10. Sixteen teams play in a one-game elimination
match. The winners of the first round go on to
play a second round until only one team remains
undefeated and is declared the champion.
4
a. Make a table of values for the number of
rounds and the number of teams participating.
b. What is the reasonable domain and the range
of this function? Explain.
c. Find the rate of decay.
d. Find the decay factor.

The function which would match the graph shown as in the task content is; y = -1/2 (x - 6) (x + 5).

It follows from the task content that; the zeroes of the parabola are; -5 and 6;

Therefore, we have that;

y = a (x - 6) (x + 5).

To determine the value of a; use the y-intercept such that we have; (0, 15).

15 = a (0 - 6) (0 + 5)

15 = -30a

a = -1/2.

Ultimately, the required function to match the graph is; y = -1/2 (x - 6) (x + 5).

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Due to inflation, a fixed quantity of money can buy 5% less every year. If camille has enough in her wallet to buy 86 movie tickets right now, the same amount of money could buy 69 movie tickets in 4 years.

Inflation is the sustained increase in the general price level of goods and services in an economy over a period of time. When inflation occurs, each unit of currency buys fewer goods and services; consequently, inflation reduces the purchasing power of money. Here, inflation reduces the purchasing power of money by 5% every year.

Let's assume that Camille has enough in her wallet to buy 86 movie tickets right now. After 1 year, the same amount of money would be able to buy 86 * (100 - 5) / 100 = 81.7 movie tickets, since the purchasing power of the same amount of money would have decreased by 5%.

After 2 years, the same amount of money would be able to buy 81.7 * (100 - 5) / 100 = 77.6 movie tickets, since the purchasing power of the same amount of money would have decreased by another 5%.

After 3 years, the same amount of money would be able to buy 77.6 * (100 - 5) / 100 = 73.7 movie tickets, since the purchasing power of the same amount of money would have decreased by another 5%.

After 4 years, the same amount of money would be able to buy 73.7 * (100 - 5) / 100 = 69.9 movie tickets, since the purchasing power of the same amount of money would have decreased by another 5%.

However, since movie tickets cannot be bought in fractional amounts, we would round down to the nearest whole number, so the same amount of money could buy 69 movie tickets in 4 years.

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Answer:

Part A:

The equation for the amount of money Nora would spend after the discount is applied on a shirt that costs d dollars is:

c = d - 0.05d

c = 0.95d

Part B:

Let x be the total value of the clothes Nora can buy before the discount is taken.

After the discount is applied, she can spend a total of $57, so we have:

0.95x = 57

x = 60

Therefore, Nora can buy a total of $60 worth of clothes before the discount is taken.

The businesswoman must invest $7,500 in the 13% fund and $22,500 in the 15% fund to earn a return of $4,350 after one year.

An equation contains one or more terms with variables connected by an equal sign.

We can use substitution or elimination method to solve when there are more than one equation.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Let's denote,

The amount invested in the 13% fund =  x

The amount invested in the 15% fund = y.

Now,

The total amount invested = $30,000,

i.e

x + y = 30000 _____(1)

The total return after one year = $4,350.

Which can be expressed as,

0.13x + 0.15y = 4350 _____(2)

Use the substitution method.

From (1),

x + y = 30000

y = 30000 - x _____(3)

Substituting y in (2)

0.13x + 0.15(30000 - x) = 4350

Solving for x.

0.13x + 4500 - 0.15x = 4350

-0.02x = -150

x = 7500

And,

y = 30000 - x

y = 30000 - 7500

y = 22500

Thus,

The businesswoman must invest $7,500 in the 13% fund and $22,500 in the 15% fund to earn a return of $4,350 after one year.

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The complete question.

A businesswoman wants to invest $30,000 in different funds that produce annual returns of 13% and 15% respectively. How much must she invest in each fund to earn a return of $4,350 after one year?

Answer:

x = 60 degrees (if x < 90 degrees).

