A small business produces soap and lotion gift baskets. Labor, utilities, and other fixed expenses

cost $6,000 a month. Each basket costs $8 to produce and sells for $20. How many baskets does

the company need to sell each month to break even?

•



Define n to be the number of gift baskets the company sells in a month

Cost Equation: C(n)= 6000 + 8n

Revenue Equation: R(n) = 20n

Cost

$

12000

11000-

10000+

9000

8000

7000-

6000

5000

4000+

3000

2000

1000-

C(n)

R(n)

100 200 300

400 500 600 700 800

TE

Answer:

Step-by-step explanation:

You want the discriminant, roots, and graph of the quadratic function ...

 f(x) = 1/2x² -2x +10

The discriminant of the quadratic function

  y = ax² +bx +c

is ...

  d = b² -4ac

The given function has a=1/2, b=-2, c=10, so the discriminant is ...

  d = (-2)² -4(1/2)(10) = 4 -20 = -16

The discriminant of -16 means there will be two distinct complex conjugate roots.

The roots are ...

  x = (-b ±√d)/(2a)

  x = (-(-2) ±√(-16))/(2(1/2)) = 2 ±4i

A graph of the function is attached.

When the skateboard's price, c, and the 7.5% sales tax are included, the simplified expression for the provided expression, c+0.075c, becomes 1.075c.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.

Here,

Given expression,

=c+0.075c

total cost=1.075c

The simplified expression for the given expression c+0.075c will be 1.075c when the skateboard cost c and the sales tax of 7.5% is added.

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Answer:

The intercepts are: (0, 3/7) and (-3/4, 0)

Step-by-step explanation:

If X=0

-4(0) + 7y = 3

7y = 3

Y = 3/7

If Y=0

-4x + 7(0) = 3

-4x = 3

X = -3/4

Answer:

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Find two convenient integer coordinates ( 0,7)  and (5,-3)

slope = (y1-y2) / (x1-x2)  

    it does not matter which point your assign as '1' or '2'

slope = (  7 - - 3 ) / (0-5) =  10 /-5  = -2

The account’s mean daily balance for April will be $105.7.

Mean is the total added values of all the data in a set divided by the number of data in the set.

The account had the following balances;

$501 for 23 days

$2428 for 3 days

$241 for 4 days.

To find the mean; add the total amount and divide by the total number of days

[tex]mean = \frac{501 + 2428 + 241}{23 + 3 + 4}[/tex]

[tex]mean = \frac{3170}{30}[/tex]

mean = $105.7

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Mr. Henderson paid a total of $98.40 for phone service and $79.20 for garbage pickup last year. To find his average cost per month for these two services, we need to divide the total amount he paid by the number of months in a year.

Since there are 12 months in a year, we can divide the total amount Mr. Henderson paid for phone service and garbage pickup by 12 to find his average cost per month. This is calculated as follows:

Average cost per month = (98.40 + 79.20) / 12

Average cost per month = 177.60 / 12

Average cost per month = $14.80

Therefore, Mr. Henderson's average cost per month for phone service and garbage pickup last year was $14.80. This means that, on average, he paid about $14.80 per month for these two services.

The solution for the inequality |r| - 3 > 2 is r < -5 or r > 5.

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

|r| - 3 > 2.

Simplify the inequality,

|r| > 5,

Implies that,

r < -5 or r > 5

Interval notation (-∞, -5) ∪ (5, ∞).

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Answer:

the answer is D. the 3 is simply a scalar multiple so multiply each term by 3

Answer:

D

Step-by-step explanation:

I believe that it's D since all you have to do is multiply 3 by each of the numbers that are supposedly n.

The measure of base angles and vertex angle are 133° and 47° respectively.

What is an isosceles triangle ?

A triangle with two equal-length sides is known as an isosceles triangle (/assliz/). The term "equilateral triangle" can refer to a shape with either exactly two sides that are the same length or at least two sides that are the same length, with the latter definition containing the equilateral triangle as an exception.

