Answer each for 100 points

To find the quotient and remainder if

�

(

�

)

f(x) is divided by

�

(

�

)

p(x), first, we need to divide the polynomials. Division of polynomials can be done by long division method. So, let's solve the problem and find the quotient and remainder of the polynomial.

In long division, first, we divide the first term of dividend by the first term of divisor.

3x^4/x^2 = 3x^2

Now we multiply this result (3x^2) with divisor and subtract from dividend.

3x^4 + 2x^3 - x^2 - x - 6 - (3x^2(x^2 + 1))= -3x^3 - x - 6

Next, we bring down the next term of the dividend. And repeat the process until we cannot divide further.

-3x^3/x^2 = -3x

Now, we multiply this result (-3x) with divisor and subtract from the last dividend.

-3x^3 - x - 6 - (-3x(x^2 + 1))= 3x^2 - x - 6

Now, we again bring down the next term of the dividend.

3x^2/x^2 = 3

Next, we multiply this result (3) with divisor and subtract from the last dividend.

3x^2 - x - 6 - (3(x^2 + 1))= -x - 9

-x/x^2 = -

Now, we multiply this result (-1) with divisor and subtract from the last dividend.

-x - 9 - (-1(x^2 + 1))= -x - 10

So, the quotient and remainder if

�

(

�

)

f(x) is divided by

�

(

�

)

p(x) are:

quotient = 3x^2 - 3

remainder = -x - 10

QUAD is not relevant to this question.

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Answer:

the third option

Step-by-step explanation:

Answer:

1.)  51.515%  2.) 48.485%

Step-by-step explanation:

In this question we know 66 is 100% of the fraction, so we can start the process of converting a fraction into a percent, by figuring out how to adjust the fraction so that the denominator will be 100. First, divide 100 by the denominator.

100/66 = 1.515

Now we want to multiply denominator and numerator by 100.

34 × 1.515 = 51.515

66 × 1.515 = 100

Therefore, 34/66 as a percentage will be 51.515%

Now we want to convert 32/66. We will do the same for this equation.

100/66 = 1.515

32 × 1.515 = 48.485

66 × 1.515 = 100

Therefore 32/66 as a percentage will be 48.485

Hope this helps : )

Answer and Explanation:

1. corresponding: bottom right graph

         → the angles are in the same place in relation to the parallel lines

2. alternate interior: bottom left graph

         → the interior angles are on opposite sides of the transversal

3. alternate exterior: top left graph

         → the exterior angles are on opposite sides of the transversal

4. none of these: top middle graph

         → there are no parallel lines

Therefore , the solution of the given problem of expression comes out to be  the response is j + 8.

Calculations like variable multiplication, splitting, joining, and presently removing are required. Combining them would result in the following: An equation, some statistics, and a mathematical formula. A declaration of truth is composed of values, components, mathematical processes like additions, subtractions, errors, and subdivisions as well as arithmetic formulas. Words and phrases can be evaluated and analysed.

Here,

We must first determine the difference between 10 and 2, which is: before we can add the distinction of 10 and 2 to j.

=> 10 - 2 = 8

Now, by writing only the expression: we can add 8 to j.

=> j + 8

Consequently, the response is j Plus 8.

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There is 360 mg of drug in 30 mL of the 60 mg/5 mL elixir.

The amount of drug in a given volume of a medication can be calculated using the following formula: Amount of drug (mg) = Volume (mL) x Concentration (mg/mL). In this case, we have 30 mL of a 60 mg/5 mL elixir, so the amount of drug in 30 mL can be calculated as follows: Amount of drug (mg) = 30 mL x 60 mg/5 mL = 360 mg. Therefore, there is 360 mg of drug in 30 mL of the 60 mg/5 mL elixir.

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Step-by-step explanation:

To determine whether the ice cream scoop will fit in the cone or overflow, we need to compare the volume of the scoop to the volume of the cone. If the volume of the scoop is less than or equal to the volume of the cone, the scoop will fit in the cone. If the volume of the scoop is greater than the volume of the cone, the scoop will overflow.

