Determine whether the statement (p∧(p⟶q))⟶q is a tautology one time by using truth table and the other time without using truth table

Answer:

7.5 cm²

Step-by-step explanation:

Dimensions of the large ∆:

[tex] base (b) = 3cm, height (h) = 9cm [/tex]

[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]

Dimensions of the small ∆:

[tex] base (b) = 2cm, height (h) = 6cm [/tex]

[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]

Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²

Answer:

4 units

Step-by-step explanation:

A transformation is the movement of a point from one position to another position. If a shape is transformed all its points are also transformed. Types of transformations are translation, rotation, reflection and dilation.

If a shape is transformed, the length of its sides and shape remains the same, only the position changes.

If Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B, the length of A'B' remains the same which is 4 unit. To prove this:

Let A be at ([tex]x_1,y_1[/tex]) and B be at ([tex]x_2,y_2[/tex]). The length of AB is:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

If AB is translated to the right by 1 unit the new points are A' at ([tex]x_1+1,y_1[/tex]) and B' at ([tex]x_2+1,y_2[/tex]). The length of A'B' is:

[tex]A'B'=\sqrt{(y_2-y_1)^2+(x_2+1-(x_1+1))^2}=\sqrt{(y_2-y_1)^2+(x_2+1-x_1-1)^2}\\\\A'B'=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

AB = A'B' = 4 units

Answer:

x ≤ [tex]\frac{9}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{4}[/tex](12x + 8) ≤ - 2x + 11 ← distribute parenthesis on left side

3x + 2 ≤ - 2x + 11 ( add 2x to both sides )

5x + 2 ≤ 11 ( subtract 2 from both sides )

5x ≤ 9 ( divide both sides by 5 )

x ≤ [tex]\frac{9}{5}[/tex]

-¼(12x+8) ≤ -2x+11

4X-¼(12x+8) ≤-2x+11

= -12x + 8 ≤ -2x + 11

-12x + 2x ≤ 11 - 8

= -10x/10 ≤ 3/-10

Answer:

3

Step-by-step explanation:

f(x)=3x-3

g(x)=-x^2+4,

f(2) = 3(2) -3 = 6-3 =3

g(-2) = -(-2)^2+4 = -4+4 = 0

f(2)-g(-2)= = 3-0 = 3

Answer:

  17 by 21 inches

Step-by-step explanation:

The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...

  L + W = 38

  LW = 357

__

Solution:

  W(38 -W) = 357 . . . . . substitute for L

  -(W^2 -76W) = 357 . . expand on the left

  -(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square

  (W -19)^2 = 4 . . . . . . . write as a square

  W -19 = ±√4 = ±2 . . . take the square root; next, add 19

  W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other

The dimensions are 17 by 21 inches.

Answer:

9%

Step-by-step explanation:

Use the rule of 72.  If you want the money to double in 8 years, it will need to be at 9 percent interest rate to reach this goal.

Answer:

federal loans = $29,000

private loans = $14,000

Step-by-step explanation:

x + y = 43000

.045x + .02y = 1585

x = 29,000

y = 14,000

Answer:

Amount of loan from federal : $ 29,000

Amount of loan from private bank : $ 14,000

Step-by-step explanation:

We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.

If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -

x + y = 43,000

At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -

0.045x + 0.02y = 1585

Let's solve the following system for x and y, the amount of each loan,

[tex]\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}[/tex] ( Substitute x = 43000 - y )

[tex]0.045\left(43000-y\right)+0.02y=1585[/tex] ( Simplify )

[tex]1935-0.025y=1585[/tex],

[tex]1935000-25y=1585000[/tex],

[tex]-25y=-350000[/tex],

[tex]y=14000[/tex],

[tex]x=29000[/tex]

Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.

Answer:

  146/45

Step-by-step explanation:

Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.

  [tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]

__

Comment on procedure

The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.

