Gwen has a home-based business making and selling scented soaps. She intially spent $96 to purchase soap-making equipment, and the materials for each kilogram of soap cost $9. Gwen sells the soap for $25 per kilogram. Eventually, she will sell enough soap to cover the cost of the equipment. How much soap will that be? What will be Gwen's total sales and costs be?

The radius of the sphere is 2.82 cm. Then the volume of the sphere will be 94.05 cubic cm.

Let r be the radius of the sphere. Then the volume of the sphere will be given as,

V = 4/3 πr³ cubic units

The surface area of the sphere is 100 square cm. Then the radius of the sphere is given as,

100 = 4πr²

r = 2.82 cm

Then the volume of the sphere is given as,

V = 4/3 x π x 2.82³

V = 1.33 x 3.14 x 22.465

V = 94.05 cubic cm

The volume of the sphere will be 94.05 cubic cm.

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Where may you be going with this?

To calculate marginal utility, you need to determine the additional utility that a consumer derives from consuming an additional unit of a good or service. This involves finding the difference in total utility before and after consuming the additional unit.

Marginal utility is the additional utility (or satisfaction) that a consumer derives from consuming an additional unit of a good or service. To calculate marginal utility, you can follow these steps:

1. Determine the total utility that a consumer derives from consuming a certain amount of a good or service.

2. Increase the amount consumed by one unit.

3. Determine the new total utility that the consumer derives from consuming the additional unit.

4. Subtract the initial total utility from the new total utility to obtain the marginal utility of the additional unit.

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Answer:

1/4

Step-by-step explanation:

400 divided by 1600 = [tex]\frac{400}{1600}[/tex]

We simplify by 400, and get the answer

1/4

Answer:

0.25 or 1/4

Step-by-step explanation:

1600/400

1600 cant go into 400 so you start with zero, add a decimal next to your zero, and carry down a 1. That then becomes 1600/4000 divide that and drop the decimal to equal 0.25.

The sum of the given temperature measures as required is; -9°C.

It follows from the task content that the sum of the given temperature measures is to be determined.

Since the given temperatures are; -10°C; 24 °C; -12°C; 8°C; -1 °C.

Therefore, the sum of the temperatures can be determined as follows;

-10°C + 24 °C + -12°C + 8°C + -1 °C

= 9°C.

Ultimately, the sum of the given temperatures is; 9°C.

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Answer:

Check below under ‘explanation’

Step-by-step explanation:

5 Units up means every point will move 5 units in the upward direction along the y- axis. Therefore the x- coordinates of every point will remain the same and only their y-coordinates will change:

Q’ = [tex](-8, -4)[/tex]

R’ = [tex](-2, -4)[/tex]

S’ = [tex](-2, 4)[/tex]

T’ = [tex](-8, 4)[/tex]

If 1 gallon equals 4 quarts then Lorraine can fill total 8 jars.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars.

First, we need to convert the 2.5 gallons of tomatoes to quarts.

As, 1 gallon = 4 quarts then

2.5 gallons = 2.5 x 4 = 10 quarts.

Now, number of quarts per jar

= 10 quarts / 1.25 quarts/jar

= 8 jars.

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Answer: 89 mm^2; Option 1

Step-by-step explanation: Solve the area of the largest rectangle by multiplying 7 and 8. That equals 56. Then do 4 times six to get the area of the medium rectangle and thats 24. Do the same thing with the small square and you get nine. Add them up to get 89.

Answer: 36

Step-by-step explanation:

g divided by 18 equals 2; g = 36 gifts.

The correct option is (3).

The fundamental ideas in number theory, measurement, and calculation are frequently referred to as "arithmetic" (which is derived from the Greek word "arithmos," "number"). (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

As per the given data:

A community toy drive for holidays was organized my Max.

Each family has to donate a total of 2 gifts.

Total number of families were equal to 18.

Let's assume the total number of gifts from all the families is g.

For finding the equation to find the total number of gifts given by all the families:

g = Gifts given by each family × Number of families

g = 18 × 2

∴ g divided by 18 equals 2; g = 36 gifts.

