f(x)=x^4+2x^3-9x^2-2x+6 and f(-4)=0 algebraically find all the zeros.

According to the solution we have come to find that, The smallest of the four consecutive integers is 18.

Consecutive integers are integers that follow each other in order, such that the difference between any two consecutive integers is always 1.

Let's call the smallest integer x. Since there are four consecutive integers, we can express the other three as x+1, x+2, and x+3.

We know that the sum of these four integers is 78, so we can write an equation:

x + (x+1) + (x+2) + (x+3) = 78

Simplifying this equation:

4x + 6 = 78

Subtracting 6 from both sides:

4x = 72

Dividing both sides by 4:

x = 18

Therefore, the smallest of the four consecutive integers is 18.

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The answer is option (d): ∅= π/2 , 2 π+ π/2, 4 π+ π/2, 6 π+ π/2. we got answer by solving sine function .

what is  sine function ?

The sine function is a mathematical function that relates the angles of a right triangle to the lengths of its sides. In particular, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse of the triangle.

In the given question,

The function y = sin(∅) equals 1 at values of ∅ where the sine function has a maximum value of 1. The maximum value of sine occurs at angles that are odd multiples of  π/2, i.e., at  π/2, 3 π/2, 5 π/2, etc.

We need to find all such values of ∅ in the interval 0 <= ∅ <= 8 π. The possible values of ∅ that satisfy this condition are:

π/2 (odd multiple of  π/2 within the interval)

2 π+ π/2 (odd multiple of  π/2 within the interval)

4 π+ π/2 (odd multiple of  π/2 within the interval)

6 π+ π/2 (odd multiple of  π/2 within the interval)

8 π (endpoint of the interval, where sin(8 π) = 0)

Therefore, the answer is option (d): ∅=  π/2 , 2 π+ π/2, 4 π+ π/2, 6 π+ π/2.

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The learner has misunderstood the concept of fractions, the misconception that the learner has is that the model they have provided does not represent a fraction.

Fractions are written using numerator (the number on top) and denominator (the number on bottom).

The model they have provided does not represent a fraction because fractions are used to compare two parts of a whole. In this model, there are only two parts, coloured dots and not coloured dots, and there is no whole to compare them to.

Therefore, the learner has misunderstood the concept of fractions and the model they have provided does not represent a fraction.

To make this model represent a fraction, it would need to represent two parts of a whole.

If the model had 12 dots and 6 were coloured, it could represent a fraction of 6/12 (or 1/2). This is because the 6 coloured dots would be 1 part of the whole which is 12 dots.

Therefore, the misconception that the learner has is that the model they have provided does not represent a fraction. The model only has two parts, coloured dots and not coloured dots.

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The misperception that the student has is that the model they have presented does not reflect a fraction; as a result, the learner has misinterpreted the idea of fractions.

When writing fractions, the denominator (the lower number) and the numerator are used. (the number on bottom).

Given that fractions are meant to compare two parts of a whole, the model they have presented does not reflect a fraction. There are only two components in this model: coloured dots and non-colored dots, and there is no whole to which they can be compared.

As a result, the learner misinterpreted the idea of fractions, and the example they gave does not accurately depict a fraction.

This model would have to depict two pieces of a whole in order to represent a fraction.

The model might represent a fraction of 6/12 (or 1/2) if it had 12 dots, of which 6 were coloured. This is because the six different colours would make up one part of the total of twelve dots.

Because of this, the learner believes that the offered model does not represent a fraction, which is a misunderstanding. The model consists of just two components: coloured dots and blank spaces.

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The number of intervals that feel that America is doing about the right amount to protect the environment is 0.487, and 0.551 intervals

To find the number of adults who feel that America is doing about the right amount to protect the environment, we need to use the confidence interval proportion formula

CI = p ± Zα/2 * √(p * (1-p)/n

where:

p = sample proportion = 519/1000 = 0.519

n = sample size = 1000

Zα/2 = the critical value for the desired confidence level = 1.96

By substuting the values, we get:

CI = 0.519 ± 1.96 * √(0.519 * (1-0.519) / 1000)

= 0.519 ± 0.032

= (0.487, 0.551)

Therefore,  (0.487, 0.551) interval feel that America is doing about the right amount to protect the environment.

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Option A : The surface area of the larger sphere is 602.88 [tex]in^2[/tex].

Let's use the formula for the surface area of a sphere: A = 4π[tex]r^2[/tex], where r is the radius of the sphere.