Answer:

C

Step-by-step explanation:

reciprocal of z=1/z

[tex]z=2(cos \frac{\pi }{4} +i sin\frac{\pi }{4} )=2e ^{i \frac{\pi } {4}\\\frac{1}{z}=\frac{1}{2e^{i \frac{\pi}{4} } }\\\frac{1}{z} =\frac{1}{2} e^{-i\frac{\pi}{4} } \\\frac{1}{z} (cos\frac{\pi}{4} -isin\frac{\pi}{4} ) \\\frac{1}{z}=\frac{1}{2} (\frac{\sqrt{2} }{2} -\frac{\sqrt{2} }{2} )\\\frac{1}{z} =\frac{\sqrt{2} }{4} -i \frac{\sqrt{2 } }{4}[/tex]

Answer:

6.034

Step-by-step explanation:

6 is a whole number.

.034 because it is 34 thousandths, not 34 hundredths.

Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

We have a line of best fit:

h = –21.962x + 114.655

As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.

Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

Learn more about the line of best fit here:

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Answer:

A. they are parallel because their slopes are equal.

Step-by-step explanation:

edge 2020

Answer:

its A in egde

Step-by-step explanation:

Answer:

19,691

Step-by-step explanation:

Answer:

2813 x 7 = 19691

Hope this helps!

Answer:

x = 6

Step-by-step explanation:

∠ DBC + ∠ ABC = ∠ ABD , substitute values

5x - 4 + 8x - 3 = 79

13x + 1 = 79 ( subtract 1 from both sides )

13x = 78 ( divide both sides by 13 )

x = 6

Answer:

B. j(kl)

Step-by-step explanation:

(jk)l

We can change the order we multiply and still get the same result

j(kl)

Answer:

Step-by-step explanation:

its B i did it

Answer:

[tex] {x}^{2} + 5x + 10[/tex]

Answer:

[tex]\large \boxed{x^2 +5x+10}[/tex]

Step-by-step explanation:

A polynomial is an expression that has variables, coefficients, and constants.

An example of a polynomial can be x² - 6x + 2.

Answer: 1.5 less than 15 is divided by a number d.

Step-by-step explanation:

Answer:

0.56 is the required probability.

Step-by-step explanation:

Time for which signal shows green light = 4 minutes

Time for which signal shows yellow light = 10 seconds

Time for which signal shows red light = 3 minutes

To find:

Probability that the signal will show green light when you reach the destination = ?

Solution:

First of all, let us convert each time to same unit before doing any calculations.

Time for which signal shows green light = 4 minutes = 4 [tex]\times[/tex] 60 seconds = 240 seconds

Time for which signal shows yellow light = 10 seconds

Time for which signal shows red light = 3 minutes = 3 [tex]\times[/tex] 60 seconds = 180 seconds

Now, let us have a look at the formula for probability of an event E:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Here, E is the event that green light is shown by the signal.

Number of favorable cases mean the time for which green light is shown and Total number of cases is the total time (Time for which green light is shown + Time for which Yellow light is shown + Time for which red light is shown)

So, the required probability is:

[tex]P(E) = \dfrac{240}{240+10+180}\\\Rightarrow P(E) = \dfrac{240}{430}\\\Rightarrow \bold{P(E) \approx 0.56 }[/tex]

The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.

Answer:

s = 17 units

Step-by-step explanation:

Given f(t) = t³ - 8t² + 27t

Differentiating f(t), we have

f'(t) = 3t² - 16 t + 27

At t = 0

f'(t) = 27

This is the required obtainaible distance, s.

Answer:

The events are independent.

The probability of showing heads on both toss is equal to 1/2

Step-by-step explanation:

The sample space for this experiment consists of 2⁴= 16 sample points, as each toss can result in two outcomes we assume that the events are equally likely.

Two events are independent in the sample space if the probability of one event occurs, is not affected by whether the other event has or has not occurred.

In general the k events are defined to be mutually independent if and only if the probability of the intersection of  any 2,3,--------, k  equals the product of their respective probabilities.

