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]
What must be the annual payment you receive in order to earn 6.3% rate of return on a perpetuity that has a price of $245.1? (Answer in $s to the nearest cent, i.E. Xx.Xx, with no $-sign or commas needed.)
Answer:
the annual payment received is 15.44
Step-by-step explanation:
The computation of the annual payment received is shown below:
As we know that
Perpetuity = Payment ÷ rate of return
$245.1 = Payment ÷ 6.3%
So, the payment is
= $245.1 × 6.3%
= 15.44
Hence, the annual payment received is 15.44
We simply apply the above formula so that the annual amount could come
Neeed helps math help no links or imma report helps 20 points
6 1/2 x 3 1/3 x 2
what’s the volume?
Answer:
1891 /3
Step-by-step explanation:
Candice has 40 bows.She shared them with her two friends Cindy received ⅜ and elsa received ⅖ which one of her friend received more hair bows and by how many.
Answer:
elsa received more bows, she received 1 bow greater than Cindy
Step-by-step explanation:
Candice has 40 bowls
She shared the bows between her 2 friends
Cindy has 3/8 of the bow
40×3/8
= 15
Elsa has 2/5 of the bow
40×2/5
= 16
Therefore elsa received more bows, she received 1 bow greater than Cindy
Order the numbers from least to greatest.
23% , 1/4 , 0.225 .
Simplify: 3+y+y+y+2
Answer:
3y + 5
I really hope this helps
advance tickets for a school play went on sale. the price of each student ticket was $4 and everyone else paid $5. on the first day, no more than $80 in tickets were sold. describe and explain the possible values of s, the number of student tickets sold, and e, the number of tickets sold to non student’s.
Answer:
0student 16non-student,
5student 12non-student,
10student 8non-student,
15student 4non-student,
20student 0non-student
Step-by-step explanation:
s student tickets, e non student
4s + 5e = 80
s e
0 16 4(0) + 5(16) = 80
5 12 4(5) + 5(12) = 80
10 8 4(10) + 5(8) = 80
15 4 4(15) + 5(4) = 80
20 0 4(20) + 5(0) = 80
help please ! I dont understand this question
Answer:
x = 4
Step-by-step explanation:
all angles in triangle add to 180
90+70=160
180-160=20
20÷5=4
The surface area of a cylinder is 500 square feet; the lateral surface area is 320 square feet. Give the area of a base.
Answer: try your best
Step-by-step explanation:
Abby pulled marbles from a large jar, recorded the color of each marble, and then replaced the marble back into the jar. The first 8 marbles that Abby pulled are shown in the table below. If Abby plans to pull 40 more marbles, how many should she expect to be red?
a. 3 of the 40 marbles will be red
b. 10 of the 40 marbles will be red
c. 24 of the 40 marbles will be red
d. 15 of the 40 marbles will be red
Answer:
A.
Step-by-step explanation:
A school ordered a trapezoidal activity table as shown in the figure. Find the area of the table. SHOW ALL
WORK!!!
60 mm
14 in
SOT
Answer:
A=630 in^2
Step-by-step explanation:
Triangles: there are two equal triangles so we can treat them as one rectangle
A = 15 * 14 = 210
Rectangle:
A=30 * 14 = 420
A_total = 210 + 420 = 630 in^2
The change in position of the ball during each play of a football game is measured in yards. Use the information below to answer questions 2-4, What integer best represents a gain of 5 yards?
Answer:
The answer is 5
Step-by-step explanation:
see atattchment please answer asap
Answer:
C
Step-by-step explanation:
Given square ABCD, which line segment could be an image of side AD using only a translation?
Answer:
The second one
Step-by-step explanation:
Line segment BC will be an image of side AD using only a translation.
Option 2 is true.
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
A figure ABCD is a square.
Now,
Since, ABCD is a square.
So, All sides of square ABCD are equal to each other.
Since, A translation occurs when a figure is moved from one location to another location without changing its size or shape.
Thus, Line segment BC will be an image of side AD using only a translation.
Therefore, Line segment BC will be an image of side AD using only a translation.
Learn more about the translation visit:
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Solve for X. Please show work
Answer:
x = 19.8
Step-by-step explanation:
Mathematically, when two triangles are similar, the ratio of their corresponding sides are equal
thus, we have it that;
16/28.8 = 11/x
16 * x = 11 * 28.8
x = (11 * 28.8)/16
x = 19.8
What is the area of a regular pentagon if its apothem has a length of 4 feet and each side has a length of 5.8 feet?
a 139.2 ft?
b. 58 ft2
C. 116 ft2
d 69.6 ft-
The area of a regular pentagon is 58 ft2. thus option B is correct.
What is apothem?Apothem for a regular polygon is a line segment that originates from the center of the regular polygon and touches the mid of one of the sides of the regular polygon.
It is perpendicular to the regular polygon's side it touches.
