Given that
x
= 7.9 m and
θ
= 54°, work out AB rounded to 3 SF.

Answer:

x= 37 , y= 143

Step-by-step explanation:

okay so to start out we must write an equation in order to find the angles of a parallelogram.

2x+2y=360 (the angles of a parallelogram always equal 360 degrees)

next, since we know that the angle for y is "y+3" we can substitute this into the equation

2x+2(y+3)=360

next, since it is given that y=3x+29 we can now substitute that into the equation

2x+2[(3x+29)+3]=360

now, SOLVE!

[tex]2x+2[(3x+29)+3]=360 \\2x+2(3x+32)=360 \\2x+6x+64=360\\8x+64=360\\8x=296\\x=37[/tex]

okay, now we know that x=37 degrees so now we must find y. this can be done by substituting 37 into (3x+29)+3 or simply, 3x+32

[tex]y=3x+32\\y=3(37)+32\\y=111+32\\y=143[/tex]

don't forget to check your work!

2(37)+2(143)=360

there you go! so x= 37 degrees and y= 143 degrees

For the given experiments , participants concluded that complexity is more on the random patterns on every trials compare to  one segment that was same for every trial.

As given in the question,

Steps for the experiment where participants manually tracked a complex pattern which consists of two segments are as follow:

In first case : One segment consists of random patterns on every trial that is on every new trial there is new random pattern which participant has to follow.

In second case : Another segment consists of same pattern on every new trial.

After conducting experiment reports conclude that repeated segment with the same pattern present more improved result compare to random patterns. As participants were aware of the same segment on each new trial.

Therefore, given experiments of participants proves the complexity is more on the random patterns on every trials compare to one segment  same for every trial.

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By plotting the obtained solutions on the graph we get graph as below.

The given system of inequalities are y >2x²+x-3 and y <-x² + 5x.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Put x=0, 1, 2 and 3 in the given inequalities, we get

Now, with y >2x²+x-3

When x=0

y >2(0)²+0-3

y >-3

When x=1

y >2(1)²+1-3

y >0

When x=2

y >2(2)²+2-3

y >7

When x=2

y >2(3)²+3-3

y >18

With the inequalities y<-x²+5x

When x=0

y<-0²+5(0)

y<0

When x=1

y<(-1)²+5(1)

y<6

When x=2

y<(-2)²+5(2)

y<14

When x=3

y<(-3)²+5(3)

y<24

By plotting the obtained solutions on the graph we get graph as below.

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The answer is g(f(x)) =(x+6)(x+2)

From the question, we have

f(x) = x + 3 and g(x) = x² + 2x - 3

g(f(x)) = g(x + 3)

=(x + 3)² + 2(x + 3) - 3

=x² + 9+6x+2x+6-3

=x² + 8x+12

=x² + 6x+2x+12

=(x+6)(x+2)

The answer is g(f(x)) =(x+6)(x+2)

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The calculation of the separation between two locations on a plane is done using the Euclidean distance formula. This equation estimates the separation between two places.

[tex]d = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }[/tex]

Our perception of space is frequently incorrect in high dimensions since it was created in two and three dimensions. Think about randomly distributing 100 points into a unit square. The range [0, 1] is used to produce each coordinate independently and evenly at random.

Choose a point, calculate the distances between it and every other point, and then chart the distribution of those distances. The points are then uniformly generated at random in a 100-dimensional unit cube when the dimension is increased. Around an average distance, the distribution of distances becomes concentrated.

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The 3x3 matrix after composite transformation of scaling by 2, a rotation of 90° about origin is [tex]\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right][/tex].

Let A=[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex] be a 3x3 matrix

scaling the matrix A by 2 then  the result will be

[tex]2A=2\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]\\\\=\left[\begin{array}{ccc}2a&2b&2c\\2d&2e&2f\\2g&2h&2i\end{array}\right][/tex]

now, rotating the resultant matrix by 90° in counterclockwise direction about the origin, we get

[tex]=\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right][/tex]

Thus, a 3x3 matrix after composite transformation of scaling by 2, a rotation of 90° about origin is [tex]\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right][/tex]

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Answer:

at an angle of 90° to a given line, plane, or surface.

