Answer:
Arithmetic Sequence
[tex]T_n = 240-60n[/tex] ---- Explicit
[tex]T_n = T_{n-1} - 60[/tex] --- Recursive
Geometric Sequence
[tex]T_n = 270* (\frac{2}{3})^n[/tex] ---- Explicit
[tex]T_n = T_{n-1} * \frac{2}{3}[/tex] ---- Recursive
Step-by-step explanation:
Given
[tex]180, 120,....[/tex]
(a) Assume it is an arithmetic sequence
The explicit formula is calculated using:
[tex]T_n = a + (n - 1)d[/tex]
Where
[tex]a = 180[/tex]
[tex]d = 120 - 180[/tex]
[tex]d = -60[/tex]
So, we have:
[tex]T_n = 180 + (n - 1)*-60[/tex]
[tex]T_n = 180 -60n + 60[/tex]
Rewrite
[tex]T_n = 180 + 60-60n[/tex]
[tex]T_n = 240-60n[/tex]
The recursive function is calculated using:
[tex]T_1 = 180[/tex]
[tex]T_2 = 120 = 180 - 60 = T_1 - 60[/tex]
[tex]T_3 = 60 = 120 - 60 = T_2 -60[/tex]
-
[tex]T_n = T_{n-1} - 60[/tex]
(b) Assume it is a geometric sequence
The explicit formula is calculated using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = 180[/tex]
[tex]r = \frac{120}{180}[/tex]
[tex]r = \frac{2}{3}[/tex]
So, we have:
[tex]T_n = 180 * (\frac{2}{3})^{n-1}[/tex]
Split
[tex]T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})^1[/tex]
[tex]T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})[/tex]
Rewrite as:
[tex]T_n = 180 * (\frac{2}{3})^n * (\frac{3}{2})[/tex]
[tex]T_n = 180 * (\frac{3}{2})* (\frac{2}{3})^n[/tex]
[tex]T_n = 180 * \frac{3}{2}* (\frac{2}{3})^n[/tex]
[tex]T_n = 90 * 3* (\frac{2}{3})^n[/tex]
[tex]T_n = 270* (\frac{2}{3})^n[/tex]
The recursive function is calculated using:
[tex]T_1 = 180[/tex]
[tex]T_2 = 120 = 180 * \frac{2}{3} = T_1 * \frac{2}{3}[/tex]
[tex]T_3 = 80 = 120 * \frac{2}{3} = T_2 * \frac{2}{3}[/tex]
-
[tex]T_n = T_{n-1} * \frac{2}{3}[/tex]
Alright another here we go, Please help!
Answer:
4x=y
Step-by-step explanation:
4x=y is your answer because if x is 5, like in the table, then 4(5) would equal 20, which is the y-value. It also works for every number in the table.
Hope this helps.
Find the area of the trapezoid shown below
Answer:
A=a+b
2h
Step-by-step explanation:
Find the distance from the point (0,0) to the line y = x – 6. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
Hi
8 POINTS I don’t understand this can anyone help?? If you answer all my other questions on BrainlyI will give you 30 points:)
Answer:
I remember my teacher saying that when you get the answer you have to * when you get the answer
HELPPPPPPPP Write the standard form of an equation
Answer:
See the Answer Below:) I am certain this is the answer
Step-by-step explanation:
In grade 8, there are 3 teachers for every 25 students. In the examination hallthe ratio of teachers to students is 15:125, Which of the following is true?
Answer:
3:25 = 15:125
15:125 is directly proportional to 3:25.
Step-by-step explanation:
Pls help which statement is true?
The first statement is true
Step-by-step explanation:
They all can be simplyfied to 3/4 including 12/16
Where can you buy a ruler that is 3 feet long?
Answer:
At a yard sale
Step-by-step explanation:
Angle ABC and angle CBD or a complementary what is the value of X
Answer:
26degrees
Step-by-step explanation:
Find the diagram attached
From the diagram, Angle ABC and angle CBD are complementary hence;
<ABC + <CBD = 90
Given
<ABC = 2x
<CBD = 38
Substitute
2x + 38 = 90
2x = 90 - 38
2x = 52
x = 52/2
x = 26degrees
Hence the value of x is 26degrees
What is the range of the function f(x) = -3x + 1 when the domain is {-2, 0, 3}?
A. all real numbers
B. {-31, -29, -32}
C. {7, 1, -8}
D. {-5, 1, -8}
Answer:
Solution given:
f(x) = -3x + 1
f(-2)=-3×-2+1=7
f(0)=-3×0+1=1
f(3)=-3×-3+1=-8
So
Range is {7,1,-8) is a required answer
Preciso de ajudar nessa questão que segue em anexo.
Answer: $85
Step-by-step explanation:
Não falo português mas tentarei ajudar.
Multiplique 6 2/3 e 3 1/7.
6 2/3 x 3 1/7 = 20 20/21
Dividir 20 20/21 e 5.
20 20/21 / 5 = 4 4/21.
Precisa de cinco latas de tinta.
5 x $17 = $85
Need answer fast thx
Answer:
50
Step-by-step explanation:
10% of 100 is 10 so times it by 5
Divide the following complex numbers 30+20i/1+5i
The volume of a cylinder is 62.8 cubic meters and the radius is 2 meters.
Find the height of the cylinder. Round to the nearest meter.
Answer:
Height: 5meters
Step-by-step explanation:
Using the formula h= V over pie/3.14r^2 = 62.8 over 3.14 times 2^2 gives us 4.99747.
The time spent by a teacher on schoolwork during the weekend is normally distributed with a mean of 6 hours and a standard deviation of 1.2 hours.
a) What amount of time do the bottom 20% of teachers work?
b) What amount of time do the top 20% of teachers work?
c) What amount of time do the middle 40% of teachers work?
