The price p, in dollars, of a certain product
and the quantity x sold obey the demand equation

p= -1/4x + 100 0≤x≤ 400

Suppose that the cost C, in dollars, of producing x units is

C = x^1/2/ 25 +600
(the square root of x over 25)

Assuming that all items produced are sold, find the cost C as a function of the price p.
[Hint: Solve for x in the demand equation and then form the composite function.]

The requried expression of 14 × 14 × 14 × 14 × 14 × 14  using exponents is 14⁶.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

As we know that while multiplying the identical terms the product is equal to the number with the sum of the exponents such as a × a = a¹⁺¹ = a².

Similarly,

14 × 14 × 14 × 14 × 14 × 14 can be written using exponents as, 14⁶

To evaluate this expression, you can use a calculator or simplify it using the laws of exponents.

Thus, the requried expression using exponents is 14⁶.

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Answer:

A. 4

General Formulas and Concepts:

Pre-Algebra

Evaluations

Order of Operations: BPEMDAS

Algebra I

Coordinate Planes

Slope Formula: \(\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}\)

Step-by-step explanation:

Step 1: Define

Identify points.

Point (0, 1)

Point (-1, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m.

Answer:

The answer is A. 4

Step-by-step explanation:

Identify points.

Point (0, 1)

Point (-1, -3)

Simply plug in the 2 coordinates into the slope formula to find slope m.

\(\displaystyle m = \frac{-3 - 1}{-1 - 0}m=−1−0−3−1\)

\(\displaystyle m = \frac{-4}{-1}m=−1−4\)

Answer:

true

Step-by-step explanation:

Answer:

m = 15/4

Step-by-step explanation:

slope (m) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (-5 , -10)

(x₂ , y₂) = (-1 , 5)

Plug in the corresponding numbers to the corresponding variables:

m = (5 - (-10))/(-1 - (-5))

m = (5 + 10)/(-1 + 5)

m = (15)/(4)

m = 15/4 is your answer.

~

Answer:

A).300763=+ 67

b) 704969= +87

c)( - 226981)= -61

Step-by-step explanation:

The values of the cube root iyf the given numbers above will be looked up in a calculator and the estimated value will be returned back.

Going through the numbers

A).for 300763

The value of the cube root = +67

B). For 704969

The value of the cube root = +89

C). For ( - 226981)

The value of the cube root= -61

Answer:

Between 3 and 3.5

Step-by-step explanation:

more than 9 and less than 16. 9 is closer to 10 making it c.

The length of the each side of the square garden of Jessica is found as 10.77 ft.

For the given question,

Jessica is making a square garden in her backyard.

The compost bought is to cover the area of the 116 ft².

The formula for the area is given as;

A = s² , where s is the length of the side of the square.

Put the values.

116 = s²

Taking square root both side.

s = √116

s = 10.77

Thus, the length of the each side of the square garden of Jessica is found as 10.77 ft.

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a) f(12.6) = 0.08(12.6) + 4.02

f(12.6) = 1.008 + 4.02

f(12.6) = 5.028

b) f(-1.09) = 0.08(-1.09) + 4.02

f(-1.09) = -0.0872 + 4.02

f(-1.09) = 4.1072

mount Saved = $2820 (answer). In other words, a 12% discount for a item with original price of $23500 is equal to $2820 (Amount Saved).

Answer:

Step-by-step explanation:

a) 2,937.5

b) 20,562.5

The fraction expression, 1/2 + 2/3 (-6), is simplified as: -7/2.

In order to simplify an expression that contains fractions, ensure you find a common denominator of the fractions involved when adding or subtracting.

Given the fractional expression, 1/2 + 2/3 (-6), simplify as shown in the steps below:

1/2 + 2/3 (-6) [Given]

Multiply:

1/2 + (2 * -6)/3

1/2 + (-12/3)

1/2 + (-4)

1/2 - 4/1

Find the common denominator and subtract

(1 - 8)/2

-7/2

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Answer:

BRAINLY POINTS

Step-by-step explanation:

Answer:

9x/4 + 30 + 5x/4

Step-by-step explanation:

\(9x/4 +30 +5x/5\)

The simplification of the expression (9/4x + 6) - (- 5/4x - 24) will be 3.5x + 30.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The expression is given below.

⇒ (9/4x + 6) - (- 5/4x - 24)

Simplify the expression, then we have

⇒ (9/4x + 6) - (- 5/4x - 24)

⇒ (9/4)x + 6 + (5/4)x + 24

⇒ (14/4)x + 30

⇒ 3.5x + 30

The simplification of the expression (9/4x + 6) - (- 5/4x - 24) will be 3.5x + 30.

