What does => mean in logic?

Answer:

y = [tex]\frac{2}{3}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (3, 4 )

m = [tex]\frac{4-2}{3-0}[/tex] = [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = [tex]\frac{2}{3}[/tex] x + 2 ← equation of line

Step-by-step explanation:

w(idth) = 2.5 inches for both boxes

h(eight) = 10 inches for both boxes

l(ength)l(arge) = 8 inches

l(ength)s(mall) = 75% of ll (=> of 8 inches)

=> ls = 8 × 75/100 = 2 × 75/25 = 2 × 3 = 6 inches

vl (volume large) = 8 × 2.5 × 10 = 200 inches³

vs (volume small) = 6 × 2.5 × 10 = 150 inches³

the difference of these two volumes is 50 inches³

the units to be used is cubic inches (inches³). we are talking about volumes. not lengths (inches), not areas (inches²).

the reason - for a volume we need to multiply 3 lengths (measured in simple inches). so, inch multiplied by inch is inch². this multiplied by inch again is then inch³.

Answer:

The largest integer is 29.

Step-by-step explanation:

Let the consecutive positive integers are x, x+1 and x+2.

The square of sum of squares of three consecutive positive integers is 2354 such that,

[tex]x^2+(x+1)^2+(x+2)^2=2354\\\\x^2+x^2+2x+1+x^2+4+4x=2354\\\\3x^2+6x+5=2354\\\\3x^2+6x- 2349=0[/tex]

It is a quadratic equation whose solution is given by :

x = 27 and x = -29

First positive integer = 27

Second positive integer = 27+1 = 28

Third positive integer = 27+2 = 29

Hence, the largest integer is 29.

Answer:

2/5

Step-by-step explanation:

Answer:

8 he would be able to give 8 kids 1 dollor and 25 cents

Answer:

X=65

Y=40

Step-by-step explanation:

2x+10=140

-10 -10

2x=130

÷2 ÷2

x=65

Y=180-140

Y=40

Answer:

%120

Step-by-step explanation:

The original cost was $10 then it went to $12, so 100 percent representing the 10, then with 2 dollars left it is 20 percent. You can check by multiplying 1.2 by 10.

Hope I helped :]

Answer:

20.00%

Step-by-step explanation:

$12-$10=$2

2/100

2/100 / 2 = 1/50

1/50=0.02

0.02×100=20%

Answer:

b = 70 degrees

c= 110 degrees

Step-by-step explanation:

The two (2) possible locations of point F include the following: F. [7, 9.5].

In this scenario, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.

Mathematically, line ratio can be used to determine the coordinates of F and this is modeled by this mathematical expression:

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Given the following parameters:

Point (x, y)= (4, 11)

Point (x, y) = (8, 9)

m:n = 3:1

Substituting the given parameters into the line ratio formula, we have;

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

F(x, y) = [(3(8) + 1(4))/(3 + 1)],  [(3(9) + 1(11))/(3 + 1)]

F(x, y) = [(24 + 4)/(3 + 1)],  [(27 + 11)/(3 + 1)]

F(x, y) = [(28)/(4)],  [(38)/(4)]

F(x, y) = [7, 9.5]

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Answer:

9x^3-17x^2-x+7

Step-by-step explanation:

Distribute the negative you'll get

(12x^3-8x^2)+(-3x^3-9x^2-x+7)

Combine like terms

12x^3-3x^3=9x^3 , -8x^2-9x^2=-17x^2 , -x , +7

Putting it all together:

9x^3-17x^2-x+7

The person that will finish the series first is;

Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.

The general equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Total pages manish has read as at today = 544 pages

He reads at the same pace and after 8 days he has read 928 pages. Thus, the equation that represents the number of pages that Manish has read is; 928 = 8m + 544

922 - 544 = 8m

m = 378/8

m = 47.25

Thus, his rate is 47.25 pages per day

The equation for Ravi is y = 51x + 594

This shows a rate of 51 pages per day

Thus, Ravi will finish first

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Answer:

19,167

Step-by-step explanation:

Laura purchased a new vehicle for 27,382

She made a down payment of 30%

27,382×30/100

= 27,382×0.3

= 8,214.6

27382-8214.6

= 19,167

Hence Laura financed 19,167

Yes, [tex]9x^2-30x +25[/tex]  is a perfect square trinomial.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial of the form [tex]ax^2 + bx + c[/tex] meets the requirement [tex]b^2 = 4ac[/tex], it is said to be a perfect square.

