A man distributes his savings of 4000 among his three sons in the ratio 4:3:3. Find the amount received by his first son.

By using the property of angle, it can be calculated that [tex]\angle EBA \cong \angle ECD[/tex]

What are angles?

Angles are a way of measuring the amount of turn between two lines or three or more planes. An angle is formed when two lines intersect or when two planes meet. It is measured in degrees, with a full circle being 360 degrees. The angle is measured in terms of the amount of turn between the two lines or planes. Angles are typically used to describe the orientation of objects in space, such as the corners of a triangle, the angle of a flight path, or the angle of the sun’s rays. Angles are also used to measure the size of an angle and the distance between two points. Angles are important in mathematics because they help to analyze the size and shape of objects, and also to help solve problems.

Here,

It is given that

[tex]\angle EBC \cong \angle ECB[/tex]

Now,

[tex]180-\angle EBC \cong 180-\angle ECB[/tex] [Angle on a straight line]

[tex]\angle EBA \cong \angle ECD[/tex]

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Answer:

[tex]x^2 - 6x + 10[/tex] or in general: [tex]a(x^2 - 6x + 10)[/tex] where "a" is any constant real number except zero.  

Step-by-step explanation:

If we're given a complex root of a polynomial to be: [tex](a+bi)\text{ or }(a-bi)[/tex], then we know that its conjugate is also a root of the polynomial: [tex](a-bi)\text{ or }(a+bi)[/tex].

So since we're given the root: [tex](3+i)[/tex], then we know that its conjugate: [tex](3-i)[/tex] is also a root. Thus we have two roots so far.

The Fundamental Theorem of Algebra simply states that any polynomial, with degree "n", will have "n" roots, which can consist of both real and imaginary solutions.

So let's say I have a polynomial: [tex]x^6+3x+2=0[/tex], this has 6 roots, according to the Fundamental Theorem of Algebra, since the degree of the polynomial is 6 (remember the degree is simply the variable with the highest degree)

Since we already have two roots, and a quadratic function has a degree of two, we know that these are all the roots the quadratic has, since the Fundamental Theorem of Algebra states that a quadratic will only have 2 roots.

We can generally express any polynomial in factored form, that is: [tex]a(x-b)(x-c)(x-d)...=y[/tex]

where "b", "c", and "d", and so on... are zeros of the function. This aligns with the behavior of zeros, since if we plug any of them into the function, then one of the factors will become zero, and since zero times anything is zero, well the entire thing is zero.

For example if I plug in "b", which is zero we get: [tex]a(b-b)(b-c)(b-d)...=y\implies a(0)(b-c)(b-d)=y\implies 0=y[/tex]

this is since plugging in zero, makes the factor: [tex]x-b[/tex] equal to zero, making the entire thing zero.

One last thing to mention is the "a" value in front which just generally determines the stretch/compression of the polynomial.

So with this information, we can write a polynomial:

[tex]a(x-(3+i))(x-(3-i))[/tex]

From here let's distribute the negative sign:

[tex]a(x-3-i)(x-3+i)[/tex]

Now this may look a bit tough to distribute, but you may notice a pattern here, we have a difference of squares. It may not be obvious, but if we make one substitution, let's say: [tex]u=x-3[/tex], then we get the equation

[tex]a(u-i)(u+i)[/tex]

The difference of squares is expressed as: [tex]a^2 - b^2 = (a-b)(a+b)[/tex], so our expression will expand out into:

[tex]a(u^2 - i^2)[/tex]

The substitution was just to make things a bit more clear, but let's just substitute x-3 back into the equation.

[tex]a((x-3)^2 - i^2)[/tex]

From here, we know that i^2 is simply -1, since: [tex]\sqrt{-1} = i, \text{ so }i^2 = -1[/tex]

We can also easily expand out the polynomial using FOIL

[tex]a((x^2 - 6x + 9) -(-1))\\a(x^2 - 6x + 9 + 1)\\a(x^2 - 6x + 10)[/tex]

You may notice the "a value, and that's just a constant, which determines the stretch/compression of the polynomial, and can be any real number, except for zero since that will make the entire thing zero regardless of what x is. For the sake of simplicity, let's just write this to be 1.

