Two UNO students want to start a business selling slushies at the Gene Leahey Mall during the summer. They will have an initial cost of $500 to buy equipment and an additional $1.25 cost for each slushie they sell. They plan to charge $3.50 for each slushie. Let C(x) represent the cost (in dollars) associated with starting and running the business and R(x) represent the revenue (in dollars) earned from sales. Let × represent the number of slushies sold
a. Write a linear function for cost.
C(x)
Write a linear function for revenue.
R(x)=


c. Find C(50). Show your work.
• Write C(50) as an (x, y) coordinate point. ——
• Write a sentence that explains the meaning of the point in the context of the problem.


D. Find R(50).
Represent R(50) as an (x, y) coordinate point. ——-
Write a sentence that explains the meaning of the point in the context of the problem?


e. If the students sell 50 slushies, do they make a profit? Use mathematical work to help explain your answer. Complete the sentence below.

If the students sell 50 slushies. do they make—— a profit? Because——

F. How many slushies do the students need to sell to break even? Use complete sentences to explain your problem solving strategy and your conclusion.


G. How many slushies do the students have to sell to make a profit of $1250? Use complete sentences to explain your problem solving strategy and your conclusion.

When we divide fractions, we multiply the first fraction by the second fraction's reciprocal.

[tex]5\div \dfrac{7}{10}[/tex]

⇒ Multiply by the reciprocal of 7/10:

[tex]= 5\times \dfrac{10}{7}[/tex]

[tex]= \dfrac{50}{7}[/tex]

⇒ If you would like, you can change this into a mixed number fraction. The whole number value from 50/7 is 7. 7 times 7 is 49, which is 1 less than 50. 1 is the numerator and 7 is the whole number:

[tex]= 7\dfrac{1}{7}[/tex]

[tex]\dfrac{50}{7}[/tex] or [tex]7\dfrac{1}{7}[/tex]

The extra amount that the store would have to pay for buying 2 hardcover and 4 paperback books instead of her original plan is $1.51

The paper back books have a discount of 25%

hence we what would be paid for in such category would be 1 - 25% charge = 75 %

price of hardcover = 17.95

price of paperback = 9.95 dollars

Isa bought 2 hardcover and 4 paper back

we are to find the cost of these items

2 x 17.95 + (4 x 9.95 x 75%)

= 35.9 + 29.85

= 65.75

We have to find the cost of the initial plan of  2 hardcover and 3 paperback books.

2 x 17.95 + 3 x 9.95 x 0.75

35.9 + 22.3875

= 58.29

This is less than 59 dollars, she would have to pay the shipping fee.

58.29 +  $5.95

= 64.23

The extra amount that she has had to pay for going with  2 hardcover and 4 paperback books is:

65.75 - 64.23

= 1.51 dollars

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Hence, the solution is [tex]-11[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

[tex]5(2x - 1) - 11x[/tex]

When [tex]x=6[/tex]

[tex]5(2x-1)-11x=5(2(6)-1)-11(6)\\=5(12-1)-66\\=5(11)-66\\=55-66\\=-11[/tex]

Hence, the solution is [tex]-11[/tex].

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The equation of the line with y - intercept (0, 6) is [tex]y = -\frac{3}{2}x + 6[/tex].

What is tangent?

The straight line that "just touches" the curve at a given point is referred to as the tangent line to a plane curve in geometry. It was defined by Leibniz as the path connecting two points on a curve that are infinitely close together.

Given:

Graph is a parabola tangent to the x-axis at (4,0) with y-intercept 6.

That is there are two points (4, 0) and (0, 6).

From these two points we have to find the slope of the line.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{0-6}{4-0} = -\frac{6}{4} = -\frac{3}{2}[/tex]

Now to use point slope form of the line.

[tex]y-y_1 = m(x-x_1)\\ y - 6 = -\frac{3}{2}(x-0)\\ y - 6 = -\frac{3}{2}x\\ y = -\frac{3}{2}x + 6[/tex]

Hence, the equation of line is, [tex]y = -\frac{3}{2}x + 6[/tex].

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Answer: The answer is y=10.

Step-by-step explanation:

4y + 10 = -10 + 6y First subtract 4y from both sides.

10 = -10 + 2y Then, add 10 to both sides.

20 = 2y Finally, divide both sides by 2.

y = 10.

