Answer:
[tex]b_n = \frac{2}{27} (9^n)[/tex]
Step-by-step explanation:
Given
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Required
An explicit rule for [tex]b_1,\ b_2,\ b_3,\ \dots[/tex]
Where [tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
We have:
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Calculate a2
[tex]a_2 = 3a_{2-1}[/tex]
[tex]a_2 = 3a_1[/tex]
[tex]a_2 = 3 * \frac{2}{3}[/tex]
[tex]a_2 = 2[/tex]
Calculate a3
[tex]a_3 = 3a_{3-1}[/tex]
[tex]a_3 = 3a_2[/tex]
[tex]a_3 = 3 *2[/tex]
[tex]a_3 = 6[/tex]
Calculate a4
[tex]a_4 = 3a_{4-1}[/tex]
[tex]a_4 = 3a_3[/tex]
[tex]a_4 = 3*6[/tex]
[tex]a_4 = 18[/tex]
Calculate a5
[tex]a_5 = 3a_{5-1}[/tex]
[tex]a_5 = 3a_4[/tex]
[tex]a_5 = 3*18[/tex]
[tex]a_5 = 54[/tex]
So:
[tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
[tex]a_1=\frac{2}{3}[/tex] [tex]a_3 = 6[/tex] [tex]a_5 = 54[/tex]
The above sequence form a geometric sequence.
Calculate common ratio (r)
[tex]r = \frac{b_3}{b_2}[/tex]
[tex]r = \frac{a_5}{a_3}[/tex]
[tex]r = \frac{54}{6}[/tex]
[tex]r = 9[/tex]
So, the explicit formula is:
[tex]b_n = b_1 * r^{n-1[/tex]
[tex]b_1=a_1[/tex], so:
[tex]b_n = a_1 * r^{n-1[/tex]
[tex]a_1=\frac{2}{3}[/tex], so:
[tex]b_n = \frac{2}{3} * 9^{n-1[/tex]
Split:
[tex]b_n = \frac{2}{3} * \frac{9^n}{9}[/tex]
[tex]b_n = \frac{2}{3*9} (9^n)[/tex]
[tex]b_n = \frac{2}{27} (9^n)[/tex]
The explicit rule is: [tex]b_n = \frac{2}{27} (9^n)[/tex]
Tim was given $100 for his twelfth birthday. He's curious to see how much it will grow to if he earns interest on it. His mother tells him that she has about $3,000 in the same kind of account and she earned $60 last year. About how much interest could Tim expect to eam in a year?
Answer:
$102
Step-by-step explanation:
3000 x Y = 3060
3060/300 = Y
Y = 1.02
100 x 1.02 = $102
Hope this helps!!
A robot’s height is 3 meters 40 centimeters. How tall is the robot in millimeters?
Answer:
3400
Step-by-step explanation:
if you add it all up in cm, which is 340cm then divide by 10 you get 3400.
Please help with this math... I learned it but don't remember how to solve
Answer:
C
Step-by-step explanation:
Look at the graph when y=5. It is a straight line that goes through 0,5 horizontally.
it crosses the y-axis at (0,5) only.
9x-12=3x show your work
Answer:
x=2
Step-by-step explanation:
given 9x-12=3x we want to solve for x
To do so we need to isolate the variable using inverse operations
to get rid of the 9x we subtract each side by 9x
9x - 9x cancels out
3x - 9x =-6x
now we have
-12=-6x
now we want to get rid of the -6
to do so we divide each side by -6
-6x/-6=x
-12/-6=2
we're left with x=2
Answer:
9x=3x+12
9x-3x=12
9x-3x=12
6x=12
x=2
solution
x=2
Which expression shows the result of applying the distributive property to 12(5y+4)?
