The function f(n)=−48⋅(-¼)^n is a geometric sequence
The recursive definition of f(n) is f(1) = 12; f(n) = f(n - 1) . -¼
How to determine the recursive formula of f(n)The function is given as:
f(n)=−48⋅(-¼)^n
Calculate f(1)
f(1)=−48⋅(-¼)^1
This gives
f(1) = 12
Calculate f(2)
f(2)=−48⋅(-¼)^2
This gives
f(2) = -3
Calculate the common ratio (r)
r = f(2)/f(1)
So, we have:
f = -3/12
Simplify
r = -1/4
Recall that: r = f(2)/f(1)
This gives
-1/4 = f(2)/f(1)
Make f(2) the subject
f(2) = -1/4* f(1)
Express 1 as 2 - 1
f(2) = -1/4* f(2 - 1)
Substitute 2 for n
f(n) = -1/4* f(n - 1)
Rewrite as:
f(n) = f(n - 1) . -¼
Hence, the recursive definition of f(n) is f(1) = 12; f(n) = f(n - 1) . -¼
Read more about sequence at:
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What is the volume of this cone?
Use a = 3.14 and round your answer to the nearest hundredth
13 mm
6 mm
how do i get the answer
Pi times radius squared times (height÷3)
if radius is 6 then 490.09
if radius is 13 then 1061.86
the last answer is 35 I just could not fit it in the pic
find the volume of 20m, 5m, 18m
Answer:
600 m³
Step-by-step explanation:
The shape we have is a rectangular pyramid:
Formula: (volume of a rectangular pyramid)
Volume = (1/3) × Base Area × height
___________________________
In our case :
Base area = L × W = 20 × 18 = 360 m²
height = 5 m
⇒ Volume = (1/3) × Base Area × height
[tex]\Longrightarrow \text{volume} \ =\ \frac{1}{3} \times 360\times 5[/tex]
[tex]\Longrightarrow \ \text{volume} \ =\ 600\ m^{3}[/tex]
Help please fast ong im begging
Answer:
(x + 3)(x + 5)
Step-by-step explanation:
Find two numbers that multiply to 15 and add to 8.
The numbers are 3 and 5.
x² + 8x + 15 = (x + 3)(x + 5)
what is 3/4 in a percent
Answer:
75%
Step-by-step explanation:
Convert the fraction into a decimal number. Multiply the obtained decimal number by 100, to get a percent value.
Answer:
3/4 in a percent is 75%
Step-by-step explanation:
To change a fraction to a decimal you divide the numerator by the denominator. In this case that would be 3 divided by 4 which is 0.75, to change the decimal to a percent you move the decimal two places to the right.
What is the solution to the following equation?
x^2 + 5x + 7 = 0
A. x = -5±√-3 /2
B. x = -5±√53 /2
C. x = -3±√-7 /2
D. x = 3±√25 /2
Answer:
A
Step-by-step explanation:
using the quadratic formula
in the picture above
Riya has 5 times as many apples as Tyler. Together they have 24 apples. How many apples does Riya have?
Answer:
Riya have 20 apples
Step-by-step explanation:
Let, Tyler have x apples
Then, Riya have 5x apples
Now, From the question,
5x + x =24
or, 6x =24
or, x = 24/6
or, x = 4
Tyler have 4 apples
Again,
Riya have 5x apples
=5*4
=20
Therefore, Riya have 20 apples
6) Out of 15 students only 10 passed the geography scam. Write the fraction of students
Who failed in the geography cam.
30 POINTS FOR THE BRAINLIEST!!! Find the indicated measures, given that
EA is a diameter.
a) mDEF=
b) mEFG=
c) mAC=
d) Explain how you found each angle measure below. Be sure to show all of your work.
I need help ya'll please:)
Answer:
Step-by-step explanation:
Please take a clearer picture couldnt read it well
Which is an example of why higher education typically has a positive return on investment (ROI)?
The jobs you can get with higher education will earn more money than jobs without a degree or certificate.
