A company produces and sells solar panels for $520. The company's daily profit, P(x), can be modeled by the function P(x) = −6x2 + 180x + 1,000, where x is the number of $5 price increases for each solar panel. Use the graph to answer the questions. Graph of function p of x equals negative 6 x squared plus 180 x plus 1,000. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 1000), increases to the vertex at about (15, 2350), and decreases through about (35, 0).

The Commutative Property of Addition is the mathematical principle at play here. we can see that  [tex]2 + 2 = 4[/tex]  and [tex]4 + 4 = 8[/tex]  , and this is due to the Commutative and Associative Properties of Addition.

The math property at work here is the Commutative Property of Addition. This property states that the order of the numbers being added does not affect the sum. In other words, a + b = b + a.

So, in the case of   [tex]2 + 2 = 4[/tex] and  [tex]4 + 4 = 8[/tex]  , we can apply the Commutative Property of Addition to rearrange the numbers being added:

[tex]2 + 2 = 4[/tex]

[tex]4 + 4 = 4 + (2 + 2)[/tex]

Then, we can use the Associative Property of Addition, which states that the grouping of the numbers being added does not affect the sum. In other words, ([tex]a + b) + c = a + (b + c).[/tex]

Applying this property to  [tex]4 + (2 + 2)[/tex] , we get:

[tex]4 + (2 + 2) = (4 + 2) + 2 = 6 + 2 = 8[/tex]

Therefore, we can see that  [tex]2 + 2 = 4[/tex]  and [tex]4 + 4 = 8[/tex]  , and this is due to the Commutative and Associative Properties of Addition.

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The value of the unknown sides and angles are;

<B = 65 degrees

b = 27

c= 13

In the triangle, Using the SOHCAHTOA rule,

such that

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have that;

sin C = c/30

sin 25 = c/30

find the value and cross multiply, we get;

c = 12. 67

< B = 180 - sum of angle A and C

<B = 180 - 115

subtract the values

<B = 65 degrees

The value of side b

sin B = b/30

sin 65 = b/30

b = 27. 19

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To find the average rate of change of the function f(x) = x² - 4x + 1 from x=3 to x = 5, we need to find the difference in f(x) between these two values and divide by the difference in x:

f(5) - f(3) / (5 - 3)

= (5² - 4(5) + 1) - (3² - 4(3) + 1) / 2

= (25 - 20 + 1) - (9 - 12 + 1) / 2

= (6) / 2

= 3

Therefore, the average rate of change of f(x) from x=3 to x=5 is 3.

Step-by-step explanation:

Given a interval x=a to x=b, the average rate of change is equal to

[tex] \frac{f(b) - f(a)}{b - a} [/tex]

where [a,b] is the interval.

Here

a is 3

b is 5 so

[tex] \frac{f(5) - f(3)}{5 - 3} [/tex]

Using the function

[tex]f(5) = 25 - 20 + 1 = 6[/tex]

[tex]f(3) = 9 - 12 + 1 = - 2[/tex]

So

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

The average rate of change of f from x=3 to x=5 is 4

The WETHIC score of 79 into a z-score is 0.33.

A WETHIC score of 62 into a z-score is 0.80.

The proportion of workers that will have a WETHIC score that is below 79 is 63%.

The proportion of workers that will have a WETHIC score that is below 62 is 21%.

1) Z score = (79-74)/15 = 0.33 , it means score is 0.33 standard deviations above the mean

2) Z score = (62-74)/15 = -0.80 , it means score is 0.80 standard deviations below the mean

3) P(X<79)

= P(Z<0.33)

= 0.6293

d) P(X<62)

= P(Z<-0.80)

= 0.2119

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The answer is 140m squared

Answer:

(fog)(x) = 7x + 9.

Step-by-step explanation:

To find (fog)(x), we need to first find the composition of f and g, which is given by f(g(x)).

So, we substitute g(x) into f(x) and simplify:

f(g(x)) = f(7x + 8)

= (7x + 8) + 1 (using the definition of f(x))

= 7x + 9

Therefore, (fog)(x) = 7x + 9.

Using sine and cosine rule, the length of fence is 19.84 feet and the number of packets to cover the garden is approximately 48

To find the value of of the length of the fence, we can either use sine rule or cosine rule.