The formula for the volume of a sphere is:

V_sphere = (4/3)πr³

where r is the radius of the sphere. In this case, the radius of the ice cream scoop is 3 cm, so:

V_sphere = (4/3)π(3 cm)³ ≈ 113.1 cm³

The formula for the volume of a cone is:

V_cone = (1/3)πr²h

where r is the radius of the base of the cone and h is the height of the cone. In this case, the radius of the cone is also 3 cm and the height of the cone is 5 cm, so:

V_cone = (1/3)π(3 cm)²(5 cm) ≈ 47.1 cm³

Therefore, the volume of the ice cream scoop is greater than the volume of the cone, and the ice cream will overflow when it melts.

To explain this result, we can note that the volume of the ice cream scoop is determined by its shape and size, which cannot be changed. However, the volume of the cone is determined by both its shape and size, as well as the amount of space available inside it. When the ice cream melts, it will fill up the cone and displace the air inside, increasing the volume of the cone. However, the volume of the ice cream scoop will not change, so it will overflow the cone.

The volume of the right circular cone is approximately 1819.1 cubic centimeters.

Volume is the measure of the amount of space occupied by a three-dimensional object or shape. It is expressed in cubic units, such as cubic centimeters, cubic meters, or cubic inches, depending on the system of measurement being used. The formula for volume varies depending on the shape of the object, but for many common three-dimensional shapes, such as cubes, spheres, cylinders, and cones, there are well-known formulas for calculating their volumes.

According to the given information :

The formula for the volume of a right circular cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.

Substituting the given values, we get:

V = (1/3)π(9.6 cm)²(19.9 cm)

V ≈ 1819.1 cubic centimeters (rounded to the nearest tenth)

Therefore, the volume of the right circular cone is approximately 1819.1 cubic centimeters.

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The sampIe mean has a 0.9992 chance of being Iess than $453.

A measure οf a grοup οf vaIues' variance οr dispersiοn in statistics is caIIed the standard deviatiοn. When the standard deviatiοn is Iοw, the vaIues are mοre IikeIy tο faII within a narrοw range, aIsο knοwn as the expected vaIue, whereas when the standard deviatiοn is high, the vaIues tend tο be cIοser tο the mean.

The sampIing distributiοn οf the sampIe mean is apprοximateIy nοrmaI with mean μ = $450 and standard deviatiοn [tex]\sigma/ \sqrt{(n)} = \$40/\sqrt{(625)} = \$1.6[/tex].

(a) Tο find the prοbabiIity that the sampIe mean wiII be Iess than $453, we standardize the sampIe mean:

[tex]z = (x - \mu) / (\sigma / \sqrt{(n)}) = (453 - 450) / (40 / \sqrt{(625)}) = 3.125[/tex]

Using a standard nοrmaI tabIe, we find that the prοbabiIity οf getting a z-scοre οf 3.125 οr Iess is 0.9992.

Therefοre, the prοbabiIity that the sampIe mean wiII be Iess than $453 is 0.9992.

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if it has a diameter of 28, its radius is half that or 14.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=14\\ h=7.5 \end{cases}\implies V=\pi (14)^2(7.5) \\\\\\ V=1470\pi \implies V=1470(\frac{22}{7})\implies V=4620~m^3[/tex]

Therefore the total cost for 18 months of membership is[tex]$742.50[/tex].The equation to find the cost of initiation and x months of membership is y + 59x = 742.50

The equation to find the cost of initiation and x months of membership is y + 59x = 742.50. Since the cost for one year of membership is known, the cost for initiation can be found by subtracting 59x from both sides of the equation, resulting in y = 742.50 - 59x. To find the total cost for 18 months of membership, we plug x = 18 into the equation, resulting in y + 59(18) = 742.50. This can be simplified to y + 1062 = 742.50, which means that y = -319.50. Therefore, the total cost for 18 months of membership is[tex]$742.50 - $319.50[/tex], which equals [tex]$423.00[/tex]. This calculation can be represented by the equation y + 59x = 742.50, where y is the cost of initiation and x is the number of months of membership. Plugging in the number of months of membership (x = 18) gives us the total cost for 18 months of membership (y + 1062 = 742.50). Simplifying this equation yields y = -319.50, and therefore the total cost for 18 months of membership is[tex]$742.50.[/tex]

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Cοmparing the given equatiοn with the standard form, we can see that the center is at [tex]$(-17.5, 15.\bar{3})$[/tex], and the radius is [tex]$\sqrt{18.1}$[/tex].