Higher paying jobs come with experience, not with earning a degree or certificate.
Higher education usually results in a lot of debt which can be difficult to afford.
The highest paying jobs come with a high school diploma which is an important reason to finish high school.
Answer:
Higher education loans generally have a positive ROI because you are building skills and work experience that can increase your future earnings. More education is correlated with higher lifetime earnings.
Step-by-step explanation:
The jobs you can get with higher education will earn more money than jobs without a degree or certificate.
What is return on investment?The term return on investment refers to the profit that one makes from an investment. Higher education is a very profitable investment for an individual.
here,
Higher education loans generally have a positive ROI because you are building skills and work experience that can increase your future earnings. More education is correlated with higher lifetime earnings.
The jobs you can get with higher education will earn more money than jobs without a degree or certificate.
The example of why higher education typically has a positive return on investment (ROI) is the jobs you can get with higher education will earn more money than jobs without a degree or certificate.
Learn more about ROI:
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The weight of a blue whale is about 250,000 pounds. Write this number in scientific notation
Answer:
250÷50=3 because I have a great day and I will be in the 3 1 4 a few days ago a friend of ours was the only thing
Step-by-step explanation:
yes maybe no more options visit in the future please reply with your family
A swimming pool is shaped like a right rectangle prism. the pool is 36 ft long and 20 ft wide. What is the total amount of water in cubic ft,needed to fill tje pool to a depth 4 ft.
Answer:
2880 ft³
Step-by-step explanation:
T o find the total amount of water that is needed to fill the pool, you have to find the volume of the pool.
Formula to find the volume of a rectangle prism is :
Volume = length × width × height
Let us solve now.
Volume = length × width × height
Volume = 36 ft × 20 ft × 4 ft
Volume = 2880 ft³
Therefore, 2880 ft³ of water is needed to fill the pool.
An airplane company flies 45 airplanes daily. The CEO collects the following passenger counts for a random sample of airplanes
from the fleet, as shown below.
119, 138, 157, 85, 157, 119, 138, 119, 157, 85
Assuming that the sample is representative of the entire fleet of airplanes, what would be the mean daily passenger count per
plane?
A. 124.75
В. 135.9
C. 127.4
D. 128.5
Frank got a gift for his sister and put it in a shoebox.
+
Note: Figure is not drawn to scale.
Now, he wants to wrap it with wrapping paper. If the length of the shoebox measures 10 in, the width measures 5 in, and the height
measures 4 in, how much wrapping paper does he need to cover the shoebox?
OA 330 sq in
ОВ.
110 sq in
OC. 440 sq in
OD. 220 sq in
Answer:
200
Step-by-step explanation:
Length times width to get the base 10 x 5 = 50 With the base multiply it by the height to get 50 x 4 = 200
to the nearest tenth what is the circumference of a bicycle tire with a radius of 11 inches? use 3.14 for pi
Step-by-step explanation:
Radius = 11 inches
⇒ Circumference = 2πr
⇒ Circumference = (2 × 3.14 × 11) inches
⇒ Circumference = 69 inches
7 raise to -2 x 3 raise to 2 = 3by7 raise to 4x
7^-2 x 3^2 = 3 x 7^4x should be your equation.
Exact form: x = 3/117649Evaluate the exponentEvaluate the exponentMultiply the numbersEvaluate the exponentMultiply the numbersDivide both sides by the same factorSimplifyDecimal form: x = 2.54995792 • 10^5I don't know if this is what you were looking for but I hope it helps.
PLEASE HELP 20 POINTS AND BRAINLIEST
Answer:
5/6, 0.83 or 83%
Step-by-step explanation:
Answer:
Probabilities
Decimal: [tex]0.91[/tex]
Fraction: [tex]\frac{91}{100}[/tex]
Percentage: [tex]91[/tex]%
Step-by-step explanation:
Writing out information
2 comedy CDs
3 science-fiction CDs
7 adventure CDs
10 random CDs
22 total CDs
The chosen CD is not a comedy.