P (A∩B) = P(A). P(B)

P (A∩B)   = 1/2. 1/2= 1/4

                                                                  Head          Tail

 P(E1)= 1/2  ----------          Coin 1               H,H              T,H

                                                                1/4                  1/4

  P(E2)= 1/2  ---------------  Coin 2             H, H               H,T

                                                                      1/4           1/4

So the events are independent.

The probability of showing heads on both toss is equal to 1/2

The sample space for this experiment consists of 2⁴= 16 sample points, out of which eight will have heads on both toss.

Or in other words ( 1/4* 1/4) = 2/4 = 1/2

Answer: -4

At 1, the parabola is at (1, 3). And at 3, it's at (3, -5). The rate of change is -4, since each time it moves right 1, it goes down 4.

Hope that helped,

-sirswagger21

Answer:

the probability of no defects in 10 feet of steel = 0.1353

Step-by-step explanation:

GIven that:

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.

Let consider β to be the average value for defecting

So;

β = 2

Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.

Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2

i.e

[tex]Y \sim P( \beta = 2)[/tex]

the probability mass function can be represented as follows:

[tex]\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}[/tex]

where;

y =  0,1,2,3 ...

Hence,  the probability of no defects in 10 feet of steel

y = 0

[tex]\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}[/tex]

[tex]\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}[/tex]

P(y =0) = 0.1353

Answer:

-5 ≤x ≤6

Step-by-step explanation:

The domain is the values that x can take

X goes from -5 and includes -5 to x =6 and includes 6

-5 ≤x ≤6

Answer:

See attached!

Step-by-step explanation:

Answer:

  x^2 +y^2 = 4y

Step-by-step explanation:

Using the usual translation relations, we have ...

  r^2 = x^2+y^2

  x = r·cos(θ)

  y = r·sin(θ)

Substituting for sin(θ) the equation becomes ...

  r = 4sin(θ)

  r = 4(y/r)

  r^2 = 4y

Then, substituting for r^2 we get ...

  x^2 +y^2 = 4y . . . . . matches the first choice

Answer:

See below.

Step-by-step explanation:

First, recall the meanings of the domain and range.

The domain is the span of x-values covered by the graph.

And the range is the span of y-values covered by the graph.

1)

So, we have here an absolute value function.

As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:

[tex]\{x|x\in\textbb{R}\}[/tex]

(You are correct!)

For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:

[tex]\{y|y\leq 7\}[/tex]

2)

We have here an ellipse.

First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:

[tex]-4\leq x\leq 6[/tex]

So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:

[tex]\{x|-4\leq x\leq 6\}[/tex]

For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:

[tex]-5\leq y\leq 1[/tex]

This represents all the y-values between -5 and 1, including -5 and 1.

In set notation, thi is:

[tex]\{y|-5\leq y\leq 1\}[/tex]

Answer:

B. More

Step-by-step explanation:

This is according to the law of large numbers

An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.

Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.

An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed

Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.

Learn more about probability here:

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Answer:

P= 2

Step-by-step explanation:

10/7p+13/8+15/2p=-909/56

Combine like terms

10/7p+15/2p=-909/56-13/8

20p+105p/14=-909-13*7/56

125/14p=-909-91/56

125/14p= -1000/56

125/14p*14/125= -1000/56*14/125

simplify

P= 8/4=2

And for #8 n =1 I answered this question it

Search

Answer:

x+10 =2

x = -8

Step-by-step explanation:

plus means add

x+10 =2

Subtract 10 from each side

x+10-10 =2-10

x = -8

Answer:

Your answer is here.Enjoy dude

Answer:

12.56 unit²

Step-by-step explanation:

The form of the circle is:

Let's bring the given to the form of a circle as above:

As per the form, we got r² = 2², so the radius of circle is 2 units.

The area of circle:

Answer:

Interquartile range is the distance between the first and third of a data.

Step-by-step explanation:

Hope it will help you :)