Round 23.492 the nearest hundredth

The end behavior of the graph of the polynomial function (x)=3x⁶+ 30x⁵ + 75x⁴ is  x→±∞, y→∞.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial function is f(x)=3x⁶+ 30x⁵ + 75x⁴

y=f(x)=3x⁴(x+5)²≥0

The zeros are 0, 0, 0,0,-5 and -5.

x-intercept ( y = 0 ): x = -5.

Local mini/max turning points ( y' = 0 ): 0 0, 0, -10/3 and -5.-,

As x→±∞, y→∞.

Hence, the end behavior of the graph of the polynomial function (x)=3x⁶+ 30x⁵ + 75x⁴ is  x→±∞, y→∞.

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Answer:

the 4th option

Step-by-step explanation:

ed2023

The value of the area of the shaded region in the circle is 4π - 8.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

The longest line which can be drawn inside the circle will be the diameter.

As per the given circle,

By Pythagoras' theorem,

LN = √(4² + 4²) = √32

Radius r = LN/2 = √32/2

Area of shaded region = area of the semicircle - the area of right angle triangle.

A = π(√32/2)²/2 - (1/2) × 4 × 4

A = (32π)/8 - 8

A = 4π - 8

Hence, "The circle's shaded region's area has a value of 4 to 8".

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As calculated from the given data the confidence interval for μ is (3.65, 3.91).

Let X_1,..,X_nX 1 ,..,X n  are n observations

from population with mean μ.

Than sample mean

= n1i=1/n∑X i​

Sample variance is defined by,

s = 1/( n-1 )∑(X i​ - mean) ²

n = sample size = 10

c = 95%

therefore ,

mean = 37.82/10

         =3.782

variance = 0.29556/9

              =0.03

Data points' variance from the mean is a measure of how they vary. A variance, according to Layman, is a measurement of how widely apart a set of data (numbers) are from their mean (average) value.

Finding the expected difference of deviation from the actual number is what is meant by variance. As a result, variance is influenced by the data set's standard deviation.

Data is more dispersed from its mean the higher the variance value, and less dispersed from mean if the variance value is low or minimal. As a result, it is referred to as a measure of data spread from mean.

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Answer:

The mean of the population with 99% confidence is between 43.1 and 46.1

Step-by-step explanation:

The mean of the population with 99% confidence and The standard deviation of the sample was 2.3, which is between 43.07 to 46.13.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.6 hours per week, X = 44.6

The standard deviation of the sample was, n = 2.3,

The confidence = 99%,

1 - α = 99%

α = 1 - 0.99

α = 0.01

Calculate the margin of the error as shown below,

[tex]E = Z_{\alpha /2} \ Mean / standard\ deviation[/tex]

E = 2.576 × 2.3 / √15

E = 1.5298

Calculate the mean as shown below,

X - E < Mean < X + E

44.6 - 1.5298 < Mean < 44.6 + 1.5298

43.07 < Mean < 46.13

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the work done by the force F on a particle moving counterclockwise around the closed path C is 9π by integral.

Green's Theorem states that:

∮C F · dr = ∫∫D (∂Q/∂x - ∂P/∂y) dA

Where C is the boundary of the region D, P and Q are the components of the vector field F, and dr is the vector differential along the boundary C.

In this case, the region D is a circle with radius 2, so we can express the boundary C as r = 2 cos θ. We also need to calculate the components of the vector field F. These are P = e^x - 3y and Q = e^y + 6x.

Plugging these values into Green's Theorem, we get integral:

∮C F · dr = ∫∫D (∂Q/∂x - ∂P/∂y) dA

= ∫∫D (e^y + 6 - (-3)) dA

= ∫∫D (e^y + 9) dA

= ∫ 0 2π ∫ 0 2 (e^2 cosθ

+ 9) (2 dθ)

= 4π ∫ 0 2 (e^2 cosθ + 9) dθ

= 9π

Therefore, the work done by the force F on a particle moving counterclockwise around the closed path C is 9π.

