Answers
Answer:
1) (Un) is a geometric sequence.
2) Un+1 - Un ≤ 0.
3) (Un) is decreasing.
4) (Un) is convergent.
5) sum = 155
Step-by-step explanation:
Un+1 = 0.5Un
U₀ = 80
1) U is a geometric sequence (reason : Un+1 = 0.5Un).
2) Un+1 - Un = 0.5Un - Un = Un×(0.5 - 1) = -0.5Un ≤ 0 (because Un ≥ 0).
Remark: use Mathematical induction to prove that Un ≥ 0
3) Un+1 - Un ≤ 0
then
Un+1 ≤ Un
then
the sequence U is decreasing.
4) U is decreasing and Un ≥ 0
Then U is convergent.
5) Since U is geometric sequence with first term U0 = 80 and common ratio = 0.5 .
Important: review the sum of consecutive terms of a geometric sequence.
Then
[tex]U_0+ U_1+ U_2+ U_3+ U_4=U_{0}\times \frac{1-\left( 0.5\right)^{5} }{1-0.5}=160\times(1-\left( 0.5\right)^{5} )=155[/tex]
Related Questions
Can someone help with this? I've been stuck on this for a while
Answers
Step-by-step explanation:
how is that math ?
anyway,
*♡ = O
●* = H
arrow up and filed triangle = E
arrow down and 3/4 circle = R
Please see attached question I am stuck on.
Answers
By looking at this problem:
⇒ must use trigonometric functions:
⇒ (look at image attached for further reference)
Let's solve:
For side 'a'[tex]sin(10)=\frac{a}{13}\\ a = 13sin(10)\\a=2.25743[/tex]
For side 'b'[tex]cos(10)=\frac{b}{13} \\b = 13cos(10)\\b = 12.80250[/tex]
Make sure to round your answer to four decimal points
Answer:
a = 2.2574b = 12.8025Hope that helps!
what is the minimum value of the function 3x^2 -4x +8
Answers
Step-by-step explanation:
f(x)=3x²-4x+8
f(1)=(3*1)²-4(1)+8
f(1)=3²-4+8
f(1)=9-4+8 or using BODMAS
f(1)=5+8 or f(1)=9-12
f(1)=13 or f(1)=-3
write 28% as a fraction
Answers
Answer:
28% as a fraction can be written in many ways. The most simplest way to convert a percentage to a fraction would just to put it over 100. For example, 50% would be 50/100 therefore 28% would be 28/100.
However, we can simplify that fraction even more by doing (28/4)/(100/4) which would give us 7/25.
Hope this helps!
What is the slope of the line passing through the points (2, 5) and (0, -4)?
Show all your work.
Leave your answer as a fraction
Answers
Answer:
slope = 9/2
Step-by-step explanation:
y2 - y1 / x2 - x1
-4 - 5/0- 2 = 9/2
An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Select the diagrams that would represent the types of animals adopted.
Alt_text
Alt_text
Alt_text
Alt_text
Alt_text
Part B
How many of each type of animals were adopted?
ferrets,
dogs,
cats
Answers
Answer:
there are 3 ferrets,15 dogs,27 cats
Step-by-step explanation:
the ratio of the three
9:5:1
the ferrets,1/15 * 45= 3
the dogs,5/15 * 45= 15
the cats, 9/15 * 45=27
PLEASE HELP!!!!!!! IMA DESPRATE!!!!!!! A radioactive isotope decays exponentially. The time it takes for half of the amount to decay is called the isotope's half-life. If an isotope has a half-life of 16 hours and you initially have 154 mg, how much will you have left after 64 hours? Round to the nearest thousandth.
Answers
Since the isotope is initially 154 mg, the amount of radioactive isotope left after 64 hours is 9.625 mg
To answer the question, we need to know what radioactive decay is.
What is radoactive decay?Radioactive decay is the spontaneous disintegration of a larger atom to a smaller one
What is half-life?Half-life of a radioactive isotope is the time it takes for the isotope to decay to half its initial value.
Amount left after n half livesThe amount left after n half lives is N = (1/2)ⁿN₀ where N₀ = initial mass of isotope.
Given that the half-life of the isotope is 16 hours, and we desire the amount present after 64 hours.