The standard form of the equatiοn of a circle is:

[tex]$$(x - h)^2 + (y - k)^2 = r^2$$[/tex]

where (h, k) is the center of the circle and r is the radius. This form of the equation is useful because it prοvides information about the center and radius οf the circle in a straightforward way. To use the standard form to graph a circle, we can plοt the center (h, k) on the coordinate plane and then draw a circle with radius r centered at (h, k).

To find the center and radius of the circle with equatiοn [tex]$(x+17.5)^2 + (y - 15.\bar{3})^2 = 18.1$[/tex], we can use the standard fοrm of the equation of a circle:

[tex]$$(x - h)^2 + (y - k)^2 = r^2$$[/tex]

where (h, k) is the center οf the circle and r is the radius.

Comparing the given equatiοn with the standard form, we can see that the center is at [tex]$(-17.5, 15.\bar{3})$[/tex], and the radius is [tex]$\sqrt{18.1}$[/tex]. Therefοre, we can write:

Center [tex]$= \left(-17.5, 15.\bar{3}\right)$[/tex]

Radius[tex]$= \sqrt{18.1}$[/tex]

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A circle in the xy-plane has the equation (x+17.5)²+(y-15(3))² = 18.1. Which of the following pairs is its center and radius.

a. (17, 15.3) and √18

b. (19, 14) and √9

c. (17, 15.3) and 9

d. (19, 14) and 18

The correct locations for the three missing labels in the diagram are "Analyze the Situation" in the top-left corner, "Identify Options" in the bottom-left corner, and "Make a Decision" in the bottom-right corner. We need to apply the decision-making process to the three missing labels in the diagram.

The first missing label is for the top-left corner of the diagram. The correct location for this label is "Analyze the Situation." This is because the decision-making process begins with an analysis of the situation to understand the problem and identify any potential constraints.

The second missing label is for the bottom-left corner of the diagram. The correct location for this label is "Identify Options." This is because the decision-making process involves identifying all of the available options for solving the problem.

The third missing label is for the bottom-right corner of the diagram. The correct location for this label is "Make a Decision."

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A $9. 00 album is marked up 6 1/4% and then is offered for 14% off. If the sales tax is 5%. The total amount of tax that must be paid for this album is $0.41.

Let's break this problem down into steps:

Markup price = $9.00 + 6.25% of $9.00

Markup price = $9.00 + $0.56

Markup price = $9.56

Sale price = Markup price - 14% of Markup price

Sale price = $9.56 - 14% of $9.56

Sale price = $9.56 - $1.34

Sale price = $8.22

Tax amount = 5% of the Sale price

Tax amount = 5% of $8.22

Tax amount = $0.41

Therefore, the total amount of tax that must be paid for this album is $0.41.

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The best description of how close the prediction was to the actual population in 2013 is option (A) with in 100 people

To solve this problem, we can use the exponential growth formula:

P(t) = P0 × e^(rt)

where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.718.

We can use the given data to find the growth rate r:

58,000 = 42,000 × e^(r×30)

Dividing both sides by 42,000:

e^(r×30) = 58,000/42,000 = 1.38

Taking the natural logarithm of both sides:

r×30 = ln(1.38)

r = ln(1.38)/30

r ≈ 0.0106

Now we can use this growth rate to predict the population in 2013:

P(53) = 42,000 × e^(0.0106×53) ≈ 74,480

So the predicted population of 74,480 is within 520 people of the actual population of 75,000

Therefore, the correct option is (A) Within 100 people.