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Answer:

The first one, G(x)=| x+4 |

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

Angles EIC and DJH are alternate exterior angles, which means they're congruent and equal.

Therefore, we can find x by setting the two angles equal to each other:

[tex]7x-4=73\\7x=77\\x=11[/tex]

Answer:

The answer is 6 days

Step-by-step explanation:

$30 - $18 = $12

$12 / $1.99 = 6.03015075377=  6 days

The nth maclaurin polynomial for the function  sinx= x -[tex]\frac{x^{3} }{3!}[/tex]+[tex]\frac{x^{5} }{5!}[/tex]-[tex]\frac{x^{7} }{7!}[/tex]+[tex]\frac{x^{9} }{9!}[/tex]

we can find this by using maclaurin series.

A relation in which involving one or more variables.It represent partial function as sum of power in one variables or by sum of power of other function.

It can be used to approximate function ,find the antiderivative of complicated function or compute on otherwise uncomputable sums.It is a type of series expansion in which all terms are non-negative integer power of the variables.

Now given a function is

f(x)=sinx             n=5

Using x=0 the given equation becomes

f(0)= sin(0) = 0

Now taking derivative of given function and using x=0

Then we have

[tex]f_{1}[/tex](x)= cosx                             [tex]f_{1}[/tex](0)=cos(0)=1

[tex]f_{2}[/tex](x)=-sinx                              [tex]f_{2}[/tex](0)=sin(0)=0

[tex]f_{3}[/tex](x)= - cosx                          [tex]f_{3}[/tex](0)= - cos(0)= -1

[tex]f_{4}[/tex](x)= sinx                            [tex]f_{4}[/tex](0)= sin(0) = 0

[tex]f_{5}[/tex](x)=cosx                             [tex]f_{5}[/tex](0)= cos(0)= 1

and so on.

Now using maclaurin polynomial series

f(x)=f(0)+x[tex]f_{1}[/tex](0)+[tex]\frac{x^{2} }{2!}[/tex][tex]f_{2}[/tex](0)+ [tex]\frac{x^{3} }{3!}[/tex][tex]f_{3}[/tex](0)+[tex]\frac{x^{4} }{4!}[/tex][tex]f_{4}[/tex](0)..............

by putting the value in the above series

sinx=0+x(1)+[tex]\frac{x^{2} }{2!}[/tex](0) +[tex]\frac{x^{3} }{3!}[/tex](-1)+[tex]\frac{x^{4} }{4!}[/tex](0)........

sinx=x -[tex]\frac{x^{3} }{3!}[/tex]+[tex]\frac{x^{5} }{5!}[/tex]-[tex]\frac{x^{7} }{7!}[/tex]...

Hence this is the 5th term maclaurin series.

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The following can be used to test the equality of two strings str1 and str2

.(str1.equalsIgnoreCase(str2))

.(str1.compareToIgnoreCase(str2)==0)

A string is a series of character in computer programming,either as a literal constant or some sort of variables.it must be enclosed in quotation for it to be recognized as a string.It is used for sorting text or character.The term string can also refer to more general arrays or other sequence data type and structures.

The string = compare two strings and is true if they are same (corresponding character are identical) but is false if they are not same.

The function equal calls string =if applied to two string.The string () compare two string character by character.if string are equal the function return to zero.

Therefore, the given test can be used to find the equality and compare of the string.

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Yes, this is true. Safety stock is an inventory strategy used to ensure that a company has enough of a particular item in stock to meet customer demand.

It is typically used to protect against unexpected changes in demand and/or supply, and is most applicable to independent demand inventory.

Safety stock is an inventory strategy used to ensure that a company has enough of a particular item in stock to meet customer demand. It is typically used to protect against unexpected changes in demand and/or supply. These changes can include anything such as supplier delays, unexpected customer orders, or seasonal fluctuations. Safety stock is most applicable to independent demand inventory, which is inventory that is driven by customer demand and not production requirements. Therefore, the statement that safety stock only applies to independent demand inventory is true.

