A new coffee shop projects that its annual profit, p(t), in thousands of dollars, over the first 6 years in business can be
approximated by the function p(t) = 0.3t² +5.5t-8 where t is measured in years.

Answer:

C = 60t + 100

Step-by-step explanation:

our flat fee is 100 dollars, meaning you're charged straight up $100, and then for each hour the electrician works, you're charged another $60

this means that 100 stays constant, while the amount of times you multiply 60 changes based on the amount of hours the electrician works

therefore, our equation will be C = 60t + 100, where C represents the total cost while t represents the hours the electrician works

for our table, we can use the equation we just found to make one

the easiest and most reasonable numbers will be 1, 2, 3, 4, and 5, because it's unreasonable to charge a proportional amount for something such as 1.2948 hours

using the equation, we plug 1, 2, 3, 4, and 5 into C = 60t+100 to find C for t

C = 160, 220, 280, 340, 400

T = 1, 2, 3, 4, 5

The graph of the quadratic equation y = -x² - 1 is on the image at the end.

Here we want to graph the quadratic function:

y = -x² - 1

To do so, we need to find some points on the quadratic equation's graph, we can evaluate the equation in sokme values of x to get that.

if x = 0

y = -0² - 1 = -1

if x = 1

y = -1² - 1 = -2

if x = -1

y = -(-1)² - 1 = -2

And so on.

Above we can see that we have the points (0, -1), (1, -2), and (-1,-2) (you could try to find more points, so the graph will be more exact).

Now just graph all the points that you have and connect them with a parabola. The graph can be seen on the image at the end.

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Answer:

340 CDs

Step-by-step explanation:

To answer this question, we're dealing with three functions for one problem, namely the revenue function, the cost function, and the profit function.

The revenue function is R(q) = pq, where p is the price of a certain good and q is the quantity sold.

The cost function is C(q) = variable cost + fixed cost, where variable costs changes depending on the quantity of goods produced and fixed cost is a one-time cost for the producer (e.g., an investment, rent, etc.).

The profit function is P(q) = R(q) - C(q) and is simply the cost function subtracted from the revenue function.

The "break-even point" is the point at which profit = $0 and the point at which cost = revenue.

From the problem, we see that Jason invested $3349 (once) for his CDs and each disk requires $3.65 for the materials so our cost function is C(q)  = 3.65q + 3349

Furthermore, we see that each disks sells for $13.50, so our revenue function is R(q) = 13.5q

Our profit function then is P(q) = 13.5q - (3.65q + 3349) = 13.5q - 3.65q - 3349 = 9.85q - 3349.

Thus, to find the break-even point, we set profit = 0 and solve for q:

[tex]0=9.85q-3349\\3349=9.85q\\340=q[/tex]

The total area of the quilt is: 112.5 square inches

The six-sided figure is given, and we can deduce the following parameters from the question:

The shape is made of a triangle and a rectangle

The side lengths derived from the question are:

The triangle on top:

base: 5 inches and height: 5.18 inches

The rectangle at the bottom:

Base: 16 inches with a height of 7.5 inches

So, we have the total area of the figure to be

Area of figure = 1/2 * 5 * 6 + 13 * 7.5

Area of figure = 112.5

Based on the parameters, the total area is 112.5 square inches

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The statement is true; Tests are weighed the most when determining a grade.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

Given in the question that:

Grade distribution

Quizzes, 30%

Homework 15%

Test, 30%

Classwork 25%

The total giving 100%.

A particular student scored the following;

87.9% on exams, 77.8% quiz, 90% Home work and 100%  on class participation

Calculating the percentages the student had for each

Exam total = 50 x 0.879 = 43.95% earned

Quiz = 30 x 0.778 = 23.34% earned

Home work = 15x 0.9 = 13.5% earned

Class participation = 5*1 = 5% earned

Total earned = 43.95+ 23.34 + 13.5+ 5 = 85.79%

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The real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.

In mathematics, a polynomial is an expression consisting of variables and coefficients, which are combined using the operations of addition, subtraction, and multiplication. A polynomial can have one or more terms, where each term is the product of a coefficient and one or more variables raised to non-negative integer powers. For example, the polynomial 2x² - 3x + 1 has three terms: 2x², -3x, and 1.