Since we have two sides and an angle, we sine rule first

a/sin A = b / sin B

[tex]\frac{33}{sin 104} = \frac{22}{sin B} \\sin B = 0.6469\\B = 40.31^0[/tex]

Using this, we can find the value of angle C

A + B + C = 180 degrees

Reason: Sum of angles in a triangle is equal to 180 degrees

104 + 40.31 + C = 180

C = 35.69 degrees

We can proceed to use cosine rule to find the length of the fence.

[tex]c^2 = a^2 + b^2 -2(a)(b)cosC\\c^2 = 33^2 + 22^2 - 2(33)(22)cos35.69\\c^2 = 393.71\\c = 19.84 ft[/tex]

Part B

Since one packet will cover 9ft², we need to know the total area of the field to determine the number of packets required.

Using heron's formula;

[tex]s = \frac{a + b + c}{2} \\s = \frac{33 + 22 + 29.84}{2} \\s = 42.42\\[/tex]

The area of the field is

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}\\A = \sqrt{42.42(42.42-33)(42.42-22)(42.42-19.84}\\A = 429.24ft^{2}[/tex]

The number of packets will be

x = 429.24 / 9

x = 47.69≅48 packets

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If f(x) is an odd function then f'(x) is an even function, a=7 and b=5.

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X.

According to our question-

dy/dx = f'(x) = limΔx→0f(x+Δx)−f(x)Δx lim Δ x → 0 ⁡

Hence, If f(x) is an odd function then f'(x) is an even function, a=7 and b=5.

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The value of x= 4.

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question-

cos(60)= x/8

x=1/2*8

x=4

Hence, The value of x= 4.

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Nathaniel hikes 6 2/5 kilometers on each of the second and third days of his hiking trip.

If Nathaniel hikes a total of 15 4/5 kilometers on a three-day hiking trip and he hikes 3 kilometers on the first day, then he must hike the remaining distance on the second and third days.

To find out how much Nathaniel hikes on the second and third days, we can start by subtracting the distance he hikes on the first day from the total distance he hikes:

15 4/5 - 3 = 12 4/5 kilometers

Since Nathaniel hikes the same distance on the second and third days, we can divide the remaining distance by 2 to find out how much he hikes on each of those days:

12 4/5 ÷ 2 = 6 2/5 kilometers

Therefore, Nathaniel hikes 6 2/5 kilometers on each of the second and third days of his hiking trip.

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We want to copy the original triangle using only two of its sides and the included angle. To do this, we'll create a new triangle with the same side lengths and angle measures as the original triangle.

To copy a triangle using two of its sides and the included angle, follow these steps:

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Answer: a

Step-by-step explanation:

Answer:

-6x + 6y = 6 (Equation 1)

-6x + 3y = -12 (Equation 2)

We can use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.

In this case, we can start by multiplying Equation 2 by 2 to eliminate the x variable:

-6x + 6y = 6 (Equation 1)

-12x + 6y = -24 (Equation 2 multiplied by 2)

Now we can subtract Equation 1 from Equation 2:

-12x + 6y = -24 (Equation 2 multiplied by 2)

-(-6x + 6y = 6) (Equation 1, with the opposite sign)

-6x = -30

Simplifying this expression, we get:

x = 5

Now we can substitute this value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:

-6x + 6y = 6

-6(5) + 6y = 6

-30 + 6y = 6

6y = 36

y = 6

Therefore, the solution to the system of equations is x = 5 and y = 6, or (5, 6) in coordinate form.

Step-by-step explanation:

Answer:

6/20 and 9/30

Step-by-step explanation:

the coordinates of M"A"T"H" are M"(1,8), A"(6,2), T"(5,4), and H"(3,4).

How to find?

The composition r x-axis ° T(7,5) first reflects the quadrilateral MATH about the x-axis and then translates it 7 units to the right and 5 units up.