Let the vertex angle to be 'x'

So, according to the question, the measure of the base angels in an isosceles triangle is 8 less than 3 times the measure of a vertex angle

    So, Base angles = (3 × vertex angle) - 8

We know that sum of all angles of a triangle is 180° and the base angles of an isosceles triangle are equal.

∴ Base angles + vertex angle = 180°

  (3 × vertex angle) - 8  + x = 180°

  3x - 8 + x = 180°

  4x = 188°

  x = 47°

∴ The vertex angle is 47° and,

Base angles =  (3 × vertex angle) - 8  

                     = 3 × 47 - 8

                     = 141 - 8

                     = 133°

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Graph with their Turning Point is shown with different degree of different degree Equation

Where a graph changes, either from increasing to decreasing, or from decreasing to increasing, is called a turning point.

Factorization Technique

The turning point of the parabola lies exactly at the midway between the (two) x-intercepts of a quadratic function, as shown by the fact that a vertical line of symmetry divides the parabola into two equal half and crosses it. In light of this, we can use a factorisation-based method to locate the solution of a quadratic equation. The process involves five steps.

Step 1: By looking at the coefficient of x2, determine if the graph is a minimum or maximum;

Factorize the supplied quadratic function in Step 2 and set it to Zero;

Step 3: Define the function's antecedents;

Take the midpoint of the pair of roots to find the x-coordinate of the turning point in step 4;

2 turning points

Let f(x)=x³+ax²+bx+c, where the coefficients a, b and c are real numbers. The figure below shows a section of the graph of y=f(x). The curve has two distinct turning points; these are located at A and B, as shown.

But there is come limitations in this case too, a function has to follow certain conditions to have two turning points.

3 turning points

If we get 4 roots of any equation it may be containing 3 turning Points.

With some limitations in this as well.

4 turning points

If we get 5 roots of any quadratic equation it may be containing 4 turning points with some limitations in this as well.

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Answer:

14

Step-by-step explanation:

x+8=? x= 6. i do know it

Answer:

7 cm.

The triangle dimensions are:  50, 27, and 7 cm

Step-by-step explanation:

The three sides of the triangle make up the entire perimeter.  Add each side and set the result equal to 84cm, the perimeter.

(7x+1) + (4x-1) + (14-x) = 84 cm

10x + 14 = 84

10x = 70

 x = 7 cm

Use x=7 to find the three dimensions:

1)  (7x+1) = 50 cm

2)  (4x-1) = 27 cm

3)  (14-x) = 7 cm

Do these add to 84 cm?

 (50+27+7) = 84 cm  YES

The water tank's illustrated prism will stand 8 meters tall.

Prisms are significant polyhedron family members with congruent polygons at the base and top.

A prism's other faces are referred to as its lateral faces. It denotes that a prism's face is not curved.

The cross-section of a prism is constant along its length. The names of the prisms are determined by their cross-sections. The best example of a prism that best represents a real-world object is a metallic nut.

A rectangular prism that best represents a real-world object is a fish aquarium.

According to our question-

The following formula will be used to determine the triangle prism's base's area:

= 1/2 × 4 × 9

= 18m²

The rectangular tank's water will be drained of the following volume:

= (6 × 6) × 4

= 144m³

As a result, the height will be determined as follows:

18 × h = 144

18h = 144

h = 144/18

h = 8m

Hence, The water tank's illustrated prism will stand 8 meters tall.

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The value of b is 20.

What is Pythagorean theorem?

The Pythagoras theorem is a mathematical law that states that the sum of squares of the lengths of the two short sides of the right triangle is equal to the square of the length of the hypotenuse.

According to the given question:

∠S and ∠Q are right angles in RSTQ quadrilateral.

RTS and RTQ are right angled triangles.