Two of your terms will be perfect squares in a perfect square trinomial. This trinomial is not a perfect square trinomial if it lacks two perfect square terms. The square root of each perfect square word should now be determined, combine the two square roots, then multiply the result by two.

This trinomial is a perfect square. The only thing left to determine is whether the middle term matches when you square (3x-5) because both [tex]9x^2=(3x)^2\ and\ 25=52[/tex] are perfect squares. The minus sign was used to at least produce a negative coefficient for the middle term.

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Answer:

2

Step-by-step explanation:

The parent graph is the one used to create a new function by any of the transformations (reflection about an axis, horizontal/vertical shifts, stretches/compressions).

Start with the square root function

[tex]f(x)=\sqrt{x}[/tex]

Multiply by 3 (vertical stretch)

[tex]h(x)=3\sqrt{x}[/tex]

Replace  x  with  x - 2 (shift to right 2 units)

[tex]g(x)=3\sqrt{x-2}[/tex]

Answer:

you would multiply 17% by  228,000

Step-by-step explanation:

you would get 177840

The constant term in the expression 2x + 3 is 3.

The term expression in math is called as the algebraic expression consists of unknown variables, numbers and arithmetic operators.

Here we have the expression 2x + 3.

Now, we have to find the constant term in the expression.

As per the definition of expression, we know that the expression has two part one is variable part and the remaining second part is the constant parts.

As the name suggest, the variable part contains the unknown value like x, y etc. that changes value of the expression depending upon the given value.

Another term is constant, where its value can't be changed.

While we looking into the given expression here we have identified that

=> 2x is the variable term because the value of the term is changed based on the value of x.

Therefore, the constant term is 3.

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The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line.

The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

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On solving the provided question we can say that the new Mean = 610 mean .

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). is 50.

What is mean?

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean).

The mean score is calculated by dividing the total number of tests taken by all of the scores. The mean will therefore rise if you give each test a higher mark. The standard deviation is calculated as the square root of the product of the power of two of all test results, multiplied by the number of tests, and then subtracted from the mean.

Each score you raise by 10 will result in a 10 change in the mean. But as there will be no change in the distance between each score and the mean, the standard deviations will also not change.

Mean = 600

Average deviation is 50.

Scores went up by 10

Mean = 610

Average deviation is 50.

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TLDs are the most common type of domain name and are typically three or more characters after the final dot in a domain name. ccTLDs are two-letter domains that represent a specific country or region.

Domain names are used to identify websites on the internet. There are two main types of domain names: top-level domains (TLDs) and country code top-level domains (ccTLDs).

TLDs are the most common type of domain name and are typically three or more characters after the final dot in a domain name. Examples of TLDs include .com, .org, .net, .edu, and .gov.ccTLDs are two-letter domains that represent a specific country or region. Examples of ccTLDs include .us for the United States, .au for Australia, .ca for Canada, .uk for the United Kingdom, and .fr for France.

When registering a domain name, users should choose a TLD or ccTLD that best suits their needs. For example, if they are targeting a global audience, they should consider a .com TLD. If they wish to target a specific country, they should consider a ccTLD.

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The parent function of a line (usually of the form y = ax + b) is y = x.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

Linear functions have x as the term with the highest degree and a general form of y = a + bx. All linear functions have a straight line as a graph. The parent function of linear functions is y = x, and it passes through the origin. The domain and range of all linear functions are all real numbers.

These functions represent relationships between two objects that are linearly proportional to each other.

Therefore, the parent function of a line (usually of the form y = ax + b) is y = x.

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==========================================================

Explanation:

We'll break things up into cases. The phrasing "at least 3" means "3 or more".

We either will have 3 kings or 4 kings.

----------------------------------------------

Case A) There are exactly 3 kings.

Use the nCr combination formula. There are n = 4 kings total and we select r = 3 of them. That gives 4C3 = 4 ways to pick the 3 kings.

Put another way: there are 4 ways to leave a certain king out of the hand.

Then we have 52-4 = 48 cards that aren't a king, and we need to fill the remaining r = 2 slots. Through the nCr formula, you should find that 48C2 = 1128

To recap, we found

That gives 4*1128 = 4512 ways to have case A happen.

----------------------------------------------

Case B) There are exactly 4 kings

4C4 = 1, so there's only one way to select all the kings. The order doesn't matter. Then we have 48 cards to pick from for the fifth slot.

Overall there are 1*48 = 48 ways to have case B play out.