60y + 4
5y + 48
17y + 16
60y + 48
Answer:
60y+48
Step-by-step explanation:
HELP NOW WILL GIVE POINTS TO IF HELPED, If the JellyBelly factory had a bagging machine that loaded 1000 jelly beans into a bag that is allowed a 0.5% error range amount. What is the range of jelly beans [x] that could be in the bag, without it being rejected? : x ,
Answer:
just search up Mathaway in your browser you will get your answer and a step by step explanation!
Step-by-step explanation:
If w= <2, -5> and y= 2,0>, find 2w+y
A. <6,-10
B. <4,-5>
C. <-10,2>
D. <-6,10>
Answer:
B
Step-by-step explanation:
F un gong jjkpjm d gjgyfgdbb
Use the diagram to complete the statements.
The measure of angle L is
70
°.
The trigonometric ratio that uses ∠M and LN to solve for NM is
.
The length of NM, to the nearest tenth, is approximately
.
» A group of 6 friends buy a video game that costs $60. They each
spend an equal amount of money. How much money does each
friend spend?
1» Let m stand for how much money each friend spends. Which equations
can be used to solve the problem? Choose ALL the correct answers.
m = 60 x 6
m= 60 = 6
m = 6 x 60
60 = 6 x m
Answer:
each friend spends $10 60 = 6 x m
Find the following arc measures for question 2
Answer:
arc BC = 16°
arc ABC = 196°
Step-by-step explanation:
arc BC = 180 - 164 = 16
arc ABC = 180 + 16 = 196
8 1/3 times 4 1/5 = ?
Answer:
35
Step-by-step explanation:
I believe the answer is 35.
Step-by-step explanation:If I am incorrect please correct me but this is what I got. Also, you never told me if it's in simplified form or in any form it should be in. Hope this somewhat helped and have a good one!
✍(◔◡◔)i need help with this !
A menu at a local diner has 12 appetizers, 8 entrees, and 4 choice of desserts. How many different meal combinations are possible when you select one appetizer, one entrée, and one dessert from the menu?
Answer:
We are to find the number of different meals that are available when we select an appetizer, an entree and a dessert. Thus, the required number of different meals is 216.
Step-by-step explanation:
PLZZZZZZZZ GIVE ME BRAINLYIST
The required number of the combination is 384. Option C is correct.
A menu at a local diner has 12 appetizers, 8 entrees, and 4 choice of desserts. How many different meal combinations are possible when you select one appetizer, one entrée, and one dessert from the menu is to be determined.
In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
For 12 appetizers, 8 entrees, and 4 choices of desserts.
The number of composite combinations that can be made = 12 * 4 * 8
= 384
The required number of the combination is 384. Option C is correct.
Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ2
A fish swims upstream a distance of 16 miles In a river with a current of 3 miles per hour. The fish returns swimming
downstream the same distance. The roundtrip up and down the river takes the fish 4 hours. Assuming that the fish
swims at a constant speed in still water, what is the fish's speed in still water?
Use only numbers. DO NOT include units!
Answer:
16÷3×4
Step-by-step explanation:
SOLVE ALL OF THAT AND THATS THE ANSWER THANK ME LATER UwUHELP ME QUICKLY PLEASE!
JUST ANSWERS!
NO EXPLANATION NEEDED!!!!!!!!!
I PUT IT DOWN AS 50 POINTS!!!!!!!!
Answer:
11. 25
12. 60
13. 93
14. 46
15. 51
16. 85
Answer:
#11
Complementary angles ad to 90°
b = 90° - 65° = 25°#12
Alternate exterior angles are congruent
b = 60°#13
Complete angle and angle addition postulate
b = 360° - (244° + 23°) = 93°#14
Vertical angles are congruent
b = 46°#15
Complementary angles add to 90°. Straight angle is 180°
b = (180° - 90°) - 39° = 51°#16
Alternate interior angles are congruent
b = 85°Suppose the points shown on the coordinate plane are vertices of a rectangle. Which statements are correct? A) The perimeter of the rectangle is 14 units. B) The perimeter of the rectangle is 28 units. C) The coordinates for the fourth vertex of the square are (5, 5). D) The coordinates for the fourth vertex of the rectangle are (−5, −6). E) The coordinates for the fourth vertex of the rectangle are (−5, −3).
