After solving the next three terms in
5120, 1280, 320, 80, …
How could you find the explicit rule?
Answers
a (n)=a1 × r^(n-1)
a1=5120
a2=1280
a3=320
a4=80
-->a2/a1=1280/5120=0.25
-->a3/a2=320/1280=0.25
-->a4/a3=80/320=0.25
ration(r) =0.25
■■■a(n)=a1 × r^(n-1)■■■
a (5)=5120×0.25^(5-1)
a (5)=5120 × 0.25 ^(4)
a (5) = 5120 × 0.00390625
a (5) = 20
Related Questions
an electrician has 4.1 meters of wire.How many strips of 7 tenths can be cut?and how much wire will be left over?
Answers
0.5 meters per strip
0.6 meters left over
This is a multi-part question you will refer back to this and other finished parts to help answer this and future questions
In 2005 a town with a population of 10,000 finds that its population is declining by a rate of 0.3% per year. Find the following Johnny was asked how long it will take the population to reach 1/2 of the original population. He answered that it would never reach half, what is the incorrect assumptions Johnny made? (answer with a
Johnny was asked how long it will take the population to reach
complete sentence) Please help.
Answers
The assumption Johnny made is that, none of the residents of the town will live up to 230.7 years.
The given parameters are:
[tex]\mathbf{a =10000}[/tex] --- the initial population
[tex]\mathbf{r =0.3\%}[/tex] -- the declining rate
Population are always modelled using exponential function.
This is represented as:
[tex]\mathbf{y = a(1 - r)^x}[/tex]
Where y represents the population in x years.
So, we have:
[tex]\mathbf{y = 10000(1 - 0.3\%)^x}[/tex]
[tex]\mathbf{y = 10000(1 - 0.003)^x}[/tex]
[tex]\mathbf{y = 10000(0.997)^x}[/tex]
When the population reaches half, then y = 5000.
So, we have:
[tex]\mathbf{5000 = 10000(0.997)^x}[/tex]
Divide both sides by 10000
[tex]\mathbf{0.5 = 0.997^x}[/tex]
Take logarithm of both sides
[tex]\mathbf{log(0.5) = log(0.997)^x}[/tex]
Apply law of logarithm
[tex]\mathbf{log(0.5) = xlog(0.997)}[/tex]
Make x the subject
[tex]\mathbf{x = log(0.5) \div log(0.997)}[/tex]
[tex]\mathbf{x = 230.7}[/tex]
This means that the population will become half the original population in 230.7 years.
The assumption Johnny made is that, none of the residents of the town will live up to 230.7 years.
Read more about exponential function at:
https://brainly.com/question/11487261
Which term of the arithmetic sequence 1, 5, 9, 13, ... is 169?
It is the
th term.
Answers
Answer:
43rd term
Step-by-step explanation:
Arithmetic sequences are basically linear functions, so the same value is added every time. So, knowing that Asub1 is equal to one, and Asubn is equal to 169 we can take 169-1 and divide by our common difference. This is four as 5-1=4 and 9-5=4.
So, (169-1)/4=42.
This is however 42 terms after Asub1, so this would be the 43rd teen of the sequence!
Use point-slope form to write the equation of a line that passes through the point
(-6,3) with slope – 2.
Answers
Answer:
y = -2x - 9
Step-by-step explanation:
Slope = - 2
Using the slope = -2 and the point (-6, 3) substitute into y= mx + b and solve for "b"
y = mx + b
3 = -2(-6) + b
3 = 12 + b
3 - 12 = b
-9 = b
The equation of the line is y = -2x - 9
Ping chooses four numbers.
The mode of these four numbers is 8, the range is 7 and the mean is 11.
Find Ping's four numbers.
Answers
8,8,15,13
I hope this helps
3. drinking 8 glasses of water a day is good for your health. if each glass of water is equivalent to 148 mL, how many liters of water you need to consume everyday.
Answers
Answer:
pap
Step-by-step explanation:
papi
Answer:
1184 mL (148×8)= 1.184 liters
this graph shows how much lisa earns babysitting compared with thge number of hours she works
Answers
Answer:
For every hour she earns 12$
Step-by-step explanation:
If your question looks like the picture, then the answer above is the right answer. If it's not, oh well, show the picture next time!
Plzzzz help meeeee plzzzz
Answers
Answer:
200
Step-by-step explanation:
The degree measure of each exterior angle of a regular octagon is represented by the expression 7x - 4. SOLVE FOR X.
Answers
Answer:
x = 4/7
Step-by-step explanation:
7x - 4
7x = 4
x = 4/7
Which one of the quotients is correct?