Given; An apothem has a length of 4 feet and each side has a length of 5.8 feet.
The area of any regular polygon can be calculated as:
Area = number of sides (n) x 0.5 x length of sides (s) x apothem (a)
Area = 5 x 0.5 x 4 x 5.8
Area = 58
Hence, the area of a regular pentagon is 58 ft2. thus option B is correct.
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The perimeter of a rectangle is 16x – 6. If the length is
5x + 2, what is the width?
Answer:
3x + 1
Step-by-step explanation:
5x + 2 × 2 = 10x + 4
do this take 16x - 6
you get 6x + 2
then divide by 2 to get the answer 3x+1
Answer:
w = 3x - 5
Step-by-step explanation:
Perimeter of a rectangle formula:
P = 2(l + w)
16x - 6 = 2(5x + 2 + w)
16x - 6 = 10x + 4 + 2w
2w = 16x - 6 - 10x - 4
2w = 6x - 10
w = 3x - 5
I'm having trouble answering this question is it possible someone can answer this ASAP?
Answer:
c. it is 185 cm squared all you do is add the sides and time them
What is the value of x in the equation 8 + x = 3?
A. −5
B. 5
C. 11
D. 24
Answer:
I think it's A
I hope this helps
helpppppppppppppppp pleaseeeeeeee
Answer:
20.25 ft
Step-by-step explanation:
9/2 = 4.5
4.5*4.5 = 20.25
help pleaseeeeeeeeeee
Answer: b
Step-by-step explanation:
Find the sum of (x + 5), (–4x –2), and (2x – 1).
PLEASE HELP!!!
Answer:
-x-2
Step-by-step explanation:
x+5 + -4x -2 + 2x -1 = -x -2
Answer:
-x + 2
Step-by-step explanation:
(x + 5), (-4x -2), and (2x -1)
x + (-4x) + 2x) + (5 + -2 + -1)
= -x + 2
Simplify completely.
(2 + 3i) + (-4+i)
Answer:
-2+4i
Step-by-step explanation:
Simplify by combining the real and imaginary parts of each expression.
The simplified form of the complex expression is -2 + 4i.
What are Complex Numbers?Complex numbers are numbers which are of the form [tex]a+ib[/tex],
where a and b are real numbers and i is the imaginary number called iota whose value is [tex]i^{2}[/tex] = -1.
Given expression is (2 + 3i) + (-4 + i).
Addition of complex numbers is defined as,
(a + ib) + (a' + ib') = (a + a') + i(b + b')
Using the definition of addition of complex numbers, given expression can be added as,
(2 + 3i) + (-4 + i) = (2 + -4) + i(3 + 1) = -2 + 4i
Hence the resulting value is -2 + 4i.
To learn more about Complex Numbers, click on the link given below :
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If the area of a triangle is 48 cm2 and the base of the
triangle is 12 cm, what is the height of the triangle?
Answer:
8
Step-by-step explanation:
Formula for height of triangle
A÷BX2
In this case, 48÷12=4×2=8
Hope you understand ☺️
Help me pleasee I’m not sure I’m doing theses correctly ?
9514 1404 393
Answer:
(d) ∠AIS
Step-by-step explanation:
The tangent SF intersects the circle at one point, point I. Any angle it forms with a chord must be a chord that terminates at point I. There are two of them: AI and CI.
The angles these chords make with tangent SF are ...
∠AIS∠AIF∠CIS∠CIFOf these, only the first (∠AIS) is listed among the answer choices.
Marta’s math textbook weighs Four-fifths of a pound less than 4 times the weight of the book she is reading for her language arts class. If the weight of the math textbook is 2 and one-fifth pounds, which shows the correct equation and value of x, the weight of Marta’s book for language arts?
4 x + four-fifths = 2 and one-fifth; x = StartFraction 7 over 20 EndFraction of a pound
4 x minus four-fifths = 2 and one-fifth; x = three-fourths of a pound
4 x + four-fifths = 2 and one-fifth; x = three-fourths of a pound
4 x minus four-fifths = 2 and one-fifth; x = StartFraction 7 over 20 EndFraction of a pound
Answer:
C
Step-by-step explanation:
pls help ill mark you brainliest
Answer:
if i am not mistaking it got to be c
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
First you subtract 325 from 75 then divide the answer by 10
is the sequence below is arithmetic {1, 8, 27,64}
Answer:
No
Step-by-step explanation:
No, because 8 - 1 ≠ 27 - 8. So, there is no common difference which is needed in order for the sequence to be arithmetic
What is a equivalent ratio
Answer:
Equivalent ratios are just like equivalent fractions. If two ratios have the same value, then they are equivalent, even though they may look very different! In this tutorial, take a look at equivalent ratios and learn how to tell if you have equivalent ratios.
Use the distance formula to slove how far the points are on the a coordinate plane. Points are (7,5)(3,2)
Answer:
distance is 5 units
Step-by-step explanation:
plug in values
