Let Tn, be the number of dots in figure.
How many dots are there in figure 30?
Look at the picture (don't mind of the highlighted ones).
Answers
Answer:
4294967293 dots
Step-by-step explanation:
Figure 1 has 5 dots.
Figure 2 has 13 dots.
Figure 3 has 29 dots.
Subtract and find different of each term:
13-5 = 829-13 = 16Let [tex]\displaystyle \large{b_n}[/tex] be sequence of difference (and the sequence appears to be geometric.)
So for [tex]\displaystyle \large{b_n}[/tex], find the common ratio which is 2.
Hence, [tex]\displaystyle \large{b_n = 8(2)^{n-1}}[/tex] - recall geometric sequence formula below:
[tex]\displaystyle \large{a_n = a_1r^{n-1}}[/tex]
The sequence of difference [tex]\displaystyle \large{b_n=8(2)^{n-1}}[/tex] can be simplified to:
[tex]\displaystyle \large{b_n=2^3(2)^{n-1}}\\\displaystyle \large{b_n=2^{n+2}}[/tex]
Now to find the original sequence:
[tex]\displaystyle \large{a_n = a_1 + \sum_{k=1}^{n-1}b_k}[/tex]
Hence:
[tex]\displaystyle \large{T_n=5+\sum_{k=1}^{n-1}8(2)^{k-1}}[/tex]
Recall:
[tex]\displaystyle \large{\sum_{k=1}^{n-1} a_1r^{n-1} =a_1\left( \dfrac{1-r^{n-1}}{1-r}\right)}[/tex]
Therefore:
[tex]\displaystyle \large{T_n=5+\sum_{k=1}^{n-1}8(2)^{k-1}}\\\displaystyle \large{T_n=5+8\left(\dfrac{1-2^{n-1}}{1-2}\right)}\\\displaystyle \large{T_n=5+8\left(\dfrac{1-2^{n-1}}{-1}\right)}\\\\\displaystyle \large{T_n=5+8(-1+2^{n-1})}\\\displaystyle \large{T_n=5-8+8(2)^{n-1}}\\\displaystyle \large{T_n=2^{n+2}-3}[/tex]
Therefore, the sequence for 5,13,29 is [tex]\displaystyle \large{2^{n+2}-3}[/tex].
Therefore, in figure 30:
[tex]\displaystyle \large{T_{30}=2^{30+2}-3}\\\displaystyle \large{T_{30}=2^{32}-3}\\\displaystyle \large{T_{30}=4294967293}[/tex]
Therefore, there are 4294967293 dots in figure 30
Related Questions
Jamie has 70 coins. They total $6.30. If they are only dimes and nickels find out how many of each she has.
Answers
Answer:
Jamie has 14 nickels and 56 dimes
Step-by-step explanation:
Start by identifying labels for the # of dimes and nickles. Lets use x for nickels and y for dimes.
From here you can make two formulas (x + y = 70) and (5x + 10y = 630) when you put them into a graphing calculator they should intersect at (14,56) which means the x = 14 and y = 56
Select the correct answer. Solve the following inequality for x.
Answers
Answer:
c. x>1
Step-by-step explanation:
-26 + 13x + 2 > 2 - 13x
-26 + 13x > -13x
13x + 13x > 26
26x > 26
= x>1
what is (1,3) rotated in 180 degrees?
Answers
Answer:
(-1,-3)
Step-by-step explaintion:
hope this helps!!
btw i just chnaged the x and y sign coordinates, thats all u needa do !!
A cylinder has a volume of 612. If the radious is multiplied by 3, what would the new volume be?
ANSWER IS NEEDED NOW!!
Answers
Answer:
the new volume is
v = 5508
6 sprinklers are shown on gridlines. each sprinkler has a diameter of 6 feet. the irrigation design for a new backyard is shown with six sprinkler heads and two walkways. which statement is true of this design? the area covered by each sprinkler head is approximately 113.10 ft2. the area covered by all the sprinkler heads together is approximately 169.64 ft2. every square foot of the yard will be watered with this design. the sprinklers would cover more area if they were in a straight line.
Answers
The area covered by all the sprinkler heads together is approximately 169.64 ft2.
We have given
6 sprinklers are shown on gridlines.
Each sprinkler has a diameter of 6 feet.
The irrigation design for a new backyard is shown with six sprinkler heads and two walkways.