Step-by-step explanation:

secx - 2 = 0

secx = 2

Now sec x = 1/cos x

So,

1/cosx = 2

cos x = 1/2

x = 60 degrees.

Answer:

The second option!

Step-by-step explanation:

Sorry if i was wrong... :(

The equation we need to use to find the number of bills in Guy Granger's stack is 5b = 4, where b is the number of bills.

What is an Equation ?

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

This equation represents the fact that each of the 5 contestants received 4 one hundred-dollar bills, so the total number of bills is

= 4 x 5

= 20

To solve for b, we need to divide both sides of the equation by 5:

5b / 5 = 4 / 5

b = 4 / 5

So, the number of bills in Guy Granger's stack is 4 / 5 * 100 = 80.

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Answer: Seed needed for the new lawn = 125 pounds

Step-by-step explanation:

Knowing the amount of seed needed for their old lawn will help Mr. and Mrs. Quigley calculate the amount of seed needed for their new lawn based on the size of the area.

First, let's calculate the area of the old lawn:

Area = length × width

Area = 10 ft × 20 ft

Area = 200 square feet

Next, we can determine the seed requirement per square foot for the old lawn:

Seed requirement per square foot = total seed needed ÷ area of the lawn

Seed requirement per square foot = 5 pounds ÷ 200 square feet

Seed requirement per square foot = 0.025 pounds per square foot

Now, let's calculate the area of the new lawn:

Area = length × width

Area = 100 ft × 50 ft

Area = 5000 square feet

To find the amount of seed needed for the new lawn, we can multiply the seed requirement per square foot by the area of the new lawn:

Seed needed for the new lawn = Seed requirement per square foot × area of the new lawn

Seed needed for the new lawn = 0.025 pounds per square foot × 5000 square feet

Therefore, Mr. and Mrs. Quigley will need 125 pounds of grass seed for their new lawn based on the calculations using the information from their old lawn.  

The value of the hypotenuse x is 19.1

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

Rise = 17

Angle = 63 degrees

The hypotenuse, x is then calculated using the following laws of sines

sin(63) = 17/x

Make x the subject

So, we have the following representation

x = 17/sin(63)

Evaluate the expression

This gives

x = 19.1

Hence, the value of x is 19.1

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Counting to 20 in Spanish is a relatively straightforward process. The first step is to learn the numbers from 1 to 10, which are:

1 - uno

2 - dos

3 - tres

4 - cuatro

5 - cinco

6 - seis

7 - siete

8 - ocho

9 - nueve

10 - diez

Once you have these numbers memorized, it's easy to continue counting up to 20. Simply add the numbers from 11 to 19 to the base number, diez.

11 - once (diez + uno)

12 - doce (diez + dos)

13 - trece (diez + tres)

14 - catorce (diez + cuatro)

15 - quince (diez + cinco)

16 - dieciséis (diez + seis)

17 - diecisiete (diez + siete)

18 - dieciocho (diez + ocho)  

19 - diecinueve (diez + nueve)

20 - veinte

As you can see, the only exception is the number 15, which has its own unique word, "quince." Other than that, all of the numbers from 11 to 19 follow the same pattern of adding "diez" to the appropriate digit. And once you reach 20, you're done! It's important to note that Spanish has gendered nouns, so when counting objects, you will need to use the appropriate article and adjective to match the gender of the noun. For example, if you are counting "dogs," you would say "uno perro," but if you were counting "cats," you would say "una gata."

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Answer:

1  uno

2  dos

3  tres

4  cuatro

5 cinco

6 seis

7 siete

8 ocho

9 nueve

10 diez

11 once

12 doce

13 trece

14 catorce

15 quince

16 dieciséis

17 diecisiete

18 dieciocho

19 diecinueve

20 veinte

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

In linear regression, one variable, called a dependent variable, is related to one or more independent variables by a linear equation.

A function has the following format: y = f(x).

In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.

That is, the input of the function is the independent variable and the output is the dependent variable.

In the case of multiple inputs, all the inputs are independent variables.

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The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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Answer:

48 miles per hour

Step-by-step explanation:

To convert Aneesha's speed from miles per hour to feet per second, we can use the formula:

speed in feet per second = speed in miles per hour * feet per mile / seconds per hour

So, Aneesha's speed in feet per second is:

50 miles per hour * 5,280 feet per mile / 3600 seconds per hour = 792 feet per second

Morris is traveling 3 feet per second less than Aneesha, so his speed in feet per second is:

792 feet per second - 3 feet per second = 789 feet per second

To convert Morris's speed back to miles per hour, we can use the formula:

speed in miles per hour = speed in feet per second * seconds per hour / feet per mile

So, Morris's speed in miles per hour is:

789 feet per second * 3600 seconds per hour / 5,280 feet per mile = approximately 48 miles per hour.

Answer:

-52

Step-by-step explanation:

If x = -2 and y = 6, then we can substitute those values into the expression:

5(2 x - 4) - 2y = 5(2(-2) - 4) - 2(6)

= 5(-4 - 4) - 2(6)

= 5(-8) - 2(6)

= -40 - 12

= -52

So, the value of the expression 5(2 x - 4) - 2y when x = -2 and y = 6 is -52.

The measure of m∠S is 116.3.

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

Parallelogram QRST.

m∠R = 63.7

Now,

We see that,

m∠R and m∠T are opposite angles.

So,

m∠T = 63.7 _____(1)

And,

m∠Q and m∠S are opposite angles.

So,

m∠Q = m∠S ______(2)

Now,

The sum of the four angles is 360.

So,

m∠R + m∠T + m∠Q + m∠S = 360

From (1) and (2),

63.7 + 63.7 + 2m∠S = 360

127.4 + 2m∠S = 360

2m∠S = 360 - 127.4

2m∠S = 232.6

m∠S = 232.6/2

m∠S = 116.3

Thus,

The measure of m∠S is 116.3.

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The diameter across this loop was 236.6 feet

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

However, if we assume that Evan ran around the loop's outer edge and not inside the loop,

we can use the formula for the circumference of a circle,

which is C = πd,

where C is the circumference, d is the diameter, and π is approximately 3.14.

We can rearrange the formula to solve for the diameter,

which is d = C/π.

Plugging in the given value for the circumference, we get:

d = 744/π ≈ 236.6 feet

Therefore, if Evan ran around the outer edge of the loop, the diameter of the circle is approximately 236.6 feet.

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You need to find a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This can be done using the extended Euclidean algorithm, and the resulting inverse is the residue of the coefficient modulo the modulus.

Finding the inverse of a modulo involves finding a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This process is important in modular arithmetic, where calculations are performed with remainders of a fixed integer modulus.

To find the inverse of a modulo, you can use the extended Euclidean algorithm, which is a method for finding the greatest common divisor of two integers.

The steps for finding the inverse of a modulo are as follows:

1. Identify the number you want to find the inverse of (let's call it "a") and the modulus (let's call it "m").

2. Use the extended Euclidean algorithm to find the greatest common divisor of "a" and "m", and the coefficients x and y such that ax + my = gcd(a,m).

3. If gcd(a,m) = 1, then "a" has an inverse modulo "m" and the inverse is given by x mod m.

4. If gcd(a,m) is not equal to 1, then "a" does not have an inverse modulo "m".

In step 3, x mod m represents the residue of x modulo m, which is the unique non-negative integer less than m that is congruent to x modulo m. In other words, it is the remainder when x is divided by m.

For example, to find the inverse of 5 modulo 7, we can use the extended Euclidean algorithm to find that 2(5) + (-1)(7) = 1. Therefore, the inverse of 5 modulo 7 is 2.

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The table is

Balloon        Helium in the tank

1                                14.4

2                                13.9

3                                13.4

4                                12.9

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given function is h = 14.9 - 0.5b  .....(i)

Where b is the number of ballon.

Putting b = 1 in equation (i)

h(1) = 14.9 - 0.5×1

h(1) = 14.4

Putting b =2 in equation (i)

h(2) = 14.9 - 0.5×2

h(2) = 13.9

Putting b = 3 in equation (i)

h(3) = 14.9 - 0.5×3

h(3) = 13.4

Putting b = 4 in equation (i)

h(4) = 14.9 - 0.5×4

h(4) = 12.9

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The dimensions of the field are length is 12 m and width is 17m  or length is 17m and width is 17m.

The area of Rectangle is length times of width.

Given that Julieta has 58 m of fencing to build a four-sided fence around a rectangular plot of land.

2(L+W)=58

2L+2W=58

Now  area of the land is 204 square meters.

LW=204

L=204/W

Now plug in this L in above equation.

2(204/W)+2W=58

408/W+2W=58

2W²+408-58W=0

2(W²-29W+204)=0

(W-17)(W-12)=0

W=17

Now plug in W as 17 in L

L=204/17=12

Hence, the dimensions of the field are length is 12 m and width is 17m  or length is 17m and width is 17m.

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Answer:

24

Step-by-step explanation:

2x3=6

6x4=24

Answer: 1 liters = 1000 cm^36 liters = 6000 cm^3Height

Step-by-step explanation:

1 liters = 1000 cm^36 liters = 6000 cm^3Height

1000 meters is equal to 3280.84 feet. To convert from meters to feet, you must multiply the number of meters by 3.28084. This is due to the fact that a meter is slightly longer than a foot.

One meter is equivalent to 3.28084 feet. Therefore, to compute 1,000 meters in feet, you must multiply 1,000 meters by 3.28084. Doing this calculation yields a result of 3,280.84 feet. The meter is the primary unit of measurement for length in the International System of Units, or SI. The SI base unit for length is the meter, which is defined as the length of the path travelled by light in a vacuum in 1/299,792,458 seconds. In other words, the meter is the distance light travels in a vacuum in 1/299,792,458 of a second. The meter is also referred to as the "meter of the air," since it is the length of the path travelled by light in the air in the same time.The foot is a unit of length in the British Imperial and US customary systems of measurement, and is equivalent to 1/3 of a yard. One foot is equal to 0.3048 meters.

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Answer: never

Step-by-step explanation:

Store A's prices are represented by the expression 25x-9

Store B's prices are represented by the expression 5(5x+8)

To find when the 2 stores charge the same rate , we set the expression equal and solve for x

25x-9 = 5(5x+8)

25x -9 = 25x + 40

Subtract 25x on both sides

-9 = 40

We cannot solve for x

So , the price of two stores never be same

Two stores never charge the same rate

The three solutions to the equation are (0, 1), (1, 12) and (2, 25)

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

y = 12x + 1

Next, we set x to 0, 1 and 2

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

y = 12 * 0 + 1

y = 1

y = 12 * 1 + 1

y = 13

y = 12 * 2 + 1

y = 25

As an ordered pair, we have

(0, 1), (1, 12) and (2, 25)

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Answer:

x = 17/32

Step-by-step explanation:

Firstly, you want to simplify by combining like terms:

4x(3+5)—10 = 4 · 3 + 5 – 10

32x—10 = 7

Add ten to both sides:

32x - 10 = 7

+10             +10

32x = 17

Divide both sides by 32:

32x = 17

/32      /32

32 divided by 32x makes x

so we get x = 17/32

(we dont divide 17/32 since we would get an irrational number (0.53125))

Answer:

-1280

Step-by-step explanation:

10×(-2)= -20

-20×(-2)= 40

4th term: 40×(-2)= -80

5th term: -80×(-2)= 160

6th term: 160×(-2)= -320

7th term: -320×(-2)= 640

8th term: 640×(-2)= -1280

Answer:

I cannot give you the answer because I need the table with the records.

Step-by-step explanation: