please help by today

The logical statement [tex]$(a \wedge b) \rightarrow(b \vee c)$[/tex] is a tautology. Hence, Option B is the most appropriate answer to the given question.

A tautology is a logical statement where the conclusion is always equivalent to the premise. No matter what the individual parts are, the result is always a true statement; i.e. a tautology is always true. The opposite of tautology is either a contradiction or a fallacy.

a. let us check the first option.

[tex](a \vee b) \rightarrow(b \wedge c)=(a+b)^{\prime}+b c[/tex]

[tex](a \vee b) \rightarrow(b \wedge c)=a^{\prime} b^{\prime}+b c[/tex]

Therefore, [tex]$(a \vee b) \rightarrow(b \wedge c)$[/tex] is a contingency and not a tautology.

b. let us check the second option.

[tex](a \wedge b) \rightarrow(b \vee c)=a b \rightarrow b+c[/tex]

[tex](a \wedge b) \rightarrow(b \vee c)=(a b)^{\prime}+b+c[/tex]

[tex](a \wedge b) \rightarrow(b \vee c)=a^{\prime}+b^{\prime}+b+c[/tex]

[tex](a \wedge b) \rightarrow(b \vee c)=a^{\prime}+1+c[/tex]   (since, b' + b = 1)

[tex](a \wedge b) \rightarrow(b \vee c)=1.[/tex]

Therefore, [tex]$(a \wedge b) \rightarrow(b \vee c)$[/tex] is a tautology.

c. let us check the third option.

[tex](a \wedge b) \rightarrow(b \rightarrow c)=(a+b) \rightarrow\left(b^{\prime}+c\right)[/tex]

[tex](a \wedge b) \rightarrow(b \rightarrow c)=(a+b)^{\prime}+b^{\prime}+c[/tex]

[tex](a \wedge b) \rightarrow(b \rightarrow c)=a^{\prime} b^{\prime}+b^{\prime}+c[/tex]

[tex](a \wedge b) \rightarrow(b \rightarrow c)=b^{\prime}+c[/tex]

Therefore, [tex]$(a \wedge b) \rightarrow(b \rightarrow c)$[/tex] is contingency but not a tautology.

d. let us check the fourth option.

[tex](a \rightarrow b) \rightarrow(b \rightarrow c)=\left(a^{\prime}+b\right) \rightarrow\left(b^{\prime}+c\right)[/tex]

[tex](a \rightarrow b) \rightarrow(b \rightarrow c)=\left(a^{\prime}+b\right)+b^{\prime}+c[/tex]

[tex](a \rightarrow b) \rightarrow(b \rightarrow c)=a b^{\prime}+b^{\prime}+c[/tex]

[tex](a \rightarrow b) \rightarrow(b \rightarrow c)=b^{\prime}+c[/tex]

Therefore, [tex]$(a \rightarrow b) \rightarrow(b \rightarrow c)$[/tex] is contingency but not a tautology.

Hence, option B is the only example of tautology.

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The judgement on each of the given scenarios are as follows;

1. Yes, enough information is given to conclude that the triangles are congruent by the side-side-side SSS congruence theorem.

2. No, the information conveyed through the triangles is not enough to conclude that the triangles are congruent.

3. Yes, the two triangles given are congruent by the HL Congruence theorem.

1. By observation: the two Triangles represented in 1. share a side and also, the two corresponding sides are congruent; it can be concluded that the two triangles are congruent.

2. Although two sides are said to be congruent in the triangles; it cannot be concluded that the triangles are congruent neither by HL nor SSS congruence theorem.

3. The two Triangles share the diagonal which is the hypothenuse of both triangles.

Additionally, one of the other side lengths of the triangles are congruent; Therefore, the triangles are congruent by the HL congruence theorem.

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Answer: Please adjust the 37. The answer would be 40.

Step-by-step explanation:

23 + 17 obviously equals 40.

for a binomial random variable x, it can only takes on two possible values, 0 or 1 is True

A binomial random variable is a discrete random variable, which means that it can only take on certain values, in this case 0 or 1. This means that the answer to the question is true. A binomial random variable is the sum of two independent Bernoulli random variables, where each Bernoulli random variable has a probability of success equal to the probability of success for the binomial random variable. This means that the binomial random variable is a summation of two Bernoulli random variables, and can only take on values of 0 or 1.

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The probability that two or more of the events will occur is 0.683594.

The probability that two or more of the events will occur is equal to 1 minus the probability that none of the events will occur. Since the probability of each event occurring is 0.25, the probability that none of the events will occur is (1 - 0.25) * (1 - 0.25) * (1 - 0.25) * (1 - 0.25) = 0.316406. Therefore, the probability that two or more of the events will occur is 1 - 0.316406 = 0.683594.

Alternatively, you can find the probability that two or more of the events will occur by adding up the probabilities of each of the ways that two or more of the events can occur.

There are four ways that two events can occur (for example, event A and event B), six ways that three events can occur (for example, event A, event B, and event C), and four ways that all four events can occur.

Thus, the probability that two or more of the events will occur is (4 * 0.25 * 0.25) + (6 * 0.25 * 0.25 * 0.25) + (4 * 0.25 * 0.25 * 0.25 * 0.25) = 0.683594, which is the same result as before.

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Answer: If your friends had 16 pizzas, the total amount of pizza sauce needed was 11/3 cups, How many pizzas could you create?

Step-by-step explanation: :D

Step-by-step explanation:

9.

x = 3

yes, that's really it.

it just means that any value is valid for y.

this line is not a function, because the one valid value for x (3) has infinitely many assigned y values.

10.

the usual equation for a line is

y = ax + b

with "a" being the slope, "b" being the y-intercept (the y-value when x = 0).

we see that b = 0, as the line goes through the origin (0, 0).

the slope is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

we see e.g. the points (0, 0) and (1, -3). I always recommend to look for points with integer coordinates.

when going from one to the other,

x changes by +1 (from 0 to 1).

y changes by -3 (from 0 to -3).

the slope "a" = -3/1 = -3.

the line equation is

y = -3x

Answer: The median of the shoe sizes is 6.5. If a shoe size of 4 is added to the data, the median will not change because it is based on the middle value in the data set and the addition of a value of 4 will not affect the middle value.

Step-by-step explanation:

Answer:

$51.20 is the cost after a 20% reduction.

Explanation:

There are two ways that this can be determined.

First, we can find what 20% of the original $64 price is and subtract the discount from the price.

20% = 0.20

0.20 ( $64) = $12.80

$64 - $12.80 = $51.20

Or

We can say that $64 is 100% of the price and subtract the 20% meaning the sale price will be 80% of the original price.

100% = 1.00 20% = .20

$64(1.00-.20) = $64(.80) = $51.20

Answer:

C

Step-by-step explanation:

The critical value for the left-tailed test is −2.0537.

For a left-tailed test, when α=0.02, the critical z-value is the value on the horizontal axis of the z- or standard normal distribution curve such that the area under the curve to the left of this critical value is 0.02.

Using a standard normal distribution table,

Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.

There are two z-score tables which are:

Now 0.5-α=0.5-0.02

=0.48

So 0.48 is closest in z score table is z=2.05

The left-tailed critical value always negative(-).

So, the value is -2.05.

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Answer: 27

Step-by-step explanation:

This is a proportion.

a = 5

b = 9

So A must equal 15. In order to get that we multiply by 3. Since we did that to A, we must also do it to B; that way we keep an equal proportion.

9 x 3 = 27

Answer:

x=-4/3

Step-by-step explanation:

Answer: d = 0

Step-by-step explanation:

     To solve this equation, we will isolate the variable.

7.5d = 2.5d

(7.5d) - 2.5d = (2.5d) - 2.5d

5d = 0

[tex]\frac{5d}{5}[/tex] = [tex]\frac{0}{5}[/tex]

d = 0

     Elena is correct when she subtracts 2.5d from each side. Since subtraction is the inverse operation of addition, we need to subtract. 7.5d and 2.5 are both like terms, so we subtract the coefficents.

The time is 8 seconds to reach the bottom of a 252-foot-long hill.