One sprinkler has a diameter of 6 feet.
So the radius is 3.
The area for one sprinkler is given by,
What is the formula for the area of the circle?
[tex]A=\pi r^{2}[/tex]
[tex]A=3.14\times 3^2\\A=28.26[/tex]
So the area covered by one sprinkler is 28.26 feet ^2.
For six sprinkler is given by
[tex]=6\times 28.26[/tex]
=169.64 ft^2
The answer is B.
The area covered by all the sprinkler heads together is approximately 169.64 ft2.
To learn more about the area visit:
https://brainly.com/question/3948796
Answer:
b
Step-by-step explanation:
What is the median of set A
Answers
Answer:
30
Step-by-step explanation:
10,10,20,20,20,20,30,30,30,30,40,50,50,60
The two numbers in the middle are 30 and 30.
30 + 30=60
60/2=30
Hope it Helps
Which of the following does NOT describe x-4?
x decreased by 4
4 less than x
xless than 4
the difference of x and 4
Answers
Answer:
x less thsn 4
Step-by-step explanation:
hope it helps
Answer: C. x less than 4
Step-by-step explanation: X is not the variable being subtracted, and 4 is the variable being subtracted, therefore the answer is C. x less than 4 because this does not describe x - 4
I need help with 5/9 divided by 3/8
Answers
Answer:
40/27 or
1 and 13/27
Step-by-step explanation:
Use Keep-Change-Flip to divide fractions.
Problem:
5/9 ÷ 3/8
KEEP the first fraction, the 5/9, just copy it exactly, no changes.
CHANGE the ÷ to ×
5/9 ×
FLIP the second fraction, the 3/8. Flip it over (reciprocal)
5/9 × 8/3
Now do this problem. You can "cancel" (which is really dividing) or multiply straight across (top×top, bottom×bottom)
5/9 × 8/3
= 40/27
This cannot be reduced. It is a perfectly good answer just like this. But since there is a larger number on top, your teacher/class/book/program, might want you to change it to a mixed number.
40/27 = 1 13/27
how many milliseconds are in a year
Answers
Answer:
3.154e+10
Step-by-step explanation:
The milliseconds unit number 31,536,000,000.00 ms converts to 1 yr, one calendar year.
Or for how many milliseconds is 365 days in a year?
The answer is one Year is equal to 31557600000 Milliseconds.
Answer:
3.154e+10, 30 billion milliseconds are in one calendar year.
Graph the line with a slope of 2/5 that goes through (3,1)
Answers
Answer:
[tex]y = \dfrac{2x}{5} - \dfrac{1}{5}[/tex]
Step-by-step explanation:
Given:
[tex]\bullet \ \ \text{Slope of line:}\ \dfrac{2}{5} \\\\ \bullet \ \text{Passes through:} \ (3, 1)[/tex]
To determine the equation of the line, we will use point slope form.
Formula of point slope form:
→ y - y₁ = m(x - x₁)Where "x₁" and "y₁" are the coordinates of the point and "m" is the slope.
Substitute the coordinates and the slope:
[tex]:\implies y - 1 = \dfrac{2}{5} (x - 3)[/tex]
Simplify the R.H.S:
[tex]:\implies y - 1 = \dfrac{2x}{5} - \dfrac{6}{5}[/tex]
Add 1 both sides:
[tex]:\implies y - 1 + 1 = \dfrac{2x}{5} - \dfrac{6}{5} + 1[/tex]
Simplify the equation:
[tex]:\implies y = \dfrac{2x}{5} - \dfrac{6}{5} + \dfrac{5}{5}[/tex]
[tex]:\implies \boxed{y = \dfrac{2x}{5} - \dfrac{1}{5}}[/tex]
Graphing the line on a coordinate plane:
In this case, we are already given a point (3, 1). We can simply plot the y-intercept [tex][\bold{\frac{-1}{5} }][/tex] on the coordinate plane. Then, we can draw a straight line through both points. It is suggested that you use a ruler to do so.
Graph attached**
Answer:
See attachment and explanation
Step-by-step explanation:
slope is x/y, which means for each x how many y's it moves by.
so,
2/5 means for every 2 x's it goes up by 5 y's.
so,
you take the point A and go right 2 and go up 5. That's the next point (5,6)
Same with the point other side of A. Go left 2 and go down 5. That's another point (1,-4)
Since, the slope 2/5 is positive, the line will be an increasing line. As shown in the attached image.