"dormers and gables that extend perpendicular to the main roofline

Step-by-step explanation:

The linear system of equation y =-6x+2 has infinitely many solutions.

The linear equation is y = -6x+2 .

Now for any value of x we find the value of y ,

at x=0 ,y = 2

at x=1 , y = -4

at x=-2 , y = 14

Hence there are infinitely many solutions on the line . All points on the straight line are solutions.

The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." In order to model real-world issues, linear equations include unknown quantities as one or more variables.

The locations where the lines or planes used to illustrate the linear equations intersect or meet are known as the solutions. The set of values for each variable in a system of linear equations is known as the solution set.

Disclaimer: the complete question is :

How many solutions does this linear system have Y =- 6x + 2?.

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The required third number of the given triad is 16.

The average is characterized as the mean worth which is equivalent to the proportion of the amount of the quantity of a given arrangement of values to the complete number of values present in the set.

Given two number are 17 and 24.

Let the third number is x,

Average of three number is 19

17 + 24 + x/3 = 19

41 + x = 57

x = 16

Thus, the third number is 16.

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In every distribution of k boxes containing n distinct objects, where box i receives ni. Let Si stand for the set that includes those ni identifiable items for i = 1, 2,..., k.

Given,

he collection of objects can be expressed equivalently as k, i = 1 Si  has the following object types: left| S 1 |right| = n 1S number of items of type 1, left |S2| right| = n 2S number of objects of type 2, and so on.

In this case, type i denotes objects that fit into box i and are therefore interchangeable. By simply permuting these sets, one can obtain all conceivable distributions of objects. kS I 1, 2, and S i

The number of distribution options is equal to the number of these permutations for i=1, 2,..., k.

n!/(n₁!,n₂!...nₐ!)

That is,

In every distribution of k boxes containing n distinct objects, where box i receives ni. Let Si stand for the set that includes those ni identifiable items for i = 1, 2,..., k.

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Case 1: Break-even units are 10000

Case 2: Fixed cost is $1,00,000

Case 3: Variable cost is $20

Case 4: The sale price is $15

Break-even in units = Fixed cost/Selling price - Variable cost

Case 1:

Sales price = $20

Variable cost = $16

Fixed cost = $40,000

Break-even point = 40000/20-16

= 10000 units

Case 2:

Sales price = $25

Variable cost = $5

Break-even units = 5000

Finding fixed cost:

5000 = Fixed cost/25-5

Fixed cost = 5000* 20

= 1,00,000

Case 3:

Sales price = $29

Fixed cost = 81000

Break-even units = 9000

Finding variable cost:

9000 = 81000/29-variable cost

2,61,000 - 9000*Variable cost = 81000

Variable cost = 20

Case 4:

Variable cost = $9

Fixed cost = $48000

Break-even units = 8000

Finding sales price:

8000 = 48000/Sales price - 9

8000*Sales price - 72000 = 48000

Sale price = $15

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Answer:The zeros of a function f correspond to the x-intercepts of its graph. If f has a zero of odd multiplicity, its graph will cross the x-axis at that x value. If f has a zero of even multiplicity, its graph will touch the x-axis at that point.

The diagonal of a cube increasing at a rate of 31.869 cm/s.

It is given that edges are increasing at a rate of 18.4 cm/s.

We know the formula of diagonal of cube which is

D = [tex]\sqrt{3}[/tex] a

where a is the edge.

Now we will differentiate the diagonal equation with respect to time er get,

[tex]\frac{dD}{dt}[/tex] = [tex]\sqrt{3}[/tex] [tex]\frac{da}{dt}[/tex]

Given that edges are increasing at a rate of 18.4 cm/s, this means

[tex]\frac{da}{dt}[/tex] = 18.4 cm/s

Therefore

[tex]\frac{dD}{dt}[/tex] = [tex]\sqrt{3}[/tex] (18.4) cm/s

[tex]\frac{dD}{dt}[/tex] = 1.732(18.4) cm/s

[tex]\frac{dD}{dt}[/tex] = 31.869 cm/s

Hence the diagonal of a cube increasing at a rate of 31.869 cm/s.

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~ xdisplay.promotion. This means that the promotion has a positive effect on unit sales, and the model can accurately predict unit sales based on whether the promotion is present or not.