----------------------------------------------

There were 4512 ways to have case A happen, and 48 ways to have case B happen.

These cases are mutually exclusive to allow us to simply add the counts:

4512+48 = 4560

This is why the final answer is 4560

2x 11 is congruent to 13 mod 16, if 3x 7 is congruent to 2 mod 16.

If 3x 7 is congruent to 2 mod 16, then 2x 11 is congruent mod 16 to what integer between 0 and 15, is inclusive.

To find the solution of 2x 11 congruent mod 16, given 3x 7 congruent to 2 mod 16, we can first use the given equation to find the value of x and then substitute it into the second equation.

First, we can solve for x in the given equation:

3x 7 is congruent to 2 mod 16

3x is congruent to 2 mod 16

x is congruent to 6 mod 16

Now that we know that x is congruent to 6 mod 16, we can substitute it into the second equation:

2x 11 is congruent to 2(6) 11 which is congruent to 13 mod 16

So the solution is that 2x 11 is congruent to 13 mod 16.

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Sandra needs to score at least 87.67% to get an average score of 85%.

Let's look at the average formula in more detail in this part and use some examples to illustrate how it may be used. The following is an example of the average formula for a specific set of data or observations: Average = (Sum of Observations) ÷ (Total Numbers of Observations).

Given, Sandra has taken 3 Test this Quarter. She has scored an 78%, 76%, and a 93%.

Now as per the question she needs 85%.

The average of the 1st three tests is 78+76+93/3 = 247/3 = 82.33

Now to get 85%, we have to average out as 82.33+x/2 = 85

x+82.33 = 85*2 = 170

x = 170-82.33 = 87.67

Hence, Sandra needs to score at least 87.67% to get an average score of 85%.

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The question is incomplete. The complete question is :

A company's Factory Overhead T-account shows total debits of $630, 000 and total credits of $716,000 at the end of the year. Determine whether there is over- or underapplied overhead using the T-account below. Prepare the journal entry to close the balance in the Factory Overhead account to Cost of Goods Sold.

Solution :

The credit of the factory overhead means Applied overhead and the debit of the factory overhead is the actual overhead incurred.

Here, applied overhead is more than the actual overhead incurred so it is the factory overheads the over appalled.

The Factory overheads

                                     Amount($)                                            Amount($)

Actual overhead          630,000             Applied overhead      716,000

Over applied                86,000

Journal entry to close balance in factory overhead

Account title and explanation                       Debit($)             Credit($)

Factor overheads                                           86,000

Cost of goods sold                                                                    86,000            

Answer:

D = (-4, -4)

Step-by-step explanation:

Given;

midpoint of line CD = M(-3, -7)

coordinate of C = (-2, -10)

The coordinate of D is calculated as follows;

C(-2, -10)---------------------M(-3, -7)--------------------D

[tex]M = \frac{D_1 + C_1}{2} \ , \ \frac{D_2 + C_2}{2} \\\\(-3, \ -7) = \frac{D_1 + (-2)}{2} , \ \frac{D_2 + (-10)}{2} \\\\(-3, \ -7) = \frac{D_1 \ - \ 2}{2} , \ \frac{D_2 -10}{2} \\\\-3 = \frac{D_1 \ - \ 2}{2} \ \ ----(1)\\\\-7 = \frac{D_2 -10}{2} \ -----(2)\\\\From \ (1): 2(-3) = D_1\ - \ 2\\\\-6 = D_1 - 2\\\\-6 + 2 = D_1\\\\-4 = D_1\\\\From \ (2) : \ 2(-7) = D_2 - 10\\\\-14 = D_2 - 10\\\\ -14 + 10 = D_2\\\\-4 = D_2\\\\The \ coordinate \ of \ D = (D_1\ , \ D_2)\\\\D = (-4 \ , \ -4)[/tex]

Therefore, the coordinate of D = (-4, -4)

The maximum height reached by the ball is 20 units at 1.2 unit time.

The extrema of a function are the maxima and minima. The highest and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, throughout its full range.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.

The equation is given as

h = [tex]-10t\x^{2} + 24t + 5.6[/tex]

Differentiating both side with respect to t we get

[tex]\frac{dh}{dt} = -20t + 24[/tex]

To reach maximum value [tex]\frac{dh}{dt} = 0[/tex]

⇒20t = 24

⇒ t = 1.2

So the maximum height reached = [tex]-10 *(1.2)\x^{2} + 24*1.2 + 5.6 = 20[/tex]

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