For the given polynomial function, the constant term is -6 and the leading coefficient is 4. Therefore, the possible rational zeroes of the function are of the form p/q, where p is a factor of -6 and q is a factor of 4.

The factors of -6 are ±1, ±2, ±3, and ±6. The factors of 4 are ±1, ±2, and ±4. So the possible rational zeroes are:

±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±3/2

To determine which of these possible rational zeroes are actual zeroes, we can use synthetic division or long division to evaluate the function at each possible zero. Doing so, we find that the actual zeroes of the function are:

x = 1/2, x = 1, x = 3/2, x = 2

Therefore, the real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.

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The value of lim x -> -1- f(x)= -1

The behavior of a function at a specific input is described by its limit, a crucial concept in calculus and analysis.

Hence,

As x approaches -1 from the left, the graph of f(x) leads you to the point (-1, 3), so the limit from the left is 3.

As x approaches -1 from the right, the graph leads to the point (-1, -3), so the limit from the right is -3.

The one-sided limits do not match, so the two-sided limit does not exist.

But f(x) is still defined at x = -1; this is indicated by the point (-1, -1). So f (-1) = -1.

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The graph below is the function f(x)

Find lim x -> -1- f(x)=

Answer: 994 beads

Step-by-step explanation:

Red Beads = 275

Blue Beads = 825 (275 x 3)

825 + 275 = 1100 beads (total)

1100 - 156 = 994 beads

On solving the given system of equations →

Eq { 1 } :  - 3x + y = 11

Eq { 2 } :  4x + 3y = 7

using substitution, we get {x} = -2 and {y} = 5.

In mathematics, a system of equations is a pair of equations which have a common set of solutions.

Given is the system of equations as -

- 3x + y = 11

4x + 3y = 7

The given system of equations is -

- 3x + y = 11

4x + 3y = 7

Now, we can write -

y = 11 + 3x

So -

4x + 3(11 + 3x) = 7

4x + 33 + 9x = 7

16x = - 26

{x} = - 2

Then, we can write -

- 3 x - 2 + y = 11

{y} = 5

Therefore, on solving the given system of equations using substitution, we get {x} = -2 and {y} = 5.

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Answer:

The correct answer is C, 428 feet.

To calculate the elevation of the marked point, we need to interpolate between the two contour lines. The difference in elevation between the two contour lines is 20 feet (440 - 420 = 20). And since the distance between the two contour lines is 0.5 inches, each 0.1 inch increment represents a 4-foot change in elevation (20 feet ÷ 0.5 inches = 40 feet per inch ÷ 10 = 4 feet per 0.1 inch).

Since the marked point is 0.2 inches from the 420-foot contour, the elevation of the marked point can be calculated by adding 8 feet (4 feet x 0.2 inches) to the 420-foot contour line: 420 + 8 = 428 feet.

We can state that the y-intercept is (0,4) and the x-intercept is after answering the given question (2,0).

The intersection point in mathematics is where the line's slope intersects the y-axis. a point where a line or curve's y-axis crosses it. [tex]Y = mx+c,[/tex]

The emphasis in the intercept form of the equation is on the line's slope (m) and y-intercept (b). The slope is m and the y-intercept is b when an equation has the intercept form (y=mx+b).

It is also possible to rewrite some equations so that they appear to be slope intercepts. For example, the slope and y-intercept are both modified to 1 if y=x is rewritten as [tex]y=1x+0.[/tex]

Slope intercept equation,

[tex]y = -2x + 4[/tex]

[tex]y = -2(0) + 4[/tex]

X-intercept is (2,0).

Therefore, The equation for the straight line is used to demonstrate this, where m denotes the slope and c the y-intercept.

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To the nearest tenth, 13.55% of people aged 29 have some form of cardiac disease.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

The function for the estimation of the percentage of heart disease is,

[tex]P =\dfrac{ 120}{1+372e^{-0.133x}}[/tex]

The percentage will be calculated as:-

[tex]P =\dfrac{ 120}{1+372e^{-0.133x}}[/tex]

[tex]P =\dfrac{ 120}{1+372e^{-0.133\times 29}}[/tex]

P= 120 / ( 1 +7.85)

P = 13.55%

Therefore, 13.55% of adults aged 29 have a heart condition, to the closest tenth.

