AXY is similar to ABC
Which of the following expressions could be used to determine the length of segment AB?

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.

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.

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 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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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 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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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 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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Answer:

The number of degrees Celsius goes down 6 every week. (-6)

Step-by-step explanation:

If the city's temperature changed the same every week, and over the period of 2 weeks it changed -12 degrees Celsius, we need to figure out how much it changed every week (c). We can do this by dividing the number of weeks (w), by the total number of Celsius it changed (t).

The equation will look something like this:

w ÷ t = c

Fitting the numbers into this equation will look something like this:

2 ÷ -12 = -6

Every week, it changed -6 degrees Celsius.

Simplifying the expression, every week it changed -6 degrees Celsius. We know this because the temperature changes the same amount every week. So if the total amount is -12, we have to divide that by 2 to get -6.

Answer:

Step-by-step explanation:

Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7

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

30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.

We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08.  The unit price for each bottle will be: The bottle having the lower price will be:-

30-ounce bottle = $6.00

One ounce bottle = 30 / 6.00 = $5.00

and

24-ounce bottle = $4.08

One ounce bottle = $24/ 4.08 = $5.88

30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

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The cost of the carpentering of the floor at the rate 12 rupees per square meter is 60 rupees.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

We have the room as a cuboid.

And its length is 6 meters and height is 3 meters.

The volume of the cuboid = length x height x width

90 = 6 x 3 x width

width = 90 / 18

width = 5 meter.

To find the cost of carpentering the floor, the rate of Rs. 12 per square meter.:

12 x width = 12 x 5 = 60 rupees.

Therefore, at the rate of 12 rupees per square meter, the cost of the carpentering of the floor is 60 rupees.

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The binary representation of each of these hexadecimal numbers is given as follows:

a) 80E = 100000001110

b) 135AB = 00010011010110101011

c) ABBA = 1010101110111010

d) DEFACED = 1101111011111010110011101101

To convert a number from hexadecimal to binary, each hexadecimal character is converted to it's respective four bit binary code, given as follows:

Then, for example:

80E hexadecimal = 100000001110.

As:

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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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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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Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306

Degree of freedom {df}=18

We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t

It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]

As we know, t distribution provides the cumulative probability

As the value of the total area under the t distribution will 1

So, we can write it as:

[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]

Now, using excel, we can easily calculate the t-critical value as follows

=T. INV ( Probability, DF)

Where Probability is the area and DF is the degree of freedom,

Now we will enter these values in excel:

=T. INV (0.95,18)

t-critical value can also be found using t table

Look up for df = 18, in very first column

Now look up for 0.05 in one tail row

Now intersect both of them to get the t-critical value

We will get it as: 2.306

So t-critical value will be =2.306

[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]

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Answer: x = 9/10 - 7/10

Step-by-step explanation:

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:

listed below

Step-by-step explanation:

5.) x=77 and y=63

6.)y=60 and x= 1230

7.)y=65 and x=92

8.)y=69 and x=175

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.

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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Answer:

Some points that are on this line are:

(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)

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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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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Answer:

x=5

Step-by-step explanation:

If p and q are parallel, then the two angles in question should be equal to one another.

So,

(3x+15)°=(8x-10)°

(3x+15)°+10°=(8x-10)°+10°

(3x+25)°=(8x)°

(3x+25)°-(3x)°=(8x)°-(3x)°

25°=5x°

5=x

So, the two angles should be (8(5)-10)° and (3(5)+15)°.  Both of these expressions equal 30°.  This makes sense, as the illustration shows that the two angles are acute.

Step-by-step explanation:

x = second number

first number = x - 6

third number = 4x

x - 6 + x + 4x = 96

6x - 6 = 96

6x = 102

x = 102/6 = 17

first number = x - 6 = 17 - 6 = 11

second number = x = 17

third number = 4x = 4×17 = 68

Answer:

[tex]27x^6y^6[/tex]

Step-by-step explanation:

The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex].  So,

[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].

Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex].  So,

[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]

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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