Hence, g divided by 18 equals 2; g = 36 gifts.

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Maria uses a coordinate grid to display the following mathematical equation = 8√ 5 (5 + 2√5)

Mathematical expression is defined. A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like add, subtract, multiplying, divisions, exponentiation, and other as-yet-unlearned operations and functions.

Mathematical operators like addition, negation, multiplication, and division are used to create expressions in writing. The mathematical equivalent of an English phrase is a correctly arranged set of mathematical characters that expresses a coherent idea.

Here, Points are,

⇒ (1, 3) (5, 7) (5, 5) (8, 9) (8, 3 ) (1, 3)

Clearly, It make pentagon.

And, Area of pentagon = 1/4 √5 (5 + 2√5) a²

Here, The side of pentagon = √ (7 - 3)² + (5 - 1)²

                                          = √4² + 4²

                                          = √32

                                          = 4√2

Thus, Area of figure = 1/4 √5 (5 + 2√5) a²

                              = 1/4 √5 (5 + 2√5) (4√2)²

                              = 8√ 5 (5 + 2√5)

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Answer:Maria uses a coordinate grid to display the following mathematical equation = 8√ 5 (5 + 2√5)

The term "mathematical expression"

Mathematical expression is defined. A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like add, subtract, multiplying, divisions, exponentiation, and other as-yet-unlearned operations and functions.

How should a mathematical expression be written?

Mathematical operators like addition, negation, multiplication, and division are used to create expressions in writing. The mathematical equivalent of an English phrase is a correctly arranged set of mathematical characters that expresses a coherent idea.

Here, Points are,

⇒ (1, 3) (5, 7) (5, 5) (8, 9) (8, 3 ) (1, 3)

Clearly, It make pentagon.

And, Area of pentagon = 1/4 √5 (5 + 2√5) a²

Here, The side of pentagon = √ (7 - 3)² + (5 - 1)²

                                         = √4² + 4²

                                         = √32

                                         = 4√2

Thus, Area of figure = 1/4 √5 (5 + 2√5) a²

                             = 1/4 √5 (5 + 2√5) (4√2)²

                             = 8√ 5 (5 + 2√5)

Step-by-step explanation:

Marcus is 30 years younger than his mother. Marcus' mother's current age is 35 years old.

To find Marcus' mother's current age, we need to use a system of equations.

Let:

x = Marcus' current age

y = his mother's current age.

We can write two equations based on the information given:

x = y - 30 (Marcus is 30 years younger than his mother)
x + 5 = 1/4(y + 5) (In 5 years, Marcus' age will be 1/4 of his mother's age)

Now we can substitute the first equation into the second equation and solve for y:

y - 30 + 5 = 1/4(y + 5)
y - 25 = 1/4y + 5/4
(3/4) y = 105/4
y = 105/3 = 35

So Marcus' mother's current age is 35 years old.

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There is No solution the system of Equation have.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Slope of Red line = Rise/ Run = 2/3

Slope of Blue line = Rise/ Run = 4/6 = 2/3

As, the two lines have the same slope and hence must be parallel, there are only two options: either they are separate lines, in which case there are no solutions, or they are the same exact line, in which case there are an endless number of solutions.

There are no answers since the two lines must be different since they are parallel and share the same slope but have separate y-intercepts.

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Answer:

the angles of the triangle are 45 degrees, 60 degrees, and 75 degrees, and they are in the ratio of 3 : 4 : 5.

Step-by-step explanation:

Let's denote the angles of the triangle as 3x, 4x, and 5x, where x is a constant.

Since the sum of the angles of a triangle is 180 degrees, we can write the following equation:

3x + 4x + 5x = 180

Simplifying this equation, we get:

12x = 180

Dividing both sides by 12, we get:

x = 15

Therefore, the angles of the triangle are:

3x = 3(15) = 45 degrees

4x = 4(15) = 60 degrees

5x = 5(15) = 75 degrees

So the angles of the triangle are 45 degrees, 60 degrees, and 75 degrees, and they are in the ratio of 3 : 4 : 5.