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The equation that describes the graphed function is given as follows:

A. y = f(-x + 3).

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function for this problem is given as follows:

[tex]y = \sqrt{x}[/tex]

The function was reflected over the y-axis, hence it is given as follows:

[tex]y = \sqrt{-x}[/tex]

Then it was moved 3 units right, hence the definition is given as follows:

[tex]y = \sqrt{-(x - 3)}[/tex]

[tex]y = \sqrt{-x + 3}[/tex]

Hence:

y = f(-x + 3), as x was replaced by -x + 3.

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Answer:

Step-by-step explanation:

-0.2x+3 / 2 = -0.6 =>

-0.2x = -(3/2) - 0.6 => (facotorize out -1)

x = ((3/2)-0.6)/0.2 =>

x = 4.5

Answer: A lot

Step-by-step explanation:

In this exercise we have to use the knowledge of excel to explain some functions that can be used, as:

In excel cell a division formula can be written as: =(A4+B4+C4+D4+E4)/5

If you track your daily earnings in an Excel spreadsheet, you can use the same spreadsheet to estimate your forecasted earnings for any period of time. You can use Excel's AVERAGE function to find out your average daily income. Multiply your average daily sales by the number of days specified to estimate how much profit you could make over time.

In mathematics, the average of a list of data represents the central value of the set of data. Mathematically defined as the ratio of the sum of all data and the number of items in the list. In statistics, the mean of a particular set of numerical data is also called the mean. For example, the average of 2, 3, 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the center value of 2, 3, and 4. So the meaning of average is to find the average of a group of numbers.

mean = sum of values ​​/ number of values

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Answer:

12 and 5

Step-by-step explanation:

12+5=17

12x5=60

Answer:

Step-by-step explanation:

5 12 step by step

The volume of a sphere is 1,436.03 cubic cm. Thus, the correct option is E.

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

V = 4/3 πr³ cubic units

Sand is contained within a spherical with a 14 centimeters diameter. Roberto emptied the sphere's contents of sand.

The radius of the sphere is given as,

r = d/2

r = 14 / 2

r = 7 cm

Then the volume of the sphere is given as,

V = (4/3) x π x (7)³

V = 1.33 x 3.14 x 343

V = 1,436.03

The volume of a sphere is 1,436.03 cubic cm. Thus, the correct option is E.

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The correct options are given below.

A. 287.2 cm³

B. 861.6 cm³

C. 1,148.8 cm³

D. 9,190.6 cm³

E. 1,436.03 cm³

Answer:

5,144,079

Step-by-step explanation:

[tex]\displaystyle CI=\mu\pm z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\CI_{99.5\%}=\mu\pm2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1=2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1\sqrt{n}=226.8056\\\\\sqrt{n}=2268.056\\\\n=5144078.01914\\\\n=5144079[/tex]

Thus, you would need a sample size of 5,144,079 to be 99.5% confident that the true population mean is ±0.1 away from it with a population standard deviation of 80.8 (aka. our margin of error).

The length of side f is 12.0 inches

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

In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°

The sum of angles in a triangle is 180 degrees

Using the above as a guide, we have the following:

E = 180 - 72 - 61

E = 47

Using the law of sines, we have

f/sin(F) = e/sin(E)

substitute the known values in the above equation, so, we have the following representation

f/sin(72) = 9.2/sin(47)

So, we have

f = sin(72) * 9.2/sin(47)

Evaluate

f = 12.0

Hence, the length is 12.0 inches

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The value of x is 21.4.

What is right-angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x. The measure of the angle opposite to height is 31°.

The sine of an angle is the ratio of height to the hypotenuse.

