

They are able to have the same value as the negative sign is simply transferred to the inside. Either way 4 is being subtracted from 3.

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3 years ago

Paulo is creating a confidence interval based on sample data for the percentage of Americans that own a dog. His work is shown b

Gekata [30.6K]

Answer:

Checked on edg. , the answer is A. Thanks!

Step-by-step explanation:

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3 years ago

Read 2 more answers

Show that 155 can be express as the sum of a power of 2 and a cube number?

son4ous [18]

$\bf \underset{155-128}{155-2^7}= 27\qquad \qquad therefore\qquad 2^7+27=155\implies 2^7+3^3=155$

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3 years ago

Given the equation y=2x+3, write a second equation that would create an independent consistent linear system

STALIN [3.7K]

Two equations will be called independent if their graphs touch only on one point (they have one solution for the x-value and one solution for the y-value), and two equations will be dependent if they touch at every point (there is an infinite number of solutions).

This definition of independent and dependent equations is shown in the following diagram. Consider that there are two lines, one red line and one blue line:

They are independent if they touch only on one point and dependent if they touch at every point (they are the same line).

In our case, we are asked to write an equation in order to create an independent consistent linear system.

Note: Consistent means that the system has a solution.

First, we graph the given equation:

$y=2x+3$

There are many different equations that will form an independent consistent linear system with this equation.

We are going to choose the following line equation:

$y=-x+1$

Because when we graph this equation next to the previous line:

We can see that they touch at one point, thus there is a solution and the system is independent --> we have created an independent consistent linear system.

Answer:

$y=-x+1$

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11 months ago