Applying Pythagorean theorem on both the triangles

sin 35° = b + 60 / RT ⇒ RT = b + 60 / sin 35°

sin 35° = 4b / RT ⇒ RT = 4b / sin 35°

Since RT is common in both equations

b + 60 / sin 35° = 4b / sin 35°

b + 60 = 4b

3b = 60

b = 20

Hence the value of b is 20

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There are the some features that make highway roads safer for drivers who are driving at higher rates of speed is :(5 correct answers)

1.Median barriers

2.Guard rails

3.Brake away signs

4.Rumble strips

5.Controlled access

Given,

In the question:

What are some features that make highway roads safer for drivers who are driving at higher rates of speed?

Now, According to the question:

There are the some features that make highway roads safer for drivers who are driving at higher rates of speed is :(5 correct answers)

1.Median barriers

2.Guard rails

3.Brake away signs

4.Rumble strips

5.Controlled access

Hence, There are above 5 highway roads safer for drivers.

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Step-by-step explanation:

The answer is in the image above

Answer:        

Step-by-step explanation:

Apply  distributive property.

5i(3+2i)

5i⋅3+5i(2i)

Multiply

3 by 5.15i+5i(2i)

Multiply

5i(2i) .

15i + 10i2

Simplify each term.

Rewrite

i2 as −1.15i+10⋅−1

Multiply

10 by −1.15i−10

Reorder

15i and −10.−10+15i

hope it helps :)

On solving the provided question, we got to know that side length of the square is 8 units.

Four sides that are equally spaced apart make up a square. Around us, a lot of things are rectangular. Equal sides and a 90° interior angle serve as a visual cue to identify a square. A closed square has four sides and exists in two dimensions (2D). A square has an equal number and parallel alignment of its four sides.

A four-sided shape known as a square has sides that are all the same length and angles that are all right angles with a 90 degree angle.

Here,

Area of square = [tex](side)^2[/tex]

64 =  [tex](side)^2[/tex]

[tex]Side = \sqrt{64}[/tex]

Side = 8 units

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Given that WXZ and YXZ are congruent based on side-angle-side congruency, we can prove the theorem that states "A point on the perpendicular bisector of a line segment is equidistant from the segment’s endpoints." This theorem is often referred to as the "Perpendicular Bisector Theorem."

The required details for "Perpendicular Bisector Theorem" in given paragraph

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a line segment, then it is equidistant from the segment's endpoints. This means that if we draw a line through a point that is perpendicular to a line segment, and that line passes through the midpoint of the segment, then the point is equidistant from the endpoints of the segment. In this case, we are given that line L is the perpendicular bisector of segment WY, and that Z is a point on L. We are also told that WXZ and YXZ are congruent based on side-angle-side congruency. Since WXZ and YXZ are congruent, it follows that WX and YX are congruent and that WZ and YZ are congruent. This means that the distances from Z to W and Y are equal, so Z is equidistant from W and Y.

Therefore, we can conclude that Z is a point on the perpendicular bisector of segment WY, and the Perpendicular Bisector Theorem is proved. The answer is C. "A point on the perpendicular bisector of a line segment is equidistant from the segment’s endpoints."

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Answer:

The y-intercept of the given line is 7/9.

Step-by-step explanation:

The y-intercept of a line is the point where the line crosses the y-axis.

So, to find the point where the line crosses the y-axis we must do x=0.

By substituting x=0 in the following equation, we get

=> 9y + 4(0) = 7

=> 9y = 7

=> y = 7/9

Hence, y = 7/9 is the y-intercept of the given line.

Anna will need 1/2 cup of onions in each pot. This is because 2/3 of a cup is equal to 4/6 of a cup, and when divided by 4 pots, the result is 1/2 cup of onions in each pot.

An ingredient is a substance that is used as part of a recipe or product formulation. Ingredients are the components of a mixture that are used to produce a food, beverage, cosmetic, pharmaceutical, or other product. Ingredients can be natural, such as water, spices, and herbs, or man-made, such as preservatives, colorings, and flavorings. The amount and type of each ingredient used in the formulation of a product determines its properties and characteristics.

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Answer: decimal form 20.5

Step-by-step explanation:

Assuming that costs increase linearly with the number of attendees, Patricia needs at least 30 people to attend the forum in order to break even.

Patricia needs 75 attendees to attend the forum in order to make a profit of 337,500.

By dividing the fixed costs by the contribution margin per unit, we are able to determine the break-even threshold in units. Divide the fixed costs by the contribution margin ratio to get the break-even threshold in dollars.

The percentage of the contribution margin to the sales revenue is known as the contribution margin ratio. Prior to the division operation, we add

the profit to the fixed cost in order to reach the goal profit.

Billing rate per participant = 10,000

Hotel charges per participant = 2,500

Contribution per participant = 7,500 (10,000 - 2,500)

225,000 is the fixed fee for the hotel room and amenities.

Break-even point in units = Contribution per unit – Fixed cost

= 30 individuals (225,000 -7,500)

Fixed cost plus profit minus contribution per unit equals break-even point in units with target profit.

Target profit = 337,500

= (225,000 + 337,500) ÷ 7,500

= 75 participants

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Without using the triangle sum theorem, the proof that shows that m∠G + m∠K + m∠GHK = 180° is proved below.

Based on the triangle angle sum theorem, all the interior angles in a triangle will add up to the sum of 180 degrees.

The complete proof that shows that m∠G + m∠K + m∠GHK = 180 degrees is explained below.

Statement                                    Reason                                          

1. GK║HJ                                     1. Given

2. ∠G ≅ ∠IHJ                              2. Corresponding angles theorem

3. ∠K ≅ ∠JHK                             3. Alternate interior ∠s theorem

4. m∠IHK = m∠IHJ + m∠JHK     4. Additive property of angle measure

5. m∠IHK = m∠G + m∠K            5. Substitution

6. m∠IHK + m∠GHK = 180°        6. Angles forming a linear pair sum of 180°

7. m∠G + m∠K + m∠GHK = 180° 7. Substitution

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Answer:

14.56 

Step-by-step explanation:

The total flowers in the garden white or pink is 8/15.

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.

In our garden, there are 2/3 total roses, making the total number of blooms that aren't roses 1/3

4/5 = 2/3 +1/3.

Since 3 is a division of 6, we must multiply by 6 to arrive at the solution.

4 x 6 =24

5 x 6 =30

24/30

Next, we calculate half of 30 and add it to get 3/3.

Then we find 1/2 of 30 and add this to make 3/3

Just like 1/2 of 2 = 1 and 2+1 = 3

30 / 2  = 15

15 + 30 =45

The answer is 24/45

We then reduce this fraction by 3 as 6 + 8 do not divide into 45

24/45 = 8/15

The total flower in the garden is 8/15

The proportion of white or pink flowers in the entire garden is 8/15.

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Answer:

Step-by-step explanation:

12x^2+17x = 5

12x^2+17x-5 = 0

(4x - 1)(3x+5) = 0

Solve (4x-1) and (3x +5)

4x - 1 = 0

4x = 1

x = 1/4

3x + 5 = 0

3x = -5

x = -5/3

x = { 1/4, -5/3 }

The solution: is C(g) = 10 + 15g, C'(g) = 80.

Monthly pricing for utilizing 2 Gigabytes of data at Company C.

Detailed explanation:

Company C's cell phone plan is $10 per month + $15 for every gigabyte of data utilized. Company D's monthly fee is $80 and includes unlimited data.

The monthly cost for using g gigabytes of data at Company C is now: C(g) = 10 + 15g.... (1)

Again, the monthly cost for using g gigabytes of data at Company D will be as follows: C'(g) = 80......... (2) (2)

Statement C(2) = 10 + 15 2 = 40 represents Company C's monthly charges for utilizing 2 Gigabytes of data use, according to equation (1).

Thanks for your question. I had an interesting time solving this.