Therefore,

sin 31° = height/hypotenuse

sin 31° = 11/x

Multiply x with both sides:

x sin 31° = 11

Divide sin 31° with both sides:

x = 11/ sin 31°

x = 21.35

x ≈ 21.4 units

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The value of 'w' in the solution of the following system of linear equations is -[tex]\frac{1}{6}[/tex]

we can solve for a variable say 'v' then put the value of 'v' in the other equations and solve them for the value of 'w'

5v + 4w = 1

5v = 1 - 4w

v = [tex]\frac{1-4w}{5}[/tex]

now, when we put the value of 'v' in the second equation, we get:

3([tex]\frac{1-4w}{5}[/tex] ) - 6w = 2

3([tex]\frac{1-4w}{5}[/tex] ) = 2 + 6w

[tex]\frac{3-12w}{5}[/tex] = 2 + 6w

3 - 12w = 10 + 30w

-42w = 7

w = [tex]\frac{7}{-42}[/tex]

w = -[tex]\frac{1}{6}[/tex]

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Answer:

14 cm

Step-by-step explanation:

The formula for circumference of a circle is 2πr, where r is the radius. In this problem, the circumference would be 2π * 7cm = 14 cm

The solution to the inequality are the region in the shaded area

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

y < 3x+3

3x-y ≤ 4

Represent properly

y < 3x + 3

3x - y ≤ 4

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0.2, 2)

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Angle b is equal to 35°, angle a and angle e are each equal to 145°

An angle is formed when two lines intersect at a point. Types of angles are acute angle, obtuse angle and right angle. Vertical opposite angles are always congruent to each other. The sum of angles along a straight line is supplementary (add up to 180 degrees)

From the diagram:

b = 35° (vertical opposite angles are congruent)

a + b = 180° (sum of angles along a straight line)

a + 35 = 180

a = 145°

a = e = 145° (vertical opposite angles are congruent)

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The ratio of the areas of the quadrilaterals is 1:2. Option A

Let's assume that the two similar quadrilaterals have side lengths of x and 2x, respectively. The ratio of their perimeters is then 2x + 2x + 2x + 2x = 8x : 2 * (2x + 2x + 2x + 2x) = 4 * 8x = 32x. The ratio of the perimeters is 2:4, so we can write the equation:

8x/32x = 2/4

Solving for x, we find that x = 4.

So the ratio of the areas of the two similar quadrilaterals is (x^2)/(2x)^2 = (4^2)/(2 * 4^2) = 16/32 = 1/2.

Therefore, the ratio of the areas of the two similar quadrilaterals is 1:2.

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The zeros of the given polynomial function are 3

Zero of a polynomial are numerical values at which the polynomial will equal zero. In other words, zeros of a polynomial are numerical values of the variable which give zero when we plug into the polynomial.

For example, for a polynomial p(x) the zeros are the value of 'x' which satisfies p(x) = 0. This means by identifying the x-intercepts, we may determine the polynomial's zeros.

In the case of a graph, we can determine the zeros of a polynomial by observing the points at which the graph line will cut the x-axis. In simple words, we can say that the x-coordinates of the points where the graph meets the x-axis are the zeros of the polynomial.  

Here we have a graph

In the given graph the polynomial function meets the x-axis three times at three different points.

Therefore,

The zeros of the given polynomial function are 3

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Answer:

To determine the balance in the Allowance for Doubtful Accounts on December 31, we first need to estimate the bad debts based on the credit sales.

Bad debts = 2% of credit sales = 2% * $400,000 = $8,000

The balance in the Allowance for Doubtful Accounts would then be equal to the estimated bad debts, which is $8,000.

Therefore, the Accounts Receivable and the Allowance for Doubtful Accounts would appear on the December 31 balance sheet as follows:

Current Assets:

Accounts receivable $120,000

Less: Allowance for doubtful accounts $8,000

Net accounts receivable $112,000

The battery will last 2.73 hours when it is fully charged

The unit rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, the unit rate is one quantity divided by the other quantity

Since Cheryl's phone battery is 55% charged and it will last for another 1.5 hours. Thus, the rate will be:

rate =   1.5 hours/55% = 3/110 hour per %

When it is fully charged, that is 100%. Thus, it will take:

Time for 100% = (3/110) * 100% = 2 8/11 hours = 2.73 hours

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Answer: a) ZY = 27

b) WY = 27

c) RX = 27

d) mWRZ = 90 degrees

e) mXYZ = 90 degrees

f) mZWY = 90 degrees

Step-by-step explanation: