Which properties determine whether a quadrilateral is a parallelogram?
A. both pairs of opposite sides of a quadrilateral are both congruent and parallel
B. one pair of opposite sides of a quadrilateral is both congruent and parallel
C. it has 4 right angles
D. one pair of opposite sides of a quadrilateral is parallel

The greatest common divisor is 12. The linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.

The extended Euclidean algorithm is an algorithm to compute integers x and y such that: ax+by=gcd(a,b)The extended Euclidean algorithm can be viewed as the reciprocal of modular exponentiation.

By reversing the steps in the Euclidean algorithm, it is possible to find these integers x and y. The whole idea is to start with the GCD and recursively work our way backwards. This can be done by treating the numbers as variables until we end up with an expression that is a linear combination of our initial numbers.

First use Euclid's algorithm to find the GCD:

3984 = 588 ×6 + 456

588 = 456×1 +132

456= 132 ×3 + 60

132 =  60×2 +12

60 = 12×5+0

The last non-zero remainder is 12.

Thus, the greatest common divisor is 12.

Now we use the extended algorithm:

12 = 132 +(-2)×60

    = 132 + (-2)×(456 + (-3)×132))

    = (-2)×456 + 7×132

    = (-2)×456 + 7×(588 +(-1)×456))

   = 7×588 + (-9)×(3984 +(-6)×588))

   = 61×588 + (-9)×3984

Thus, a = -9 and b = 61.

Thus, the linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.

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Answer: 15 - h - 3

Step-by-step explanation:

The equation of the function described as;  y = 7 sin ( 4x + π/2 ) + 3

The general equation of the sine curve can be written as;

y = a sin ( nx + α ) + b

where : a is the amplitude, n = 2π/period, b = shift in the direction of y

            α°= shift in the direction of x

We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.

 Thus,

a = (maximum - minimum)/2 = (10 - -4)/2

a = 7

 n = 2π/period = 2π/(π/2)

n = 4

 b = maximum - a = 10 - 7

b= 3

To find α as y-intercept = 10

y = 10 at x = 0

Substitute in the general function;

y = a sin ( nx + α ) + b

10 = 7 sin ( 4*0 + α ) + 3

Thus, we have;

sin α = 1

α = π/2

So, the equation of the function described is;

 y = 7 sin ( 4x + π/2 ) + 3

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The correct answer is A) y = 9000x + 65,000.

The correct answer is A) y = 9000x + 65,000.

The house has increased in value by 54,000 ($119,000 - $65,000) over 6 years (change in x), so the slope must be 9000 (54,000/6).

The equation y = 9000x + 65,000

models the value of the house after x years, where y is the value of the house,

9000x is the slope of the equation,

and 65,000 is the y-intercept.

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The value of z such that 7% of the area under the standard normal curve lies to the right of z is approximately -0.4

To find the value of z such that 7% of the area under the curve lies to the right of z, we need to find the value of z such that 43% of the area lies to the left of z.

This value of z is known as the 43rd percentile of the standard normal curve.

We can use a table of the standard normal distribution, also known as the z-table, to find the value of z corresponding to the 43rd percentile.

According to the z-table, the value of z corresponding to the 43rd percentile is approximately -0.4

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When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.

Here,

let length be l and width be w.

l=3w+8

l*w=256

(3w+8)*w=256

3w²+8w=256

3w²+32w-24w-256=0

3w(w-8)+32(w-8)=0

(3w+32)(w-8)=0

w=-32/3, 8

w=8 inch

l=3*8+8

l=32 inch

The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.

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The time management skill and amount of work done is an example of positive correlation.

Correlation or dependency pertains to any statistical link involving two random variables or bivariate data, whether causal or not. Although the term "correlation" can refer to any form of link, in statistics it is most usually used to refer to the degree to which two variables are statistically linearly associated.

The link between the heights of parents and their children, as seen in the enough that demand curve, and the correlation between the price of an item and the quantity of items that buyers are willing to acquire are examples of dependent phenomena.

The Pearson product-moment correlation coefficient (PPMCC), sometimes known as "Pearson's correlation coefficient," is the most commonly used measure of two-value dependency.

It is computed by dividing the covariance ratio of the two variables in our numerical dataset by the square root of their variances. The covariance of the two variables is simply divided by the product of their standard deviations in mathematics. The coefficient was calculated by Karl Pearson from Francis Galton's similar but slightly different idea.

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Answer:

Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.

Step-by-step explanation:

The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

Now, According to the question:

The given sphere is of radius R.

Let h be the height and r be the radius of the cylinder inscribed in the sphere.

We know that:

Volume of cylinder

V = [tex]\pi R^2h[/tex]    .....(1)

In right Triangle OBA

[tex]AB^2 + OB^2 = OA^2[/tex]

[tex]R^2 + \frac{h^2}{4} = r^2[/tex]

So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]

Putting the value of [tex]R^2[/tex] in equation (1), We get

V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]

V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex]   ....(2)

dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)

For, Stationary point, dV/dh = 0

[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0

[tex](r^2 - \frac{3h}{4} )[/tex]   => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]

Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]

[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex]   = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0

Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]

Maximum volume is :

[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]

[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

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Option D is the correct answer, Universal Instantiation is The implicational rule of inference that permits us to derive a specific instance from a universal statement.

It is the process of deriving an individual statement from a general one by replacing the variable with a name or another referring expression called Instantiation.

Universal Instantiation is also called universal specification or universal elimination, it is a valid rule of inference from the truth about each member of a class of individuals to the truth about a particular individual of that class.

Example: "No humans can fly. John Doe is human. Therefore John Doe can not fly."

∀xA⇒A(x↔a}

for every formula A and every term a, where A(x↔a}  is the result of substituting a for each free occurrence of x in A. A(x↔a} is an instance of

∀xA.

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The angle A is an obtuse angle of the regular polygon.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The interior angle of a polygon is [(n-2)180°]/n.

Where n is the number of sides of the polygon.

The number of sides of the polygon is 8.

The measure of the interior of the polygon is [(8-2)180°]/8

= 135°

The obtuse angle is an angle that more than 90°.

Therefore angle is an obtuse angle.

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Answer:

70

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.

Answer:

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Therefore, the equation of the line with slope -4 and y-intercept 2 is y = (-4)x + 2.

The required probability is P(X≥3) =0.3234

The average number of winning tickets that the woman buys each month is 2.

The binomial probability distribution is a discrete type of probability distribution with two parameters, n, and p. The probability mass function of the distribution is used to get the required probability. The average value of the winning number is the expected value of the binomial distribution.

The probability mass function of the binomial distribution is defined as:

[tex]P(X=x)=\frac{n}{x} p^{x} (1-p)^{n-x} , x =0,1,2,3,....,n.[/tex]

Given that,

n = 20

p = 0.10

The required probability is P(X≥3)

P(X≥3) = 1-P(X<3)

P(X≥3)= 1-P(X=0)-P(X=1)-P(X=2)

P(X≥3)= 1- 0.1216- 0.270- 0.285

P(X≥3) = 0.3234

The mean of the distribution is defined as μ=n*p= 20*0.10= 2

The average number of winning tickets that the woman buys each month is 2.

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The rate of change of the line that contains the two points (-1, -4) and (5, 4) is 4/3.

The rate of change for a line is the slope, the rise over run, or the change in over the change in.

The slope of line can be calculated using the formula, slope =(y2-y1)/(x2-x1).

The given coordinate points are (-1, -4) and (5, 4).

Now, slope = (4-(-4))/(5-(-1))

= (4+4)/(5+1)

= 8/6

= 4/3

Therefore, the slope of a line is 4/3.

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The ratio of rainy days to total days written as a percent will be 75%.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.

Since in the last 24 days, it rained 18 days.

Number of rainy days = 18.

Number of total days = 24

The ratio of rainy days to total days written as a percent will be:

= Number of rainy days / Total days × 100

= 18/24 × 100

= 3/4 × 100

= 75%

Therefore, the ratio is 3:4 which is 75%.

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The graph of the equation y = (1/3)x + 2 is passing through points  

(3, 3) and ( -3, 1).

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A linear equation y = (1/3)x + 2.

Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.

When x = 3, y = 3 ⇒ (3, 3).

When x = - 3, y = 1 ⇒( -3, 1).

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Answer:

  x = 15

Step-by-step explanation:

You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.

The angle sum theorem tells you the sum of angles in a triangle is 180°.

  U +V +W = 180°

  (3x -10)° +(6x +5)° +(4x -10)° = 180°

  13x -15 = 180 . . . . . . . divide by °, collect terms

  13x = 195 . . . . . . . add 15

  x = 15 . . . . . . . divide by 13

The value of x is 15.

A. The top cycle in this case is a -> b -> c -> a.

B. The agenda that wins the candidate is:

First vote:

a vs b -> a wins

Second voice:

versus. c -> a wins

The agenda that Candidate B wins is:

First vote:

b vs c -> b wins

Second Voice:

b vs a -> b wins

The agenda that Candidate C wins is:

First vote:

c vs a -> c wins

Second Voice:

c vs b -> c wins

C. Using the Borda count system, the candidates' scores are as follows:

a:

18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)

b:

18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)

c:

18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)

d:

12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)

e:

12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)

f:

12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)

g:

6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)

Therefore, candidates a, b, and c tie for first place with 18 points each.

D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.

E. The candidate with the worst score in the Borda count is  g of 6 points.

F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:

a:

15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)

b:

15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)

c:

15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)

Day:

10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)

e:

10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)

f:

10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)

In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.

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The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.

As per the given data,

we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.

We know that,

Probability(Event) =Number of Favorable Outcomes/Total number of

                                Outcomes = x/n.    

Total number of Outcomes is 52 (given)

So,  we will calculate Number of Favorable Outcomes as follows:

The total no. of King in deck of card is 4

The total no. of queen in deck of card is 4.

