Use a system of equations to find the quadratic function
f(x) = ax^2+ bx + c
that satisfies the equations. Solve the system using matrices.

f(1) = 3, f(2) = 12, f(3) = 25

In order for the expected value of a mega ball ticket to be zero, the grand prize needs to be at least $4,105,724.49.

The term "value" can have different meanings depending on the context in which it is used. Generally, value refers to the worth or usefulness of something, often measured in terms of money, time, or other resources.

To calculate the expected value of a mega ball ticket, we need to multiply the probability of winning each prize by the value of that prize, and then sum up the products:

Expected value = (1/302575350) x $40,000,000 + (24/302575350) x $1,000,000 + (325/302575350) x $10,000 + (7800/302575350) x $500 + (20800/302575350) x $200 + (499300/302575350) x $10 + (436617/302575350) x $10 + (3399723/302575350) x $4 + (817712/302575350) x $2 + (297842418/302575350) x $0

Expected value = $0.65444

This means that if you were to buy every possible combination of numbers (all 302,575,350 of them), the expected value of a ticket would be $0.65444.

To calculate the amount the grand prize needs to be in order to break even, we need to set the expected value equal to zero and solve for the prize:

0 = (1/302575350) x (Prize - $2.00) + (24/302575350) x ($1,000,000 - $2.00) + (325/302575350) x ($10 - $2.00) + (7800/302575350) x ($500 - $2.00) + (20800/302575350) x ($200 - $2.00) + (499300/302575350) x ($10 - $2.00) + (436617/302575350) x ($10 - $2.00) + (3399723/302575350) x ($4 - $2.00) + (817712/302575350) x ($2 - $2.00) + (297842418/302575350) x ($0 - $2.00)

Simplifying this equation, we get:

0 = (1/302575350) x Prize - $0.01359

Solving for the prize, we get:

Prize = $0.01359 x 302575350

Prize = $4,105,724.49

Therefore, in order for the expected value of a mega ball ticket to be zero, the grand prize needs to be at least $4,105,724.49.

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After 6 years, the investment is whort $4,051.97

We know that this can modeled by an exponential equation of the form:

y = A*(1 + r)^x

Where A is the initial amount and r is the rate at which the investement grows (in decimal form)

Then we can write the equation as:

y = 2700*(1 + 0.07)^x

Where x is the number of years.

Then after 6 years, the investment is whort:

y = 2700*(1 + 0.07)^6 = 4,051.97

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-32t + 220

= -32(12) + 220

-384 + 220 =

-164

first step is to take the derivative. next is to plug in 12 into the function

For 15 feet below the sea level, the value of temperature reads is,

⇒  10.8 degree cooler

Given that;'

Rob finds that every 2.5 feet below sea level, the value of temperature reads 1.8 degree cooler.

Hence, For 15 feet below the sea level, the value of temperature reads is, x

Thus, We can formulate;

⇒ 2.5 / 1.8 = 15 / x

⇒ 25/18 = 15/x

⇒ x = 15 × 18 / 25

⇒ x = 10.8 degree cooler

Thus, For 15 feet below the sea level, the value of temperature reads is,

⇒  10.8 degree cooler

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Rewriting the equation for x gives[tex]x = \sqrt[4]{13}[/tex]

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

x = 13^1/4

To rewrte the equation for x, we introduce radicals

By pronounciation, x = 13^1/4 means that the value of x is 13 raised to the power of 1/4 i.e. the fourth root of 13

When rewritten, we have

[tex]x = \sqrt[4]{13}[/tex]

Hence, the solution is [tex]x = \sqrt[4]{13}[/tex]

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4f - 6v is equal to the vector <36, -16>.

To find 4f - 6v, we need to perform scalar multiplication on both vectors and then subtract the result.

Scalar multiplication of a vector by a scalar k is simply multiplying each component of the vector by k. For example, if we have the vector <a, b>, then k times that vector would be <ka, kb>.