Answer:

Below

Step-by-step explanation:

1.235 <= Weight < 1.245    before rounding

given a triangle with side of  lengths of 5 and 8 then c^2 =89 inequality describes all possible lengths of the third side

In the right triangle of sides a, b, and c

a^2 + b^2 = c^2

Since a = 5 and c = 8

Substitute them in the given rule

we get

25+64= c^2

89= c^2

Take a square root for both sides

c= sqrt 89

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Answer:

25,456

Step-by-step explanation:

   592                       2 x 3 = 6       9 x 3 = 27 (You put the 7 in the tens place)

x     43                     (And add 2 to the hundreds after multiplication)

______             5 x 3 = 15    15 + 2= 17    (So you add 1 to the thousand place)

   1776                                      Which would be 1776

2368

Now we do the same thing but with 4 this time, and we wont use the ones place because were putting the numbers in the tens place to start with since it's 40                        2 x 4 = 8 (Goes in tens place)

          9 x 4 = 36 (6 goes in hundreds place and 3 to thousands place)

5 x 4 = 20       (So 2 goes into the ten thousands place, and 3 to thousands place)

                                                     So it would be 2368

Answer:

Step-by-step explanation:

SolutionFinal answers are given below.

Back-up Theory and Details of calculations follow at the end.

Part (a)

Estimate of the slope for the least-squares regression line = - 0.0073  Answer 1

InterpretationFor every increase of 1 pound in car’s weight, the fuel efficiency would reduce by 0.0073 mpg.  Answer 2

Part (b)

Correlation coefficient, r = - 0.9438  Answer 3

Interpretation An r-value of - 0.9438 indicates that there is a strong inverse linear relation between car’s weight and fuel efficiency.

Negative sign implies that as car’s weight increases, the fuel efficiency would come down.Answer 4

Part (c) The estimated regression equation is: Fuel efficiency = 45.4705 – 0.0073 x car’s weight. Substituting car’s weight = 2684 in the above equation, the estimated fuel efficiency = 25.83.So, residual = 24.5 – 25.84 = - 1.23.

Thus, Residual for a car weighing 2684 pounds and having an average fuel efficiency of 24.5 mpg= - 1.23 Answer 5

Part (d)

Substituting fuel efficiency = 20.2 in the above regression equation, the estimated car’s weight = 3461Estimate of the weight of a car whose fuel efficiency is 20.2 mpg = 3461 pounds Answer 6

It can be said that authoritarianism has been a coexistence problem because it is based on domination and violates many norms and rights.

Without a doubt, authoritarianism has a negative impact on coexistence, because it focuses on many behaviors and thoughts that go against many values and good principles.

Let's keep in mind that authoritarianism is a type of behavior where an individual places his will above others, this undoubtedly generates a conflict in coexistence.

¡Hope this helped!

Authoritarianism is a form of government characterized by strong central power and limited political freedoms.

It is a coexistence problem because it often leads to the suppression of individual rights, freedoms, and diversity of opinion.

In an authoritarian regime, the government exercises strict control over all aspects of society, including the media, education, and civil society organizations.

This can result in the suppression of dissenting voices and the persecution of those who express views that are critical of the government.

The difference between the two population means is estimated at -1.05.

Null Hypothesis: The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

The information presented here represents the golfers' first and final round scores.

a. α= 0.10 is the significance level.

The following hypothesis test can be created:

Hypothesis of nullity H₀ μₐ= 0

This suggests that the population means of the first round and final round are identical.

Alternative formulation: Hₐ μₐ≠0

This suggests that the population means of the first round and final round are different.

The test statistic is now:

t=(d-meanₐ)[tex]\sqrt{n}[/tex]/sₐ

Excel can be used to determine the test statistic.