The total no. of ace in  deck of card is 4.

The total no. of jack in deck of card is 4.

Therefore, the number of favorable outcomes is 4+4+4+4= 16

Now, putting values in the above stated formula of probability, we get:

Probability= 16/52=4/13

Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.

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Standard deviation will be √3.3516 .

To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².

After that , we have to calculate the Xbar by using

Xbar = ∑fiXi / N

for which we need the value of fi , Xi and N

N = 100

fiXi = 6478

we have calculated the values from the given data ,

Therefore ,

Xbar = 6478 / 100

= 64.78

Var(X) = αx² - ∑fiXi² / N - (Xbar²)

= 419980 / 100 - (64.78)²

= 4199.80 -4196.4484

=3.3516

Thus,

standard deviation ax = √var(X)

= √3.3516

Therefore , the standard deviation will be  √3.3516

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Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.

To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest. Most loans with simple interest rates are auto loans and short-term personal loans.

A = $6,250.00

I = A - P = $1,250.00

Formula: A = P(1 + rt)

First, convert R percent to r decimal, which is equal to 5%/100 or 0.05 per year.

Fixing our equation

A = 5000(1 + (0.05 × 5)) = 6250 \sA = $6,250.00

Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.

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Answer: x = 9/10 - 7/10

Step-by-step explanation:

The value of BC = 25 using properties of triangle.

What are properties of triangle ?

Let us discuss here some of the properties of triangles.

1. A triangle has three sides and three angles.

2. The sum of the angles of a triangle is always 180 degrees.

3. The exterior angles of a triangle always add up to 360 degrees.

4. The sum of consecutive interior and exterior angle is supplementary.

Properties for isosceles:

Isosceles triangles are those triangles that have at least two sides of equal measure.

1. Two equal sides and two equal angles.

2. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.

3. The side opposite the vertex angle is called the base and base angles are equal.

Using 1st property,

in given triangle two angles are equal then opposite side will also be equal.

So, AB = AC

i.e. 4x+4 = 6x-14

4+14 = 6x-4x

18 = 2x

x = 9

Putting value of x in BC

BC = 2*9 +7

     = 18+7

     = 25.

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Using a system of equations, the number of seats in the upper section of the racetrack is 3,600.

A system of equations, also called simultaneous equations, is two or more equations solved concurrently.

We can use any of the following methods to solve simultaneous equations:

In this situation, after forming the equations, we can use substitution and elimination methods to solve them.

Racetrack charge per lower seat = $85

Racetrack charge per upper seat = $60

Racetrack charge per field ticket = $35

Let lower seats = x

Let upper seats = 3x

Let field tickets = y

4x + y = 22,800 ... Equation 1

y = 22,800 - 4x ...Equation 3

85x + 60(3x) + 35y = 948,000

85x + 180x + 35y = 948,000 ... Equation 2

Substitute Equation 3 in Equation 2 to eliminate y:

85x + 180x + 35(22,800 - 4x) = 948,000

85x + 180x + 798,000 - 140x = 948,000

125x = 948,000 - 798,000

125x = 150,000

x = 1,200

Determining the number of seats:

Seats in the Lower section = 1,200

Seats in the Upper section = 3,600 (1,200 x 3)

Field tickets, y = 22,800 - 4x

y = 22,800 - 4(1,200)

= 18,000

Check:

85x + 180x + 35y = 948,000

85(1,200) + 180(1,200) + 35(18,000) = 948,000

102,000 + 216,000 + 630,000 = 948,000

948,000 = 948,000

Thus, based on simultaneous equations, there are 3,600 seats in the upper section of the racetrack.

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If 1+3+5+7+…+49 =625, then the value of 2+4+6+8+…+50 = 650.

What is arithmetic series?

A series of numbers called an arithmetic progression or sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Here, we have

Given:  1+3+5+7+…+49 =625

We have to find the value of 2+4+6+8+…+50.

Here, we calculate the sum of all even numbers and we get

2+4+6+8+…+50 = 650

Hence, if 1+3+5+7+…+49 =625, the value of 2+4+6+8+…+50 = 650.

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According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.

A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.

The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.

Given that John paid $485 to build a deck.

And he will pay $25 per hour to his brother for building the deck.

one hour of work costs John $25 + $485 .

Total cost of building deck = $25 × h number of hours + $485

3 hour of work costs $25 × 3 = $75 + $485 = $560

8 hour of work costs = $25 × 8 = $200 + $485 = $685

12 hour of work costs = $25 × 12 = $300 + $485 = $785

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The complete question is-

John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?

h c

0 485

3 510

8 535

12 560

h c

0 510

3 535

8 560

12 585

h c

0 485

3 560

8 685

12 785

h c

0 510

3 585

8 710

12 810

Answer:

1000

Step-by-step explanation:

If any of the digits 0-9 can be used then there are 10^3 possible codes.

10^3 = 1000