The number of half-lives after 64 hours is n = time/half-life
= 64 h/16 h
= 4
Since we have 154 mg of isotope present, N₀ = 154 mg
Given that
n = 4 and N₀ = 154 mgSubstituting the values of the variables into N, we have
N = (1/2)ⁿN₀
N = (1/2)⁴ × 154 mg
N = 154 mg/16
N = 9.625 mg
So, the amount of radioactive isotope left after 64 hours is 9.625 mg
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PLEASE HELP ASAP
what is an equation of the line that passes through the points (2,-3) and (2,6)
Answers
Answer:
x = 2
Step-by-step explanation:
The two points have the same x-coordinates, so lie on the same vertical line:
x = 2
!!!!HELPPPP!!!! if cos theta = - square root 3 over 2 and pi < theta < 3 pi over 2, what are the values of sin theta and tan theta?
will mark Brainliest for correct answers .
i’m in a final pls help
Answers
Answer:
Option 4
Step-by-step explanation:
In Quadrant IV,
tan = +vecos = -vesin = -veIf cosθ = -√3/2, then :
sinθ = -1/2tanθ = √3/3solve the equation -8=7x+2/5
Answers
Answer:
-6/5 = x
Step-by-step explanation:
Multiply by 5 to get rid of fractions:
-40 = 35x + 2
Subtract by 2 to get all terms on one side:
-42 = 35x
Divide by 35 to get x term:
-42/35 = x
-6/5 = x
Which is least? 1.26 ÷ 0.3 OR 7.84 ÷ 5.6
Answers
so clearly...the 2nd one is the least
hope it helps...!!!
Answer:
7.84 / 5.6 is least
Step-by-step explanation:
1. 1.26 / 0.3
= 4.2
2. 7.84 / 5.6
= 1.4
answer of 1. is 4.2 and 2. is 1.4
1.4 is less than 4.2
In parallelogram EFGH if GE=30 find GJ.
Answers
Answer:
GJ = 15
Step-by-step explanation:
ParallelogramGE = 30
GE is the diagonal.
In a parallelogram, the diagonal bisect each other
GJ = GE ÷ 2
= 30 ÷ 2
GJ = 15
Which is a coeffecient
Answers
Answer:
B is a coefficient
Step-by-step explanation:
Coefficient of 2O2 is 2.
B = 2
Find the 4th term of the geometric sequence whose first term is 3 and common ratio is 2.
Answers
The 4th term of the geometric sequence whose first term is 3 and the common ratio is 2 is 24.
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is a
and the term by which we multiply the previous term to get the next term is r then the sequence would look like
a, ar, ar², ar³,...., arⁿ
Thus, the nth term of such sequence would be aₙ = a₁ × r⁽ⁿ⁻¹⁾ (you can easily predict this formula, as for the nth term, the multiple r would've multiplied with initial terms n-1 times).
Given the first term of the sequence is 3, while the common ratio is 2, therefore, the fourth term of the geometric sequence can be written as,
aₙ = a₁ × r⁽ⁿ⁻¹⁾
a₄ = 3 × 2⁽⁴⁻¹⁾
a₄ = 3 × 2³
a₄ = 24
Hence, the 4th term of the geometric sequence whose first term is 3 and the common ratio is 2 is 24.
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Find the approximate values of the five-number summary for the data set represented by this box plot.
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Please hurry!!!
Answers
Answer: Minimum: 0
Quartile Q1: 22.5
Median: 50
Quartile Q3: 77.5
Maximum: 100
Step-by-step explanation:
Please help I’m not sure about this one x=106
Answers
Answer:
Question?
Step-by-step explanation:
where is the Question?
The executive summary component of a business plan is to describe
a where the funds to start and operate your business will come from, when you expect to see
profit, and how much profit you expect to see
b. the size of the market, how your business will fit into the market, and how your business will
stand out from other businesses in the market
c. the 'big picture behind your business, what your business has to offer the consumer, and why
your business will be successful
d. how your business will be organized and what type of management or department structure
your business will have
Please select the best answer from the choices provided
ΟΑ
О В
ОС
Answers
Answer:
Executive summary describes the 'big picture behind your business, what your business has to offer the consumer, and why
Step-by-step explanation:
B is right
The figure shows a planter Mrs Washington uses for flowers please help fast
Answers
Answer:
67.5 ft^3
Step-by-step explanation:
7.5 * 2 * 3.5 + 3 * 2.5 *2 = 67.5 ft^3
Calculate (C ∘ F) for the month
Answers
To calculate temperature (C ∘ F) Celsius to Fahrenheit for the month, use the following expression.
[tex]^oC=\dfrac{5}{9}(^oF-32)[/tex]How to convert Celsius to Fahrenheit?
Temperature is the way to express the hotness or coldness of a body or object surface. The scales of measuring temperature are:
Celsius FahrenheitKelvinTo convert Fahrenheit to Celsius, we use the following formula.
[tex]^oF=^oC\times\dfrac{9}{5}+32[/tex]
The formula to convert Celsius to Fahrenheit is
[tex]^oC=\dfrac{5}{9}(^oF-32)[/tex]
Now, there is no data given in the problem. Thus, the above formula for any data can be used to convert the unit of temperature measurement.
