Determine the net sales when: operating expenses = $57,750,
gross margin = $56,650, and net loss = 1%.

Answer:

2500

Step-by-step explanation:

Total spectator 9500

Men 6375

Women and children = 9500-6375= 3125

Women X

Children 4X

If women and children = 3125

4x + X = 3125

5x = 3125

Divide both sides by 5

X = 625

Women 625

Children 625x4 = 2500

The term 3x² in the quotient is the result of dividing 3\(x^{4}\) by x²

On dividing 3x^4 by x² we get the following by the long division method

x² | 3x^4 | 3x² --------> quotient

    -(3x^4)

    ______

         0

Thus the quotient is 3x² as mentioned in the question and the remainder is 0. Long division is a method to find out the quotient and remainders on dividing number, algebraic expression by another. As shown above, on the right-hand side we get the quotient and at the bottom, the remainder is obtained.

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Answer:

The flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.

Step-by-step explanation:

We can use the following formula to calculate the flow rate:

Flow rate (mL/hr) = Volume to be infused (mL) / Time of infusion (hr)

First, we need to convert the total volume of 2 liters to mL:

2 liters = 2000 mL

Next, we can plug in the values:

Flow rate = 2000 mL / 16 hours

Flow rate = 125 mL/hr

Therefore, the flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.

Answer: {g,h}={−3,−4}

Step-by-step explanation:

System of Linear Equations entered :

[1]           6g-2h=-10

 [2]           11=h-5g

Equations Simplified or Rearranged

[1]    6g - 2h = -10

  [2]    5g - h = -11

// Solve equation [2] for the variable  h  

  [2]    h = 5g + 11

// Plug this in for variable  h  in equation [1]

  [1]    6g - 2•(5g+11) = -10

  [1]    -4g = 12

// Solve equation [1] for the variable  g  

  [1]    4g = - 12

  [1]    g = - 3

// By now we know this much :

   g = -3

   h = 5g+11

// Use the  g  value to solve for  h  

   h = 5(-3)+11 = -4

and your solution is

{g,h} = {-3,-4}

Answer:

38.5 is the volume

Step-by-step explanation:

3.5x4=14

14x5.5=77

now you divide by two because it's a triangle

Answer: The Union of two sets will be all elements without duplicate elements. So G U H ={apple , orange , banana , grape , duruan ,pear , strawberry}

Step-by-step explanation:

"U" is the union of two sets. The no of values in Union of two sets G , H

is G U H = G + H - (G ∩ H)

To learn more about sets notation,

Answer:

The sum is 7/3.

Step-by-step explanation:

hope that helps

The area of triangle JHK is 4.18 units²

A triangle is a polygon with three sides having three vertices. There are different types of triangle, we have;

The right triangle, the isosceles , equilateral triangle e.t.c.

The area of a figure is the number of unit squares that cover the surface of a closed figure.

The area of a triangle is expressed as;

A = 1/2bh

where b is the base and h is the height.

The base = 2.2

height = 3.8

A = 1/2 × 3.8 × 2.2

A = 8.36/2

A = 4.18 units²

Therefore the area of triangle JHK is 4.18 units²

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The specific value that the mean reading speed of a random sample of second-grade students will exceed cannot be determined solely based on the given information.

The statement mentions a "chance" but does not provide any specific information about the distribution or standard deviation of the reading speeds. Without knowing the variability of the data, it is not possible to determine a precise value that the mean reading speed will exceed.

To estimate the value, we would need additional information such as the standard deviation or a confidence interval. With this information, statistical techniques such as hypothesis testing or confidence intervals could be used to determine the likelihood of the mean reading speed exceeding a particular value.

Therefore, without more information, we cannot determine the exact value that the mean reading speed of a random sample of second-grade students will exceed. The statement implies that there is a possibility, but without additional data or assumptions, it is not possible to provide a specific value.

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Mi use structure ji builds a right rectangular prism with 14-centimeter cubes in the bottom layer with no gaps or overlaps. if there are 8 layers,  The volume of the right rectangular prism is 14 x 14 x 8 = 1,536 cm3.

To get this answer, I first determined the number of cubes in the bottom layer. Since the bottom layer contains 14 cubes, the total length of the base of the prism is 14 cm. The height of the prism is 8 layers, so the total height of the prism is 8 cm. To calculate the volume of a right rectangular prism, you need the base length, the width, and the height. Since all three of these measurements are given, the volume can be calculated by multiplying the base length (14 cm) by the width (14 cm) by the height (8 cm). The result is 1,536 cm3.

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mi use structure ji builds a right rectangular prism with 14-centimeter cubes in the bottom layer with no gaps or overlaps. if there are 8 layers, what is the volume of the right rectangular prism?