This will result in: 0.10<P<0.20.

b. The 90% confidence level is the primary margin of error. This indicates that there is no discernible difference, and the result is -1.05.

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James owns on owns only 5 percent of the business capital.

We should know that percentage deals with number of ratios as a fraction of 100

James = $10,000

One partner = $10,000

Other two partners = ($90,000+90,000)=$180,000

Total capital invested = $)10000+10000+90000+90000)

Total investment = $200,000

James proportion= [tex]\frac{10,000}{200,000} *\frac{100}{1}[/tex]

Simplifying this to have James percentage of investment as 5 percent

James =5%

In conclusion James has only 5% of the business investment

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5.25 option c is the test statistics for the given data.

Given,

The observed values;-

A: 36

B: 42

C: 60

D: 14

E: 8

Total =160

 To verify the following claim, a chi square test must be performed:

H0: The proportions for the final grades are the same.

H1: The final grade proportions varies from one another.

The level of significance assumed for this case is α = 0.01  

The statistic to check the hypothesis is given by:  

X² = ∑ⁿi = 1 (Oi - Ei)²/Ei

Now all that remains is to use the following formula to determine the predicted values, Ei = % × total

And the calculations are given by:  

EA = 0.25 × 160 = 40

EB = 0.25 × 160 = 40

EC = 0.4 × 160 = 64

ED = 0.05 × 160 = 8

EF = 0.05 × 160 = 8

Here, the statistics;-

X² = (36 - 40)²/40 + (42 - 40)²/40 + (60 - 64)²/64 + (14 - 8)²/8 + (8 -8)²/8

= 16/40 + 4/40 + 16/64 + 36/8 + 0/8

= 5.25

 Therefore,

The test statistics for the given data is option c 5.25

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We use Z-Distribution for large sample sizes, The reduced sample size is 200.

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.

confidence interval = 0.06

Sample size= 400

new interval of confidence = 0.03

new sample size = 400/0.06 * 0.03

=200

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Answer:

Step-by-step explanation:

To find the y-intercept of the equation y - 6 = -2(x + 5), we can set x equal to 0, since the y-intercept is the point where the graph of the equation crosses the y-axis.

Substituting 0 for x, we get:

y - 6 = -2(0 + 5)

y - 6 = -2(5)

y - 6 = -10

y = -4

Therefore, the y-intercept of the equation y - 6 = -2(x + 5) is (0, -4). This means that the graph of the equation crosses the y-axis at the point (0, -4).

a) The relative extrema of the function h(x)=cos((2π/3)x) on the interval [0, 2] are given as follows:

b) The absolute extremas of the function h(x)=cos((2π/3)x) on the interval [0, 2] are given as follows:

Relative extrema are all the turning points on the graph of a function, which are the points in which the derivative of the function is zero, hence the function behavior's may change from increasing to decreasing or vice versa.

From the graph given by the image at the end of the answer, the extremas of the function are given as follows:

These are also the absolute extremas, as there are only one minimum extrema and one maximum.

If there were multiple extremas, we would have that:

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The approximate number of bricks he will use for the entire building is; 1596 bricks

We are given that;

- Tim is building a brick wall that will be 4 feet high and 57 feet long.

- It takes 7 bricks to build 1 square foot of the wall.

The area of the building is gotten by applying the area of a rectangle which is;

Area of building = Length * Width

Thus;

Area = 4 * 57

Area = 228 square foot

Now, we are told that it takes 7 bricks to build one square foot of wall. Thus;

Number of bricks required here is;

N = 228 * 7

N = 1596 bricks

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The complete question is;

Tim is building a brick wall that will be 4 feet

high and 57 feet long. It takes 7 brick to build 1 square foot of wall

(Area = Length x Width)

Approximately how many bricks will he use for the entire building?