To find the image of M(-6,-3) after reflection about the x-axis, we flip the sign of the y-coordinate to get M'(-6,3). Then, we translate M' 7 units to the right and 5 units up to get the coordinates of M":

M" = T(7,5) ∘ M' = (7 + (-6), 5 + 3) = (1, 8)

Similarly, we can find the coordinates of A", T", and H":

A' = (-1, 3) → A" = T(7,5) ∘ R(x-axis) ∘ A' = (7 + (-1), 5 - 3) = (6, 2)

T' = (-2, 1) → T" = T(7,5) ∘ R(x-axis) ∘ T' = (7 + (-2), 5 - 1) = (5, 4)

H' = (-4, 1) → H" = T(7,5) ∘ R(x-axis) ∘ H' = (7 + (-4), 5 - 1) = (3, 4)

Therefore, the coordinates of M"A"T"H" are M"(1,8), A"(6,2), T"(5,4), and H"(3,4).

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The expected number of students who classify the crown shapes as medium is approximately 38.3.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To find the expected number of students who classify the crown shapes as medium, we need to use the assumption that the distributions of responses from the professionals and the students are the same. We can use the row and column totals to calculate the expected counts.

First, let's calculate the marginal totals for the students:

The total number of students is 91.

The total number of students who classified the crown shapes as low is 43.

The total number of students who classified the crown shapes as medium is 39.

The total number of students who classified the crown shapes as high is 9.

Now let's calculate the expected counts for the students who classified the crown shapes as medium:

The total number of classifications for the medium category is 87 (from the table).

The proportion of classifications in the medium category made by the professionals is 48/109.

The expected number of classifications in the medium category made by the students can be calculated as (proportion from professionals) x (total number of student classifications) = (48/109) x 87 = 38.3 (rounded to one decimal place).

Therefore, the expected number of students who classify the crown shapes as medium is approximately 38.3.

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Sue needs to sell 16 rings to make her revenue equal to her expenses

Revenue is the total income generated by a company or organization from its sales or operations. It is the amount of money that a business earns from selling its products or services, or from other sources such as investments or interest on deposits.

Let's assume that Sue sells x rings.

The revenue generated by selling x rings = $6x

The total expenses for selling x rings = $2.50x + $56

To find the number of rings that Sue needs to sell for her revenue to equal her expenses, we need to set the revenue equal to the expenses and solve for x.

6x = 2.5x + 56

Subtracting 2.5x from both sides, we get:

6x - 2.5x = 56

Simplifying the left side, we get:

3.5x = 56

Dividing both sides by 3.5, we get:

x = 16

Therefore, Sue needs to sell 16 rings to make her revenue equal to her expenses.

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Answer:

ти можеш загуглити в інтернеті, і все

The perimeter of the triangle is therefore P= 45 cm.

A triangular prism is a prism composed of two triangular bases and three rectangular sides. It is a pentahedron.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.

We know that the volume of a prism is given by

V = Bh, where B is the area of the base and h is the height of the prism. In this case, we have V = 1950 cm³ and h = 20 cm.

So, we can solve for B:

B = V/h = 1950/20 = 97.5 cm².

The base of the triangular prism is a triangle with height 13 cm, so we have

B = 1/2bh = 1/2(13)(b) = 97.5.

Solving for b, we get b = 2B/h = 2(97.5)/13 = 15 cm.

Since all sides of the triangle are equal, we have b = c = 15 cm.

The perimeter of the triangle is therefore P = 3b = 3c = 3(15) = 45 cm.

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Answer:

[tex]( - 28 \infty )[/tex]

Step-by-step explanation:

We have already found the solution to the inequality, but since we want to represent the solution in interval notation, we have changed it.

hopefully this helps! :)

Answer:

A (-6, -4),(-3,-3)

Step-by-step explanation:

Formula for slope of a line is y2-y1/x2-x1

If you plug each equation in:

-3-(-4)/-3-(-6)=1/3

1/3 is the perpendicular slope of -3

the rounded color remains the original colour:: 9e034e

The color code #9e034e represents a shade of deep pink or magenta. To round this color to the nearest tenth, we need to convert the hexadecimal code to its corresponding RGB values and then round those values.

Converting #9e034e to RGB gives us (158, 3, 78).

Rounding each of these values to the nearest tenth gives us (158, 3, 78), which is the same as the original color. Therefore, the rounded color is still #9e034e.

As for the mention of "A" in the question, it's unclear what context it refers to. If it's related to the color, it might mean that the color is used to represent the letter "A" in a certain context. However,

The question doesn't provide enough information to determine the exact meaning of "A."n summary, the rounded color #9e034e remains the same as the original color, and the mention of "A" in the question is unclear.