Answer: σ: 2.76

Step-by-step explanation:

Count, N: 5

Sum, Σx: 125

Mean, μ: 25

Variance, σ2:  7.6

Steps

look at attached pic for formula

σ^2 = \(\frac{Σ(xi - μ)^{2} }{N}\)

\(\frac{(21 - 25)2 + ... + (29 - 25)2}{5}\)

⇒ \(\frac{38}{5}\)

⇒ 7.6

σ =  \(\sqrt{7.6}\)

⇒   2.756809750418

⇒ or 2.76

The z-score that separates the bottom 86% from the top 14% is 1.08 (option B).

Z-score is the number of standard deviations from the mean value of the reference population.

To find the z-score we can use a z-score table or calculator:

Z-score table can be used to calculate the area under a normal bell curve for a binomial normal distribution.

It shows the area to the left of a given z-score, so we can look for the area closest to 0.86 in the table. The z-score that corresponds to this area is 1.08.

Alternatively, we can use a calculator to find the inverse of the standard normal Cumulative Distribution Function (CDF). The CDF gives the area to the left of a given z-score, so we can use the inverse CDF to find the z-score that corresponds to a given area. In this case, we want the z-score that corresponds to an area of 0.86:
z = invNorm(0.86)

  = 1.08

Therefore, the z-score that separates the bottom 86% from the top 14% is 1.08 (option B).

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x²+ 1 is the minimal polynomial that vanishes at x and so x is a root of x²+ 1.

(a) To show that g = 2x + 1 is a primitive element in F by calculating all powers of 2x + 1,

The order of F = GF (9) is 9 - 1 = 8, which means that the powers of 2x+1 we calculate should repeat themselves exactly eight times.

To find the powers of 2x+1 we will calculate powers of x as follows: x, x², x³, x⁴, x⁵  x⁶, x⁷, x⁸

Now we will use the equation

2x + 1 = 2(x + 5) = 2x + 10,

so the powers of 2x+1 are:

2(x + 5) + 1 = 2x + 10 + 1

= 2x + 11; (2x + 11)²

= 4x^2 + 44x + 121

= x + 4; (2x + 11)³

= (x + 4)(2x + 11)

= 2x^2 + 6x + 44;

(2x + 11)⁴ = (2x² + 6x + 44)(2x + 11)

= x² + 2x + 29; (2x + 11)⁵

= (x² + 2x + 29)(2x + 11)

= 2x³ + 7x² + 24x + 29;

(2x + 11)^6 = (2x^3 + 7x₂ + 24x + 29)(2x + 11)

= 2x⁴ + 4x³+ 7x^2 + 17x + 22; (2x + 11)⁷

= (2x^4 + 4x^3 + 7x^2 + 17x + 22)(2x + 11)

= x^3 + 2x² + 23x + 20; (2x + 11)⁸

= (x³ + 2x^2 + 23x + 20)(2x + 11)

= 2x^3 + 5x² + 26x + 22 = 2(x³ + 2x^2 + 10x + 11) = 2(x + 1)(x² + x + 2)

Therefore, all the powers of 2x+1 are different from one another and so g = 2x + 1 is a primitive element in F.

(b) We want to find the minimal annihilating polynomial of a = x, which is the monic polynomial of least degree with coefficients in Z3 that vanishes at x.

Now, we see that x² + 1 is the minimal polynomial that vanishes at x and so x is a root of x²+ 1.

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Step-by-step explanation:

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations. For example, 3x² − 2xy + c is an algebraic expression. Since taking the square root is the same as raising to the power, is also an algebraic expression.

Step-by-step explanation:

we solve for x

15x-(2/x)>1. /*x

15x^2 -2 > x. /-x

15x^2 -x -2 > 0

Solve the quadratic at zero

15x^2 -x -2=0

using the quadratic formula

x1,2 = [1+-sprt((-1)^2-4(15)(-2))]/2(15)

= [1+- sqrt (121)]/30

= [1+-11]/30

x1= 12/30= 2/5

x2= -10/30= -1/3

therefore this positive parabola is greater than zero or positive when

x< -1/3 and x> 2/5

Answer:

Right 3.5 units

Step-by-step explanation:

Well, the coordinates go (x,y) so just plug it in..

(3.5, 0)

Go across (to the right) 3.5 and up 0, that's it.

Hope this helps :)

Answer:

Create a scatterplot

Step-by-step explanation:

Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology.

He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has 4 children; the 2 oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son Mike Sullivan, III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than 10 books. He owns a travel agency and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where he enjoys gardening.

Michael Sullivan, III has training in mathematics, statistics and economics, with a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series which he writes with his father, Michael Sullivan.

Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series. When not in the classroom or writing, Michael enjoys spending time with his 3 children, Michael, Kevin and Marissa, and playing golf. Now that his 2 sons are getting older, he has the opportunity to do both at the same time!