Answer:

-3

3

Step-by-step explanation:

0.1x^2-0.6x+0.9=0

(1/10)(x^2+6x+9)=0

(1/10)(x+3)^2=0

x=-3

2x^2-12x+18=0

2(x^2-6x+9)=0

2(x-3)^2=0

x=3

The solution of the equation 0.1x²-0.6x+0.9=0 is -3 and 2x²-12x+18=0 is 3.

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given the system of equation as;

0.1x²-0.6x+0.9=0

2x²-12x+18=0

Solving by completing the square:

0.1x²-0.6x+0.9=0

(1/10)(x²+6x+9)=0

(1/10)(x+3)²=0

x=-3

2x²-12x+18=0

2(x²-6x+9)=0

2(x-3)²=0

x=3

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The interest rate on this loan will be 5%.

Given that Eileen takes a student loan of 10,000 with simple interest to pay back after 10 years. If the estimated payment is 22,000.

The interest on the loan will be:

= $22000 - $11000

= $11000

The interest rate on this loan will be:

Rate = Interest / Principal × Time

Rate = 11000 / (22000 × 10)

Rate = 11000 / 220000

Rate = 5%

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The greater unit rate of the two functions is 2. The greater y-intercept of two functions is 6.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

From the given table, (0, 5) and (5, 15)

Here, slope(m)=(y2-y1)/(x2-x1) =(15-5)/(5-0)

= 10/5

= 2

Substitute m=2, (x, y)=(0, 5) in y=mx+c, we get

5=2(0)+c

c=5

Substitute m=2, c=5 in y=mx+c, we get

y=2x+5 --------(I)

From the graph, (-4, 0) and (0, 6)

Here, slope(m)=(6-0)/(0+4)

= 3/2

= 1.5

Substitute m=1.5, (x, y)=(0, 6) in y=mx+c, we get

6=1.5(0)+c

c=6

Substitute m=1.5, c=6 in y=mx+c, we get

y=1.5x+6 --------(II)

Therefore, the greater unit rate of the two functions is 2. The greater y-intercept of two functions is 6.

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We need to use the concept of Relative Abundance. Relative Abundance of A,B and C are 14.28,57.14 and 28.57% respectively.

The percentage of an organism of a specific sort in relation to the overall number of organisms in the area is known as relative abundance. Relative species abundances frequently follow particular patterns, some of the most well-known and extensively researched patterns in macroecology. Over a large variety of biological ecosystems, relative species abundances exhibit relatively similar patterns. Most species are rare (represented by a single individual in a community sample), while only a small number of species are prolific, according to a histogram of the number of species represented by 1, 2, 3,..., n individuals.

(M1)(x) + (M2)(1-x) = M(E) is the formula for Relative Abundance.

A weighs 12g, B weighs 16g and C weighs 24g.

A customer buys 1 apple A, 3 apples B and 1 apple

So assume A,B and C as different isotopes of apples.

Relative Abundance of A=12/84 ×100⇒14.28%

Relative Abundance of B=48/84 ×100⇒57.14%

Relative Abundance of C=24/84 ×100⇒28.57%

We need to use the concept of Relative Abundance. Relative Abundance of A,B and C are 14.28,57.14 and 28.57% respectively.

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The standard equation of a circle is [tex](x-1)^{2} + (y+5)^{2}= (\sqrt{3})^{2}[/tex]. The equation of the circle in general form is (x-1)² + (x-1)² = 3.

Standard form of circle equation is (x – a)² + (y – b)² = r²

General form of Equation of a Circle.

x² + y² + 2gx + 2fy + c = 0, for all values of g, f and c.