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

We have,

riding at a speed of 18mi/h when she starts down a long hill,

The distance she travels in feet can be modeled by d(t) = 4t² + 18t,

252 foot - long hill

I attempted the problem and I got 12.5 seconds.. but im not sure if im right

Use the quadratic formula to find t.

d(t) = 4t² + 18t,

d(t)=400

4t² + 18t =400

4t² + 18t -400=0          

2t²+9t-200=0          

x= 8; -25/2  

Hence, the time is 8 seconds to reach the bottom of a 252-foot-long hill.

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we often predict the probability of an event happening in the future based on how easily we can recall a similar type of event from the past. this is known as the  availability bias

When faced with an instant choice requirement, the availability heuristic enables people to make decisions fast. When you are trying to decide, a lot of connected incidents or circumstances could pop into your head right away. You can conclude that some events are more common or likely than others as a result.

You tend to overestimate the possibility and likelihood of similar situations happening in the future and give this information more weight. When you're attempting to decide or pass judgement on the world around you, this can be useful. Would you argue, for instance, that words in the English language that start with the letter t or with the letter k are more numerous?

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The equilibrium price is 12 and the equilibrium quantity is 400.

It should be noted that on order to fund equilibrium price and quantity, we've to equate the quantity supplied and demanded. This will be:

Qd = 1060 - 55p

Qs = -200 + 50p

Qd = Qs

1060 - 55p = -200 + 50p

Collect like terms

-55p - 50p = -200 - 1060

-105p = -1260

Divide

p = 1260 / 105

p = 12

The equilibrium price is 12

Equilibrium quantity = -200 + 50p

= -200 + 50(12)

= -200 + 600

= 400

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Answer:

−3.5, −0.3, 0.6, 3.3

Step-by-step explanation:

This is because negative numbers are less than positive numbers, and numbers with a smaller absolute value are less than numbers with a larger absolute value. Therefore, the smallest number in the given list is −3.5, followed by −0.3, 0.6, and finally 3.3. When we put the numbers in this order, we get the correct order from least to greatest.

the area of the triangle ABC is found by using the formula 1/2 * (base * height). Here, the base is 0 and the height is 1. Thus, the area of the triangle ABC = 0.5.

Let x = 0, y = 1 in 5x2y = 31

31 = 0

Thus, the point B is (0, 0).

The area of the triangle ABC = 1/2 * (0 * 1) + (0 * 1) + (1 * 0) = 0.5.

The equation of line L is given as 5x2y = 31. To find the point B, we need to substitute x = 0 in the equation. Doing so, we get 31 = 0, which means that the point B lies on the y-axis at (0, 0).

Next, since the line M is perpendicular to L and passes through A, we can assume that it is a horizontal line passing through (0, 1). Thus, the point C is the point of intersection of L and M, which is (1, 0).

Finally, the area of the triangle ABC is found by using the formula 1/2 * (base * height). Here, the base is 0 and the height is 1. Thus, the area of the triangle ABC = 0.5.

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Answer:

~8.5

Step-by-step explanation:

Knowledge Needed

Pythagorean Theorem:

[tex]a^2+b^2 = c^2[/tex]

Plug in 2 known values to solve.

Question

[tex]a^2+b^2 = c^2\\(8)^2 + (3)^2 = c^2[/tex]

64 + 9 = c^2

c^2 = 73

Find the square root of both sides.

[tex]\sqrt{c^2} = \sqrt{73}[/tex]

c = [tex]\sqrt{73}[/tex]

~8.5

Answer:

c = 8.5

Step-by-step explanation:

The Pythagorean theorem is

[tex]a^{2} +b^{2} =c^{2}[/tex]

Since we know a and be, we simply square them, then add those values together, and take the square root of the final value

[tex]8^{2} = 64[/tex]

[tex]3^{2} = 9[/tex]

[tex]64 + 9 = 73[/tex]

[tex]\sqrt{73} = 8.5[/tex]

c = 8.5

Therefore, in order for them to enjoy a party, they must be rewarded a minimum of 26 extra times.

The equals sign (=) must appear in an equation. You can think of an equation as having a left and a right side since there will be a mathematical expression on either side of it. Consider an equation to be a set of scales. Although you can use different amounts on either side, for it to be solved, each side must be equally balanced. An unknown will always be present in an algebraic equation. This is symbolized by a symbol, such x, y, or z.