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Answer: 10 marbles

Step-by-step explanation:

First, arrange all the numbers of marbles that the student picked in a ratio

red:green:blue

7:2:11

When adding all the coloured marbles that the student picked together, you get 20 marbles or "parts" as you would usually say in ratio.

Then, it would be helpful to rewrite the ratios as fractions, with 20 as the denominator:

[tex]\frac{7}{20}:\frac{2}{20}:\frac{11}{20}[/tex]

However, the bag contains 100 marbles so we should have 100 as the denominator instead of 20.  20 is a fifth of 100, so in this case, we would multiply everything (the numerator and the denominator) by 5:

[tex]\frac{7*5}{20*5} :\frac{2*5}{20*5} :\frac{11*5}{20*5}[/tex]

[tex]\frac{35}{100}:\frac{10}{100}:\frac{55}{100}[/tex]

Therefore, you could predict you would get 35 red marbles, 10 green marbles, and 55 blue marbles.

The values of f(x) for x = 1, 2, 3, 4, 5, ,,,, are 5, 10, 15, 20, 25, 30, , , ,

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

f(x) = 5 √x²

√x² = x

f(x) = 5x

For x = 1, 2, 3, 4, 5, ,,,,,,

f(1) = 5

f(2) = 10

f(3) = 15

f(4) = 20

f(5) = 25

Thus,

The final expression is f(x) = 5x.

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Answer:

$420

Step-by-step explanation:

To find the original price, we need to determine how much the sale price was discounted, and then add that amount back to the sale price. Since the sale price was 68% less than the original price, the discount was 100% - 68% = 32% of the original price.

To find the amount of the discount, we multiply the original price by the discount percentage: 32% * original price = $134.40

Dividing both sides of the equation by the discount percentage gives us the original price: original price = $134.40 / (32% * 1) = $134.40 / 32% = $420.

Therefore, the original price of the sofa was $420.

After finding the point from the given function, we draw the graph. The graph of the given function is given below:

In the given question, Bart is required to pass out 80 flyers for an upcoming event. He passes out an average of 10 flyers per minute.

The situation can be represented using the function f(x)=80-10x

where x represents time in minutes.

We have to create a graph of the situation.

To create the graph we firstly find the value of f(x) for x=0,1,2,3,..............

The given function is f(x) = 80-10x

Now put x = 0

So f(0) = 80-10(0)

f(0) = 80-0

f(0) = 80

Now put x = 1

So f(1) = 80-10(1)

f(1) = 80-10

f(1) = 70

Now put x = 2

So f(2) = 80-10(2)

f(2) = 80-20

f(2) = 60

Now put x = 3

So f(3) = 80-10(3)

f(3) = 80-30

f(3) = 50

Now put x = 4

So f(4) = 80-10(4)

f(4) = 80-40

f(4) = 40

Now the table is

x                  0               1               2               3               4

f(x)               80             70           60            50              40

Firstly we denote the point in the graph then we connect the all point to form a graph.

The graph of the given function is given below:

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The quadrant in which u/2 lies is II quadrant.

What is Quadrant?

Quadrant is a business intelligence tool that helps companies extract, analyze, and visualize data from multiple sources in real-time. It enables users to create actionable insights to improve decision-making, optimize operations, and increase profitability. Quadrant provides an intuitive platform for teams to uncover hidden trends and correlations in data, develop predictive models, and generate reports. It also allows users to customize dashboards and create interactive visualizations. Quadrant simplifies data analysis and helps teams make more informed decisions.

a) tan(u) = -3/4, 3π/2 < u < 2π

[tex]\frac{3\pi }{2} < u < 2\pi \\\\270^{o} < u < 360^{o}\\\\Dividing\ both\ side\ by\ 2\\\\135^{o} < \frac{u}{2} < 180^{o}[/tex]

u/2 lies in II quadrant.

b) We have half angle formula's,

      [tex]sin(\frac{u}{2} )= \sqrt[]{\frac{(1-cos\\ u)}{2} } \\[/tex]

         [tex]sin \frac{u}{2} = \frac{3}{5}[/tex]

      [tex]cos(\frac{u}{2} )= \sqrt[]{\frac{(1+cos\ u)}{2} } \\[/tex]

         [tex]cos\frac{u}{2} =\frac{4}{5}[/tex]    

      [tex]tan(\frac{u}{2} )= \sqrt[]{\frac{(1-cos\ u)}{sin \ u} } \\[/tex]

      [tex]tan(\frac{u}{2} )= \frac{3}{4}[/tex]

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The volume of a cube with a side length of 3.75 m is D. 52.73 m³.