The equation of a circle is

(x-h)²+ (y-k)² = r²

So, it's given that radius,

r = √3

h=1 and k=-5

So, by substituting all values to the standard equation of a circle is :

[tex](x-1)^{2} + (y+5)^{2}= (\sqrt{3})^{2}[/tex]

The equation of the circle in the general form is written as :

(x-1)² + (x-1)² = 3

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Answer: C. 1 unit down. 2 units to the right

Step-by-step explanation:

A

5-1=4

34+5=39

5-1=4

5+5=10

Answer:

[tex]A)g-1=4\\g=4+1\\g=5[/tex]

Step-by-step explanation:

[tex]A)g-1=4\\g=4+1\\g=5\\\\B)34+g=50\\g=50-34\\g=16\\\\C)g-1=15\\g=15+1\\g=16\\\\\\D)g+5=15\\g=15-5\\g=10\\So the only Option remaining is A) which the correct answer[/tex]

Answer:

[tex]x=5, y=2[/tex]

Step-by-step explanation:

[tex]4x+y=22 \implies 24x+6y=132 \\ \\ 8x-6y=28 \\ \\ 32x=160 \\ \\ x=5 \\ \\ \implies 4(5)+y=22 \implies y=2[/tex]

The equations that are correct are a = 1/2(-2b + 2c -d) and c = a + b + d/2. The correct options are  C. c = a + b + d/2 and D. a = 1/2(-2b + 2c -d)

From the question, we are to solve the equation for each variable

The given equation is

a + b = c - d/2

Solving for a

a + b = c - d/2

a = -b + c -d/2

Multiply through by 2

2a = -2b + 2c -d

By multiplying both sides by 1/2, this can be written as

a = 1/2(-2b + 2c -d)

Solving for b

a + b = c - d/2

b = -a + c - d/2

Multiply through by 2

2b = -2a + 2c - d

By multiplying both sides by 1/2, this can be written as

b = 1/2(-2a + 2c - d)

Solving for c

a + b = c - d/2

a + b + d/2 = c

Therefore,

c = a + b + d/2

Solving for d

a + b = c - d/2

Multiply through by 2

2a + 2b = 2c - d

d = 2c  - 2a - 2b

d = -2a - 2b + 2c

Hence, a = 1/2(-2b + 2c -d) and c = a + b + d/2  are correct

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In the accompanying proof, the reason (5) is SAS theorem.

In the given question,

Given: AB || DC

AB=DC

Prove: m∠DAC = m∠BCA

The statement used to prove this conditions are:

Statement                        Reason

AB || DC                            (1) Using the Quadrilateral Rule

AB=DC                             (2) Opposite sides are equal

m∠BAC = m∠DCA           (3) Alternate interior angles Theorem

AC=AC                              (4) Common Side

∆ADC≅∆CBA                   (5) SAS Theorem

m∠DAC = m∠BCA            (6) Alternate interior angles Theorem

We have to explain in the accompanying proof, what is reason (5).

So, in the accompanying proof, the reason (5) is SAS theorem.

In the proving we first prove one side equal, then angle equal and at last again one side equal.

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Answer:

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

Total length we need is the sum of the perimeter and two diagonals of the square.

Perimeter:

Diagonals:

Total length:

Number of rolls:

The new yearly salary will be $31,694.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year.

And, The employee was just promoted and received a 15% raise.

Now,

Since, Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year.

And, The employee was just promoted and received a 15% raise.

Hence, The salary for 13.25 hours = 13.25 × 2080

                                                     = $27,560

And, The employee was just promoted and received a 15% raise.

Hence, The new salary = $27,560 + 15% of 27,560

                                    = 27,560 + 4134

                                    = $31,694

Thus, The new salary = $31,694

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When a die is loaded so that the probability of one side appears twice as often as the other five, the number "1" will be the most frequent result when the die is rolled.

When a die is loaded so that one side appears twice as often as the other five, the number that comes up most often when the die is rolled is "1". This is because the loaded die has an unequal probability of rolling each number, with one side being twice as likely to come up as any of the other five sides. This means that the chances of rolling this particular number are twice as great as the chances of rolling any of the other five numbers. For this reason, the number "1" will be the most frequent result when the die is rolled.The probability of rolling the number "1" is 2/7, while the probability of rolling any of the other five numbers is 1/7. Therefore, the number "1" is twice as likely to come up as any of the other five numbers when the die is rolled.

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Answer: 2

Step-by-step explanation: hope it helps