Both equations are true when x = 1 and y = 1, so the solution is correct.

What are system of equations ?

A system of equations is a set of two or more equations that are to be solved simultaneously. The equations in the system share common variables, and the solution to the system is a set of values for those variables that satisfy all of the equations in the system.
To solve this system, we need to find the values of x and y that satisfy both equations at the same time. This means that any solution we find must work in both equations simultaneously.

According to the question:
To solve the system:

x + y = 2 ...(1)

x - y = 0 ...(2)

We can add equations (1) and (2) to eliminate y:

(x + y) + (x - y) = 2 + 0

2x = 2

x = 1

Substituting x = 1 into equation (1):

1 + y = 2

y = 1

Therefore, the solution to the system is x = 1 and y = 1. We can check the solution by substituting the values into both equations

x + y = 2

1 + 1 = 2 (true)

x - y = 0

1 - 1 = 0 (true)

Both equations are true when x = 1 and y = 1, so the solution is correct.

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Answer:

Step-by-step explanation:

To find x + 1/x, we need to first find the value of x.

Given, x = 2-√3

To simplify x + 1/x, we need to find the value of 1/x.

1/x = 1/(2-√3)

Multiplying the numerator and denominator by the conjugate of the denominator, we get:

1/x = (2+√3)/(2-√3)(2+√3)

1/x = (2+√3)/(4-3)

1/x = 2+√3

Now, substituting the values of x and 1/x, we get:

x + 1/x = (2-√3) + (2+√3)

x + 1/x = 4

Therefore, the answer is option a) 4.

The population will reach 12000 bacteria after 56.4 minutes and other solutions are listed below

We can use the formula for exponential growth, which is given by:

N = N0 * e^(kt)

where N is the final population, N0 is the initial population, k is the growth rate constant, and t is time.

To find the initial size of the culture, we can use the values given at 15 minutes and 40 minutes:

100 = N0 * e^(15k)

1800 = N0 * e^(40k)

Dividing the second equation by the first, we get:

18 = e^(25k)

Taking the natural logarithm of both sides, we get:

k = ln(18)/25

Solving for k, we get:

k = 0.1156

Substituting this value of k into the first equation, we can solve for N0:

100 = N0 * e^(15 * 0.1156)

N0 = 17.65

Therefore, the initial size of the culture was 17.65 bacteria.

To find the doubling period, we use the fact that the population doubles when t increases by a certain amount, which we'll call T. That is:

N0 * e^(kT) = 2N0

Dividing by N0 and taking the natural logarithm of both sides, we get:

T = ln(2)/k

Solving for T, we get:

T = ln(2)/k ≈ 6.00 minutes

Therefore, the doubling period is approximately 6 minutes.

To find the population after 115 minutes, we can use the formula with the values of N0, k, and t:

N = N0 * e^(kt) = 17.65 * e^(0.1156 * 115) ≈ 10477448.92

Therefore, the population after 115 minutes is approximately 10477448.92 bacteria.

To find when the population reaches 12000, we set N equal to 12000 and solve for t:

12000 = 17.65 * e^(0.1156t)

Dividing by 17.65 and taking the natural logarithm of both sides, we get:

ln(12000/17.65 ) = 0.1156t

Solving for t, we get:

t ≈ 56.42 minutes

Therefore, the population will reach 12000 bacteria after approximately 56.4 minutes.

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The probability that a given person drank between 40 and 45 glasses of water is 13.5%.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number outcomes.

between 40 and 45 glasses of water.

First, we need to standardize the values of 40 and 45 using the z-score formula:

z1 = (40 - 50) / 5 = -2

z2 = (45 - 50) / 5 = -1

Next, we look up the area under the standard normal distribution curve between z = -2 and z = -1. We can use a standard normal distribution table or a calculator to find this area, which is approximately 0.135.

Therefore, the probability that a given person drank between 40 and 45 glasses of water is 13.5%.

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Answer:

they have equal shape calculate the number

Answer:

3√2

Step-by-step explanation:

9 + 9 = 18

square root of 18 is

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Answer:

It's y = 3x + 1 :)