Answer:
[tex]f(n) = 96 * 0.5^n[/tex]
Step-by-step explanation:
Given
[tex]f(3) = 12[/tex]
[tex]f(n) = 0.5 * f(n-1)[/tex]
Required
Write as an explicit function
When n = 3, we have:
[tex]f(3) = 12[/tex]
[tex]f(3) = 0.5 * f(3-1)[/tex]
[tex]f(3) = 0.5 * f(2)[/tex]
Substitute: [tex]f(3) = 12[/tex]
[tex]12 = 0.5 * f(2)[/tex]
Solve for f(2)
[tex]f(2) = 12/0.5[/tex]
[tex]f(2) = 24[/tex]
So, we have;
[tex]f(3) = 12[/tex]
[tex]f(2) = 24[/tex]
Since it is a geometric sequence, calculate the common ratio (r)
[tex]r = \frac{f(3)}{f(2)}[/tex]
[tex]r = \frac{12}{24}[/tex]
[tex]r = 0.5[/tex]
Calculate the first term using:
[tex]r = \frac{f(2)}{f(1)}[/tex]
Solve for f(1)
[tex]f(1) = \frac{f(2)}{r}[/tex]
[tex]f(1) = \frac{24}{0.5}[/tex]
[tex]f(1) = 48[/tex]
The explicit function is then calculated as:
[tex]f(n) = f(1) * r^{n-1[/tex] ----nth term of a gp
[tex]f(n) = 48 * 0.5^{n-1[/tex]
Split the exponent
[tex]f(n) = 48 * \frac{0.5^n}{0.5^1}[/tex]
[tex]f(n) = 48 * \frac{0.5^n}{0.5}[/tex]
[tex]f(n) = 96 * 0.5^n[/tex]
When the input is 5, what is the output for the square function?
Answer:25
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
A table is on sale for 33% off. The sale price is $603.
What is the regular price?
Help please
Answer:900
Step-by-step explanation:
603*100/(1-33)
900
0.051x40(0.5+0.01)x40 using distributive property
Answer:
41.616
Step-by-step explanation:
There are approximately 25,000 polar bears worldwide. Some scientists estimate that the polar bear population has been declining at a yearly reduction rate of 1%. What equation would model this situation?
A - p (t) = 25,000 (1.99)^t
B - p (t) = 25,000 (.099)^t
C - p (t) = 25,000 (0.99)^t
D - p (t) = 25,000 (0.01)^t
Answer:
i think d
Step-by-step explanation:
Ms. Young acquired a loan of $40,000 at her local bank. The loan has a simple interest rate of 6% per year. What is the amount of interest that Ms. Young will be charged on the loan at the end of 5 years.
Answer:
12.000
Step-by-step explanation:
40000x6= 240000/100= 2400x5
The volume of a cylinder is 980 in cubed.
The height of the cylinder is 20 in. What is the radius of the cylinder?
Express your answer to the nearest hundredth.
9514 1404 393
Answer:
3.95 in
Step-by-step explanation:
The volume is given by ...
V = πr²h
Solving for radius, we get ...
r = √(V/(πh))
For the given numbers, the radius is ...
r = √(980 in³/(π·20 in)) = 7/√π in ≈ 3.95 in
The radius of the cylinder is about 3.95 inches.
Liliana correctly answered 92% of the questions on a geography quiz. Lu answered 47 of 50 questions correctly. Who earned the higher score? Explain.
Answer:
Lu
Step-by-step explanation:
.....................m
HELP ME PLEASE!!1 I WILL GIVE !20 POINTS! AND BRAINLIST PLEASE I DON'T UNDERSTAND THIS AND ITS DUE SOON EPLAIN YOUR ANSWERS TOO PLEASE
Answer: Question 11 is q/s
Step-by-step explanation:
Answer:
Step-by-step explanation:
The two triangles are similar because of their angles. Both of the triangles contain a 90 degree angle, a angle, and 90-a angle.
There are 3 red marbles, 4 blue marbles, 2 green
marbles, and 6 clear marbles in a burlap bag. One
marble is randomly pulled from the bag. What is
the probability the marble was green?
Answer:
2 out of 15 chance its green
Step-by-step explanation:
there's 15 marbles in total and 2 are green
The height of the right circular cylinder shown below is 10 feet and its base has a radius of 4 feet. A. B. C. D.
Answer:
502.4ft^3
Step-by-step explanation:
Given data
Height= 10ft
radius= 4 ft
Hence the volume for the cylinder can be gotten as
v= πr^2h
v= 3.14*4^2*10
v=3.14*16*10
v=502.4ft^3
Therefore the volume of the cylinder is 502.4ft^3
When Anne had one cat, she needed to serve 1/8 of a can of cat
food each day. Now that Anne has adopted a second cat, she
needs to serve a total of 4 cans each day. How much extra food
is needed to feed the second cat?
Simplify your answer and write it as a fraction or as a whole or
mixed number.
Answer:
Abc= D= 2.94C
Step-by-step explanation:
Simplify the expression
[tex]5( \frac{1}{5} x - 1)(5x - \frac{1}{5} )[/tex]
What is the value of x in the figure? Enter your answer in the box.
Answer:
X = 65
Step-by-step explanation:
2(65) + 15 = 145
ur welcome
There are 12 dogs and 15 cats at the pet store. Find the ratio of cats and dogs
Answer:
15:12
Step-by-step explanation:
hope this helps!
The ratio of dogs and cats at the pet store is 12:15 and in simplest form, it is 4:5.
What is Ratio?When evaluating two or more numbers, the phrase ratio is used in mathematics. When one quantity is contrasted with another, it is used to show how big or tiny it is.