Hence, to calculate temperature (C ∘ F) Celsius to Fahrenheit for the month, use the following expression.
[tex]^oC=\dfrac{5}{9}(^oF-32)[/tex]
Learn more about the temperature measurement here:
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A triangle has vertices T(3, 7), U(6, -6), and V(5, -9).
The image of the triangle has vertices T'(8, 1), U'(-5,
4), and V'(-8, 3).
Which transformations could have produced the
image?
OT(1.-2) ° Ty=x
Ory=x0 T(1, -2)
O Ta. -2) o Ro, 180°
O
O Ro. 180
Ta. -2)
Answers
Step-by-step explanation:
y=2x find the value of y and x
Rita earns $19.00 per hour. If she gets a 5% raise, what will be her new hourly wage?
A. $19.05
B. $24.00
C. $19.95
D. $18.05
Answers
Answer:
C.
Step-by-step explanation:
Find 5% of 19:
19 x 0.05 = 0.95
0.95 + 19 = 19.95
answer is C. 19.95
Please help thanks! Will give brainiest
Answers
Answer:
Colinear points: Points that lie on the same line.
Coplanar points: Points that lie in the same plane.
Plane: a flat, 2D surface with no height.
1. Three colinear points: A, B, E
2. Four coplanar points: A, B, C, E
3. A plane containing E: plane S
4. Two points and a line that lie in Plane T: Points F & G, Line L
5. Two planes that contain l: S and T
which is the graph of f(x)=3√x
Answers
Answer: The first graph
Step-by-step explanation:
It's the first one. I don't know how to explain, haha.
Randy is starting a beehive so that he can have fresh
honey. He decides to check the current population of bees
in the hive by marking 160 bees. Later, Randy collects 240
bees and observes that 30 of them are marked. What is the
BEST estimate for the bee population?
Answers
Answer:
1,280
Step-by-step explanation:
Are the triangles similar?
Answers
Answer:
No, because the sides lengths are not proportional.
Step-by-step explanation:
What is the SAS similarity theorem ?By definition, two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional.
What is the AA similarity theorem ?If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
They both have an angle of 70°This lies between sides of 6/9 and 9/18 respectively for the triangles6/9 = 2/3 and 9/18 = 1/2Hence, the sides are not proportionalThey are not similar(50 + brainiest if correct!)
From each square we can construct a second square, whose area is double that of the first square.
Construct from the square abcd below a second square, whose area is double the area of the square abcd.
Answers
Answer:
So the first thought would be to make the length and width twice the size of the original square but this would actually cause us to multiply the area by 4.
The second thought was to raise one of the sides to be twice the length or width and that would give us the correct answer since we are just multiplying it by 2. If side AB is the only one that can move then we would just extend that side twice the original length.
What is the third angle on a triangle with angels of 45 and 45?
Answers
- - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]
what is the third angle of a triangle with angles of 45 and 45?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]
Angles in a triangle always add up to [tex]\bold{180\textdegree}[/tex].
❖ Here we are given 2 angles:-
45 and 45, which add up to 90.
❖ Subtract 90 from 180:-
90
✶ So the angles are 45, 45 and 90.
Good luck.
- - - - - - - - - -- - - - - - - - - - -- - - - - - - - - -
Answer:
90 degrees.
Step-by-step explanation:
As there are 180 degrees in a triangle
third angle = 180 - 45 - 45 = 90 degrees.
Frank bought a pair of gloves for $9.95 and a hat for $5.25. What is the best estimate of much he spent?
$15.00
$10.00
$5.00
$25.00
Answers
Answer:
$
15.00
Step-by-step explanation:
Round the costs of the gloves and hat. $9.95 is very nearly $10. And even though $5.25 is over $5 , it is still very close. $10+$5 is $15. This is the estimate.
Twice the difference of a number and 6 is 5
Use the variable x for the unknown number
Answers
To rewrite a word equation as a numerical equation, we can recognize certain keywords and change them into numbers or operations.
twice = multiply by 2difference = subtract'a number' = let this be xis = equalsSolving the QuestionWe're given:
Twice the difference of a number and 6 is 5⇒ twice = (2 ×)
⇒ difference of a number and 6 = (x - 6)
⇒ is 5 = ( = 5)⇒ 2(x-6) = 5
To solve for x, isolate the variable:
2(x-6) = 5
2x-12 = 5
2x = 17
x = [tex]\dfrac{17}{2}[/tex]
Answer[tex]\dfrac{17}{2}[/tex]
Which of the following is the correct factorization of the polynomial below?