The amount of carbon dioxide will you prevent from entering the atmosphere in one year is 280028 lb

We are given 1.37 pounds of carbon dioxide per kWh

Using a 100-watt light bulb daily for 8 hours, for a year, the amount of carbon dioxide produced will be:

100 × 1.37 × 8 ×365 = 400040 lb

Using a 30-watt CFL bulb for 8hrs/ day for a year, the amount of carbon dioxide produced will be:

30× 1.37 × 8 × 365 = 120012 lb

Therefore, carbon dioxide prevented:

= 400040-120012

= 280028 lb

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Answer:

B. y > 4x + 2

Step-by-step explanation:

The area of the graph above the dotted line is shaded; therefore, this inequality is greater than. The dotted line's slope is 4, hence x is multiplied by 4, and its y-intercept is at 2, hence + 2 on the right side.

As per the question, the solution to the equation f(x) = a(x-h)2+k is y = 3(x+5)2 -1.

Equations are mathematical expressions with two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be similar to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a simple fundamental equation.

As per the given values mentioned in the question,

a=3, b=30, c=74.

To fix this issue, employ the Vertex Formula,

(-b/(2a)) , f(-b/(2a))

-b/(2a)

= -(30)/(2 × 3)

h = -5.

f(-b/(2a))

= 3(-5)² + 30(-5) + 74

k = 75 +-150 +74

k = -1.

Vertex, V = (h,k)

V = (-5,-1).

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The solution to the inequality r - 6 > −11 will be r > -5.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Based on the information, the solution to the inequality r - 6 > −11 will be solved thus:

r - 6 > −11

Collect the like terms

r > - 11 + 6

r > -5

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Answer:

8.35

A company orders 25 boxed lunches from a deli for $208.75

Given:

[tex]25\\208.75[/tex]

We need to find the cost.

Therefore, we need to work on the numbers we are given:

Therefore, the unit cost is 8.35

well, the decrease is really 30000 - 24500 = 5500.

now, if we take the 30000 to be the 100%, what is 5500 off of it in percentage?

[tex]\begin{array}{ccll} a&b\\ \cline{1-2} 30000 & 100\\ 5500& x \end{array} \implies \cfrac{30000}{5500}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 60 }{ 11 } ~~=~~ \cfrac{ 100 }{ x }\implies 60x=1100\implies x=\cfrac{1100}{60}\implies x=\cfrac{55}{3}\implies x=18\frac{1}{3}[/tex]

The wire used for the triangular pendant can have a cost more than 664.65 USD and less than 791.25 USD.

In this problem we find the case of a triangle, in which the length of two sides are known and we need to determine the range of costs associated to the set of all possible triangles. This can be derived by the geometric system described in the image attached below. The minimum and the maximum costs of the pendant:

θ = 0°

l = 10.5 cm - 2.5 cm

l = 8 cm

s = 10.5 cm + 8 cm + 2.5 cm

s = 21 cm

C = (31.65 USD / cm) · (21 cm)

C = 664.65 USD

θ = 180°

l = 10.5 cm + 2.5 cm

l = 13 cm

s = 10.5 cm + 2.5 cm + 12.5 cm

s = 25 cm

C = (31.65 USD / cm) · (25 cm)

C = 791.25 USD

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The predicted number of coffee sales, in hundreds of dollars, for an average daily temperature of 32 degrees is of:

63.34.

The definition of the line of best fit in this problem is given as follows:

y = -0.68x + 85.1.

The variables in the context of this problem are defined as follows:

Hence, for an average daily temperature of 32 degrees, the estimate of the number of coffee sales is given as follows:

y = -0.68(32) + 85.1 = 63.34 thousand dollars.

The problem is incomplete and is given by the image at the end of the answer.

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Answer:

A.

Step-by-step explanation:

the symbol means "congruent".

that means that both shapes have the same angles and the custodian same side lengths (even if the shape is turned in sine way, to you can reorient in a way, so that it will cover the other shape 1:1).

the only triangle with the same measurements everywhere is A. triangle EFG.

B and C (RST and XYZ) are similar triangles with ABC. the angles are the same, and all side lengths have the same scaling factor to the other shape.

D (KLM) is nothing at all to ABC.