Let's call the radius of the smaller sphere "r1" and the radius of the larger sphere "r2". We know that the surface area of the smaller sphere is 200.96 [tex]in^2[/tex], so we can set up the equation:

4π[tex]r1^2[/tex] = 200.96

Solving for r1, we get:

r1 = √(200.96 / 4π) ≈ 2.8

A2 / A1 = [tex](r2 / r1)^2[/tex]

A2 = [tex]A1 (r2 / r1)^2[/tex]

We know A1 = 200.96 [tex]in^2[/tex] and r1 ≈ 2.8, and we want to find r2, so we can use the formula for the volume of a sphere to relate r1 and r2:

(4/3)π[tex]r1^3[/tex] = (4/3)π[tex]r2^3[/tex]

Solving for r2, we get:

r2 = [tex]r1 (3)^(1/3)[/tex] ≈ 3.3

Now we can plug in the values for A1, r1, and r2:

A2 = [tex]200.96 (3.3 / 2.8)^2[/tex] ≈ 301.44

Therefore, the larger sphere has a surface area of roughly 301.44 in2, making answer choice C appropriate.

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Using the given information, the volume of the sphere is approximately 1521.88 cubic units, rounded to the hundredths place

From the question, we are to determine the volume of the sphere.

Let's start by using the formula for the circumference of a circle,

C = 2πr,

Where C is the circumference

and r is the radius.

Since the circumference of the great circle is given as 14π, we can solve for the radius as follows:

14π = 2πr

Dividing both sides by 2π, we get:

r = 7

Now, we can use the formula for the volume of a sphere,

V = (4/3)πr³

Where V is the volume

and r is the radius.

Substituting the value of r that we found, we get:

V = (4/3)π(7)³

V = (4/3)π(343)

V = 4/3 * 1141.45

V = 1521.88

Hence, the volume of the sphere is 1521.88 cubic units.

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The probability that there are 3 people between x and y is 1/659470.

The total number of ways in which x and y can stand in a line with 10 other people is (12C2) = 66.

To find the number of ways in which there are exactly 3 people between x and y, we can treat x and y as a single entity and arrange them along with the 10 other people in 8 available spots in the line. This can be done in (8C1) = 8 ways.

Within this arrangement, there are 3 spots where x and y can be placed with 3 people between them,

Once x and y have been placed in one of these 3 spots, the remaining people can be arranged in the remaining spots in

10!/(10-8)! = 1814400 ways.

So the number of ways in which there are exactly 3 people between x and y is,

8 * 3 * 1814400 = 43545600.

Therefore, the probability that there are 3 people between x and y is,

43545600/66 = 659469.69 (rounded to 2 decimal places)

So, the probability is approximately 1 in 659470 or 1/659470.

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Answer:

The point of reflection has coordinates:

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

Use the graph to determine the point A and given line.

Point A has coordinates (4, 3).

Use two points on the line to get its slope:

It gives us the y-intercept of b = 1 and slope of:

The line is:

We know he line of reflection is equidistant from the original point A and its image A'.

The line segment AA' is perpendicular to the line of reflection and the point of intersection is the midpoint of AA'.

Now, let's determine the midpoint of AA'.

The segment AA' has a slope of m = 1/2 as the perpendicular slope to the given line, they are opposite-reciprocals.

Use coordinates of A and the slope to determine the line AA', using point-slope equation:

Find the intersection of the two lines, by solving the system:

The y-coordinate:

The point of intersection is (0, 1).

Use midpoint equation to determine the coordinates of the reflected point A'(x, y):

So the point A' is (- 4, - 1).

By working with the exponential equation we will get:

i) N = 1000

ii) k = -0.02

iii) t = 34.66 seconds

Here we know that the equation:

[tex]N = 1000*e^{-k*t}[/tex]

models the population at a time t.

i) When t = 0, we have:

[tex]N = 1000*e^{-k*0}\\N = 1000*1\\N = 1000[/tex]

That is the initial population of bacteria.

ii) at t = 0, the rate of decay is -20 /min

the differentiation of the exponential gives:

[tex]N' = -k*1000*e^{-k*t}[/tex]

And evaluating that in t = 0 should give -20., then:

[tex]-20 = -k*1000*e^{-k*t}\\\\-20 = -k*1000\\-20/1000 = -k\\-0.02 = -k\\0.02 = k[/tex]

That is the value of k.

iii) Here we need to solve the equation:

[tex]500= 1000*e^{-0.02*t}\\\\0.5 = e^{-0.02*t}\\\\ln(0.5) = ln(e^{-0.02*t})\\\\ln(0.5) = -0.02*t\\\\ln(0.5)/ -0.02 = t\\ \\34.66 = t[/tex]

So it will take 34.66 seconds to reach half of the initial population.

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According to given information, the truck has 4.75 pounds of sand when it arrives at the yard.

What is distance?

Distance is a numerical description of how far apart objects or points are. It is a scalar quantity that is typically measured in units such as meters, kilometers, miles, etc. Distance is a fundamental concept in geometry, physics, and other fields of science and engineering.