Here,

Given: Given: To reward her students for good behavior, Mrs. Morton fills a marble jar with three marbles.

if there are 24 marbles in the jar. When r denotes the quantity of additional rewards for the class, then the necessary equation is 24 + 3r 100.

If we can figure it out, we'll obtain the minimum number of marbles the jar holds—24.

In order to solve the problem, take 24 away from both sides.

=> 3r ≥100 -24

=> 3r  ≥76

=> r  ≥76/3

=> r ≥ 25.33

=> r≈ 26

Therefore, in order for them to enjoy a party, they must be rewarded a minimum of 26 extra times.

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Answer:

The measure of each interior angle of a regular polygon with 7 sides is about 128.6.

Step-by-step explanation:

hope this helps

If the y-intercept is 4, the point version would be written as (0,4).

What is a point?

In classical geometry, a point may be a primitive notion that models a particular location in area, and has no length, width, or thickness. In trendy arithmetic, a point refers additional typically to a part of some set referred to as an area.

Main body:

As the y-intercept is 4 , so x intercept is 0 according to which the point becomes (0,4)

as x  =0 and y = 4.

hence ,  the point version would be written as (0,4).

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Answer: B

Step-by-step explanation: TRUST

The horizontal component of the force vector is 260 pounds, and the vertical component is 150 pounds. (Option B).

To find the horizontal and vertical components of the force vector, we can use trigonometry. The horizontal component is the force acting in the direction parallel to the ground (x-axis), and the vertical component is the force acting in the direction perpendicular to the ground (y-axis).

Given that the force is 300 pounds and makes a 30° angle with the ground, we can calculate the components as follows:

Horizontal component (F_horizontal) = Force * cos(angle)

Vertical component (F_vertical) = Force * sin(angle)

Inserting in the values:

Horizontal component (F_horizontal) = 300 pounds * cos(30°)

Vertical component (F_vertical) = 300 pounds * sin(30°)

Now, let's calculate:

Horizontal component (F_horizontal) = 300 pounds * 0.866 (rounded to 3 decimal places, cos(30°) ≈ 0.866)

F_horizontal ≈ 259.8 pounds

Vertical component (F_vertical) = 300 pounds * 0.5 (rounded to 3 decimal places, sin(30°) ≈ 0.5)

F_vertical ≈ 150 pounds

Therefore, the required components of the force vector are approximately 260 pounds and 150 pounds.

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Answer:

1) 35.07

2) 123.6

3)3.9

4) 102.83

5)97.5

6)6.93

Using the concept of ratios, there is 15 more blue balls

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.

The ratio of white to blue balls is 3:5

The number of white bulbs is 45

let's calculate the number of blue balls to determine the total number of balls.

3 + 5 = 8;

(3 / 8) * x = 45

3x = 45 * 8

3x = 360

x = 360 / 3

x = 120

The total number of balls is 120.

The number of blue balls ;

5/8 * 120 = 75

To change ratio to 1 : 3 in respect to white and blue balls;

1 + 3 = 4

The number of blue balls can be calculated as;

3 /4 * 120 = 90

The number of blue balls now is 90 balls

There will be 90 - 75 =  15 balls

There's 15 more blue balls

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There are 10 frames, thus the probability of Hoffman rolling a strike in a single frame is 0.5. The probability of Hoffman rolling a perfect game is 0.000779.

The probability of Hoffman rolling a perfect game is the sum of the probabilities of him rolling a strike in each of the 10 frames.

There are 10 frames, thus the probability of Hoffman rolling a strike in a single frame is 0.5.

To calculate the probability of Hoffman rolling a perfect game, we must multiply 0.5 by 10, which is equal to 0.5. This gives us a probability of 0.000779 or 0.000779 rounded to six decimal places.

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Answer: 2280000000

Step-by-step explanation: Yes, I know it is a long number, but 10 cubed = 10 x 10 x 10, which simplified, would be 100 x 10, which is 1000. So, now you do 2.4 x 1000 to get 2400. Now you take that and multiply that by 9.5. Then, you do 10 to the 5th power, which is 100000. Now, you connect it all together, to get 2280000000. Hopefully, I did it right, if not I am sorry :/