Solving probability for each
Decimals rounded to nearest 100th
Comedy:
[tex]2:22\\0.09\\\frac{2}{22}[/tex]
Science-fiction:
[tex]3:22\\0.14\\\frac{3}{22}[/tex]
Adventure:
[tex]7:22\\0.32\\\frac{7}{22}[/tex]
Random:
[tex]10:22\\0.45\\\frac{10}{22}[/tex]
Finding the total of the non-comedy
[tex]0.14+0.32+0.45=0.91[/tex]
[tex]0.91=91[/tex]%
Conclusion
Probabilities
Decimal: [tex]0.91[/tex]
Fraction: [tex]\frac{91}{100}[/tex]
Percentage: [tex]91[/tex]%
Rewrite the fraction with the indicated denominator.
Answer:
I believe the answerwould be 18/21.
Please let me know if I'm correct!
Hope this helps you!
Hey there!
6/7 = ?/21
= 6/7 = x/21
CROSS MULTIPLY the FRACTION
6(21) = x(7)
6(21) = 7(x)
126 = 7x
7x = 126
DIVIDE 7 to BOTH SIDES
7x/7 = 126/7
CANCEL out: 7/7 because it give you 1
KEEP: 126/7 because it help solve for the x-value
NEW EQUATION: x = 126/7
SIMPLIFY IT!
x = 18
Therefore, your answer is: 18
BECAUSE 18/21 is equivalent to 6/7 and they both give you approximately 86% (or simply 0.86) if you’re rounding your percentage/decimal form
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
NEED HELP WITH THIS MATH PROBLEM QUICK!!!
Answer:
[tex]\implies m\angle A =42\degree[/tex]
Step-by-step explanation:
Quadrilateral ABCD is inscribed in circle with center O.
-> Quadrilateral ABCD is cyclic.
Opposite angles of a cyclic quadrilateral are supplementay.
[tex]\implies m\angle B + m\angle D = 180\degree[/tex]
[tex]\implies (2x)\degree + (3x-5)\degree = 180\degree[/tex]
[tex]\implies (5x-5)\degree = 180\degree[/tex]
[tex]\implies 5x-5= 180[/tex]
[tex]\implies 5x= 185[/tex]
[tex]\implies x= \frac{185}{5}[/tex]
[tex]\implies x= 37[/tex]
[tex]\implies m\angle A =(x+5)\degree[/tex]
[tex]\implies m\angle A =(37+5)\degree[/tex]
[tex]\implies \huge{\orange{m\angle A =\boxed{42}\degree}}[/tex]
Determine the number of solutions of each system of equations.
Answer:
no solutions
Step-by-step explanation:
x+y = 5
-2x-2y = 10
Multiply the first equation by 2
2x+2y =10
Add this to the second equation
2x+2y =10
-2x-2y =10
0 =20
This is not true so there are no solutions
What is the geometric mean of 25 and 2
Answer:
Geometric Mean of 2 and 25: 7.0711Given that log Cart 2) + log, b=0 and ing (a-2) 16g, b=actl Show = "feetfiad Metult possible velers of a cand is where a, b er (a that 92 442480 an 2 it soln
Answer:
12+12 log2) b=34) 54+90)=10000+32+54=9000
Step-by-step explanation:
I know the answer I am a math tutor at Elomantry High Scholl Teaching for 6 years now
IM NOT SURE HOW TO SOLVE THIS CAN SOMEBODY HELP ME
Answer:
The y-intercept is the point (0, 128).
The x-intercepts are the points (-4, 0) and (-8, 0).
As x → ∞, y → ∞.
As x → -∞, y → -∞.
Step-by-step explanation:
To find the y-intercept, substitute 0 for x and solve for y.
P(x) = (x + 4)²(x + 8) P(0) = (0 + 4)²(0 + 8)P(0) = (4)²(8)P(0) = 16 * 8 P(0) = 128The y-intercept is (0, 128).