The initial amount of sand the truck carried is 9.35 pounds.

The amount of sand the truck loses on the way is 4.6 pounds.

Therefore, the amount of sand the truck has when it arrives at the construction yard is:

9.35 - 4.6 = 4.75 pounds.

So the truck has 4.75 pounds of sand when it arrives at the yard.

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Answer:

1/2

Step-by-step explanation:

a dice has 6 sides

even sides are: 2 4 6

odd sides are:  1 3 5

because there the same amount of even/odd sides is 1/2 or 3/6

The standard error to be used in the formula of a confidence interval for the difference in proportions is 0.07.

The estimated standard deviation of a statistical sample population is known as the standard error (SE) of a statistic.

By utilising standard deviation, the standard error is a statistical concept that assesses how well a sample distribution represents a population. In statistics, the difference between a sample mean and the population's actual mean is known as the standard error of the mean.

The standard error's primary function is to indicate how divergent the population mean will be from the sample mean. Because it aids in determining how well the standard data reflect the entire population, the standard error is significant. We may readily draw reliable conclusions by calculating the standard error in order to determine how representative our sample is of our population.

56 out of 100 boys = P1 = 0.56

43 out of 100 girls = P2 = 0.43

The formula for standard is given by,

[tex]S.E=\sqrt{\frac{P_1(1-P_1)}{n1} +\frac{P_2(1-P_2)}{n2} } \\=\sqrt{\frac{0.56(1-0.56)}{100} +\frac{0.43(1-0.43)}{100} } \\\\= \sqrt{\frac{0.2464}{100} +\frac{0.2451}{100} } \\\\=\sqrt{0.004915} \\=0.07[/tex]

Therefore, the standard error is 0.07.

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The equation that will likely have the graph attached is

The first step will be checking the y intercepts of the equations. Considering the graph the y intercept is in the positive hence equation in d is eliminated

Another factor is vertex, solving for the vertex of the remaining equations would show the equation that has a vertex that would be in that position

Otherwise plot the graph of all the equations and match the likely equations to the graphs

Matching the equations to their graphs shows that graph of y = 3x² - 2x + 1 is attached

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Answer:

3x² + 3x - 6

Step-by-step explanation:

(3x - 3)(x + 2)

each term in the second factor is multiplied by each term in the first factor, that is

3x(x + 2) - 3(x + 2) ← distribute parenthesis

= 3x² + 6x - 3x - 6 ← collect like terms

= 3x² + 3x - 6

The probability that a sample of five parts from a production process that produces 3% defective parts contains exactly two defective parts is approximately 0.2834.

To find this probability, we can use the binomial probability formula:

P(X = 2) = (5 choose 2) * 0.03^2 * (1 - 0.03)^3

Where "X" is the number of defective parts in the sample, "5 choose 2" represents the number of ways to choose 2 defective parts out of 5, and 0.03 and (1 - 0.03) represent the probabilities of selecting a defective and non-defective part, respectively.

Using a calculator, we can simplify and compute:

P(X = 2) = (5 choose 2) * 0.03^2 * 0.97^3

= 10 * 0.0009 * 0.9127

≈ 0.0081

Therefore, the probability is approximately 0.0081 or 0.81%.

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Answer:

[tex]9(x - 1)(x-3)[/tex]

Step-by-step explanation:

[tex]9 {x}^{2} - 36x + 27[/tex]

[tex]9x(x - 1) - 27(x - 1)[/tex]

[tex](x - 1)(9x - 27)[/tex]

9(x-1)(x-3)

The value of x in the rhombus is - 96.

A rhombus is a quadrilateral with 4 sides equal to each other. The opposite sides of a rhombus are parallel. The opposite angles are congruent. The diagonals are perpendicular and they bisect each other. The adjacent angles are supplementary.

Therefore,

m∠TXU = (-x - 6) degrees

Hence,

-x -6 = 90

add 6 to both sides of the equations

-x -6 = 90

-x -6 + 6 = 90 + 6

-x = 96

Therefore,

x = -96

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Using SAS congruence theorem, the triangles PQT and RST are congruent. By using the sum of all angles in triangle STR, the measure of angle STR (or arc SR) is found to be 100 degrees.

Draw a circle and label the radii QT and PT.

Identify that angle PQT measures 40 degrees, which makes triangle PQT an isosceles triangle with angles QPT and PQT both measuring 40 degrees.

Recognize that triangle RST is also isosceles with angle RST equaling angle SRT.

Note that ST and TQ are equal in length, as are PT and TR.

Deduce that angles PQT and STR are also equal since they are opposite angles of congruent triangles.

Apply the SAS congruence theorem to conclude that triangles PQT and RST are congruent.

Recognize that angles PQT, RST, QPT, and SRT all measure 40 degrees since they are congruent angles in congruent triangles.