The division is used to compare the two numbers in a ratio. The term "antecedent" in this context refers to the dividends and "consequent" to the divisor.
As per the given data provided in the question,
Total number of dogs in the pet store, D = 12
Total number of cats in the pet store, C = 15
The ratio of dogs to cat be,
D:C = 12:15
Now, the ratio in simplest form,
D:C = 4:5
To know more about Ratios:
https://brainly.com/question/13419413
#SPJ2
6x – 9 = 33 Check
please and thank you
Answer:
x = 7
Step-by-step explanation:
6x - 9 = 33
6x = 33 + 9
6x = 42
x = 42 / 6
x = 7
6x - 9 = 33
6 x 7 - 9 = 33
42 - 9 = 33
33 = 33
Hope that helps!
Answer: x=7
Step-by-step explanation:
6x-9=33
for x
6x=33+9
6x=42
x=42/6
x=7
for checking put value of x
6*7-9=33
42-9=33
33=33
Which associations best describe the scatter plot?
Select each correct answer.
A. Nonlinear association
B. Negative association
C. Linear association
D. Positive association
Answer: i think hope this helps
Step-by-step explanation:
How many lines of symmetry does a kite have
0
1
3
2
Answer:
1 i think hope this can help you with your problem
Answer:
1
Step-by-step explanation:
Kailey wrote 8,912,000 in scientific notation as 89.12 times 10 Superscript 5. Which statement best describes Kailey's work?
Answer:
Could You Please Explain More?
Step-by-step explanation:
The sum of the length and width of a rectangle is more than 15 units. The length is 3 units more than the width, x. Which model and solution is correct for this situation?
Answer: [tex]6, 9\ \text{units}[/tex]
Step-by-step explanation:
Given
The Sum of length and width is [tex]15\ units[/tex]
length is 3 units more than the width
width is [tex]x[/tex]
length is [tex]x+3[/tex]
Their sum is 15
[tex]\Rightarrow x+x+3=15\\\Rightarrow 2x=12\\\Rightarrow x=6\ \text{units}[/tex]
Length is [tex]x+3=9\ \text{units}[/tex]
Width is [tex]x=6\ \text{units}[/tex]
Do 2b+b and 3b have the same value for all values of b
Answer:
Expression 2b+b and 3b have same values for all values of b.
Step-by-step explanation:
Given the two expression 2b+b2b+b and 3b3b and values of b as 1, 2 and 3.
Consider first expression that is, 2b+b2b+b .
Substituting the value of b=1b=1 ,
2\left(1\right)+\left(1\right)=2+1=32(1)+(1)=2+1=3 ....1
Substituting the value of b=2b=2 ,
2\left(2\right)+\left(2\right)=4+2=62(2)+(2)=4+2=6 ....2
Substituting the value of b=3b=3 ,
2\left(3\right)+\left(3\right)=6+3=92(3)+(3)=6+3=9 ....3
Consider second expression that is, 3b3b .
Substituting the value of b=1b=1 ,
3\left(1\right)=33(1)=3 ....4
Substituting the value of b=2b=2 ,
3\left(2\right)=63(2)=6 ....5
Substituting the value of b=3b=3 ,
3\left(3\right)=93(3)=9 ....6
For value of b=1, equation 1 and equation 4 are same, for value of b=2, equation 2 and equation 5 are same and for value of b=3 equation 3 and equation 6 are same.
Therefore both expression are same for all values of b.
Step-by-step explanation:
Hope it helps you!
just follow me for more!
I'm willing to help you
hi guys this one is one whole question it just couldent fit please help
Answer:
Pentagon and rhombus
Step-by-step explanation:
The question is: Which best describes the first step in evaluating the expression 4· 53+1 (8-5)Cubed 3
Answer:
Subtract [tex]8 - 5[/tex]
Step-by-step explanation:
Given
[tex]4 . \frac{53 + 1}{(8 - 5)^3}[/tex]
Required
The first step to evaluate the expression
The first step is to evaluate the expression in brackets.
From the question: The expression in bracket is: [tex]8 - 5[/tex]
So, the first step is to subtract [tex]8 - 5[/tex]
What is the answer to this question please
Answer:
450cm3
Step-by-step explanation:
10 times 5 times 9
Answer:
Simple . the cuboid have to go to GYM to Work out the Volume . 1+2= 11 Answer
im confused on this problem
Answer:
y = 54, x = 62
Step-by-step explanation:
plz mark helpful, 5 str, and give brailiest, thx!
Find the slope of the line that passes through the points (0,-5) and (-2,-3).
Answer:
the slope is -1
Step-by-step explanation:
formula for slope is (y2-y1)/(x2-x1)
lets say (-2,-3) is (x2,y2)
-3-(-5)=2
-2-0=-2
2/-2=-1
What is the solution to this inequality?
4(2x + 2) + 12 > 100
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
What is the solution to
this system of linear
equations?
Change this fraction into a decimal: 20/25
.8
.08
.008
.0008
Answer:
0.8
Step-by-step explanation:
20/25=80/100=0.8
Need help need help
at a pizza shop you can choose thick or thin crust red or white sauce and toppings a pepperoni and cheese or vegetarian. create a tree diagram to display the same space
Answer:
Total 2*2*3 = 12 outcomes
------------------------------------------------------------------------
> thick, white, pepperoni
White > > thick, white, cheese
> thick, white, vegetarian
Thick > >
> thick, red, pepperoni
Red > > thick, red, cheese
> thick, red, vegetarian
------------------------------------------------------------------------
> thin, white, pepperoni
White > > thin, white, cheese
> thin, white, vegetarian
Thin > >
> thin, red, pepperoni
Red > > thin, red, cheese
> thin, red, vegetarian