To find the x-intercept, substitute 0 for y and solve for x.
0 = (x + 4)²(x + 8)Set the first term, (x + 4)², equal to 0.
0 = (x + 4)²0 = x + 4 -4 = xx = -4Set the second term, (x + 8), equal to 0.
0 = x + 8 -8 = xx = -8The x-intercepts are the point (-4, 0) and (-8, 0).
Look at the degree and leading coefficient of the polynomial to determine the end behavior, and therefore you can determine how y behaves as x gets closer to infinity.
Since the degree of the polynomial is odd (3) and the leading coefficient is positive, the graph falls to the left and rises to the right.
So, as x → ∞, y → ∞ and as x → -∞, y → -∞.
If you want to verify this, plug the equation into your calculator and look at the graph. How does it behave as you look at negative x-values? How about for positive x-values?
what is the difference between 3/4 and 2 1/4
Answer:
3/4 simplified is 3/4 but when 2 1/4 is simplified it is 9/4. Off the bat we know there is a big difference. Also, 2 and 1/4 is irrational and 3/4 and rational.
A certain laptop is really popular and sells for $209. Since sales are so good, the store raises the price by 12%. What is the cost of the laptop after the markup?
How is 1-n/2n-2 written in lowest terms
Answer:
- 1/2
Step-by-step explanation:
I assume this is (1-n) / (2n-2)
(1-n) / (-2)(1-n)
-1/2
find the value of n such that x^2-19x+n is a perfect square trinomial.
Answer:
1st option
Step-by-step explanation:
x² - 19x + n
using the method of completing the square
add ( half the coefficient of the x- term )² to x² - 19x
x² + 2(- [tex]\frac{19}{2}[/tex] )x + (- [tex]\frac{19}{2}[/tex] )²
with n = (- [tex]\frac{19}{2}[/tex] )² = [tex]\frac{361}{4}[/tex] , then
(x - [tex]\frac{19}{2}[/tex] )² ← a perfect square trinomial
Find a degree 3 polynomial with real coefficients having zeros 3 and 1 − 4i and a lead coefficient of 1. Write P in expanded form.
[tex]\text{Let,}\\\\~~~~~~~x=1-4i,\\\\\implies x-1 = -4i\\ \\\implies (x-1)^2 =(-4i)^2\\\\\implies x^2 -2x +1 = -16\\\\\implies x^2 -2x +1 +16 = 0\\\\\implies x^2 -2x +17=0\\\\\text{So,}~ x^2 -2x +17 ~\text{is a factor of the 3 degree polynomial.}\\ \\\text{The polynomial is,}\\\\P(x) = (x-3)(x^2 -2x +17)\\\\~~~~~~~=x^3-2x^2+17x -3x^2 +6x -51\\\\~~~~~~~=x^3 -5x^2 +23x -51[/tex]
need a good explanation, i dont get how to get the answer.
Fifteen years ago, Russell bought his house for $141,000. The house’s property value has decreased by 1.6% per year ever since then. If Russell sells his house, how much is it worth, to the nearest hundred dollars?
a.
$110,700
b.
$107,200
c.
$67,100
d.
$37,900
Answer:
141000 * (1 - 0.016)^15 = 110699.48 = A 110700
Step-by-step explanation:
1st year depreciation = 141000 - (141000 * 0.016) = 138744
2nd year depreciation = 138744 - (138744 * 0.016) = 136524.096
3rd year depreciation = 136524.096 - (136524.096 * 0.016) = 134339.710464
etc. unitl you reach the 15th year
Basically we calculate 1.6% of the current value of the house and subtract that from the current value for each year for 15 years.
The equation used in the answer is a faster way to approach your answer instead of calculating for each year.
You'd multiply your initial value by the difference in percentage (note well that since it is decreasing in value we subtract the decimal equivalent to 1.6% which is 0.016, from 1 where one represents 100% and then raise the difference gained to the power of the amount of years which would be 15.