Point A has coordinates (4, -1)
Point B has coordinates (9, 7)
Work out the coordinates of the midpoint of the line AB.
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad B(\stackrel{x_2}{9}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 9 + 4}{2}~~~ ,~~~ \cfrac{ 7 -1}{2} \right)\implies \left(\cfrac{13}{2}~~,~~\cfrac{6}{2} \right)\implies \left( 6\frac{1}{2}~~,~~3 \right)[/tex]
Please I need help and I'm struggling on this question
Answers
Answer:
D
Step-by-step explanation:
The combined expenses for year 3 and 4 are 600,000 + 700,000 which equal 1,300,000. The combined income for year 3 and 4 are 400,000 + 600,000 which equal 1,000,000. 1,300,000 (the combined expenses for year 3 and 4) is also 300,000 greater than 1,000,000 (the combined income for years 3 and 4)
Sofia buys a two-gallon bottle of juice for $35.84. what is the unit rate of the cost of the juice per fluid ounce?
how many fluid ounces of juice did sofia buy?
Answers
Answer:
$0.14 per fl oz /// 256 fl oz of juice.
Step-by-step explanation:
The number of fluid oz per gallon = 128
2 gallons = 256 fl oz
$35.84/256= $0.14.
--------------------------------------
1 gallon = 128 fl oz.
128x2 = 256
2 gallons = 256 fl oz.
ten less than 40% of a number is -4
Answers
Answer:
Number is "n" (.40* n)-10=-4
Step-by-step explanation:
i found this off of the Internet hope this helps
What is the center and radius of the circle?
Answers
Answer:
Center = (5,-3) radius = sqrt (36) = 6
Step-by-step explanation:
WILL GIVE BRAINLIEST, THANKS, AND 5STARS!
PLEASE HELP ME ANSWER THIS QUESTION
Answers
Answer:
h(.5)= -16(.5)^2 + 50
= 46
Angelique makes beaded jewelry. The graph below shows the number of beads on varying cord lengths.
Jewelry
A graph has cord length (inches) on the x-axis and number of beads on the y-axis. A line has a regression equation of y = 2.52 x + 1.61.
A necklace contains 88 beads. Based on the information above, which is the best estimate for the cord length?
21 inches
26 inches
34 inches
36 inches
Answers
Answer:
26
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
Congruent to angle B
Answers
Answer:
-------------------
Step-by-step explanation:
while the other answer is not wrong in this case, it is not complete.
"congruent angle" means the angles are equal.
so, yes, diagonally down is one, but also at exactly the same 2 spots over at the intersection point of the blue line with the second parallel red line.
Pentagon A is rotated 180° about its center and then translated to create pentagon B.
What is the value of x?
Answers
The value of x after the simultaneous rotation and translation of pentagon A to create pentagon B is 110°
What is the translation of plane figures?A plane figure translation is an isometry that translates each position of the figure at a distance and in a direction indicated by the vector.
It is also regarded as a sort of transformation that involves sliding each point in a plane figure at an identical distance in a similar direction.
From the attached image, the value of x after the simultaneous rotation and translation of pentagon A to create pentagon B is 110°.
Learn more about the translation of plane figures here:
https://brainly.com/question/2467920
Betty sits 9 feet from the fulcrum and weighs 100 pounds. How far should Ginger sit if she weighs 125
pounds?
Answers
Answer:
7.2 feet
Step-by-step explanation:
Torque is calculated by T=Frsin(theta). Betty's total torque is 9 x 1000 (mg) = 9000. Since ginger weighs 125 pounds, 9000 = (125 x 10) x r. Solve for r and get 7.2 feet.
Write a word problem that must be solved with division and includes 2/7 as the dividend and 4 as the divisor.
Answers
The word problem is
A Cake has 2/7 part left.iF it's shared between 4persons how much each get ?
Let's solve it
Let each get x
x=2/7÷4x=2/7×1/4x=1/14Answer:
See below ~
Step-by-step explanation:
Mitch is given 2/7 of a cake as a prize for winning a contest. He would like to share it among him and his 3 friends. How much of a whole cake do each of them get?