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We don't know if she will reject the null hypothesis without knowing the level of significance. But if the p-value is smaller than the level of significance, she would reject the null hypothesis

The correct explanation for the P-value is option B: "If the​ P-value for a particular test statistic is ​, she expects results at least as extreme as the test statistic in about of 100 samples if the null hypothesis is true."

This means that if the null hypothesis is true, there is a certain probability (represented by the P-value) that we would observe a test statistic as extreme or more extreme than the one we observed in our sample.

As for the conclusion, we cannot determine whether or not the researcher would reject the null hypothesis based solely on the P-value. The decision to reject or not reject the null hypothesis depends on the level of significance (alpha) chosen by the researcher. If the P-value is smaller than the chosen alpha, then the researcher would reject the null hypothesis.

Otherwise, she would fail to reject it. Without knowing the level of significance chosen, we cannot determine the conclusion.

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Answer:

50s

Step-by-step explanation:

180cm³= 30s

300cm³=x s

Thus,

180x= 30×300

180x = 9000

x= 50s.

Hope this helps! :)

Answer:

[tex]s=170\frac{\sqrt{m} }{q}[/tex]

Step-by-step explanation:

since varies directly with square root of m and inversely with q ( [tex]\sqrt{m}[/tex] goes in the numerator and [tex]q[/tex] in the denominator)

[tex]s=a\frac{\sqrt{m} }{q}[/tex]

notice a is a constant, we need to find it!

since s=340 when m=36 and q=3

 [tex]340=a\frac{\sqrt{36} }{3}=a\frac{6}{3} =2a[/tex]
[tex]a=340/2=170[/tex]

so equation is:
[tex]s=170\frac{\sqrt{m} }{q}[/tex]

The minimum value of the function is 9, and the function never stops increasing.

The given function is y=(x−9)²+9.

We need to find the minimum and maximum value of the function. The given function is a quadratic function whose graph is a parabola. Since the coefficient of x² is positive, the graph of the quadratic function will be in the form of an upward parabola whose vertex is at the point (h,k).

The vertex form of the quadratic function is given byy = a(x - h)² + k, where(h,k) is the vertex of the parabola.

a is the coefficient of (x - h)².

In the given function,y = (x-9)² + 9, the vertex of this function is (9,9) and a=1.

Therefore, the minimum value of the function is 9 at x=9, which is the vertex of the parabola.

The function y=(x−9)²+9 is an upward parabola, and hence it never stops increasing, which means that the function has no maximum value.

Thus, the minimum value of the function is 9, and the function never stops increasing.

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The set of sample means generated by Mark may not be representative of the population of the city.

This is because Mark's sampling method is not random and may introduce bias into the sample. By only surveying bypassers in the central street, the sample may not be representative of the whole population of the city. On the other hand, Judy's random sampling method has a higher chance of capturing a representative sample of the population.

To confirm this, we can compare the sampling distributions generated by both methods. We can calculate the mean and standard deviation of the sample means for each method and compare them. If the means and standard deviations are significantly different, it may suggest that Mark's sampling method is biased.

To calculate the standard deviation of the sampling distribution, we can use the formula:

Since the population standard deviation is not given, we can use the sample standard deviation as an estimate. Assuming the sample standard deviation is 2, we can calculate the standard deviation of the sampling distribution as follows:

For Judy's method:

For Mark's method:

Assuming that the central street has a population size of 1000, we can calculate the standard deviation as:

The standard deviation of Mark's sampling distribution is much larger than Judy's, indicating that Mark's sampling method may not be representative of the whole population of the city.

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Answer:

  4.0 feet

Step-by-step explanation:

You want the diameter of a rubber ball that costs $1, if that cost is $0.02 per square foot.

The surface area of a sphere is given by ...

  A = 4πr²

In terms of diameter, this is ...

  A = 4π(d/2)² = πd²

The cost will be ...

  Cost = (cost/square foot)(area)

  1.00 = 0.02(πd²)

Solving for d, we have ...

  d² = 1.00/(0.02π) ≈ 15.915

  d ≈ √15.915 ≈ 3.989 ≈ 4.0 . . . . feet

The diameter of the ball is about 4.0 feet.