Answers
Answer:
B
Step-by-step explanation:
B is correct 24r11 one ................
If 'r' represents remainder then the correct answer is option A. The quotient is 24 & the remainder is 13.
Steps are in the attachment.
____
RainbowSalt2222 ☔
F(4p + 3) = 8 - 5(4p + 3)
Answers
=============================
[tex]\large\bold{Equation:}[/tex]
[tex]\large\sf{F(4p + 3) = 8 - 5(4p + 3)}[/tex][tex]\large\bold{Solution:}[/tex]
Let's solve for f
[tex]\large\sf{F(4p + 3) = 8 - 5(4p + 3)}[/tex]
1st step: Factor out variable f
[tex]\large\sf{F(4p+3)=−20p−7}[/tex]2nd step: Divide both sides by 4p+3
[tex]\large\sf{ \frac{F(4p + 3)}{4p + 3} = \frac{ - 20p - 7}{4p + 3} }[/tex][tex]\large\sf{F = \frac{ - 20p - 7}{4p + 3} }[/tex][tex]\large\bold{Answer:}[/tex]
[tex]\large\tt{F = \frac{ - 20p - 7}{4p + 3} }[/tex]===================================
How is it? Hope you appreciate and understand my answer. Have a great and nice day ahead!!
^^
A homeowner collects data about the amount of oil, in gallons, used to heat the house per month for 5 months and the average monthly temperature, in degrees Fahrenheit, for those months. The scatter plot shows the data. The function best fits these data.
Use the function A(t)to determine which of the following statements are true. Select all that apply.
A The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 ° F.
B The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 ° F.
C The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 ° F.
D The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F. The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 ° F.
E The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.
Answers
They are doing the calculations, we can say that the alternatives are:
A) True
B) False
C) False
D) False
E) True
For this exercise, the equation should be used:
[tex]A(t)=-1.4t+96[/tex]
So analyzing the first given statement we will have to:
[tex]A(t)=-1.4t+96\\t=10\\A(t)=-14+96=82[/tex]
Based on the calculations, this statement is true, for the second statement we will have:
[tex]A(t)=-1.4t+96\\t=15\\A(t)=-21+96=75[/tex]
From the calculations this statement is false, so for the alternative we will have:
[tex]A(t)=-1.4t+96\\t=55\\A(t)=-77+96=19[/tex]
From the calculations this statement is false, so for the alternative we will have:
[tex]A(t)=-1.4t+96\\t=0\\A(t)=96[/tex]
Based on the calculations, this statement is true.
Learn more: brainly.com/question/516840
i need help please ill give u brainlist to who ever answer
Answers
Still won his election by a margin of 7 to 2 his opponent had 3492 votes how many votes did Steve have
Help ASAP
Answers
Answer:
12,222 votes
Step-by-step explanation:
7 x 3492= 24,444
24,444/2= 12,222
Steve has 12,222 votes.
marcus piano teacher wanted him to practice 1.5 hours before she saw him on friday afternoon he practiced 18 minutes on monday 23 minutes on tuesday 16 minutes on wednesday and 13 minutes on thursday. how long did he have to practice on friday morning to meet his goal? what fraction of an hour is that? pls help 15 if correct
Answers
he would have to practice 20 minutes on friday
18 + 23 + 16 + 13 = 70
1.5 hours = 90 minutes
90-70 = 20 minutes
2/9
what is? -6 = x + 6
this is one step equation addition / subtraction
Answers
[tex] \: \: \: \: \: [/tex]
x = - 12
refer to the attachment
refer to the attachmenthope it helps[tex]\sf \longmapsto-6 = x + 6[/tex]
Flip the equation[tex]\sf \longmapsto \: x+6=−6[/tex]
Subtract 6 from both sides[tex]\sf \longmapsto \: x+6−6=−6−6[/tex]
[tex]\sf \longmapsto \: x=−12[/tex]
[tex] \boxed{ \sf \: x=−12}[/tex]
PLZ HELP ASAP! I'LL GIVE BRAINLIEST AND POINTS JUST HELP PLZ
plz no links
Divide these numbers in scientific notation.
(9.6*10^-8) divided by (3*10^-7)
Answers
Answer:
3.2 *10^-1
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]\dfrac{9.6*10^{-8}}{3*10^{-7}}==\dfrac{9.6}{3}*10^{-8-[-7]}\\\\\\= 3.2*10^{-8+7}\\\\\\=3.2*10^{-1}[/tex]
A:B is equivalent to 11:5.
Answers
Answer:
yeeeeee
Step-by-step explanation:
Mary goes to the bakery with $35. She purchases 2 loaves of bread for $3 each and a cake for $15. She plans to spend the remainder of her money on cookies that cost $1.25 each.