The Tracking Signal in Week 3 is -1.8.

The Tracking Signal in Week 3 can be calculated by using the following formula:

Tracking Signal = (Sum of Forecast Errors) / (Mean Absolute Deviation)

First, we need to calculate the forecast errors for each week:

Week 1 Forecast Error = Actual Demand - Forecast = 50 - 49 = 1
Week 2 Forecast Error = Actual Demand - Forecast = 54 - 56 = -2
Week 3 Forecast Error = Actual Demand - Forecast = 58 - 60 = -2

Next, we need to calculate the Mean Absolute Deviation (MAD):

MAD = (|1| + |-2| + |-2|) / 3 = (1 + 2 + 2) / 3 = 5 / 3 = 1.67

Finally, we can calculate the Tracking Signal:

Tracking Signal = (1 + -2 + -2) / 1.67 = -3 / 1.67 = -1.8

Therefore, the Tracking Signal in Week 3 is -1.8.

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The slopes for the given pairs of points are:

To find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the formula:

slope = (y2 - y1) / (x2 - x1)

Using this formula for each pair of points, we get:

(19, 3), (20, 3)

slope = (3 - 3) / (20 - 19) = 0/1 = 0

(3,0), (-11, -15)

slope = (-15 - 0) / (-11 - 3) = -15 / -14 = 15/14

(19,-2), (-11, 10)

slope = (10 - (-2)) / (-11 - 19) = 12 / (-30) = -2/5

(6, -10), (-15, 15)

slope = (15 - (-10)) / (-15 - 6) = 25 / (-21) = -25/21

(12,-18), (-15, -18)

slope = (-18 - (-18)) / (-15 - 12) = 0 / (-27) = 0

(3,-20), (5, 8)

slope = (8 - (-20)) / (5 - 3) = 28 / 2 = 14

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The table shows the number of pounds, x, of coffee ordered and the total price, y, in dollars, of each order. X 5 6 7 10 y $35 $42 $49 $70 Which best represents the units for the rate of change (rise over run) in the table? a.dollars. b.dollars per pound. c.pounds b.pounds per dollar

To find the units for the rate of change (rise over run), we need to determine the change in y (rise) divided by the change in x (run) for any two points in the table.

Let's choose the first and last points in the table, (5, $35) and (10, $70), respectively. The change in y is $70 - $35 = $35, and the change in x is 10 - 5 = 5. So the rate of change (rise over run) is:

rise/run = $35/5 = $7

Therefore, the best representation for the units of the rate of change is dollars per pound, as the rate of change indicates how much the price changes for every pound of coffee ordered. So the answer is (b) dollars per pound.

Answer: To find the height of the flagpole, we can use the fact that the angles of depression and elevation are complementary angles, meaning that they add up to 90°.

Let's call the height of the flagpole "h". Then, we have:

h - 6 = h * tan(4°) (the height difference between Javier and the bottom of the flagpole)

and

h = 6 + h * tan(25°) (the height of the top of the flagpole as seen by Javier).

By substituting the first equation into the second, we can find h:

h = 6 + h * tan(25°)

h = 6 + h / tan(65°)

h * tan(65°) = 6 + h

h * tan(65°) - h = 6

h = 6 / (tan(65°) - 1)

Using a calculator, we find that h = approximately 43.3 feet. Rounding to the nearest foot, the height of the flagpole is 43 feet.

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients and factoring is the process of breaking down a polynomial into simpler units

A polynomial is an expression consisting of variables and coefficients, which are combined using only addition, subtraction, and multiplication. For example, 3x^2 + 2x - 1 is a polynomial, where x is the variable, 3 and 2 are coefficients, and ^2 and ^1 are exponents.

Factoring is the process of breaking down a polynomial into simpler units, which can be multiplied together to obtain the original polynomial. The simplest units are usually linear expressions, which have the form ax + b, where a and b are coefficients. For example, the polynomial 3x^2 + 2x - 1 can be factored into (3x - 1)(x + 1) by identifying two linear expressions that when multiplied together produce the original polynomial.

