Kensington was selling Girl Scout cookies and a customer offered her a deal. The customer would place three $1 bills, one $5 bill and one $10 bill in a bag. Kensington would reach into the bag and take one bill from the bag and get paid that instead of the $5 it would cost for one box of Girl Scout cookies. Should she take the deal? Or should she insist on getting the regular cost of $5?

The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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The degree solutions of the equation are 51.82 degrees and 128.17 degrees

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

cos² (x) + cos (x) − 1 = 0

Let y = cos(x)

So, we have

y² + y - 1 = 0

When solved graphically, we have

y = ±0.618

This means that

cos(x) = ±0.618

Take the arccos of both sides

x = cos-1(±0.618)

Evaluate

x = 51.82 degrees and 128.17 degrees

Hence, the angles are 51.82 degrees and 128.17 degrees

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The number of different frames you can create, if There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from, is 12.

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from,

Calculate the total number of frames, we can create as shown below,

The number of frames = different styles available for blue color × shades of blue

The number of frames = 4 × 3

The number of frames = 12

Thus, the number of frames you can create is 12.

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The factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

To determine the factors of the polynomial x^3 - 12x^2 - 2x + 24 by grouping, we can follow these steps:

Step 1: Group the terms in pairs. In this case, we can pair the first two terms and the last two terms:

(x^3 - 12x^2) + (-2x + 24)

Step 2: Factor out the greatest common factor from each pair. From the first pair, we can factor out x^2, and from the second pair, we can factor out -2:

x^2(x - 12) - 2(x - 12)

Step 3: Notice that we now have a common binomial factor of (x - 12) in both terms. Factor out this common binomial factor:

(x - 12)(x^2 - 2)

Therefore, the factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

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Answer:

-64

Step-by-step explanation:

-9(5-2) -111÷3

PEMDAS says parentheses first

-9(3) -111÷3

Then multiply and divide from left to right

-27 -111÷3

-27 -37

Now add and subtract from left to right

-64

Answer:

The Answer Will Be D

Step-by-step explanation:
The fuel economy of a car is modeled by the function f(s) = -0.009s² +0.699s +12 where s represents the speed of the car, measured in miles per hour.We need to find the fuel economy of the car when it travels at an average of 20 miles an hour.f(20) = -0.009(20)² +0.699(20) +12f(20) = -0.009(400) +13.98f(20) = 9.6The fuel economy of the car when it travels at an average of 20 miles an hour is 9.6 miles per gallon.Therefore, the answer is option D. 22.38 miles per gallon.

The company's March expected cash receipts from current and prior credit sales are $97,660.

The cash receipts represent the receipts from cash sales and the cash collections from credit sales.

Each period's cash receipts depend on the company's cash collection history based on estimated collections from credit customers.

Cash sales percent = 30% of sales

Credit sales percent = 70% of sales (100% - 30%)

Collections on credit:

The month of sales = 25%

The second month = 55%

The third month = 15%

                               January    February    March

Project Sales:        $74,000    $99,000  $109,000

Credit Sales:         $51,800     $69,300   $76,300

Cash receipts:

Cash sales (30%) $22,200     $29,700   $32,700

Collections on credit:

1st month (25%)      12,950         17,325     19,075

2nd month (55%)                       28,490     38,115

3rd month (15%)                                           7,770

Total cash receipts in March                 $97,660

Thus, the company's March expected cash receipts from current and prior credit sales are $97,660.

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The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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Among the given options, 90 degrees (option A) is not a solution to the equation sin(2θ) = 1. The equation sin(2θ) = 1 represents the values of θ for which the sine of twice the angle is equal to 1. To determine which option is not a solution, we need to evaluate each choice.

A) 90 degrees: If we substitute θ = 90 degrees into the equation sin(2θ) = 1, we get sin(180 degrees) = 1. However, sin(180 degrees) is actually 0, not 1. Therefore, 90 degrees is not a solution to the equation sin(2θ) = 1.

B) 45 degrees: Substituting θ = 45 degrees gives sin(90 degrees) = 1, which is true. Therefore, 45 degrees is a solution to the equation sin(2θ) = 1.

C) 225 degrees: When we substitute θ = 225 degrees, we get sin(450 degrees) = 1. However, sin(450 degrees) is also 0, not 1. Thus, 225 degrees is not a solution to sin(2θ) = 1.

D) -135 degrees: Similarly, substituting θ = -135 degrees gives sin(-270 degrees) = 1. However, sin(-270 degrees) is 0, not 1. Hence, -135 degrees is not a solution to the equation sin(2θ) = 1.

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Answer:

  660 in²

Step-by-step explanation:

The area of this figure looks like it is best computed by subtracting the areas of the empty corners from the area of the "bounding box."

The overall dimensions of the figure are ...

  horizontal: 31 in + 10 in = 41 in

  vertical: 13 in + 7 in = 20 in

Then the area of the bounding box is ...

  A = LW = (41 in)(20 in) = 820 in²

__

The area of the upper left empty space is ...

  A = (6 in)(5 in) = 30 in²

The area of the lower right empty space is ...

  A = (10 in)(13 in) = 130 in²

Then the area of the figure is ...

  total shaded area = (820 -30 -130) in² = 660 in²

__

Additional comment

The formula for the area of a rectangle is ...

  A = LW . . . . . . where L is the length, and W is the width

Solution:

Draw the whole rectangle.

Refer to image~

Subtract the area of the unshaded region from the rectangle's area.

The length οf each side οf the dilated rectangle is 63 cm.

Dilatiοn is a transfοrmatiοn that changes the size οf the οbject withοut affecting its shape. It invοlves stretching οr shrinking an οbject unifοrmly alοng all its dimensiοns by a fixed scale factοr.

(a) Tο find the length οf each side οf the dilated image, we need tο multiply the οriginal dimensiοns by the scale factοr οf 3.5.

The length οf the dilated rectangle wοuld be:

Length = 18 cm x 3.5 = 63 cm

The width οf the dilated rectangle wοuld be:

Width = 8 cm x 3.5 = 28 cm

Therefοre, the length οf each side οf the dilated rectangle is 63 cm fοr the length and 28 cm fοr the width.

(b) Tο draw the new image A'B'D'C, we can use the fοllοwing steps:

Draw a rectangle with a length οf 63 cm and a width οf 28 cm.

Draw a vertical line thrοugh the midpοint οf the rectangle, dividing it intο twο equal halves.

Label the midpοint οf the line as O, which is the center οf dilatiοn.

Draw lines cοnnecting each cοrner οf the οriginal rectangle tο the center οf dilatiοn.

Extend each line tο dοuble its length, passing thrοugh the center οf dilatiοn and ending at A', B', C', and D'.

Cοnnect the endpοints οf each line tο fοrm the dilated rectangle A'B'D'C.

The resulting image shοuld lοοk like a larger rectangle that is centered arοund the midpοint O and is 3.5 times larger than the οriginal rectangle.

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Therefore, the starting value of the house was £724,492.37 (rounded to two decimal places).

A fraction is a mathematical expression that represents a part of a whole. It is expressed as two numbers separated by a line or a slash, with the number on top called the numerator and the number on the bottom called the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. Fractions can be used to represent quantities such as lengths, distances, time, weight, and many other things in the real world. They are an important concept in mathematics and are used in a wide range of applications, from basic arithmetic to advanced calculus and beyond.

Here,

Let's denote the starting value of the house by x.

After the first year, the value increased by 9%, so the value became 1.09x.

After the second year, the new value decreased by 4%, so the value became 0.96(1.09x) = 1.0464x.

We know that this final value is £758,640, so we can set up an equation and solve for x:

1.0464x = 758640

x = 758640 / 1.0464

x ≈ 724492.37

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there are 120 different ways a sequence of 10 coin flips can consist of exactly 3 heads and the rest tails.

To solve this problem, we can use the formula for combinations. The number of ways to choose k items from a set of n items is given by the formula n choose k, which is written as C(n,k) or sometimes as nCk.

In this case, we want to choose 3 heads from a set of 10 coin flips. The number of ways to do this is C(10,3) = 120.

Once we have chosen the 3 heads, the remaining 7 flips must all be tails. There is only one way to arrange 7 tails, since they are all the same.

Therefore, the total number of sequences that consist of exactly 3 heads and the rest tails is 120.

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The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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Answer:

It is 2/3 or 0.666666667

Answer:

the answer is is 2/3

Step-by-step explanation:

hope this helped

\(\text{First term,}~ a = 8\\\\\text{Common ratio,}~ r= \dfrac{32}8 = 4\\\\\text{nth term} = ar^{n-1} \\\\\text{9th term} = 8\cdot 4^{9-1}\\\\\\~~~~~~~~~~~~~=8 \cdot 4^8\\\\\\~~~~~~~~~~~~~=524288\\\\\text{The 9th of the geometric sequence is 525288.}\)

there you go i think

Answer:

discount rate = change divided by original price: (3.80-3.67)/3.80 = 0.0342 = 3.4%

Step-by-step explanation:

Answer:

240 ft

Step-by-step explanation:

When she stops, her velocity is 0.  The first time that happens is at t = 3 minutes.  Her position at that time is equal to the area under the curve.

You can use area of a trapezoid, or you can split the shape into two triangles and a rectangle.  Watch your units!  Speed is given in ft/s, and time is given in minutes.

Using trapezoid area:

A = ½ (1 min + 3 min) (2 ft/s)

A = ½ (60 s + 180 s) (2 ft/s)

A = 240 ft

Answer:

15$

Step-by-step explanation:

The value of the variable 'x' in the given isosceles right angle triangle is 2√2. By applying the Pythagoras theorem, we get the required value.

An isosceles right angle triangle has a right angle and equal lengths of two sides. (the other two angles are also the same in measure for an isosceles triangle).

Given triangle has two angles of 45° and one angle of 90°, then the triangle is "an isosceles right angle triangle.

It is also given that, hypotenuse h = 4 and the opposite side is given by x.

Since it is an isosceles right triangle, the two sides are also equal in measure.

I.e., opposite side length = adjacent side length = x

Then, applying the Pythagoras theorem, we get

h² = (opp)² + (adj)²

⇒ (4)² = x² + x²

⇒ 16 = 2x²

⇒ x² = 8

∴ x = 2√2

Thus, the value of the length x = 2√2.

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It can be said that the percentage is 6 of the squares have shops.

What are Percentage?

A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

We know that there are 100 blocks/squares and there are 6% of the community with shops so

All we have to calculate is 6% of 100

6/100 * 100 = 6

So, it can be said that 6 of the squares have shops.

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The transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

An isometric transformation is one that keeps the angles and distances between the original and changed shapes the same. There are numerous techniques that can be used to alter any image in a plane.

The two figures are isometric only if they are congruent. In the given figure the angles remain the same however the lengths of the side are transformed as the figure is dilated.

Hence, the transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

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The preparation of the branch's income statement for Santosh & Co. Chennai is as follows:

Branch of Santosh & Co. Chennai

For the year ended December 31, 2018

Sales revenue            $40,300

Cost of goods sold         4,200

Gross profit                 $36,100

Expenses:

Office expenses $36,000

Salaries                    3,600

Total expenses         $39,600

Loss                             $3,500

An income statement is a financial statement prepared at the end of an accounting period to determine the profit or loss generated by a business or branch.

The profit or loss is the difference between the total revenue and the total expenses for the accounting period.

Credit sales at branch 40,000

Office expenses by Head office 36,000

Cash remittance to branch for petty cash 9,000

Goods sent to Branch 7,200

Salaries paid by head office 3,600

Debtors 31.12.2018 30,000

Petty cash on 31.12.2018 16,200

Cash sales at branch 300

Stock of 31.12.2018 3,000

Sales revenue   $40,300 ($40,000 + $300)

Cost of goods sold $4,200 ($7,200 - $3,000)

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Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

The exponential function that can model the county population, y, x decades after Tiana was born, is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 in 6.6 decades after Tiana was born.

The definition of the exponential function is presented as follows:

\(y = a(b)^x\)

In which the parameters of the exponential function are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the function is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 when y = 600000, hence:

\(y = 641000(0.99)^x\)

\(600000 = 641000(0.99)^x\)

\((0.99)^x = \frac{600000}{641000}\)

\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)

\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)

\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)

x = 6.6 decades.

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If X ~ Exponential(µ), then the mean of X is 1/µ. So if the mean of X is twice the mean of Y, then the mean of Y is 1/(2µ), so that Y ~ Exponential(2µ).

We're given that

P(X > 50) = 1 - P(X ≤ 50) = 1 - Fx (50) ≈ 0.7788

==>   Fx (50) = P(X ≤ 50) ≈ 0.2212

where Fx is the CDF of X, which is given for 0 ≤ x < ∞ to be

Fx (x) = 1 - exp(-µx)

Solve for µ :

1 - exp(-50µ) ≈ 0.2212   ==>   µ ≈ -ln(0.7788)/50 ≈ 0.005

Then we have

P (Y > 40) = 1 - P (Y ≤ 40) = 1 - Fy (40)

where Fy is the CDF of Y,

Fy (y) = 1 - exp(-2µy)

so that

P (Y > 40) ≈ 1 - exp(-2 × 0.005 × 40) ≈ 0.3297