Volume is described as the space occupied within the boundaries of an object in three-dimensional space.

Volume is the product of the length, width, and height of a three-dimensional space.

A cube is a three-dimensional space of equal lengths.

The side length of the cube = 3.75 m

The volume of a cube = a³ where a is the side length

= 3.75 m³

= 3.75 x 3.75 x 3.75

= 52.734375 m³

= 52.73 m³

Thus, the volume of the cube cannot be 7.50 m³, 11.25 m³, or 14.06 m³, but 52.73 m³.

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30 is the correct answer.

The square root of 50 is 5x sqrt of 2 and the multiplied by 3 becomes 15 times 2 = 30 because the two square roots of 2 multiplied together become 2.

5 x 3 x 2 = 30

The constant of proportionality in the relationship is 3/2

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

X Y

2 3

6 9

The above represents the table of values

Since the data on the table of values represents a proportional relationship, then the constant of proportionality is

Constant of proportionality = Y/X

So, we have

Constant of proportionality = 3/2

Hence, the constant of proportionality is 3/2

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The likelihood that a random cumulative variable will fall within a specific range of values rather than taking on a single value is specified by the Probability Density Function.

The probability density function (PDF), also known as the density of a continuous random variable, is a function whose value at any specific sample (or point) in the data point (the range of potential values for the random variable) can be understood as having given a relative likelihood that the value of something similar to the random variable would be closer to that sample.

There is no absolute probability that a random variable will take on any specific value because there are an unlimited number of alternative values to begin with. However, the PDF value at two samples can be used to estimate how much more likely it is for the random variable to have that particular value in any given draw.

The Cantor distribution, which although having no discrete component, does not assign positive probabilities to any specific locations, and discrete random variable probability distributions do not all have a density function.

A distribution has a density function if and only if the cumulative distribution function F(x) is fully continuous. In this case, F is typically always differentiable, and its derivative can be used to symbolize the probability density.

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a. 68 %  between $147,700 and $152,300 if the standard deviation is $2300

b. 2.5 % more than $154,800 if the standard deviation is $2400

Given that:

Prices of a certain model of a new home are normally distributed with a mean of $150,000.

Using the 68-95-99.7 rule ,  find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.

Let X = prices of a certain model of a new home

SO, X ~ Normal ( μ = 150,000 , σ = 2,300 )

z score probability distribution for normal distribution

Z = X - μ / σ  

where μ population mean price = $150,000

σ  standard deviation = $2,300

According to 68-95-99.7 rule;

Around 68% of the values in a normal distribution lies between μ - σ and μ +σ .

Around 95% of the values occur between  μ - 2σ and μ + 2σ  .

Around 99.7% of the values occur between  μ - 3σ and μ + 3σ.

Find the z scores for both given values

Z = X - μ / σ  

  =   [tex]\frac{147,700 - 150,000}{2,300}\\ \\ \\[/tex]

 = -1

Z = X - μ / σ  

  = [tex]\frac{152,300 - 150,000}{2,300}[/tex]

 = -1

The z score indicates that the category of between  μ - σ and μ +σ .

Therefore , this represents that percentage of buyers who paid between $147,700 and $152,300 is 68%.

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Answer:

c) To find Shane's overall average number of jumps completed, we need to add up the total number of jumps he completed at each height and divide by the total number of jumps he attempted.

At the lowest height, Shane completed 3 out of 3 jumps, for a total of 3 completed jumps.

At the middle height, Shane completed 5 out of 6 jumps, for a total of 5 completed jumps.

At the highest height, Shane completed 3 out of 4 jumps, for a total of 3 completed jumps.

