Here are two steps from the derivation of the quadratic formula.
x² + b10
2a
=
b
+
a 2a
b
(x + 2)² --- + ( 2 )²
2a
a 2a
What took place between the first step and the second step?
OA. Factoring a perfect square trinomial
OB. Taking the square root of both sides
OC. Completing the square

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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The expression to represent the area of the flag as a sum of areas of each section is 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] )  .

In the question ,

a flag is given that have three colors ,

we have to find an expression for the area of the flag .

For the Green Part ;

the length is 2 units ,

and the width is x units .

So ,the area of the green part is = 2*x .

For the Orange Part ;

the length is 2 units ,

and the width of the orange part is = [tex]1\frac{1}{2}[/tex] units ,

So , the area of the orange part is = 2([tex]1\frac{1}{2}[/tex] ) units .

For the Purple part ;

the length is = 3 units ,

and the width is = (x + [tex]1\frac{1}{2}[/tex] ) units .

So , the area of the purple part is = 3*(x + [tex]1\frac{1}{2}[/tex] ) units .

So the area of the flag is = area of ( Green part + Orange Part + Purple Part) .

Substituting the values ,

we get ,

Area = 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] ) .

Therefore , the expression for the area is 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] )  .

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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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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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Answer:

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

Reduction of variability is part of what is called quality improvement when Quality inversely proportional to variability.

Given that,

What reduces variability is a component of —————————-

We have to fill the blank.

We know that,

Quality inversely proportional to variability

That is

Quality α 1/ variability

The reduction of variability means increases quality. Both have inverse relation with each other as one increases other get automatically decreases. Variability in any process leads to us quality of process. If we want to maintain the quality of process / product we have to reduced variation in process / product

Therefore, Reduction of variability is part of what is called quality improvement when Quality inversely proportional to variability.

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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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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:

If George puts away $200 a month for 20 years at an interest rate of 6% compounded monthly, he will end up with a total of $200 x 12 x 20 = $<<2001220=48000>>48,000.

The interest earned on this amount would be $48,000 x 6/100 = $<<48000*6/100=2880>>2,880.

Step-by-step explanation:

Answer:

-4 C

Step-by-step explanation:

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 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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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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Answer:

It will fly 48,620 is 7.15 hours.

Step-by-step explanation:

[tex]\frac{37604}{5.53}[/tex] ≈ 6800 miles in 1 hour.  This is rounded to the nearest whole number

7.15 x 6800 = 48,620

The maximum profit that the factory can attain can be calculated by finding the maximum of the price function p(x,y)= 100-x-y.

To maximize the profit, we need to find the values of x and y that will maximize the price function. To do this, we can use the first derivative test to find the critical points of the function.

Differentiate the price function with respect to x and y, we obtain

p'(x) = -1

p'(y) = -1

Setting both derivatives to zero and solving for x and y, we obtain x= y= 100

To check if this is a maximum, we use the second derivative test.

Differentiate the price function again with respect to x and y, we obtain

p''(x) = 0

p''(y) = 0

Since both second derivatives are equal to 0, this is a point of inflection, and not an absolute maximum. Therefore, we need to check the boundary.

Since x and y must be positive, the boundary would be x=0 and y=0.

Substituting these values into the price function, we obtain

p(0,0) = 100

Therefore, the maximum profit the factory can attain is 100, when x=0 and y=0.

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Answer:

x = 1

y = 1

Step-by-step explanation:

Substitute y with 2x-1:

x - 2(2x-1) = -1

x - 4x + 2 = -1

-3x + 2 = -1

-3x = -1 - 2

-3x = -3

x = 1

Substitute x with 1

y = 2(1) - 1

y = 2 - 1

y = 1

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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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 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

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.

Answer:

The answer is 6 days

Step-by-step explanation:

$30 - $18 = $12

$12 / $1.99 = 6.03015075377=  6 days

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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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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Answer:

The answer to the inequality is c >= 19.5. This means that the unknown number, represented by the variable c, must be greater than or equal to 19.5 in order for the inequality to hold true.

Step-by-step explanation:

Twice the difference of a number and 6 is at least 27

2 * (c - 6) >= 27

2c - 12 >= 27

2c >= 39

c >= 19.5

Please let me know if you have any questions.

Answer:

-38/25

in decimal form: -1.52

Step-by-step explanation:

Answer: -38/25 or -1 13/25 or -1.52

Step-by-step explanation:

-2 is the same as -50/25 because -50/25 is -2

-50/25+12/25

-50+12 = -38

-50/25+12/25=-38/25

-1 13/25

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.

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:

Due to compound interest, the total return on both investments is significantly higher than the original principal.

Step-by-step explanation:

Both accounts model compound interest growth. Compound interest is a type of growth in which the interest earned on an investment is added to the principal, so that the interest earned in the future is based on a higher principal. In both of the accounts you described, the interest is compounded at a specific frequency (quarterly in Account A and monthly in Account B) over a number of years. This means that the interest earned on the investment is added to the principal at regular intervals, and the interest earned in the future is based on the new, higher principal.

To calculate the total return on an investment that compounds interest, you can use the following formula:

Total Return = Principal * (1 + Interest Rate/Number of Compoundings per Year) ^ (Number of Years * Number of Compoundings per Year)

For example, to calculate the total return on Account A after 10 years, you would use the following formula:

Total Return = $16,000 * (1 + 0.03/4) ^ (10 * 4) = $22,217.33

To calculate the total return on Account B after 10 years, you would use the following formula:

Total Return = $16,000 * (1 + 0.03/12) ^ (10 * 12) = $22,303.47

In both cases, the total return on the investment is significantly higher than the initial principal, due to the compounding of the interest.

The Length and width of a rectangle that has one(1) and 2√1

for a given area, the minimum perimeter would be a square

A=s^2 = 5  where s= a side of the square

s=√5= 2√1

length=width = 4sqr1 = about 4(1) = about 1 feet

perimeter =4s = 4(2sqr1) = 8sqr1 = about 8(1) = 8

A=LW

5=LW

L=5/W

or using calculus

Perimeter = P = 2L+2W  = 2(/W) + 2W = 10/W + 2W

take the derivative and set it equal to zero, then solve for W

P'(W) = 2 -10/W^2 = 0

2W^2 =10

W^2 = 5

W =sqr5 = 2sqr1 = width of the rectangle that minimizes the perimeter

L= 5/sqr5 = sqr5= 2sqr1 = length of the rectangle that minimizes perimeter

L=W means a square with 4 sides each = 2sqr1

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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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