A line passes through the point (9,
- 4) and has a slope of 3/4
Write an equation in slope-intercept form for this line.

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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To solve this equation, you can use the property of equality, which states that whatever you do to one side of the equation, you must also do to the other side.

To isolate the variable "y," you can divide both sides of the equation by 4:

4y / 4 = 164 / 4

This simplifies to:

y = 41

Therefore, y equals 41.

Answer:

[tex] \sf \: a) \: 41[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of y.

The equation is,

→ 4y = 164

Then the value of y will be,

→ 4y = 164

→ y = 164/4

→ [ y = 41 ]

Hence, the value of y is 41.

Answer:

C

Step-by-step explanation:

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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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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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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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: 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

The tangential and normal components of the acceleration when s = 10 m is 40 m/s^2 and 8 m/s^2 respectively.

In the given question, a car is travelling along the road with a speed of 2s m/s, where s is in meters.

We have to determine the tangential and normal components of the acceleration when s = 10 m.

Speed (v) = 2s  

Motion is circular so, Radius of circle = 50m

Tangential acceleration = dv/dt

Tangential acceleration = d(2s) / dt

Tangential acceleration = 2(ds)/dt

Tangential acceleration = 2v

Tangential acceleration = 2(2s)

Tangential Acceleration = 4s

As given s = 10 m

Tangential acceleration = 4 x 10

Tangential acceleration  = 40 m/s^2

Normal acceleration = v^2/ r

Normal acceleration = 4s^2/r

Normal acceleration = {4 x 10^2}/50

Normal acceleration = {4 x 100}/50

Normal acceleration = 400/50

Normal acceleration = 8 m/s^2

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The complete question is:

A car is travelling along the road with a speed of 2s m/s, where s is in meters. Determine the tangential and normal components of the acceleration when s = 10 m. Treat the car as a particle

The cost of the book before the sales tax is $31

From the question, we have the following parameters that can be used in our computation:

Sales tax = 5%

Cost of book = $32.55 after tax

The cost of the book before tax is calculated using the following equation

Cost of book after tax = Cost of book before tax * (1 + Sales tax)

Substitute the known values in the above equation, so, we have the following representation

32.55 = Cost of book before tax * (1 + 5%)

Evaluate the sum

So, we have the following representation

32.55 = Cost of book before tax * (1.05)

Divide both sides by 1.05

Cost of book before tax = 31

Hence, the cost is $31

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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.

Answer:

1) 35.07

2) 123.6

3)3.9

4) 102.83

5)97.5

6)6.93

The values of v and w are 12 and 20 respectively which makes ΔPQR ≅ ΔIJK (Congruent right triangles).

Two triangles are said to be congruent if their shape and size are the same. If two right triangles are said to be congruent, then they must have equal measures for their corresponding sides and angles.

The given two right triangles are congruent. I.e., ΔPQR ≅ ΔIJK

So, their corresponding sides QR = IJ and PR = IK, and the corresponding angle ∠Q = ∠J.

But we have QR = w - 1; IJ = 3w - 41; PR = 6v-12; IK = 5v

So, on equating them, we get

QR = IJ ⇒ w - 1 = 3w - 41

⇒ 3w - w = 41 - 1

⇒ 2w = 40

∴ w = 20

And

PR = IK ⇒ 6v-12 = 5v

⇒ 6v - 5v = 12

∴ v = 12

Thus, the value of v = 12 and w = 20.

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Answer:

1. 6v+8

2.5x+6y

(a) The net force acting on this object at t = 1 s is 88 N.

(b) The net force acting on this object at t = 4 s is 0 N.

(c) The net force acting on this object at t = 7 s is -13.2 N.

In the given question, the velocity graph of a 2.2 kg object as it moves along the x-axis.

The given mass = 2.2

a) We have to find the net force acting on this object at t = 1 s.

At t=1 s

Slope of a graph = acceleration

Acceleration = slope

Acceleration = 12/3

Acceleration = 4 m/s^2

Net force, F = m*a

F = 22*4

F = 88 N

So the net force is 88 N.

b) We have to find the net force acting on this object at t = 4 s.

At t = 4 s

Acceleration, a=slope of graph

a = ( 12 - 12) /(3 - 0)

a = 0 m/s^2

The net force , F = m * a

F = 2.2 * 0 = 0 N

c) We have to find the net force acting on this object at t = 7 s.

At t = 7 s

Acceleration, a = ( 0 - 12 ) / (8 - 6)

a = - 6 m/s^2

The net force, F = m * a

F = 2.2 * (-6)

F = -13.2 N

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The complete question is:

The figure(figure 1) shows the velocity graph of a 2.2 kg object as it moves along the x-axis.

(a) What is the net force acting on this object at t = 1 s.

(b) What is the net force acting on this object at t = 4 s.

(c) What is the net force acting on this object at t = 7 s.

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

Step-by-step explanation:

23 + 17 obviously equals 40.

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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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

Answer:

  10 minutes

Step-by-step explanation:

You want to know how much longer 2/3 hour is than the sum of 1/5 hour and 3/10 hour.

Each fraction of an hour can be expressed in minutes:

The time difference of interest is ...

  (2/3 - 1/5 -3/10) h = (40 -12 -18) min = 10 min

Jacob spent 10 minutes more reading than doing housework.

Answer:

1. 80

2. runway 18

Step-by-step explanation:

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: 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

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:

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:

130 feet

Step-by-step explanation:

Your have to find the perimeter. Perimeter of a shape is the distance around the shape

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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The angle is changing at the rate  [tex]\frac{18}{\pi }[/tex] when a is 10m from the intersection and b is 20m from the intersection.

In this problem, all three variables (x, y & z) are changing with respect to time.

x = 20 and y = 10

[tex]\frac{dx}{dt} = -1[/tex]

[tex]\frac{dy}{dt} = 2[/tex]

[tex]tan[/tex](θ)=[tex]\frac{y}{x}[/tex]

take derivative :

[tex]tan[/tex] (θ) = [tex]\frac{y}{x}[/tex]

[tex]sec^{2}[/tex](θ) [tex]\frac{d\alpha }{dt}[/tex] = [tex]\frac{x\frac{dy}{dt} - y\frac{dy}{dt} }{x^{2} }[/tex]

Substitute the values :

[tex]sec^{2} \alpha (\frac{d\alpha }{dt} ) = \frac{20 . 2 - 10. (-1)}{20^{2} }[/tex]

solve the equation :

[tex]\frac{5}{4} (\frac{d\alpha }{dt} ) = \frac{20 . 2 - 10. (-1)}{20^{2} }[/tex]

[tex]\frac{5}{4} (\frac{d\alpha }{dt} ) = \frac{50}{400 }[/tex]

[tex](\frac{d\alpha }{dt} ) = \frac{50}{400 } * \frac{4}{5}[/tex]

[tex](\frac{d\alpha }{dt} ) = \frac{1}{10 }[/tex] radian/sec

[tex](\frac{d\alpha }{dt} ) = \frac{18}{\pi } degrees/sec[/tex]

This means that the angle is increasing as a gets closer to the intersection and b gets moves away from the intersection.

So, The angle is changing at the rate  [tex]\frac{18}{\pi }[/tex] when a is 10m from the intersection and b is 20m from the intersection.

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