Product details

Publisher ‏ : ‎ Pearson; 4th edition (8 January 2018)

Language ‏ : ‎ English

Hardcover ‏ : ‎ 1224 pages

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The graph represents the relationship between the number of games downloaded and the total cost in dollars. The ratio of total cost to the number of games downloaded is $2.50 per game.

The given graph shows the relationship between the number of games downloaded and the total cost in dollars of the downloads. It can be observed that when 2 games are downloaded, the total cost is $5.

To determine the ratio of total cost to the number of games downloaded, we divide the total cost by the number of games.

This results in a ratio of $2.50 per game downloaded. Thus, the ratio of total cost (in dollars) to the number of games downloaded is $2.50 per game.

This means that on average, each game downloaded costs $2.50.

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Answer:

-4

Step-by-step explanation:

khan academy

The area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².

The area of the circle is the space occupied by it. It can be given as,

\(A=\pi r^2\)

Here (r) is the radius of the circle.

In this diagram, three concentric circles' rectangle.

The radius of the smallest circle is 3.

\(r_1=3\rm\unit\)

Thus, the area of it is,

\(A=\pi (3)^2\\A=28.27\rm\; unit^2\)

Let suppose the mid-point of the rectangle is D. Here, OB is the diagonal of the rectangle in which,

\(OD=BD\)  

The radius of the yellow ring's outer face from point O is,

\(r_3=OD+BD\\r_3=OD+OD\\r_3=2OD\\\)

OD is the radius of the small circle, which is 3 units long. Thus,

\(r_3=2\times3\\r_3=6\rm\; units\)

The line segment OC is the radius of the white circle from point O. In the triangle COB from the Pythagoras theorem, the radius r₂ of the middle circle is,

\(r_2=\sqrt{r_3^2-r_1^2}\\r_2=\sqrt{6^2-3^2}\\r_2=3\sqrt3\)

Thus, the area of the yellow ring is,

\(A_y=\pi r_3^2-\pi r_2^2\\A_y=\pi (6)^2-\pi (3\sqrt{3})^2\\A_y=28.27\rm\; unit^2\)

The area of white ring is,

\(A_w=\pi r_2^2-\pi r_1^2\\A_w=\pi (3\sqrt{3})^2-\pi (3)^2\\A_w=56.55\rm\; unit^2\)

Hence, the area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².

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The fraction 4 4/5 cannot be represented as whole number

The number is given as:

Number = 4 4/5

The above number is a fraction, where the denominator is a not 1

Fractions that have denominators not 1, and fractions that do not have equal numerator and denominator cannot be represented as whole numbers

This means that:

4 4/5 cannot be represented as whole numbers

Hence, the fraction 4 4/5 cannot be represented as whole number

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To find the average rate of change of a function from x1 to x2, you need to calculate the difference in the function's values at x1 and x2, and divide it by the difference in the x-values. The formula for average rate of change is (f(x2) - f(x1)) / (x2 - x1).

The average rate of change measures the average rate at which a function is changing over a given interval. To calculate it, you subtract the function's values at the starting point (x1) and ending point (x2), and then divide it by the difference in the x-values. This gives you the average rate of change for the interval from x1 to x2.

Example: Let's say we have a function f(x) = 2x + 3. To find the average rate of change from x1 = 1 to x2 = 4, we substitute these values into the formula: (f(4) - f(1)) / (4 - 1). Simplifying, we get (11 - 5) / 3 = 6 / 3 = 2. Therefore, the average rate of change of the function from x1 = 1 to x2 = 4 is 2.

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Therefore, the car's gas mileage is approximately 5.83 miles per gallon.

To calculate the gas mileage, we divide the total number of miles traveled (350 miles) by the total number of gallons of gas consumed (60 gallons).

The gas mileage formula is: Gas mileage = Total miles / Total gallons.

In this case, the car traveled a total of 350 miles and consumed a total of 60 gallons of gas.

Dividing 350 miles by 60 gallons gives us approximately 5.83 miles per gallon.

The gas mileage, measured in miles per gallon (mpg), can be calculated by dividing the total number of miles traveled by the total number of gallons of gas consumed. In this case, the gas mileage would be:

Gas mileage = Total miles / Total gallons

Gas mileage = 350 miles / 60 gallons

Gas mileage ≈ 5.83 miles per gallon

This means that for every gallon of gas consumed, the car can travel approximately 5.83 miles.

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Answer:

1/42

Step-by-step explanation:

Adding a negative is the same as subtracting a positive.

6/7 + (-5/6) =

= 6/7 - 5/6

Now you need a common denominator. The LCD of 6 and 7 is 42.

= 36/42 - 35/42

= 1/42