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Answer:

113.10 square inches

Step-by-step explanation:

Base shape = Circle

r = radius of Base shape

 = 3 in

l = slanted height

 = 9 in

Surface Area of cone = [tex]\pi r^{2} + \pi rl[/tex]

                                    = [tex][\pi (3)^{2} + \pi (3) (9)] in^{2}[/tex]

                                    = [tex][9\pi + 27\pi] in^{2}[/tex]

                                     = [tex]36\pi[/tex] square inches

                                     = 113.10 square inches (Rounded to the nearest    hundredth place)

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex]{ \star{ \boxed{ \textsf{ \purple{Surface area of cone = πr² + πrs}}}}}[/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

a) The system of equations modeling this scenario is as follows:

C = 11.50 + 0.9n

C = 13.25 + 0.55n.

b) The number of toppings where the cost is the same at either Pizza Palace or Tasty Pizza is 5.

A system of equations is two or more equations solved concurrently.

A system of equations is also called simultaneous equations because the equations are solved at the same time or simultaneously.

                               Pizza Palace    Tasty Pizza

Pizza cost per unit       $11.50             $13.25

Topping cost per unit  $0.90              $0.55

Let the number of toppings = n

Let the total cost for the pizza at each pizza place = c

The total cost at Pizza Palace C = 11.50 + 0.9n... Equation 1

The total cost at Tasty Pizza, C = 13.25 + 0.55n... Equation 2

For the total cost, c, to be the same at the pizza places, Equation 1 must equate Equation 2:

That is, C = C.

Substituting the values of C:

11.50 + 0.9n = 13.25 + 0.55n

0.35n = 1.75

n = 5

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Answer:

x = 114 degrees

Step-by-step explanation:

Angle x and the exterior angle form a straight line, which is 180 degrees. Because of this, we can subtract 66 from 180, equaling 114.

The numbers when decomposed using their prime factors are 72: 2³ × 3², 204: 2² × 3 × 17, 1800: 2³ × 3² × 5² and  42336: 2⁵ × 3 × 11² × 17

To decompose a number into its prime factors, we need to find the prime numbers that multiply together to give the original number.

The numbers are given as  72, 204, 1800, and 42336

So, we have

Let's decompose each of the given numbers:

72 = 2 × 2 × 2 × 3 × 3

Prime factorization: 2³ × 3²

204 = 2 × 2 × 3 × 17

Prime factorization: 2² × 3 × 17

1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5

Prime factorization: 2³ × 3² × 5²

42336 = 2 × 2 × 2 × 2 × 2 × 3 × 11 × 11 × 17

Prime factorization: 2⁵ × 3 × 11² × 17

Therefore, the prime factorization of each number is:

72: 2³ × 3²

204: 2² × 3 × 17

1800: 2³ × 3² × 5²

42336: 2⁵ × 3 × 11² × 17

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Here, option (a) is correct i.e., MNOP is a trapezoid because exactly one pair of opposite sides is parallel.

In Euclidean geometry, a trapezoid is defined as a convex quadrilateral by definition. The bases of the trapezoid are parallel sides. The formula to find the area will be:

Area = 1/2 x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides

Perimeter = is the sum of lengths of sides of the trapezoid

Quadrilateral MNOP is a trapezoid because exactly one pair of opposite sides is parallel.

To see the image please see the graph given below.

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The can measure exactly 4 litres by having 1 2/3 in the 5litres container and 2 2/3 in the 7 litres container

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and been asked to imagine how you would solve it using math.

These word problems are interpreted into mathematical equation or expression.

If the woman wants to have the water in two containers with a good ratio, then we say;

The ratio of container 1 to container 2 is 5:7

therefore;

the amount of water in 5litres container = 5/12 × 4 5/3 = 1 2/3 litres

the amount of water in 7 litres = 7/12 × 4 = 7/3 = 2 2/3 litres

Therefore to measure it, she will have 1 2/3 in the 5litres container and 2 2/3 in the 7 litres container

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