Regression models are statistical models that are used to forecast a continuous result information based on one or more predictor variables. These models are employed to comprehend how the predictor and outcome variables relate to one another as well as to forecast the result variable. In disciplines like economics, finance, and psychology, regression models are frequently employed to forecast variables like future sales or psychological health. Regression models can be either linear or nonlinear, and they can also have numerous predictor variables. These models typically include an intercept and a slope for each predictor variable, which are used to calculate the predicted outcome.

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The sum of the first 30 terms of this arithmetic expression (A.P)  will be -30.

Let the first term of the Arithmetic progression be a

And the common difference of this progression be d

An be the nth term of the progression

Sn be the sum of the first nth term of the progression

As we know,

Sn = n/2( 2a + (n-1)d)

S11 = 11/2(2a + (11-1)d)

S11 = 11/2(2a + 10d) = 11(a + 5d)

As S11 = 19

Therefore, 19 = 11(a + 5d)

19 = 11a + 55d………….(i)

Again, S19 = 11 = 19/2 ( 2a + 18d )

11 =19( a + 9d)

11 = 19a + 171d………(ii)

Now, multiplying equation (i) by 19 and (ii) by 11 and then subtracting them, we get

361 = 209a + 1045d

121 = 209a + 1881d

240 = -836d

d = -240/836 = -60/209

Putting the value of d in equation (i), we get

11a - 55x60/209 = 19

11a = 3300/209 + 19

11a = 7271/209

a = 661/209

Therefore sum of first 30 terms are S30 = 30/2(2(661/209)+29(-60/209))

S30 = 15(1322/209 -1740/209) = 15 (-418/209) = 15(-2) = -30

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Three consecutive even integers can be written with difference of two.

The even integers are defined as the numbers that are completely divisible by two. The complete division means that the result of division will be zero. The even integers are always present after a gap of one number in between.

This means that there is a difference of two numbers between integers. Firstly of all, the first even number is two. Following it four. There is a gap of number that is three. Hence, to find the consecutive even integers, add number two to the number.

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After calculating the individual discount and coupon percentages of the actual price, we find out that the final price of the new computer monitor is $40.

It is given to us that -

The new computer monitor is regularly priced at $200

It is now on sale for 25% off

After the sale discount, we can also use 20% off coupon

We have to find out the final price of the computer monitor.

The initial price of the new computer monitor = $200

After the sale discount of 25% off is applied to the product, the new price of the monitor can be calculated by finding out

25% of $200 = 0.25 * 200 = $50

Now, after calculating the price of the monitor after the sales discount, we have to find out the final price after the 20% off coupon is applied.

So, 20% of $50 = 0.20 * 50 = $10

So, we can conclude that after the sales discount and after a coupon of $10 off is applied, the final price of the computer monitor is -

$50 - $10

= $40

Thus, calculating the individual discount and coupon percentages of the actual price, we find out that the final price of the new computer monitor is $40.

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Answer:

[tex]7-8x+4y=-21[/tex]

Step-by-step explanation:

[tex]2x-y=7 \implies 8x-4y=28 \\ \\ \implies 7-8x+4y=7-28=-21[/tex]

It is proved that every natural number can be expressed as the sum of distinct powers of 2 using strong induction.

Natural numbers are those in mathematics that are utilized for counting and ordering. Cardinal numbers are those used for counting, while ordinal numbers are those used for ranking. The positive integers, also referred to as non-negative integers, are a subset of the natural numbers. A few examples are 1, 2, 3, 4, 5, 6,.... In other words, the set of all whole numbers other than 0 (i.e., 23, 56, 78, 999, 100202, etc.) is known as the natural numbers.

Here,

The statement is obviously true for n=0.

Assume that we are given an n≥1 and that it is true for all m with 0≤m<n.

When n=2^m then m<n and therefore m=∑k2^pk with finitely many pk, all of them different. It follows that n=∑2^(pk+1) with all pk+1 different.

When n=2^(m+1) with an m as before then n=2^0+∑k2^(pk+1) with all pk+1 different and different from 0.

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Answer:

deductive

Step-by-step explanation:

The required read time taken by the John in the given question is 2 hours.

A ratio can be characterized as the relationship or examination between two quantities of a similar unit to check how greater is one number than the other one.