Which number is equivalent to 6^2x6^3
Answer: 6^5
Step-by-step explanation:
What is the volume of a cylinder that has a radius of 2 meters and height of 10 meters? Use 3.14 for π
Answer:
125.66
Step-by-step explanation:
The formula for the volume of a cylinder is V=Bh, V=πr2h, or πr2h
==
π π
r 2
2 2 ≈
Vh 10125.66371
I'm not good at explaining it but this should be the answer
Which equivalent expression can be used to solve the quotient 2/3 divided by 4/5
Answer:
5/6
Step-by-step explanation:
Divide it
The equivalent expression can be used to solve the quotient 2/3 divided by 4/5 is 5/6.
What is division?Division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing.
The equivalent expression that can be used to solve the quotient 2/3 divided by 4/5 is;
[tex]= \dfrac{\dfrac{2}{3}}{\dfrac{4}{5}}\\\\=\dfrac{2}{3} \times \dfrac{5}{4}\\\\=\dfrac{1}{3} \times \dfrac{5}{2}\\\\=\dfrac{5}{6}[/tex]
Hence, the equivalent expression can be used to solve the quotient 2/3 divided by 4/5 is 5/6.
Learn more about division here;
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On a map 1 cm represents 40 km. the real life distance between two places on the map is 360km what is the distance between these two places on the map
On a second map the distance between the same two places is 4cm what real life distance does 1 cm represent on the second map?
A bag of colored candies had 38 brown candies, 6 red pieces, 19 yellow pieces, 8 blue pieces, 17 orange pieces, and 12 green pieces. How many green pieces would you expect to find in a bag of 250 candies?
Answer:
138
Step-by-step explanation:
Stock Market At the beginning of the day the stock market goes up 50 1/2 points and stays at this level for most of the day,
At the end of the day the stock market goes down 120 3/4 points from the high at the beginning of the day. What is the total
change in the stock market from the beginning of the day to the end of the day
The total change in the stock market is
(Type an integer, roer fra tim
points
Answer: -70 1/4
Step-by-step explanation:
50 1/2 - 120 3/4
hoped this helped
ello i need help -^-
Answer:
d =90 e=52 f=52
Step-by-step explanation:
The angle that are crosppsinding have equal angle.
like f=e.
Stella rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase describes the probability that she will roll a number less than or equal to 5? \text{impossible}impossible \text{certain}certain \text{unlikely}unlikely \text{likely}likely
The probability of getting a number less than or equal to 5 is 5/6.
What is probability?"Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one".
For the given situation,
Stella rolls a standard six-sided die, numbered from 1 to 6.
The sample space for rolling a single die = {1, 2, 3, 4, 5, 6}
⇒[tex]n(s)=6[/tex]
The event is getting a number less than or equal to 5.
E = { [tex]{1, 2, 3, 4, 5}[/tex] }
⇒[tex]n(e)=5[/tex]
Thus the probability of getting a number less than or equal to 5,
[tex]P(e) =\frac{n(e)}{n(s)}[/tex]
⇒[tex]P(e)=\frac{5}{6}[/tex]
Hence we can conclude that the probability of getting a number less than or equal to 5 is 5/6.
Learn more about probability here
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Help would be nice! Question is can you help me?
All you have to do is find the surface area, free brainliest if you get it right simple as that
No links or stuff like that
Otherwise I will eat your family :)
Answer:
84
Step-by-step explanation:
you just got to do 12 * 14 , then divide by 2. so the answer is 84
for the entire thing, the area would be 480
PLEASE HELP ME IT' S FOR TODAY!!!
Answer:
x=55
Step-by-step explanation:
125+125=250
250+2x=360
2x=110
x=55
Answer:
55
Step-by-step explanation:
There are many ways to solve this problem; however, I used the one I believe to be the fastest and easiest, but you can still use a different way.
I solved this by using the fact that the green angle (m<125) and the red angle (x) make a straight line. All straight lines equal 180 degrees; therefore, this line must equal 125+x=180. Then, you can subtract 125 from both sides of the equation. That leaves x=55.
dillon pays x dollars to get a haircut. he gives the stylist a 15% tip. the expression representing his total cost is x + 0.15x
Answer:
B) 1.15x, adding 15% to the cost of haircut is same as to multiply cost by 1.15
Step-by-step explanation:
Given expression = x + 15% of x
x + (15/100) x = x + 0.15x
= (1+ 0.15) x = 1.15x
15% = 0.15 , added to x = 1.15x
Janelle sells necklaces and bracelets online. She sells each necklace for $16 and each bracelet for $12. What expression represents the total amount of money Janelle made last month from selling a necklaces and bracelets
Pls help
Answer:
Y = 16a + 12b
Step-by-step explanation:
Given:
Cost of each neckless = $16
Cost of each bracelet = $12
Find:
Equation for the following state
Computation:
Assume;
Number of neckless sale in a month = a
Number of bracelet sale in a month = b
Total amount she earn = Y
So,
Total amount she earn = (Cost of each neckless)(Number of neckless sale in a month) + (Cost of each bracelet)(Number of bracelet sale in a month)
Y = (16)(a) + (12)(b)
Y = 16a + 12b
am
Solve the proportion.
14
y +9
10
15
y = [?]
Enter
Answer:
5
Step-by-step explanation:
What percentage (nearest whole percent) is budgeted for entertainment if $200 is allotted from a total budget of $1260 ?
simplify 3/36 will choose brainliest
Answer:
3/36 simplified is 1/12
Hope this helps!