Factoring is an important tool in algebra, as it can help to simplify expressions, solve equations, and identify the roots of a polynomial.

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By the analysis of histogram , 40% percent of the cars was less than 20 years old or more than 40 years old.

The histogram may be seen here. Each column lists the age range at the bottom and the number of automobiles in that age group on the left.

The number of vehicles in the first two columns from the left (age 0-9 and 10-19) and the last two columns (age > 40) must be added together to determine the percentage of vehicles with less than 20 years or more than 40 years of age (age 40-49 and 50-59).

The total number of requested vehicles is equal to 8 that is (3 + 2 + 0 + 3).

The total number of automobiles must now be determined (by adding the cars in each column): 3 + 2 + 8 + 4 + 0 + 3 = 20

The ratio of the number of automobiles of the specified age to the total number of cars must then be calculated and converted into a percentage.

[tex]\frac{8}{20}[/tex][tex]= 0.40 = 40%[/tex]

40% percent of the cars was less than 20 years old or more than 40 years old.

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Charlie reads [tex]2\frac{1}{7}[/tex]  pages per minute.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Charlie reads [tex]1\frac{3}{7}[/tex] pages every [tex]\frac{2}{3}[/tex] minute.

Therefore, His unit rate can be obtained by dividing the number of pages by the amount of time which is,

= [tex]\frac{1\frac{3}{7}}{\frac{2}{3}}[/tex] pages per minute.

= (10/7)×(3/2) pages per minute.

= 30/14 pages per minute.

= 15/7 pages per minute.

= [tex]2\frac{1}{7}[/tex] pages per minute.

Q. Charlie reads quickly he reads [tex]1\frac{3}{7}[/tex] pages every [tex]\frac{2}{3}[/tex] minute, His unit rate of page per minute would be?

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Answer: (Give brainliest)
a = 4.5
type of segment = Angle Bisector
property = property of XT/WY = XY/WZ

Step-by-step explanation:

The radius of the circle is 7 centimeter.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We have to find the radius r of the circle when area is 153.9 square centimeter.

A=πr²

153.9=3.14r²

Divide both sides by 3.14

153.9/3.14=r²

49.01=r²

Take square root on both sides

r=7

Hence, the radius of the circle is 7 centimeter.

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(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the non-homogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the no non-homogeneous part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

(c) y'' + 2y = −8x + 14

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

is 8x + (7/2)

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Answer:

He will need 6/5 cans of paint.

The answer could also be written as 1 1/5 cans of paint or 1.2 cans of paint.

Step-by-step explanation:

Since 2/5 filled 1/3 of the room, he will need 3 times that amount.

2/5 * 3/1 = 6/5

Answer:

30 degrees.

Step-by-step explanation:

Angles must add up to 180 so,

180 - 150 = 30.

Answer:=3

Step-by-step explanation:  For 2x-5y=3 substitute

Answer:

8

Step-by-step explanation:

0+3+6+9+11+13+14 = 56

56/7 = 8

a(x) = b(x) * (3x² - 10x + 21) + (8x - 8)

To divide the polynomial a(x) by b(x), we can use long division as follows:

    3x - 6

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

x² + 2 | 3x² - 4x² + x

- (3x³ + 0x²)

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

-4x² + x

- (-4x² - 8)

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

8x - 8

Therefore, the quotient is 3x - 6, and the remainder is 8x - 8.

a(x) = b(x) * (3x - 6) + (8x - 8)

   -2 | 3 -4  1  0

      |    -6 20 -42

      |-------------

      | 3 -10 21 -42

The numbers on the bottom row represent the coefficients of the quotient, which are 3, -10, 21. The last number on the bottom row, -42, is the remainder. Therefore, the quotient is:

3x² - 10x + 21

8x - 8

a(x) = b(x) * (3x² - 10x + 21) + (8x - 8)

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Answer: 2

Step-by-step explanation:

List all the factors:

14:

1 x 14

2 x 7

46:

1 x 46

2 x 23

Two is the only greatest number that can go into both 46 and 14.