Sasha read = 2(mike  read)

given, mike read 5 hours

Then, Sasha = 10 hours

Similarly,

Tom read = (Sasha read)2/5

Tom read = 4 hours

Now, john read = (Tom read)/4 = 4/2

John read = 2 hours

Thus, read time of John is 2 hours.

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There are [tex]\frac{60!}{57!}[/tex] ways we can do it.

Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,

the president can be select in 60c1 = [tex]\frac{60!}{1! 59!}[/tex]

                                                           = [tex]\frac{60 *59!}{1*59!}[/tex]

                                                           = 60 ways

After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.

and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.

∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58

              =  [tex]\frac{60 * 59 * 58 * 57!}{57!}[/tex]

              =  [tex]\frac{60!}{57!}[/tex]

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If length of AZ=8 units and the length of ZX=4, then the length of the side XB is 6 units

Consider the triangle ABC

The points X and Y are on the line AB and Y is on the line AC

The lines XY and BC are parallel

Therefore

AX / XB = AY / YC

Similarly, the lines ZY and XC are parallel

AZ /  ZX = AY /  YC

Therefore the the proportion will be

AX / XB = AZ / ZX

The length of the line AX = AZ + ZX

= 8 + 4

= 12 units

Then the proportion will be

12 / XB = 8 / 4

Cross multiply the terms

12 × 4 = 8 × XB

XB = (12 × 4) / 8

XB = 48 / 8

XB = 6 units

Hence, the length of the side XB is 6 units

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The effective tax rate for a taxable income of $63,42 using the marginal tax rate chart rounded to the nearest hundredth is 15.18%.

The correct answer option is option C

Income = $63,425 and marginal rates

Find tax payable amount:

Amount taxable = $10275 -$0

= $10275

Tax payable = 10% of 10275

= 0.1 × 10275

=$1027.5

Amount taxable = $41,175 - $10,276

= $30899

Tax payable = 12% of 30899

= 0.12 × $30899

= $3707.88

Amount taxable = $89,075 - $41,176

= $22249

Tax payable = 22% of 22249

= 0.22 × $22,249

= $4894.78

Total tax payable amount = $10275 + $3707.88 + $4894.78

= $9630.16

Effective tax rate = (Total tax payable amount/ income) × 100

= ($9630.16 / $63,425) × 100

= 15.18%

Therefore, the effective tax rate for a taxable income of $63,425 is 15.18%.

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The required greatest difference between the estimate and the true value is 45.

Given that,
Ethan needs to add together two whole numbers and wants to estimate the answer first. He rounds both numbers to 1 significant figure, which gives him 300 and 600 and adds them together to get an estimate of 900.

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

Here,
For the estimated number 900, the least number that can be rounded to the number 900 is 855,
Now,
Difference  = 900 - 855 = 45

Thus, the required greatest difference between the estimate and the true value is 45.

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Answer: Northeast - unless you are at the South Pole, in which case you are still facing North.

Step-by-step explanation

Sequence:

Facing North

90 degrees left = facing West

180 degrees right = facing East

reverse = facing West

45 degrees left = facing Southwest

reverse = facing Northeast

Answer:

18 ÷ 2/3 = 27

-5/6 ÷ 9/10 = -0.925

No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero

A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.

Given,

No, X or y-axis scale does not have to always start at zero.

A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.

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Answer:

It is data outside what you would expect.

Step-by-step explanation:

An example would be if I asked everyone is a class how many dogs they dad living with them.  I would expect to get answers like 0, 1, 2, 3 or 4.  If someone answered 115 that would be be an outlier, it is outside all of the data that I have collected.

The area of the parcel of land is 226934.799 square feet.

Given:

a triangular parcel of land has sides of lengths 590 feet, 980 feet and 1423 feet.

a).

Let a = 590 , b = 980, c = 1423  lengths

s = semi-perimeter

= 1/2(a+b+c)

= 1/2(590+980+1423)

= 1496.5

s-a = 1496.5-590

= 906.5

s-b = 1496.5-980

=516.5

s-c = 1496.5-1423

= 73.5

Heron's formula for area:

A = [tex]\sqrt{(s(s-a)(s-b)(s-c))}[/tex]

= √1496.5(906.5)(516.5)(73.5)

= √51499402997.4

≈ 226934.799

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