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Answer:

Step-by-step explanation:

\( \sf{2(6x - 1) = - 38}\)

Distribute 2 through the parentheses

⇒\( \sf{12x - 2 = - 38}\)

Move constant to right hand side and change it's sign

⇒\( \sf{12x = - 38 + 2}\)

Calculate

⇒\( \sf{12x = - 36}\)

Divide both sides of the equation by 12

⇒\( \sf{ \frac{12x}{12} = \frac{ - 36}{12} }\)

Calculate

⇒\( \sf{x = - 3}\)

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

1.

\(2x^2+16x +30\\\\\mathrm{Factor\:out\:common\:term\:}2:\\\quad 2\left(x^2+8x+15\right)\\\\\mathrm{Factor}\:x^2+8x+15:\\\quad \left(x+3\right)\left(x+5\right)\\\\\\=2\left(x+3\right)\left(x+5\right)\)

2.

\(-4x^2+8x+32\\\\\mathrm{Factor\:out\:common\:term\:}-4:\\\quad -4\left(x^2-2x-8\right)\\\\\mathrm{Factor}\:x^2-2x-8:\\\quad \left(x+2\right)\left(x-4\right)\\\\=-4\left(x+2\right)\left(x-4\right)\)

Answer:

(-1,-3)

Step-by-step explanation:

See the attached worksheet.  First step is to apply the transformation.  Modifiy the x and y points as per the instructions.  The transformed triangle is shown in blue and the coordinates are listed.  As the directions indicate, it is slipped down by 2 and to the left by 3 (y-2 and x-3).

Next, convert the x values so that they are reflected across the y axis.  The table shows that all x values are the negative of their original values.  The reflected triangle is shown in red.

The new point Z is (-1,-3).

Compute the speed of the car:

\(\dfrac{2\pi\,\rm ft}{1\,\rm rev} \cdot \dfrac{13\,\rm rev}{1\,\rm s} \cdot \dfrac{1\,\rm mi}{5280\,\rm ft} \cdot \dfrac{3600\,\rm s}{1\,\rm h} = \dfrac{195\pi}{11} \dfrac{\rm mi}{\rm h} \approx 55.6919 \dfrac{\rm mi}{\rm h}\)

So after 1 hour, Sal will have driven about 56 mi.

The area of the triangle AOB is 9√3 square units

The triangle AOB is an equilateral triangle with the following parameters:

Side length, x = 6

Angle, y = 60

The area of the triangle is then calculated using:

Area = 0.5 * x^2 * sin(y)

So, we have:

Area = 0.5 * 6^2 * sin(60)

Evaluate

Area = 18 * 0.5√3

Evaluate the product

Area = 9√3

Hence, the area of the triangle AOB is 9√3 square units

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The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

Math

Step-by-step explanation:

12

Answer:

0.875

Step-by-step explanation:

7/8

0.875

Answer:

0.434 seconds

Step-by-step explanation:

Distance = 60 feets 6 inches

Speed of baseball = 95mph

Time taken : distance / speed

6 inches = 0.5 feets

60 feet 6 inches = 60.5 feets

Convert 60 feet 6 inches to miles

1 mile = 5280 feets

x = 60.5 feets

5280x = 60.5

x = 60.5 / 5280

x = 0.0114583 miles

Hence,

60.5 feets = 0.0114583 miles

Hence,

Time taken = 0.0114583 miles / 95 mph

Time taken = 0.0001206 hour

Converting to seconds :

0.0001206 * 3600

= 0.4342105 seconds

0.434 seconds

The time Jodie have left to match the record of Mandy is 15.11 seconds

Jodie:

= 40.25 seconds

Time spent on the rope = 12.84 seconds

Total time spent = 40.25 seconds + 12.84 seconds

= 53.09 seconds

Total time she have left to match the record = Mandy's obstacle course - Total time spent

= 68.2 seconds - 53.09 seconds

= 15.11 seconds

Therefore, the time Jodie have left to match the record of Mandy is 15.11 seconds

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Answer:

quadrant IV

Step-by-step explanation:

In the image, these are where each quadrant is and labelled. If you plot ( 3,-4) on the grid, it will end up in quadrant IV.

(a) Product of disjoint cycles is α = (1 3 4 5 2)(6)(7 8), (b) Product of transpositions is β = (1 2 7 3)(4 8 6 5) is even, (c) αβ = (1 4 5)(2 7 3)(6)(8) and the reverse order of the transpositions is β^(-1) = (3 7 2 1)(5 6 8 4).

