In a game show, players play multiple rounds to score points. Each round has 3 times as many points available as the previous round.




Round 0 1 2 3 n

Points 25 75 225 675



Which equation shows the number of points available, p, in round n of the game show?

Answers

Answer 1

Answer:

[tex]p = 25(3)^n[/tex]

Step-by-step explanation:

Given

Round 0 1 2 3

Points 25 75 225 675

Required

Determine the equation

Let n = rounds and p = points.

So, we have:

[tex](n_1,p_1) = (0,25)[/tex]

[tex](n_2,p_2) = (1,75)[/tex]

[tex](n_2,p_2) = (3,225)[/tex]

The above shows a geometric progression.

So, we solve using

[tex]p = ab^n[/tex]

In [tex](n_1,p_1) = (0,25)[/tex]

n = 0 and p = 25

Substitute these values in [tex]p = ab^n[/tex]

[tex]25 = ab^0[/tex]

[tex]25 = a*1[/tex]

[tex]25 = a[/tex]

[tex]a = 25[/tex]

In [tex](n_2,p_2) = (1,75)[/tex]

n = 1 and p = 75

Substitute these values in [tex]p = ab^n[/tex]

[tex]75 = ab^1[/tex]

[tex]75 = ab[/tex]

Substitute 25 for a

[tex]75 = 25*b[/tex]

Make b the subject

[tex]b = \frac{75}{25}[/tex]

[tex]b = 3[/tex]

So, we have:

[tex]a = 25[/tex] and [tex]b = 3[/tex]

The equation [tex]p = ab^n[/tex] becomes

[tex]p = 25(3)^n[/tex]

Answer 2

     Equation representing the number of points 'P' in 'n' games will be [tex]P=25(3)^{n}[/tex].

Explicit formula of the Geometric sequence:a, ar, ar², ar³........arⁿ

       There is a common ratio of 'r' in each successive term to the

       previous term.

       Therefore, it's a geometric sequence.

Explicit formula of a geometric sequence is given by,

       [tex]T_n=ar^{n-1}[/tex] (For n ≥ 1)

       Here, [tex]a=[/tex] First term

       [tex]r=[/tex] Common ratio

       [tex]n=[/tex] nth term

Given in the table,

Common ratio (r) of any successive term to the previous term,

        [tex]r=\frac{75}{25}=3[/tex]

First term of the sequence 'a' = 25

Explicit formula of the sequence will be,

[tex]P=25(3)^{n}[/tex] [For n ≥ 0]

       Therefore, equation representing the number of points 'P' in 'n' games will be [tex]P=25(3)^{n}[/tex].

Learn more about the geometric sequence here,

https://brainly.com/question/11385300?referrer=searchResults


Related Questions

Solve for r in terms s, t, u, v.
su=rtv

Answers

Answer:

r = su/tv

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right  

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Step-by-step explanation:

Step 1: Define

su = rtv

Step 2: Solve for r

[Division Property of Equality] Divide tv on both sides:                               su/tv = rRewrite/Rearrange:                                                                                         r = su/tv
Making r subject of formula, we get:

r = su/tv

a(-6)=-42
solve for a

Answers

Answer:

7

Step-by-step explanation:

Answer:

A = 7

Step-by-step explanation:

You would take -42/-6 because that will tell you what x -6=-42

-42/-6 = 7

Also. you have to remember that a negative divided or multiplied by a negative = a positive

please help my friend, he's struggling on math ​

Answers

Answer:

question 1 = 37 covers , 535 dollars

question 2 = 32 covers , 460 dollars

Expression = 69 covers , 995 dollars

Step-by-step explanation:

You would take the number of covers and multiply it by 15 because 15 dollars is how much they sold each cover for.

and then for the expression wasnt sure what to do but from what i could see you added up the totals.

Hope this helped him :)

also tell me what his snap is BAHA okay lemme stop.

Ryan ordered some books online and spent a total of . Each book cost and he paid a total of for shipping. How many books did he buy?

Answers

Answer: 12 books

Step-by-step explanation:

First you need to remove the cost of shipping from the total amount:

= 75 - 3

= $72

The above is the total amount spent on the books without shipping.

If each book cost $6, the total number of books bought is:

= 72 / 6

= 12 books

Work out the size of angle X

Answers

Answer:

117

Step-by-step explanation:

180-101 = 79

180-(79+38)

180-117

63

180-63=117



PLEASE HELPPPPPPPP....?.......
If a+b=15 and ab=54 then find
1)
[tex] {a}^{2} + {b}^{2} [/tex]
2)
[tex](a - b )^{2} [/tex]
3)
[tex]a ^{2} - {b}^{2} [/tex]

Answers

Answer:

a = 9

b = 6

I hope you can do the rest yoyrself, as I coulsnt find how to type it out ;-;

Answer:

1) 117

2) 9

3) 45 or -45

Step-by-step explanation:

a=9

b=6

1) a²+b²=9²+6²=81+36=117

2) (a-b)²=(9-6)²=3²=9

3) a²-b²=81-36=45

It’s also possible that a=6 and b=9, in which case

1) (same)

2) (same)

3) 36-81=-45

I WILL MARK BRAINLIEST PLEASE HELP ASAP!!!!! Sketch a new graph of this relationship. The equation is y=7/4x​

Answers

Answer:

Step-by-step explanation:

Find the value of x.

Answers

Answer:

Step-by-step explanation:

8/18=x/24

18x=192

x=10.667(correct to three decimal places)

Find all of the roots of the following quartic equation:
h(x)= x^4 - 2x^3 - 9x^2 + 18x

Answers

x4)-(2•(x3)))-32x2)+18x
STEP
2
:

Equation at the end of step
2
:

(((x4) - 2x3) - 32x2) + 18x
STEP
3
:

STEP
4
:
Pulling out like terms

4.1 Pull out like factors :

x4 - 2x3 - 9x2 + 18x =

x • (x3 - 2x2 - 9x + 18)

Checking for a perfect cube :

4.2 x3 - 2x2 - 9x + 18 is not a perfect cube

Trying to factor by pulling out :

4.3 Factoring: x3 - 2x2 - 9x + 18

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -9x + 18
Group 2: x3 - 2x2

Pull out from each group separately :

Group 1: (x - 2) • (-9)
Group 2: (x - 2) • (x2)
-------------------
Add up the two groups :
(x - 2) • (x2 - 9)
Which is the desired factorization

Trying to factor as a Difference of Squares:

4.4 Factoring: x2 - 9

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3
Check : x2 is the square of x1

Factorization is : (x + 3) • (x - 3)

Final result :
x • (x + 3) • (x - 3) • (x - 2)

please help me on this will give you brainliest!!

Answers

Answer:

0.926

Step-by-step explanation:

Since it ask as decimal you will have to 0. and then the number which 926. Hope this helps, thank you !!

Dan was thinking of a number. Dan adds 10 to it, then doubles it and gets an answer of 56.6. What was the original number

Answers

Answer:

23.3 is the answer to this question

19.- Según la gráfica ¿Cuál es la rapidez media entre 4 s y 8 s?
A. 8 m/s
B. 1 m/s
C. 0,5 m/s

Answers

Answer:

B. 1m/s es la respuesta correcta

-10(d+1)=-14
What is the value of d

Answers

Answer:

[tex]d=\frac{2}{5}[/tex]

Step-by-step explanation:

-10 (d+1) = -14

-10d -10 = -14

-10d = -14 + 10

-10d = -4

d = 4/10

d= 2/5

D=2/5

Decimal form : d= 0.4

v
8
IZ
13
10
U
What is the LCM (least common multiple) of 2 and 7

Answers

Answer:

14

Step-by-step explanation:

Answer: 14

Step-by-step explanation:

The greatest common multiple of 2 and 7 is 1, because they are both prime numbers (numbers that cannot be divided by anything other than one or themselves).

Why bother with the greatest common multiple?

There's a very sneaky formula you can do to calculate the LCM with this.

[tex]lcm(a, b) = \frac{|a * b|}{gcd(a, b)}[/tex]

where lcm(a, b) = the least common multiple of integers a and b (1)

a = integer a (2)

b = integer b (7)

gcd(a, b) = greatest common divisor of integers a and b

So let's use it, we have all the available numbers.

[tex]lcm(a, b) = \frac{|2 * 7|}{1} = 14[/tex]

92 divided by 11 with remainder

Answers

Answer:

8 remainder 4

3(2h+5)+4 so i dont get what it is, can someone help please?

Answers

Answer:

An linear equation in one variable

Step-by-step explanation:

Variable:h

Equation:6h+19

An isosceles triangle has an angle that measures 56º. Which other angles could be in that
isosceles triangle? Choose all that apply.
HELP PLEASE I NEED THIS

Answers

Answer:

The other angles can be 56°, 68°, or 62°.

Step-by-step explanation:

If the 56° angle is one of the two congruent angles, then the remaining angles are 56° and 180-2(56) = 68°

If the is 56° Is not congruent to either of the other angles, then each of the remaining two angles is (180-56)/2 = 62°.

The other angles can be 56°, 68°, or 62°.

This another nae for fraction or quotient.It can also be written in the forms 'a:b' and a to b', where a and b are numbers.

Answers

Answer:

The answer is "Ratio".

Step-by-step explanation:

A ratio indicates how often a number contains a different number. Whenever the calculation of two quantities, as often happens, is indeed a measurement ratio without dimension. It is called a quotient of two volumes, which is calculated by using various units.

It is the relationship among two or more elements of financial reports is calculated by ratios. These also are efficient when the outcomes are presented several times. It allows you to monitor the performance of your company over time and to detect signs of injury.

Which statement is correct?
O A.
The opposite of the opposite of 6 is 6.
OB.
The opposite of the opposite of 1 is 1.
O C.
The opposite of the opposite of 3 is 0.
O D.
The opposite of the opposite of 5 is.

Answers

Answer:

I think its OB but I'm not sure

Step-by-step explanation:

Simplify (6w + 5.2) + (12.2 + 2.3w)

Answers

Answer:

The answer is 8.3 W + 17.4

If you click on the image it will show you how to solve the equation and I hope this helps you.

Lauren took 12 hours to read a 360 page book use the unit rate to determine how many hours it will take her to read 150

HELPP PLEASEE

Answers

Answer:

360 divied by 2.4 = 150

Step-by-step explanation:

Kris has 3 daughters who all live in different cities across Georgia. She wants to live somewhere that is an equal distance from each of her daughters. She mapped out the 3 cities and drew a triangle connecting them. How can she find a point on the map that is an equal distance from all 3 cities?


construct the incenter

construct the orthocenter

estimate the best place

construct the circumcenter

Answers

Answer: D) construct the circumcenter

===========================================================

Explanation:

Consider triangle ABC. The vertex points are at A,B,C. These represent the three cities in which the three different daughters live. Constructing the circumcenter will produce a circle such that all three points A,B,C are on that circle. Let's say that D is the center of that circle.

This means that AD, BD, CD are all radii of this same circle. Radii of the same circle are the same length, which is why point D is equally distant from A,B,C. If the mother lives at point D, then she will travel the same distance to visit any three of her daughters. See the note below.

To construct the circumcenter, we form perpendicular bisectors to segments AB, BC and AC. Technically you only need two of them. All three of these perpendicular bisectors intersect at point D.

-------------

Note: Keep in mind that roads aren't completely straight, so that means we'll have to factor in the curvature of each road. But to keep things simple, we assume each road is a straight line segment.

Pls help me i need your help to do it pls

Answers

The answer is 39 because the measurement of CBA is 90 so if CBD is 51 then u have to take away 51 out of 90

Answer: 39°

Step-by-step explanation:

This is a right triangle, meaning one of the angles is a 90° angle. Angle CBA in this case is the 90° angle. In order to figure out the measure of ABD, you subtract the measure of CBA by the measure of CBD, which is 51°.

90 - 51 = 39

Thus, the measure of ABD is 39°

The length, in millimeters of each side of a square shaped electronic chip is a rational number. What statement is true about the length of the diagonal of the chip

Answers

Answer:

The diagonal is irrational because it is a product of a rational and an irrational number

Step-by-step explanation:

The options are not given. However, the question is still answerable.

Given

Shape: Square

Length: Rational

Since the side length is said to be rational, I'll answer the question based on whether the diagonal is rational or not.

Having said that:

The diagonal (d) of a square with side length (l) is calculated using Pythagoras theorem.

[tex]d^2 = l^2 + l^2[/tex]

[tex]d^2 = 2l^2[/tex]

Take positive square root of both sides

[tex]d = \sqrt{2l^2}[/tex]

Split:

[tex]d = \sqrt{2} * \sqrt{l^2}[/tex]

[tex]d = \sqrt{2} *l[/tex]

Recall that the side length (l) is rational.

However, [tex]\sqrt 2[/tex] is irrational.

So, the product of l and [tex]\sqrt 2[/tex] will be irrational

Hence:

The diagonal is irrational

What is m_8 if m_4= 50 degrees?

Answers

50 degrees because the lines are parallel

HELP ME RN PLEASEEEE!!!!!!!!
how many 3/8 are in 8, explain how you know

Answers

Answer:

exactly 21 sets of 3/8 fit into 8

Step-by-step explanation:

Basically you just draw 8 boxes split them in 8ths and you end up with 21 sets of 3/8

can someone please help its due soon.ill give brainliest!

Answers

Answer:

z = 17.5

Step-by-step explanation:

To get the value of z, we use the bisector theorem

7/z = 6/15

6z = 7 * 15

6z = 105

z = 105/6

z = 17.5

what is the appoximate distance between points d and e round your answer to the nearest hundreth

Answers

The distance between the 2 points is approximately 8.25
What she or he said have a good day

Sam's two new aquariums each hold exactly 200 gallons of water. One aquarium will hold small fish and the other will hold large fish. Now he needs new fish for his aquariums.

•He will buy 5 small fish for every 10 gallons of water in the aquarium.
•He will buy 8 large fish for every 40 gallons of water in the aquarium.

What is the total number of fish Sam will have? What will be the ratio of Sam's small fish to large fish? Show or explain the steps you used to solve this problem.

Answers

In the 1st one he will have 100 small fishes. 200/10=20. 20x5=100
In the 2nd one he will have 40 large fishes. 200/40=5. 5x8=40
Sam will have a total of 140 fishes. 100+40=140
Ratio=40/100=4:10

The length of a rectangle is 3 times as big as the width. If beth increases each dimension by 4, write an expression to represent the new area, a, of the rectangle.

Answers

Answer: See explanation

Step-by-step explanation:

Let the width of the rectangle be x.

The length of a rectangle is 3 times as big as the width. Length = 3x

New width = x + 4

New length = 3x + 4

The new area will be:

a = (3x + 4)(x + 4)

a = 3x² + 12x + 4x + 16

a = 3x² + 16x + 16

Other Questions
The term "stateless," when used in the study of world geography, would most likely be associated with which of thefollowing locations?A. RussiaB. USAC. PalestineD. JapanNeed help ASAP Two students are using estimation to determine reasonable solutions to the expression 89.1 times 9.3. Katie uses the expression 90 times 10. Amaya uses the expression 89 times 9. Which is the best comparison of the estimates and the actual product? Solve the inequality and graph the solution.4x - 5 7 ________ use statistics to anticipate customers withdrawals. ________ use statistic to calculate probable life expectancy to help them set rates. What does the use of fourteen dogs suggest about Hal, Charles, and Mercedes?They are ignorant.They are insecure.They have a strong team.They are ambitious. I don't what to doOnly 1-9 the path of a toy rocket is modelled by the equation y=-x^2+6x+2, where x is the horizontal distance, in metres, travelled and y is the height, in metres, of the toy rocket above the ground. what is the maximum height of the toy rocket? at what horizontal distance does the maximum height occur? The militia who could be ready in a"moment's notice" were called what?A. QuickmenB. MinutemenC. InfantryD. Speedmen 80 times 30 plus 60 equals Explain how the Persian empire treated people Please help me with this assignment I need you to write it for me please Im in Spanish 2B so you cant really use translatorHere are some stuff in my vocabulary sheet Corn, turkey, garlic, black pepper, bacon, flour, onion, cinnamon, shrimp, beef, seafood, butter, oil All theses are in Spanish you have to use the words, after, then, add, teaspoon, cooking pan, cooking pot, stove, oven, Cup, bowl, mix, boil, fry, peel , and then you say if its good or not you can just fake that part, and the words that I said are on my vocabulary list you dont have to use those words you just have to use some of those those were just examples of the word in my vocabulary list you can do more than that you just have to put any food that will fit in a recipe the stuff that I said was in my vocabulary sheet was an example of stuff you can use ok please help. Use substitution to solve the system of equations.3 - 5y = 3622 + y = -16 1.PART A: Which of the following identifies a central idea of the text?A. Black women had an immense impact on the success of the Civil RightsMovement but were frequently disrespected and went unacknowledgedbecause of their gender.B.While black women made significant contributions to the Civil Rights Movement,they were unable to participate to the extent that men did because of theirresponsibilities at home.C. Black women were prevented from contributing to the Civil Rights Movementbecause men feared they would have to endure violence.D. While black women believed that gender equality was more important thanracial equality, men pressured them to take up the fight for racial equality. Most of the property in command economies is owned by the points (-1,r) and (2,1) lie on a line with slope -4 find the missing coordinate how do different types of motion affect forces? Does (0,5) make the equation y = 7x true? Answer each question by using the appropriate direct object pronoun. 1.Preparaste la leccin? = S, yo_2.Vas a mirar televisin? = S, yo_3.Quieres beber t? = S, yo_4.Viste a Juan? = S, yo_5.Puedes hablar espaol? = S, yo_6.Ests mirando el programa? -S, yo_7.Estn comprando los boletos? = S, nosotros_8.Deseas ver la pelcula? = No, yo no_9.Vas a montar bicicleta? = No, yo no_10.Ests llevando guantes? = No, yo no_ Juanita has a 20% of the money that she needs to buy a new bicycle if she has a $52 how much money does the bicycle cost? How many seconds would it take to drive to Miami if I go 75 mph the whole way? (use 675 miles for the distance)