Using this definition, we can find:

4f = 4<12, 2> = <48, 8>

6v = 6<2, 4> = <12, 24>

So, 4f - 6v = <48, 8> - <12, 24> = <36, -16>

Therefore, 4f - 6v is equal to the vector <36, -16>.

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Answer:

Step-by-step explanation:  70.7

Given:

r=46

angle from arc =88

Formula and Explanation of formula:

You want to find the proportion/precent of the circle you want to find and multiply it by the full length of the circle, which is the circumference.  

[tex]L=\frac{Part of circle}{full circle} Circumference\\\\\\L=\frac{Part of circle}{full circle} 2\pi r[/tex]

Plug Given into Formula:

[tex]L=(\frac{88}{360})(2)\pi (46)[/tex]     Plug into calculator

L =  70.7

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=46\\ \theta =88 \end{cases}\implies s=\cfrac{(88)\pi (46)}{180}\implies s=\cfrac{1012\pi }{45}\implies s\approx 70.65[/tex]

You would pay Ghana cedi 270.00 for the phone during the sale.

To calculate this:

40% of Ghana cedi 450.00 is 0.40 x 450 = Ghana cedi 180.00

Subtracting this discount from the original price gives:

Ghana cedi 450.00 - Ghana cedi 180.00 = Ghana cedi 270.00

The largest number is 145, the middle number is 95 and the smallest number is 60.

Given that, the sum of three miners is 300, the largest exceeds the middle one by 50 and the smallest by 85.

Let the three numbers be x, y and z.

Here, the largest number is x, middle number is y and smallest number be z.

y=x-50, z=x-85

Here, x+y+z=300

x+x-50+x-85=300

3x-135=300

3x=435

x=145

y=95 and z=60

Therefore, the three number are 145, 95 and 60.

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Answer:

25480

Step-by-step explanation:

Hopefully it's right.

The value matched to the correct expression is

1 + 5 = 6

2 + (1 + 3)² = 18

4 + 8(2) = 20

4³ = 64

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

1 + 5

2 + (1 + 3)²

4 + 8(2)

4³

Evaluating the expressions, we have

1 + 5 = 6

2 + (1 + 3)² = 18

4 + 8(2) = 20

4³ = 64

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Answer: g(x)= -|x|

.

Step-by-step explanation:

a|x-h|+k  

> this form shows the shifts, stretches and reflections

> If there is a h or k, the vertex has shifted to (h, k)

> "a" is your stretch

> if there is a - in front, the function has been refected

The image you gave is facing upside down so it's been reflected.  There has been no other changes the (h, k) is (0,0) and there has been no stretch

g(x)= -|x|       just put a negative in front to show reflection.

The equation of the line is determined as; y = (2/3)x + 22/3.

The general equation of line is written as;

y = mx + b

Where;

The slope is calculated as;

m = (y₂ - y₁) / (x₂ - x₁)

m = (14 - 4 ) / (10 + 5)

m = 10/15

m = 2/3

The y intercept is calculated as;

y = mx + b

4 = 2/3(-5) + b

4 = -10/3 + b

b = 4 + 10/3

b = 22/3

The equation of the line is determined as;

y = (2/3)x + 22/3

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When the number of classes is 1, football is less expensive.

When the number of classes is 2, 3, or 4, basketball is less expensive.

In order to determine the sport which is less expensive, we would have to calculate the total cost for a basketball program by substituting the number of classes (x) into the function which models it as follows;

y = 9x + 10

When the number of classes x = 1, the total cost is given by;

y = 9(1) + 10

y = $19.

Therefore, a total cost of $19 is greater than $15 for a football program.

When the number of classes x = 2, the total cost is given by;

y = 9(2) + 10

y = $28.

When the number of classes x = 3, the total cost is given by;

y = 9(3) + 10

y = $37.

When the number of classes x = 4, the total cost is given by;

y = 9(4) + 10

y = $46.

Therefore, a total cost of $46 is less than $60 for a football program.

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The shorter sides of Monica's wrapping paper measure 8 inches. Therefore, the correct option is A. 26 2/3 inches.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

We can set up a proportion to solve for the shorter sides of Monica's wrapping paper. Let x be the length of the shorter sides of Monica's paper. Then we have:

x/34 = 2/17

To solve for x, we can cross-multiply:

x = 34 * (2/17) = 4 * 2 = 8

Therefore, the shorter sides of Monica's wrapping paper measure 8 inches.

Alternatively, we can simplify the proportion first by dividing both sides by 2:

x/17 = 1/2

Then, we can solve for x by cross-multiplying:

x = 17 * (1/2) = 8

Either way, the answer is the same. Therefore, the correct option is A. 26 2/3 inches.

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A and B are mutually exclusive events, so PA) is 11/20.

Given that, P(B)=1/5 and P(A or B)=3/4.

For mutually exclusive events A and B

That is, P(A or B) = P(A) + P(B)

Here, 3/4 = P(A)+1/5

P(A)=3/4 - 1/5

P(A)=(15-4)/20

= 11/20

Therefore, P(A)=11/20

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Answer:

63.67

Step-by-step explanation:

nice one, this got me thinking some time

The solution is :

The length of the rectangle is L=18cm

The width of the rectangle is W=10cm

We have,

Given data

let the length be x

L=x

Width= x-8

W= x-8

Perimeter= 56cm

But we know that the perimeter is expressed as

P=2L+2W

substitute our data

56=2(x)+2(x-8)

56=2x+2x-16

56+16=4x

72=4x

divide both sides by 4

x= 72/4

x=18cm

Hence the Length is 18cm

L=18cm

The width= 18-8

W=10cm

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complete question:

Arectangle has a width that is 8 centimeters less than its length. The perimeter of the rectangle is 56 centimeters. Find both the width and length of the rectangle. Show your work.

The equation is solved and the distribution property is given by

a) A = 5x + 15

b) B = x² - 3x

c) C = x² + 6x + 8

d) D = x² - 10x + 25

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

A = 5 ( x + 3 )

On simplifying the equation , we get

A = 5 ( x ) + 5 ( 3 )

A = 5x + 15

b)

B = x ( x - 3 )

On simplifying the equation , we get

B = x ( x ) - x ( 3 )

B = x² - 3x

c)

C = ( x + 4 ) ( x + 2 )

On simplifying the equation , we get

C = ( x + 4 ) ( x ) + ( x + 4 ) ( 2 )

C = x² + 4x + 2x + 8

C = x² + 6x + 8

d)

D = ( x - 5 ) ( x - 5 )

On simplifying the equation , we get

D = ( x - 5 ) ( x ) + ( x - 5 ) ( -5 )

D = x² - 5x - 5x + 25

D = x² - 10x + 25

Hence , the equations are solved

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The smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent is 4000.

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain. Probability theory is widely used in the analysis of statistical data, such as in the study of the behavior of populations or financial markets.

To calculate the smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent, we must first calculate the probability of not finding any green apples. This can be done by finding the probability of selecting four red apples from the basket. With four red apples and an unspecified number of green apples, the probability of selecting four red apples is 4/N, where N is the total number of apples in the basket.

To find the smallest number of green apples, we must set the probability of selecting four red apples equal to 0.001 and solve for N. This gives us:

N = 4/0.001

Therefore, the smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent is 4000.

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The answer of the given question based on the equation is , the unknown number is 6.

An equation is the  mathematical statement that asserts equality of the two expressions. It typically consists of the two expressions separated by equal sign " = ". The expressions can include variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Solving an equation involves finding the value(s) of the variable(s) that make the equation true.

The statement can be translated into an equation as follows:

2(y - 2) = 8

Simplifying the equation, we can distribute the 2 on the left-hand side:

2y - 4 = 8

Then, we can add 4 to both sides to isolate the variable:

2y = 12

Finally, we divide both sides by 2 to solve for y:

y = 6

Therefore, the unknown number is 6.

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The rectangular prism with length of the base is 4 units, the width of the base is 3 units, and the height is 5 units is shown below.

Since the volume of the rectangular prism is 60 cubic units and the height is 5 units, we can find the length and width of the base by dividing the volume by the product of the height and base. That is,

Volume = Length * Width * Height

60 = Length * Width * 5

Length * Width = 12

We can choose any two numbers whose product is 12 as the length and width of the base. Let's choose 3 and 4 for simplicity. Then, the rectangular prism would look like as shown in picture where the length of the base is 4 units, the width of the base is 3 units, and the height is 5 units.

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Answer:

In this situation, [tex]t[/tex] (time) is the independent variable, and [tex]p[/tex] is the dependent variable, since calculating it relies on [tex]t[/tex]. In a real-world context, [tex]p[/tex] represents the number of hard drives sold in [tex]t[/tex] number of years.

Value of x is 2 in the circle .

What in Geometry Is the Definition of a Circle?

A circle is a curved, two-dimensional form that may be created by connecting points in a plane that are spaced the same fixed distance apart from a fixed point in the same plane. The circle's centre is that specific fixed location.

                              The diameter and radius of a circle are measured from the centre to its circumference and from one point on the circumference to another point that passes through the centre, respectively. In the actual world, a pizza foundation is among the most prevalent instances of a circular.

In circle,

          3 * (x + 2) = x * 6

           3x + 6 = 6x

             6 = 3x

            x = 2

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The value of the sin A in simplest radical form is 0.651 units

From the Figure,

We have the following information :

The triangle in the image is Right angle triangle.

The value of side AB is [tex]\sqrt{85}[/tex].

The value of side BC is 6.

The value of side CA is 7.

And we know that :

In the Right angle triangle, One angle is 90 degree.

So, The value of angle ABC is 90 degree.

For solving, we use the sin law:

Sine law-The law of sine can be used to calculate the remaining sides or angle of the triangle when 2 or more sides or angle are known.

[tex]\frac{AB}{SinC} =\frac{BC}{Si nA }[/tex]

Plug all the values in above formula:

[tex]\frac{\sqrt{85} }{Sin 90} =\frac{6}{Sin A}[/tex]

Now, Solving value of Sin A

Sin A = (6 × sin 90)/[tex]\sqrt{85}[/tex]

Sin A = 6 /[tex]\sqrt{85}[/tex]

Sin A = 0.651

Hence, the value of the sin A in simplest radical form is 0.651 units.

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Answer:

72 such cuboids are required to make a perfect cube.

Step-by-step explanation:

V = l x w x h

V = 12 cm x 9 cm x 8 cm = 864 cm^3

edge length = V^(1/3) = (864 cm^3)^(1/3) = 12 cm

V_cube = edge length^3 = 12 cm^3

number of cubes = V_cuboid / V_cube = 864 cm^3 / 12 cm^3 = 72

Therefore, 72 such cuboids are required to make a perfect cube.

The solution of the sine function sin(5π/12) is (√6 + √2)/4.

As per the sum and difference identity for sine, which states:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

To find sin(5π/12), we can express it as the sum or difference of two angles whose sine values we know.

One possible way is to use the fact that:

5π/12 = π/4 + π/6

So we have:

sin(5π/12) = sin(π/4 + π/6)

Using the sum identity, we get:

sin(π/4 + π/6) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6)

We know that sin(π/4) = cos(π/4) = √2/2 and sin(π/6) = 1/2, so we can substitute:

sin(π/4 + π/6) = (√2/2)(√3/2) + (√2/2)(1/2)

simplify the expression:

sin(π/4 + π/6) = (√6 + √2)/4.

Therefore, sin(5π/12) = sin(π/4 + π/6) = (√6 + √2)/4.

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The circular is around 305 cm in circumeference.

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle.

Substituting d = 97 cm and using the value of π to be 3.14159, we get:

C = πd

C = 3.14159 × 97 cm

C ≈ 304.731 cm

Rounding this to 3 significant figures, we get:

C ≈ 305 cm

Therefore, the circumference of the circle is approximately 305 cm.

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