(a) To express α as a product of disjoint cycles, we observe the cycles by tracing the numbers in α. Starting with 1, we see that α(1) = 3, α(3) = 4, α(4) = 5, α(5) = 2, α(2) = 1, α(6) = 6, α(7) = 8, and α(8) = 7. From this, we can write α as a product of disjoint cycles: α = (1 3 4 5 2)(6)(7 8).

(b) To express β as a product of transpositions, we consider the pairs of numbers that are swapped by β. We have β(1) = 2, β(2) = 7, β(7) = 3, β(3) = 1, β(4) = 8, β(8) = 6, β(6) = 5, and β(5) = 4. Thus, we can write β as a product of transpositions: β = (1 2 7 3)(4 8 6 5).

To determine whether β is even or odd, we count the number of transpositions. In β, we have four transpositions, so β is even.

(c) To compute αβ, we perform the composition of the two permutations. We substitute the values of β into α, starting with 1: α(β(1)) = α(2) = 1. Continuing this process, we find αβ = (1 4 5)(2 7 3)(6)(8).

To find β^(-1), we reverse the order of the transpositions: β^(-1) = (3 7 2 1)(5 6 8 4).

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The graph of the piecewise function is given at the end of the answer. From the graph, and from it's concepts, we have that:

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For this problem, the function has two definitions, as follows:

Both are decreasing linear functions, with the definition opening a space at x = 0, between y = 0 and y = -2, as shown in the graph. The closed interval, due to the equal sign, is at x = 0.

In a graph, the domain and the range are found as follows:

Hence, for the function in this problem, we have that:

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Answer:

A.) -5

Step-by-step explanation:

Slope Formula --->     \(m = \frac{y_2 - y_1}{x_2 - x_1}\)       m = slope

\(m = \frac{2 - (-3)}{-2 - (-1)}\)

Eliminate negatives:

\(m = \frac{2 + 3}{ -2 + 1}\)

Solve:

\(m = \frac{5}{-1}\)

Simplify:

\(m = -5\)

Answer:

Step-by-step explanation:

if it's talking about between the numbers 75 to 97, then it's 22.

It takes Tran approximately 0.1 hours, or 6 minutes time, to travel 3 miles at a speed of 33 miles per hour.

What is the time of travels?

To find the time it takes for Tran to travel 3 miles at a speed of 33 miles per hour, we can use the formula:

time = distance / speed

Substituting the given values, we get:

time = 3 miles / 33 miles per hour

time ≈ 0.0909 hours

Rounding to the nearest tenth, we get:

time ≈ 0.1 hours

Therefore, it takes Tran approximately 0.1 hours, or 6 minutes, to travel 3 miles at a speed of 33 miles per hour.

What is speed of travel?

Speed of travel refers to how fast an object is moving relative to a reference point, usually measured in units of distance per unit of time, such as miles per hour or kilometers per hour.

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True. The equation Ax = 0 gives an explicit description of its solution set.

When A is a matrix and x is a vector, the equation Ax = 0 represents a homogeneous system of linear equations. The solution set of this system consists of all vectors x that satisfy the equation and make the left-hand side equal to zero.

The explicit description of the solution set can be obtained by using techniques such as Gaussian elimination or matrix factorizations. These methods allow you to perform row operations on the augmented matrix [A | 0] to obtain the reduced row echelon form. The reduced row echelon form reveals the structure of the solution set by identifying pivot and free variables.

If there are no free variables (all columns of A are pivot columns), then the solution set consists of only the zero vector, x = 0. In this case, the solution set is a singleton set {0}.

If there are one or more free variables, you can express the solutions in terms of those variables. The free variables introduce parameters that allow for infinitely many solutions. The explicit description of the solution set will involve expressing the dependent variables (those corresponding to pivot columns) in terms of the free variables.

In summary, the equation Ax = 0 gives an explicit description of its solution set, either as the singleton set {0} or as a set of vectors expressed in terms of free variables.

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In given word problem ending time of the play is 10.50 AM.

What is word problem?

 A comprehensive list of math word problems focuses on addition, subtraction, multiplication, division and more specific operations. life scenario. This means that children must be familiar with vocabulary associated with familiar mathematical symbols in order to understand word problems.

Here starting time of play = 9:05 AM

It took 1 hour 45 minutes to end the play. Then ,

=> 9 hour  05 minutes

    1 hour   45 minutes +

=> 10 hour 50 minutes.

Hence ending time of the play is 10.50 AM.

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Answer:

Step-by-step explanation:

The base of the prism is triangle with base of 6 yd and hight of 6 yd.

The hight of the prism is 10 yd.

Therefore, the volume of the prism:

\((\frac12\cdot8\cdot6)\cdot10=240\ yd^3\)