What is the greatest number of cookies that Mary can buy?
HELPPPP
Answers
Answer:
The greatest number is 11
Step-by-step explanation:
It is 11 because 3+3=6+15=21
35-21=14
14/1.25=11.2
hope this helps
-4/4 plus 160 percent plus 1/5
Answers
Answer:
-1 + (1.6) + 0.2
Step-by-step explanation:
-1 + 1.6 = 0.2 = 0.8
Answer:
-1 + (1.6) + 0.2
Step-by-step explanation:
-1 + 1.6 = 0.2 = 0.8
Can someone please tell me how to subtract 1 3/8 by 3/4
Answers
Answer:
13/8-3/4. LCM=2×2×2=8
= find the LCM of the denominators. 2 8 4
= 13 -6 /8 2. 4. 2
= 7/8 2 2. 1
; 1. 1
(I’m having trouble with this question, it would be greatly appreciated if I could have some help, thank you)
What is the equation of a line that is parallel to – 2x + 3y = -6 and passes through the point (-2, 0)?
Answers
Answer:
y = 2/3x + 4/3
Step-by-step explanation:
you need to know the slope of the line -2x + 3y = -6 because parallel lines have the same slopes
let's put the equation in y=mx+b format (slope-intercept format)
-2x + 3y = -6
add 2x to each side to get:
3y = 2x - 6
divide each side by 3 to get:
y = 2/3x - 2
the equation now shows us the slope is 2/3 and the y-intercept is (0,-2)
now we use y=mx+b again and use the point (-2,0) and the m=2/3 to get the y-intercept ('b' value) of the equation that is parallel:
0 = 2/3(-2) + b
0 = -4/3 + b
b = 4/3
equation would be:
y = 2/3x + 4/3
Please help with this question.
Thanks.
Answers
Answer:
10
Step-by-step explanation:
E = V + 1/2mv^2
700 = 300 + 1/2*8*v^2
400 = 4v^2
100 = v^2
v = 10
solve pls brainliest
Answers
Answer:
I=Prt
(I= interest
P=principle amount
r=rate per year in decimal form
t=time period)
●I = Prt
I = 8000×(2/100)×6
I = 8000×0.02×6
I =$960
BRAINLIST PLS
Step 4: Plot the y-intercept.
Answers
Plot the y-intercept. The point will be (0, b).
Find the slope=m of the equation y = mx + b.
Make a single step, using the rise and run from the slope. ...
Then:
Connect those two points with your line.
Mom bought a bag of 12 apples. She discovered that 1/6 of the apples were spoiled. How many apples were spoiled? How many unspoiled apples does Mom have?
Answers
cos135° =
A.√2/2
B.-√2/2
C.-1/2
Answers
we have cos135° = -√2/2
so B is the correct answer
ok done. Thank to me :>
what is the answer help
Answers
Answer:
$29.88
Step-by-step explanation:
$12.45 / 5
$2.95 each pound
2.95 * 12
29.88
Question is atttached below
Answers
Answer:
A. 20·60
Step-by-step explanation:
The product of force and distance is ...
[tex]F\cdot D=(20\text{ m})\cdot\dfrac{60\text{ kg$\cdot$m}}{\text{s}^2}=\dfrac{20\cdot60\text{ kg$\cdot$m$^2$}}{\text{s}^2}=\boxed{20\cdot60\text{ J}}[/tex]
Write each expression without using exponents.
a.
[tex]5 \frac{2}{3} [/tex]
b.
[tex]4 - \frac { 3}{2} [/tex]
Answers
5⅔ = ...
= (3 × 5 + 2)/3
= (15 + 2)/3
= 17/3
[tex] \: [/tex]
B.)4 - 3/2 = ...
= 4 - 1,5
= 2,5 <==> 2½
[tex]5 \frac{2}{3} [/tex]
[tex]=\frac{5 \times 3 + 2}{3} [/tex]
[tex] = \frac{15 + 2}{3} [/tex]
[tex] = \frac{17}{3}[/tex]
[tex]4 - \frac{3}{2} [/tex]
[tex] = \frac{4}{1} - \frac{3}{2} [/tex]
[tex] = \frac{4 \times 2}{1 \times 2} - \frac{3}{2} [/tex]
[tex] = \frac{8}{2} - \frac{3}{2} [/tex]
[tex] = \frac{8 - 3}{2} [/tex]
[tex]= \frac{5}{2}[/tex]
[tex] = 2 \frac{1}{2} \: \: \: or \: \: \: 2,5[/tex]