A school club uses a telephone chain to inform members of changes in plans. The club president calls 2 members, each of whom calls 2 members, and so on. The process must be repeated 5 times. How many members are in the club?

Answers

Answer 1

Answer:

63 members

Step-by-step explanation:

Since each person calls 2 persons each, there is an exponential increase of 2 for each level. Since it starts with the president as 1 person, and increases exponentially by 2 for each level of phone call, we have a geometric progression of first term, a = 1 and common ratio r = 2. Since the process of phone calls must be repeated 5 times, our last term is 2⁵. So, our geometric progression is 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ = 1 + 2¹ + 2² + 2³ + 2⁴ + 2⁵

We now sum the geometric progression

The sum of a geometric progression with r > 1 is

S = a(rⁿ - 1)/(r - 1)

substituting r = 2, a = 1 and n = 6 since we have 6 terms, we have

S = 1(2⁶ - 1)/(2 - 1)

= (64 - 1)/1

= 63

So, we have 63 members in the club.

We could have also found this by summing up individually the terms in the series. We have 1 + 2¹ + 2² + 2³ + 2⁴ + 2⁵ = 1 + 2 + 4 + 8 + 16 + 32 = 63


Related Questions

ummmmmmmmmmmmmm... what is 24=5 + 6x

Answers

You subtract 5 from 5 and whatever you do on one side you do to the other so 24 would be 19. Now you have 19=6x you now have to cancel out six by dividing 6 by 6 whatever you do to one side you do to the other so now 19 divided by 6 is 3.16666667 round that to 3.2 so (x = 3.2)
the answer is 19/6 simplified it’s 3 1/6 or in decimal version it’s 3.16

What would it be help plz

Answers

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

It would be Choice 3 A counterclockwise rotation of 180° about the origin.

It's a rotation because the others can't be true a reflection wouldn't be across it diagonally. The 270° rotation would rotate into three quadrants while a 180° only goes into two quadrants.

Will mark as brainlist


Nicholas has some cans at home to donate to the soup kitchen, but decides to start a can drive at his school to see if others will help. The equation representing this is y = 235x + 15, where x is the number of days, and y is the number of cans collected.

Which statements are true based on the equation given. Select all that apply.
Nicholas had 235 cans at home.
The school collected 235 cans a day.
Nicholas had 15 cans at home.
The school collected 15 cans daily.

Answers

#3 Nicholas had 15 cans at home.

Answer:

b c d

Step-by-step explanation:

i think

Which word best completes the sentence?
Select the word from the pull-down menu.
from which to carve a statue
The sculptor selected a granite Choose
Choose...
bilocation
bisector
monolith
monomania

Answers

Answer:

ok the answer is acualy monolith bc i took the test

Step-by-step explanation:

a monolith is a upwright stone structure

Answer:

monolith

Step-by-step explanation:

there's no explanation

what is 14 divided by 3?​

Answers

4.6666 or 4.6 repeated

Answer:

14 divided by 3 would be 4.67

Step-by-step explanation:

What is the equation of a line through the points (0.9) and (3, 0)?
9-0
because m-
0-3: -3x + 9
9-0
because m-
0-3:y=-3x + 3
3-0
because m 0-9:-*
Giy--+9
3-0
because m-

Answers

Answer:

m=   -3

equation=  -3x+9

distance=   9.48   or 3 root 10

Step-by-step explanation:

hope this helps i couldnt understand the options

I need help on this math question?!

Answers

Answer:

X intercept = (-2,0) Y intercept = (0,2)

Step-by-step explanation:

Find the slope of the line passing through the points (-7, 8) and (5, -7)

Answers

Answer:

5/4

Step-by-step explanation:

the equation for slope is:

y² - y¹

m= x² - x¹ , except the ones and twos are at the bottom by the x. if you plug into the equation you get:

-7 - 8

m= 5 - (-7) = 5 + 7. that equation equals

-15. 5

m = 12 = 4

Slope of the line passing through the points (-7, 8) and (5, -7) is  [tex]\frac{-5}{4}[/tex]

What is slope of the line?

The slope of a straight line between two points says ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex])can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter 'm'.

As we know that slope of line (m)  passing through ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) is given as

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

As the line passing through the points (-7, 8) and (5, -7)

m = [tex]\frac{-7-8}{5-(-7)}[/tex]

m = [tex]\frac{-15}{12}[/tex]

m = [tex]\frac{-5}{4}[/tex]

Hence, slope of the line passing through the points (-7, 8) and (5, -7) is  [tex]\frac{-5}{4}[/tex]

Learn more about slope of the line here

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how do i solve this ? and wut is the answer?

Answers

Answer:

1. b = ad - c

2. y = C/B - A/Bx

Step-by-step explanation:

What's the domain and range

Answers

Domain- All of the input or x values in a function. In (3,6) , 3 would be the domain
Range- All of the actual output or y values in a function. In (3,6) , 6 would be the range

4/5 = 17/x
Find x please!!
*ratios and proportions*

Answers

Answer:

So, first you need to set up a proportion and cross multiply. This allows you to  get an equation which you can solve for x.

Step-by-step explanation:

[tex]\frac{4}{5}[/tex] × [tex]\frac{17}{x}[/tex]  

Cross multiply to get 4x = 85

Next, isolate the x variable by dividing the 4 on both sides. This leaves you with x = 21.25.

Answer: x = 21.25

10% of the number is 15 what is the number

Answers

Answer:

10

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

first make 10% a decimal (0.1)

then set up an equation

0.1x=15

solve for x

x= 15/0.1

Kevin bought 3 bags of gravel to cover the bottom of his fish tank. Kevin used 27 pounds of gravel to cover the bottom of the tank. How many pounds of gravel are left over?

Answers

Answer:

Remain gravel = (3x - 27) pound

Step-by-step explanation:

Given:

Number of bags Kevin have = 3

Used gravel = 27 pound

Find:

Remain gravel

Assume;

Each bag carry x pound of gravel

So,

Total gravel = 3x

Remain gravel = Total gravel - Used gravel

Remain gravel = (3x - 27) pound

help me and u will get 25 points ​

Answers

Answer:

5 = 12

10 = 24

15 = 36

20 = 48

25 = 60

Step-by-step explanation:

They both increase at a proportional rate, where minutes increase by 5 each time, and the dishes washed increase by 12. With this in mind, the graph goes:

5 = 12

10 = 24

15 = 36

20 = 48

25 = 60

Hope this helped!

PLEASE HELP I NEED THIS BEFORE 2PM! Arrange the letters a, b, &c from LEAST TO GREATEST. *
1 point
50°
60°
a, b, c
O b, a, c
Ocb, a
O b, c, a
O a, c, b
O c, a, b

Answers

Answer:

5th choice) a , c , b

Step-by-step explanation:

Find the last angle measurement. Note that the total angle measurement of the interior angles of a triangle = 180°.

It is given that two of them are 50 & 60. Find the last measurement:

180 - (50 + 60) = 180 - 110 = 70.

Note that to find the sides without proper measurements, the angles OPPOSITE of the sides determine the value. The greater the angle's value, the greater the opposite side's measurement value.

In this case, side a will be the least as it is opposite of 50°, side c will be next as it is opposite of 60°, and side b will be the greatest as it is opposite of 70°.

~

Ms. Cuevas has 115 students. Today 40% of them wore jeans to school.

PART A: How many of the students wore jeans?

Answers

Answer:

46 students

Step-by-step explanation:

Set up a proportion

X/115= 40%/100%

Multiply 115 by 40

Divide by 100

A circular pizza with diameter of 10 inches. The pizza is in a square box with side lengths of 14 inches. In square inches, how much of the box is empty?

Answers

Answer:

117.45 in²

Step-by-step explanation:

Given that:

Diameter of circular pizza = 10 inches

Length of square box = 14 inches

Area of a square = a²

Where a = side length

Area of square = 14² = 196 in²

Area of circle :

pi * r²

Pi = 3.142 ; r = d/2 = 10/2 = 5 inches

Area of circle = 3.142 * 5² = 78.55 in²

Amount of the box which is empty :

196 in² - 78.55 in² = 117.45 in²

Find two fractions equivalent to each fraction of 8/10

Answers

Answer:

4/5, 16/20

Step-by-step explanation:

two fractions equivalent to 8/10 are 8/10 (the original fraction itself), 16/20 (obtained by multiplying by 2), and 4/5 (obtained by dividing by 2).

To find two fractions equivalent to 8/10, we can simplify 8/10 to its simplest form and then multiply or divide the numerator and denominator by the same number to find equivalent fractions.

Step 1: Simplify 8/10 to its simplest form:

The greatest common divisor of 8 and 10 is 2. Dividing both the numerator and denominator by 2, we get 4/5.

Step 2: Find equivalent fractions:

We can multiply or divide the numerator and denominator of 8/10 by the same number to find equivalent fractions. Here are two possibilities:

Multiplying both numerator and denominator by 2:

8/10 * 2/2 = 16/20

So, two fractions equivalent to 8/10 are 8/10 (the original fraction itself), 16/20 (obtained by multiplying by 2), and 4/5 (obtained by dividing by 2).

Learn more about fractions here

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Which pairs of triangles are similar? Check all that apply.

-△ABC ~ △DEF
-△DEF ~ △GHI
-△GHI ~ △ABC
-△GHI ~ △JKL
-△JKL ~ △ABC

Answers

Answer:

Umm.. I think the second one in the first two pairs and the last one on the bottom

Step-by-step explanation:

I don't know for sure tho.. I'm sorry if it's wrong

The pair of triangles that are similar are △DEF ~ △GHI and △JKL ~ △ABC

Given:

△ABC

length = 20

Base = 14

length / base = 20/14

= 10/7

△DEF

length = 10

Base = 8

length / base = 10/8

= 5/4

△GHI

length = 12

Base = 15

length / base = 15/12

= 5/4

△JKL

length = 10

Base = 7

length / base = 10/7

Therefore, the pair of triangles that are similar are △DEF ~ △GHI and △JKL ~ △ABC

Learn more about triangles:

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6x + 9= 4x + 25 solve for x pls

Answers

Answer:

x=8

Step-by-step explanation:

6x+9=4x+25

so subtract 9 from both sides

6x=4x+16

subtract 4x from both sides

2x=16

divide both sides by 2

x=8

Answer:

x=8

Step by Step:

combine like terms

divide both sides

Given f(x) = -x - 2, find x when f(x) = 12.

Answers

Step-by-step explanation:

f(x) = -x-2

in finding x we need to implies that we already know f(x) = 12

therefore:

f(x) = -12 - 2

we need to know this laws that - × - is = +

this give us to the final answer:

12 + 2 = 14

Answer:

14

Step-by-step explanation:

y = 12

12 = x - 2

14 =x

Express the ratio 8:12 in lowest terms​

Answers

Answer:

2:3

Step-by-step explanation:

Find the greatest common fcator then divied taht by both of the numbers and boom you have your answer.

Hope this helps!

The lowest ratio (or the lowest equivalent ratio) of 8:12 is 2:3
Divide both sides (8 and 12) by 4 (biggest factor of both numbers) and get 2:3

Question 6: Order the rational numbers in descending order:
1/4, 4 x 10-2 , 0.004 , 4 , 40% .
Please help me!

Answers

Answer:

4*10-2, 4, 40%, 1/4, 0.004

Step-by-step explanation:

4*10-2=38

1/4=.25

4=4

.004=.004

40%=.40

Solve the equation.
2(11t+1.5t) = 12 – 5t

Answers

Answer: t=0.4

Step-by-step explanation: 22t+3t=12-5t

25t=12-5t

30t=12

t=0.4

In this question, we multiply the equation and calculate the value by adding/subtraction, and the further calculation can be defined as follows:

Given:

[tex]\bold{2(11t+1.5t) = 12- 5t}[/tex]

To find:

Solve the equation=?

Solution:

[tex]\to \bold{2(11t+1.5t) = 12- 5t}\\\\\to \bold{22t+3.0t = 12- 5t}\\\\\to \bold{22t+3.0t +5t= 12}\\\\\to \bold{30t= 12}\\\\\to \bold{t= \frac{12}{30}}\\\\\to \bold{t= \frac{4}{10}}\\\\\to \bold{t= 0.4}\\\\[/tex]

Therefore the final answer is "0.4"

Learn more:

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help me plez
Select the correct answer. Which line has a y-intercept of 2 and an x-intercept of -3? W.
A-W
B-X
C-Y
D-Z

Answers

Answer:

its A

Step-by-step explanation:

yw. i think its A .W

Answer:

A is the correct answer

W is the correct graph

Tickets for a celebrity golf tournament were sold before the tournament and on the day of the tournament. After reviewing
ticket sales, the tournament director found that 150 fewer tickets were purchased on the day of the tournament than
before the tournament. A total of 898 tickets were sold. How many tickets were sold on the day of the tournament?
314 tickets
O 374 tickets
0 524 tickets
748 tickets

Answers

374 tickets were sold on the day of the tournament

Answer:

B

Step-by-step explanation:

took test :)

Complete the point-slope equation of the line through (-8,-8) and (-7,9).
Use exact numbers.

Answers

Step-by-step explanation:

m=Y2-Y1/X2-X1

m=9--8/-7--8= 16/15

y-b=m(x-a)

y--8=16/15(x--8)

y+8=16/15(x+8)

15y+120=16(x+8)

15y+120=16x+128

15y=16x+8

y=16/15x+8/15

Lebron james is 6 feet 9 inches tall.There are 2.54 centimeter in 1 inch.What is lebron’s height in centimeters

Answers

Answer:

205.74 cm

Step-by-step explanation:

First convert feet to inches.

6x12+9=81

next multiply that by 2.54

that gives you the answer 205.74

Answer:

205.74 cm

Step-by-step explanation:

Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers to 21

Answers

Answer:

The set of real numbers is all numbers that can be shown on a number line. ... It also includes rational numbers, which are numbers that can be written as a ratio of two integers, and irrational numbers, which cannot be written as a the ratio of two integers.

If f(x) = 6x – 4, what is f(x) when x = 8?
A 2
B 16
C 44
D 52

Answers

52

hope it helps and give brainliest if my answer helps...

Answer:

c.44

Step-by-step explanation:

when x= 8 => f(8) = 6.8-4 =44

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