Answer: 1001000

Step-by-step explanation:

IF A= 65

   H=72

   BINARY OF H= 72 = 1001000

The table of values that could be used to graph g(x), a reflection of f(x) across the x-axis is table (c)

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

f(x) = One-third(6)x

When this statement is represented as an equation, we have the following representation

f(x)= 1/3(6)ˣ

The transformation is given as

A reflection of f(x) across the x-axis

This means that

g(x) = -f(x)

So, we have

g(x) = -1/3(6)ˣ

What this means is that the values of f(x) are negated to get g(x)

The table that represents this is table (c)

Hence, the table of values is table (c)

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Answer: C

Step-by-step explanation:

Answer:

$4.84 per pound

Step-by-step explanation:

divide 12.10 by 2.5 and you get 4.84, which is the price per pound

Answer:

12.1 × 2.5 = 30.25

Step-by-step explanation:

12.1 × 2.5

12.1 has 1 decimal place

2.5 has 1 decimal place

Therefore, the answer has 2 decimal places

= 30.25

Answer:

A peace sign has one line of symmetry.

The one line is up and down in the center.

Hope this helps! :D

Step-by-step explanation:

The discount percentage offered on the new video game as of a sale is 75%.

For the stated question-

The listed price on the video game = $46.

price paid exclusive of tax = $34.50.

Let 'x' be the percentage discount of the listed price.

Then,

x% of 46 = 34.50

x = 34.50 x 100 / 46

x = 75%

Thus, the discount percentage offered on the new video game as of a sale is 75%.

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The evaluated expression of 24 / b + 8 when b = 9 is [tex]10\frac{2}{3}[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) .

In other words, an expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

Therefore, let's evaluate 24 / b + 8 when b = 9

Hence,

[tex]\frac{24}{9}+8 = \frac{24+ 72}{9}=\frac{96}{9} = 10\frac{6}{9}=10\frac{2}{3}[/tex]

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If the population grows 3% every year, then each year's population is 103% of the previous year's population.  This gives us the exponential function:    

        [tex]f(x) = 17000 (1.03)^x[/tex]

17000 for the current population, 1.03 growth factor for the 103%, raised to the x power because we'll need 103% of 103% of 103% and so on until we multiply by 103% for the correct number of years.

[tex]f(10) = 17000(1.03)^{10} \approx 22846.578448850072648[/tex]

Following standard math rounding this would round to 22,847 people.  

If you argue that last 0.57844 of a person really round up, you could argue that this is really 22,846 people.

Answer: See the attachment

Step-by-step explanation: You would use the formula y=mx+b and since b is the y-intercept you would plug that into the equation and then plug in 3/4 as m resulting in

y=3/4x -1 then you just graph it!

Place a point on -1 in the y axis, (0,-1) then go up three units up and four units right, (4,2)

The amount you have after 18 months is $ 1143.96 .

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

[tex]A=P {(1 +\frac{r}{n})^{nt} }[/tex]

Given:

P = 1000 , r in decimal  = 0.09 ,

n = 12 ,  t = 1.5 ( 18 months = one and a half years).

Substituting the values into the formula:

A = 1000 ( 1 + 0.09/ 12 ) ^[12 ( 1.5 )]          

  ≈ 1000 ( 1.143960 )          

  = 1143.960

Rounding to the nearest cent, we get $ 1143.96 .

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Answer:

t = 60

t/4+5=20

Step 1:

multiply both sides of equation by 4 to separate t from the fraction t/4.

t + 20 = 80

Step 2:

Subtract 20 from both sides of the equation ( you have to put constant values on the same side)

t= 80 - 20

Step 3:

Do the math

80-20=60 so t=60

Step-by-step explanation:

hope this helps! please give brainiest ^^^

Answer:

D x = 3 y = 4

(3.4)

Step-by-step explanation:

See below

[tex]\begin{array}{ccll} books&\$\\ \cline{1-2} 12 & 8\\ 3& x \end{array} \implies \cfrac{12}{3}~~=~~\cfrac{8}{x} \\\\\\ 4 ~~=~~ \cfrac{ 8 }{ x }\implies 4x=8\implies x=\cfrac{8}{4}\implies x=2[/tex]

Answer:

2$

Step-by-step explanation:

If 12 paperback books could be purchased for 8$,

We need to divide by 4 on each side to find the answer.

Therefore, 3 paperback books costs 2$.

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Supplementary angles are angles that have a sum of 180 degrees. They are formed on a straight line.

Looking at the given diagram, we can notice how angle SUV and SUT are supplementary angles. We know this because they form the straight line, VT.

We are given angle SUT, which is 58 degrees.

Because angles SUV and SUT have a sum of 180 degrees, we can solve for angle SUV by subtracting 58 from 180:

180 - 58 = 122

Therefore, angle SUV is 122 degrees.

122 degrees

Answer:

Angle SUV = 180 - 58

= 122° (adjacent angles on a straight line)