In total, Shane completed 3 + 5 + 3 = 11 jumps out of a total of 3 + 6 + 4 = 13 jumps attempted.

His overall average number of jumps completed is 11 / 13, or approximately 0.85 jumps.

d) Since Shane's average number of jumps completed is greater than one-half (0.5), the eighth graders should be awarded 50 points

Step-by-step explanation:

For your other question A and B for A Correct! To find the total distance thrown by Claire and Grace, you first converted the mixed numbers 5/8 and 3/5 to fractions with a common denominator (in this case, 40), then added those fractions together to find the total distance in fraction form. Finally, you converted the fraction 49/40 back to a mixed number and added it to the whole number distances thrown by Claire and Grace to find their total distance.

The total distance thrown by Claire and Grace is 82 feet 9/40 inches, or approximately 82.225 feet.                                                                                                               For B also Correct! Since the total distance thrown by Claire and Grace is not greater than 83.7 feet, the eighth graders should be awarded 50 points.

The philosopher who thought that the existence of human beings is not reduced to the realization of an essence thought by God has been Jean-Paul Sartre.

This character was a Frenchman who had several professions and stood out in different branches, Jean-Paul Sartre was:

Jean-Paul Sartre is recognized for being an exponent of existentialism and humanist Marxism, among his thoughts, he himself thought that man exists to the extent that he is realized.

¡Hope this helped!

The length of the side AB of the triangle ACB will be equal to 12.72.

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices.

Triangles can be divided into a variety of categories according to their sides and angles.

As per the given information in the question,

As we can see, the triangle ACB in the figure,

AC = 9 cm

Angle = 45°

cos θ = B/H

cos 45° = 9/H

1/√2 = 9/H

H = 12.72 cm

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Answer:

A checking account is the best place to leave your money because of the high interest rates.

Therefore, the area of rectangular house is  138.684 [tex]m^{2}[/tex].

The size of a region on a planar or curved surface can be expressed mathematically using the idea of area. The term "surface area" refers to the area of an open surface or the perimeter of a three-dimensional object, whereas the term "plane area" refers to the area of a shape or planar lamina.

Here,

Given :

the length of the rectangular house =15.24 m

the width of the rectangular house = 9.1 m

thus, we find the area of rectangular house

Using formula,

=> Area= length * width

=> Area = 15.24 * 9.1

=>  Area = 138.684 [tex]m^{2}[/tex]

Therefore, the area of rectangular house is  138.684 [tex]m^{2}[/tex].

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Answer: C. [tex]y=2(x+4z)[/tex]

Step-by-step explanation:

[tex]m=\frac{0-8z}{-4z-0}=2\\\\\therefore y=2x+8z=2(x+4z)[/tex]

The value of s is 17.

What is the Pythagorean theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given

AB = 5, BD = 15

We have to find AD.

By applying the Pythagorean Theorem, we get

AB² + BD² = AD²

5² +15² = AD²

AD² = 289

AD = 17

Hence, the value of s is 17.

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The value of c in the equation A is 7 and the value of d in the equation B is 5

The first equation is

[tex]\sqrt{448x^c}=8x^3 \sqrt{7x}[/tex]

Move the term 8x^3 inside the square root

[tex]\sqrt{448x^c}=\sqrt{7x(8x^3)^2}[/tex]

Multiply the terms in the equation

[tex]\sqrt{448x^c}=\sqrt{448x^7}[/tex]

Here the both terms are equal. Therefore the value of x^c and the x^7 will be equal.

Then the value of c = 7

Part 2

The second equation is

[tex]\sqrt[3]{576x^d}=4x\sqrt[3]{9x^2}[/tex]

Move the term 4x inside the square root

[tex]\sqrt[3]{576x^d}=\sqrt[3]{9x^2(4x)^3}[/tex]

Multiply the terms in the equation

[tex]\sqrt[3]{576x^d}=\sqrt[3]{576x^3}[/tex]

Here the both terms are equal. Therefore the value of x^d and the x^5 will be equal

Then the value of d = 5

Therefore, the value of c = 7 and the value of d = 5

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