Use the fact that the sum of all angles in triangle STR equals 180 degrees to determine that the measure of angle STR (or arc SR) is 100 degrees.

Therefore, the measure of angle STR (or arc SR) is 100 degrees.

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The figure is attached below

The overlap of the doors is 20% of the width of the doorway.

In the given context, the function f(t) = 13.5 sin(5 * 2πt) + 20 describes the vertical position of a point on the bicycle wheel, in inches, at any given time t in seconds.

The amplitude of the sine function, which is 13.5 in this case, determines the maximum displacement or distance of the point on the wheel from its equilibrium position (the midline).

In other words, the point on the wheel moves up and down by a maximum distance of 13.5 inches from the center of the wheel as it spins. This means that the diameter of the wheel is twice the amplitude, which is 27 inches.

So, 13.5 is the amplitude of the sine function and represents the maximum displacement of the point on the bicycle wheel from its equilibrium position.

Answer:

The 13.5 in this context is the amplitude of the sine function. It represents the maximum displacement of the point from its equilibrium position.

The function f(t) = 13.5 sin (5 * 2πt) + 20 describes the vertical position of a point on the wheel as a function of time. The sine function represents the cyclical motion of the point. The amplitude of the sine function is 13.5, which means that the point will move a maximum of 13.5 inches above or below its equilibrium position.

Step-by-step explanation:

3 divided by 2 is equal tο 1 and 1/2.

A divisiοn divides a larger number intο smaller grοups with the same number οf cοnstituents. It is οne οf the basic mathematical οperatiοns. Hοw many tοtal grοups will be fοrmed, fοr example, if 20 students need tο be divided intο five grοups fοr a spοrting event?

It is easy tο address such challenges thanks tο divisiοn and cοοperatiοn. In this scenariο, multiply 20 by 5. The UTCMe is gοing tο be 20 x 5 = 4. There will be fοur grοups οf five students each. Yοu may cοnfirm this number by multiplying 4 by 5 and getting the answer 20.

When dividing 3 by 2, we get a quοtient οf 1 with a remainder οf 1. Tο write this quοtient as a mixed number, we take the quοtient (1) as the whοle number part οf the mixed number and write the remainder (1) as the numeratοr οf the fractiοnal part.

Then, the denοminatοr οf the fractiοnal part is the same as the divisοr (2) in the οriginal divisiοn prοblem.

So, the mixed number form of 3 ÷ 2 is:

1 1/2

Hence, 3 divided by 2 is equal to 1 and 1/2.

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For given Semi-circle shaped window,  the distance around the window is 38.55 inch.

What exactly is a circle?

A circle is a closed two-dimensional shape in which all points on the boundary are equidistant from a single point called the center. It is formed by taking all points in a plane that are a fixed distance (called the radius) away from the center. The distance around the circle's boundary is called the circumference, and the distance from the center to any point on the boundary is the radius.

Now,

As radius of semicircle = 7.5 in and

Circumference is given by = πr⇒3.14*7.5=23.55 inch

Perimeter of window= πr+D

D=diameter

P=23.55+15

P=38.55 inch

Hence,

         the distance around the window is 38.55 inch.

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Answer:

  90.0 cm²

Step-by-step explanation:

You want to know the area of the composite figure shown.

The vertical side and hypotenuse of the right triangle are 9 cm and 15 cm. These have the ratio 9/15 = 3/5, so we know this triangle is a 3-4-5 right triangle with a scale factor of 3. The missing side length is 3·(4 cm) = 12 cm.

So, the figure is a trapezoid with a top base of 4 cm, a bottom base of 4+12 = 16 cm, and a height of 9 cm. Its area is ...

  A = 1/2(b1 +b2)h

  A = 1/2(4 cm +16 cm)(9 cm)

  A = 90 cm²

The area of the figure is 90.0 cm².

__

Additional comment

In case you don't recognize the 3:4:5 side ratio, you can figure the base of the triangle using the Pythagorean theorem:

  a² +b² = c²

  a² = c² -b² = 15² -9² = 225 -81 = 144

  a = √144 = 12 . . . . . length of CD in cm

Other useful Pythagorean triples you will see are {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.

Answer:

ans is 1.

7+3×n+3×1-8

then u get the frst option

other options are wrong 10 n never possible

Step-by-step explanation:

Area of each of the ends    pi r^2   there are TWO

  TWO x  pi ( 7^2)   = 98 pi     in^2

SIDE area is   circumference ( pi * d )   *   height ( 2)

        Side =  pi ( 7x2) * 2   = 28 pi   in^2

Total  =  98 pi  +  28 pi  =  126 pi     in^2      <=====exact answer

                                       = 395.84    in^2      <===== approx answer