Solving
Cake in hand = 2/7Number of people = 4Cake per person = Cake in hand / no. of peopleCake per person = (2/7) / 4Cake per person = 2/28 = 1/14 of the cake8. Find the Mean Absolute Deviation of the set: 10, 5, 7, 14, 19, 32, 25
Answers
Answer: 16
to find the mean you have to add all the numbers up and divide it by how many numbers are in the set
Answer:
[tex] \frac{10 + 5 + 7 + 14 + 19 + 32 + 25}{7} \\ = 16[/tex]
if 15 mini pizzas cost 25 dollars how much would 25 mini pizzas cost?
Answers
Answer:
41.75
Step-by-step explanation:
First we divide :)
25/15 = 1.67
Now we multiply!!
1.67 x 25 = 41.75
Have an amazing day!!
Please rate and mark brainliest!!
if a thing is not a flower, then it is not a plant.
shorthand
Answers
Answer:
False, plants can be anything, take grass and trees and cacti, plant just need photosynthesis.
Step-by-step explanation:
You see, plants aren't based on if they are a flower or not
Find the sale price Original price: $50 Discount: 15% Sale price: $
Answers
A lender estimates the closing costs on a home loan of $90,000 as listed below. closing cost charge loan origination $180 title insurance $365 attorney’s fees $795 inspection $300 recording fees $120 escrow $980 the actual closing costs were: closing cost charge loan origination $180 title insurance $340 attorney’s fees $830 inspection $375 recording fees $150 escrow $1,000 evaluate the lender's good faith estimate as a percentage of the loan amount. a. the lender made a very good estimate; it was within 0.25% of the actual closing costs. b. the lender made a fairly good estimate; it was between 0.25% and 0.5% from the actual closing costs. c. the lender made a somewhat poor estimate; it was between 0.25% and 0.5% from the actual closing costs. d. the lender made a very poor estimate; it was between 0.5% and 0.75% from the actual closing costs.
Answers
Based on the details above, the lender's good faith estimate is one that is within 0.25% of the actual closing costs.
What is good faith estimate?A Good Faith Estimate commonly referred to as GFE, is known to be a kind of situation where a lender is given to a person as one request or apply for a form of reverse mortgage.
Note that the Lenders often needs a Good Faith Estimate (GFE) for about a period of three business days one getting the loan application. This will explain your loan terms and costs linked with the loan.
From the above, , the lender's good faith estimate is one that is within 0.25% of the actual closing costs and thus can tell the costs linked with the loan.
Learn more about good faith from
https://brainly.com/question/24725464
Answer:
is D. the lender made a very poor estimate; it was between 0.5% and 0.75% from the actual closing cost
Step-by-step explanation:
I saw the answer on quizlet
Last year, 351 children signed up to play football in Johnston County. Each single team had 27 players on its roster.
How many football teams were there in Johnston County?
13 teams
14 teams
15 teams
16 teams
Answers
Answer:
13 teams
Step-by-step explanation:
You have 351 children, and each team has 27 players.
Putting this into an equation you get:
351 ÷ 27 = x
x = 13
A straw forms a cylinder with a length of 270 millimeters and a diameter of 6 millimeters. What is the volume of the straw in cubic millimeters? Round your answer to the nearest hundredth.
Answers
The volume of the cylindrical straw of diameter 6 mm and length of 270 mm is 7630.20 mm³
Volume of a cylinder
volume of a cylinder = πr²h
Therefore,
r = radius of the baseh = height of the cylinderHence,
radius = r = 6 / 2 = 3 mm
volume of the cylinder = 3.14 × 3² × 270
volume of the cylinder = 3.14 × 9 × 270
volume of the cylinder = 7630.2 mm³
Therefore, the volume of the straw is 7630.2 mm³
learn more on cylinder here: https://brainly.com/question/15723055
#SPJ1
A quantity p varies jointly with r and s. which expression represents the constant of variation, k? prs startfraction p over r s endfraction startfraction r s over p endfraction p r s
Answers
Answer:
k = p/(rs)
Step-by-step explanation:
The equation that represents p varying jointly with r and s will be ...
p = k·r·s . . . . . . . . for some constant of variation k
__
Solving this equation for k gives ...
k = p/(rs) . . . . . divide by the coefficient of k
Q. Find the area of the figure. 10 cm2 12 cm2 20 cm2 24 cm2
Answers
Answer:
[tex]24cm^{2}[/tex]
Hope This Helps! :) Please give Brainliest if it does!