Write a polynomial function f of least degree that
has rational coefficients, a leading coefficient of 1,
and the given zeros.
5. -4, 1, 2
6. -6, -1, 3
7. 7, 1+ i
8. 2i, 1-i

By using trigonometry, it can be calculated that

Value of x is [tex]\frac{2\pi}{3}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

Trigonometry is a very important tool in mathematics.

Trigonometry has a very good application in heights and distance.

Trigonometry has also a very good application in calculus and differential equation and also in physics, trigonometry plays a very vital role

Here,

The trigonometric equation is

4cos x + 2 = 0 where 0 ≤ x ≤ π

4cos x = -2

cos x = [tex]-\frac{2}{4}[/tex]

cos x = [tex]-\frac{1}{2}[/tex]

cos x = cos [tex]\frac{2\pi}{3}[/tex]

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

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The minimum number of dogs that have a mass of more than 24kg is 6 and the maximum number of dogs that could have a mass of more than 24kg is 18  

Using fundamental algebraic principles, rearrange the function to get the value of x at the derivative value of 0. The maximum or minimum will be at the vertex of the function, which is indicated by the response's x-coordinate. Rewrite the answer into the original function to determine the minimum or maximum.    

Here we have

The given shows the masses of various dogs  

Mass (x) kg          frequency  

0 ≤ x < 10                    2

10 ≤ x < 20                  7

20 ≤ x < 30                12

30 ≤ x < 40                 6      

a) The minimum number of dogs that have a mass of more than 24kg.

If we observe the given table the mass of 24 kg will lie in class intervals 20 ≤ x < 30, 30 ≤ x < 40                      

In class interval 20 ≤ x < 30, mass ranges from 20 kg to 30 kg there is a possibility that the mass of dag will be less than 24 since it started from 20 kg,  

In class interval 30 ≤ x < 40, mass ranges from 30 kg to 40 here there is no possibility that the mass will be less than 24 kg.

So here we can take the frequency of class interval 30 ≤ x < 40 as the Minimum value or number of dogs that could have a mass of more than 24 kg

Therefore,

The minimum number of dogs that have a mass of more than 24kg is 6

b) The maximum number of dogs that have a mass of more than 24kg.

In the above case since we are calculating minimum value, we didn't consider class interval 20 ≤ x < 30.

In this case, to get the maximum value or a maximum number of dogs we will consider class interval 20 ≤ x < 30 as there is a possibility that the mass could be more than 24 kg

In class interval 30 ≤ x < 40 the mass will always be more than 24 kg.

Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18

Therefore,

The maximum number of dogs that could have a mass of more than 24kg is 18  

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The coordinates of the intersection with the x-axis are

(8,0), and the coordinates of the point where x = -3, (-3 0).

What are the coordinates of the axis?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

We have,

The graph shows the sketch of y = f(x).

The graph crosses the y-axis at the point (0,-2), and the x-axis at the point (8,0).

The coordinates of the intersection with the x-axis are:

x = 8

y = 0

The coordinates of the point where x = -3,

y = 0.

Hence, the coordinates of the intersection with the x-axis are

(8,0), and the coordinates of the point where x = -3, (-3 0).

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Answer:

q. point of intersection

Step-by-step explanation:

Both systems in two variables contains two lines that may be intersecting, parallel, or the same line.

It will take Omari 7 months to pay off the computer.

What is a percentage?

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

To find the amount of the down payment, multiply the price of the computer by the down payment percentage:

down payment = $1,099 * 20% = $219.80

The remaining balance on the computer after the down payment is:

remaining balance = $1,099 - $219.80 = $879.20

To find the total number of months it will take Omari to pay off the computer, divide the remaining balance by the monthly payment:

total months = $879.20 / $144/month = 6.1 months

Since it is not possible to have a fraction of a month.

Hence, it will take Omari 7 months to pay off the computer.

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The pressure of 28 inches of mercury occurs about 50 miles far the eye.  

The measurement of air pressure in a certain location is called barometric pressure, which is the force of air pressing down on the surface of the globe, the oceans, and the land. .

p(x) =0.48ln (x + 1) + 27

Lets take P(50)

P(50)= barometric pressure at 50 miles from the eye of the hurricane P(50) as x

P(50) = 0.48 ln (50 + 1) + 27

P(50) = 0.48 ln (51) + 27

P(50) = 0.48 x 3.9318 + 27

where,

ln(51) = 3.9318

P(50) = 28.89

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Time taken by the bicyclist is 8 hours.

Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Given slope = 35 / 2 = 17.5

Distance = 140 miles.

then time is calculated by 140 /17.5

 = 8 hours

The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.

As x grows, there are 4 different sorts of slopes: negative, positive, zero, and undefined. The "average rate of change" can also be thought of as the slope of a line.

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For the third part of the batch, 1 :1/2 gallon of yellow is needed and for the second batch part 1/4 gallon is needed.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Since we know that there should be the same amount of yellow and green (they are each 1/4 of the recipe) and there is a half a gallon of green there should same amount the yellow. Hence, the answer is 1/2 gallon.

For the second part of the question, we know that 2 gallons is 1/4 of the recipe, and we know that 1/4 * 2= 1/2 (2/4) we just have to multiply 2 by 2 and get 4, our answer.

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Answer:

third part of the batch 1 :1/2 gallon of yellow Second batch part 1: 4

Step-by-step explanation:

have a nice day.

The following excel commands would give you the critical value is T.INV(0.95,25)

What is excel commands?

The following describe the commands in Excel: They carry out tasks the same way users do. They can change Excel settings, open, close, and edit documents, start recalculations, and other actions that users may perform (within the bounds of the interface being utilized). Excel's command menu interface is called the Ribbon. It logically and visually groups together frequently used actions. These make up the Ribbon's principal components. Related groupings of commands are grouped together by tabs.

Population sd is not available so we have to use t test.

0.95 is for upper bound and 25 is df of t test.

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a) The mean of this distribution is of: 0.35.

b) The standard error of this distribution is of: 0.0382.

The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has mean and standard deviation defined as follows:

(the standard deviation can also be called standard error).

The sample size and the proportion for this problem are given as follows:

n = 156, p = 0.35.

Then the standard error for this distribution is calculated as follows:

s = square root(0.35 x 0.65/156) = 0.0382.

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The taylor series as per the power series operation is sin(x) = 0 + 1x + 0x + −1/3!+3 + 0x

given,

f(x) = sinx

c = 3pi/4

the required series will be .

f(x) = f(c) + f' (c)( x-c ) + f''(c)/2! + .... f x n(c)/n! (x-c)^n

f(c) = sin(c)

     = sin(3pi/4)

      = 1/2

on solving the equation becomes,

sin(x) = 0 + 1x + 0x + −1/3!+3 + 0x

Assume that f(x) is a real or composite function and that it is a differentiable function of a real or composite neighbourhood number. The following power series is then described by the Taylor series.

The Taylor series can be expressed using sigma notation, where f(n)(a) = nth derivative of f n! = factorial of n.

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On solving the question, we got that - Maricopa Success invested $45000 in stocks, Maricopa Success invested $75000 in bonds and Maricopa Success invested $50000 in CD's.

A theorem of equality between two expressions consisting of equations, variables and/or numbers. Essentially, equations are problems, and the development of mathematics has been driven by attempts to find answers to these problems in a systematic way. The equations vary in complexity from simple algebraic equations (containing only addition or multiplication) to differential, exponential equations (containing exponential terms), and integral equations. They are used to express many of the laws of physics. See also system of equations.

Equations -

s + b + C = 170000

11.4s + 4.4b + 3.25C = 1005500

b = C + 25000

And,

Rearrange::

s + b + C = 170000

1140s + 440b + 325C = 100550000

0 + b - C = 25000

Now,

Use any method you know to solve the system to get:

stocks = 45000

bonds = 75000

CD's = 50000

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Answer: Yes.

Step-by-step explanation:  3/8 and 1 1/2 of a fourth are equivalent amounts. To see why, you can use a common denominator to compare the two fractions. If we convert both fractions to eighths, then 3/8 becomes 3/8 and 1 1/2 of a fourth becomes 6/8. Since 3/8 and 6/8 are both equal to 3/4, it follows that 3/8 and 1 1/2 of a fourth are also equal.

The pressure of 28 inches of mercury occurs at 6.03 miles from the eyes of the hurricane

From the question, we have the following pressure function that can be used in our computation:

f(x) = 0.48 ln(x + 2) + 27

Also from the question, we have

Pressure = 28 inches

This means that

f(x) = 28

So, we have the following equation

0.48 ln(x + 2) + 27 = 28

Subtract 27 from both sides

0.48 ln(x + 2) = 1

Divide 0.48 from both sides

ln(x + 2) = 2.083

Take the exponent of both sides

x + 2 = 8.03

So, we have

x = 6.03

Hence, the distance is 6.03 miles

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Answer:

Step-by-step explanation:

Although the answer is correct, the Step 3 is not correct.

The polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that the zeroes of the polynomial are, x= -2, x=7

The polynomial expression is obtained as,

=(x+2)(x-7)

=x²-7x+2x+14

=x²-5x+14

Thus, the polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14.

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Answer:

C(-6, -3)

Step-by-step explanation:

In a square, all four sides have the same length and all four angles have the same measure (90 degrees). Therefore, the line segments connecting the vertices of a square are all perpendicular to each other and all have the same length.

Since the line segment AB has a length of 8 (the difference in the y-coordinates is 8) and a horizontal component (the difference in the x-coordinates is 0), the line segment CD must also have a length of 8 and a horizontal component of 0. This means that the x-coordinate of point C is the same as the x-coordinate of point A, which is 2.

The line segment CD also has a vertical component equal to the difference in the y-coordinates of points D and A, which is 5 - (-3) = 8. Therefore, the y-coordinate of point C is the same as the y-coordinate of point D minus 8, or -3.

Therefore, the coordinates of point C are (-6, -3).

The value of the coefficients a, b, and c will be 2, 2, and negative 24. And the sign will be (<).

Let a, b, c, and d are the zeroes of the polynomial.

Then the polynomial is given as,

⇒ (x - a)(x - b)(x - c)(x - d)

The degree of the polynomial will be greater than or equal to the number of zeroes.

From the graph, the zeroes are -4 and 3. Then the factor of will be (x + 4) and (x - 3). Then the polynomial 'y' is given as,

y = a(x - 3)(x + 4)

At (1, -20), we have

- 20 = a(1 - 3)(1 + 4)

- 20 = a (-2)(5)

a = 2

Then the inequality is given as,

y < 2(x - 3)(x + 4)

y < 2(x² + x - 12)

y < 2x² + 2x - 24

The value of the coefficients a, b, and c will be 2, 2, and negative 24. And the sign will be (<).

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We have a two-tailed test, as we are testing if the mean is different of a value.

The t-distribution is used, as we have the standard deviation for the sample, and the parameters are given as follows:

Using a t-distribution calculator, the critical value is of:

t = ± 1.7109.

The equation for the test statistic is defined as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

In the context of this problem, the values of these parameters are of:

[tex]\overline{x} = -34.3, \mu = 0, s = 42.9, n = 25[/tex]

Hence the value of the test statistic is of:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{-34.3 - 0}{\frac{42.9}{\sqrt{25}}}[/tex]

t = -4.

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f(m) = 3 * 1.09 * m = 3.27 * m

A:

solve f(m) = 5.98 to find how long it takes for fish to reach that length

5.98 = 3.27 * m

m = 5.98/3.27 = 1.83 months

A reasonable domain would technically depend on other factors like standard deviation, however, a domain of [0,3] could be reasonable without further information.

B:

The y intercept (0 because f(0)=0 ) represents the length of fish at the beginning of the marine biologists study, or when the number of months is zero

C:

Rate of change equals the change in y over the change in x.

[tex]\frac{f(8)-f(2)}{8-2}=\frac{26.16-6.54}{6}=\frac{19.62}{6}=3.27\frac{cm}{month}\\[/tex]

This represents the average number of cm the length of the fish change per month in the interval [2, 8]

The correct option for the equation is C.

What is equation?

An equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main Body:

Using distance=rate multiplied by time as the  formula,  

mountaineer climbed 1,000 feet at a rate of x feet per hour  

1000 = xt₁           <--eq.1  

"He climbed an additional 5,000 feet at a different rate."  

5000 = x't₂         <--eq.2  

"This rate was 10 feet per hour less than twice the first rate."  

x' = 2x - 10 <--eq.3  

We now have 3 equations/expressions to solve for the number of hours:  

From eq. 1 and 2:  

Total time = t₁ +t₂ = t

t = 1000/x + 5000/x'  

but x' = 2x - 10  

t = 1000/x + 5000/(2x-10)  

t = 1000/x + 5000/[2(x-5)]  

t = 1000/x + 2500/(x-5)

Hence correct option is C.

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Using the Final Exam Grade formula above, I want a 90 in the class and I currently have an 85 . The final is worth [tex]$40 \%$[/tex] of the term grade.

First, convert the weight of the final exam from percent to decimal: [tex]$40 \div 100=0.40$[/tex]

[tex]$$\begin{gathered}F=\frac{90-((1-0.4) \times 85)}{0.4} \\F=\frac{90-((0.6) \times 85)}{0.4} \\F=\frac{90-51}{0.4} \\F=\frac{39}{0.4} \\F=97.5\end{gathered}$$[/tex]

So if I have an 85 in the class, I want a 90, and the final exam is worth 40%, I need a 97.5 to get a 90 in the class.

Using the Final Class Grade formula above, [tex]$F=88.6, w=15$, and $C=91$.[/tex]

First, convert the weight of the final exam from percent to decimal: 15 div 100=0.15

So I went into the final with a class grade of 91 . I got 88.6 on the final which was worth $15 \%$ of the course grade. My final grade in the class was 90.64.

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The value of x = 3.8 cm and y = 3.44 cm

What are some examples of consistency?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

What are the five different types of congruence?
Two triangles are congruent if they satisfy all five conditions for congruence. Right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).

This can be solve by congruence

these two triangle can be congruent by AAS

so x = 3.8 com

in this triangle we have all angle 60 degree

so this is an equivalent triangle

hence down side = 3.8 cm

hence y = (3.8)^2-(1.6)^2 = 14.44 - 2.56 = √11.88 = 3.44

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The linear systems has the ordered pair (1, 1)as a solution will be x + y = 2 and x - y = 0. Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let's check all the options, then we have

A)  x + y = 2 and x - y = 0

Add both equations, then we have

x + y + x - y = 2 + 0

2x = 2

x = 2 / 2

x = 1

Then the value of the variable 'y' is calculated as,

1 - y = 0

y = 1

Then the solution of the equations is (1, 1).

The linear systems has the ordered pair (1, 1)as a solution will be x + y = 2 and x - y = 0. Then the correct option is A.

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The missing option is given below.

A) x + y = 2 and x - y = 0

B) x + y = 2 and x + 2y = 0

C) x + y = 0 and x - y = 2

D) None of the above

Answer: y= 0.64x

Step-by-step explanation:

Take 3.52 divided by 5.5 = $0.64 per pound of potato

y is the total cost, x is the number of pound

y= 0.64x

Answer:

c. |11|

Step-by-step explanation:

When it comes to absolute value, we're talking about the distance from 0. Even though 11 is greater than -19 and -34, the distance from 11 and 0 is smaller than the distance from -19 and 0 and the distance from -34 and 0.

|11-0|=11

|0-19|=19-0=19

|0-34|=34-0=34

[tex]\fbox{x=$\dfrac{-7}{6}$ }[/tex]

Flip the equation:

[tex]-6x-5=2[/tex]

Add 5 to both sides:

[tex]-6x-5+5=2+5[/tex]

[tex]-6x=7[/tex]

Divide both sides by -6:

[tex]\dfrac{-6x}{-6} =\dfrac{7}{-6}[/tex]

[tex]x=\dfrac{7}{-6}[/tex]

Step-by-step explanation:

[tex](8 - 12) \times (8 \times 4) + {7}^{2} \\ [/tex]

[tex]( - 4) \times (32) + 49[/tex]

[tex] -12 8 + 49 =79 [/tex]

$23.76 is the value of XYZ stock when the required return is 12 percent.

percentage, a relative value indicating hundredth parts of any quantity.

Let the price per share be P

growth rate, g = 8% = 0.08

D = Next years dividend = $0.88 × 1.08 = $0.9504

Required rate of return r = 12% = 0.12

P=D/r-g

P=0.9504/0.12-0.08

P=$23.76

Hence,$23.76 is the value of XYZ stock when the required return is 12 percent.

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