Answer:
A
Step-by-step explanation:
Answer:
I beleive it is A and C i just took the test!
Step-by-step explanation:
yourwelcome! :)
Did Sammy eat more blueberries on Monday or on
Monday or on Tuesday? Explain
your reasoning.
Answer: Sammy says he was hungry on Monday so that's why he ate more blueberries than Tuesday
Step-by-step explanation:
Help please. I need this in a few minutes
Answer:
Step-by-step explanation:
34.
The side lengths of the base of a triangular prism are 5 meters, 8 meters, and 10 meters. The height of the prism is 16.5
meters.
Answer:
379.5
Step-by-step explanation:
A prism is a three-dimensional shape where there are two identical bases and rectangular or parallelogram faces.
The lateral surface area of a triangular prism is given as:
= (add all three side lengths) x height of the prism
The lateral surface area of a triangular prism in square meters is
379.5 square meters.
What is a prism?A prism is a three-dimensional shape where there are two identical bases and rectangular or parallelogram faces.
We have,
Triangular prism:
The side lengths of the base of a triangular prism are 5 meters, 8 meters, and 10 meters.
The height of the prism is 16.5 meters.
The lateral surface area of a triangular prism is given as:
= (add all three side lengths) x height of the prism
= (5 + 8 + 10) x 16.5
= 23 x 16.5
= 379.5 square meters.
Thus,
The lateral surface area of a triangular prism in square meters is 379.5 square meters.
Learn more about prism here:
https://brainly.com/question/12649592
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A3-inch candle burns down in 5 hours. How far has it burned after 8
hours? Use the dropdown menu to state your answer as a decimal, mixed
number, or improper fraction.
Answer:Assuming a 3-inch diameter, pillar candles of 3, 4 and 6 inches in height will burn for 45, 60 and 75 hours, respectively. Three-inch Party Lite pillar candles will burn 30-35 hours; 5-inch, 65 to 70 hours; and 7-inch, 90 to 95 hours. The three-wick 6-by-5-inch candles burn for more than 100 hours.
Step-by-step explanation:
find the value of given expression
[tex] \sqrt{369 \times 369} [/tex]
Answer:
√{369×369}=√369²=369 is your answer
Answer:
your answer will be 369
Step-by-step explanation:
......
Sabrina has a rectangular swimming pool in her backyard. She fills it with water to the depth of 4 feet. The water in the pool has a volume of 1600 cubic feet. What are the possible dimensions of the swimming pool with the given depth? Select ALL that apply. WHAT IS THE ANSWER????? PRETTY PLS AND THANK YOU
Answer: [tex]20\times 20, 16\times 25, 10\times 40[/tex]
Step-by-step explanation:
Given
The volume of the pool is [tex]1600\ ft^3[/tex]
Depth of water is [tex]d=4\ ft[/tex]
Suppose A is the base of the pool
[tex]\Rightarrow V=A\times d\\\Rightarrow 1600=A\times 4\\\Rightarrow A=400\ ft^2[/tex]
This area can be written as
[tex]\Rightarrow A=10\ ft\times 40\ ft\ or\\\Rightarrow A=16\ ft\times 25\ ft\ or\\\Rightarrow A=20\ ft\times 20\ ft[/tex]
Find the tangents of the acute angles in the right triangle. Write each answer as a fraction 61,11,60
Answer:
[tex]tan(S)= \frac{28}{45}[/tex]
[tex]tan(R) = \frac{45}{28}[/tex]
Step-by-step explanation:
Given
[tex]RS = 53[/tex]
[tex]ST = 45[/tex]
[tex]RT =28[/tex]
See attachment for triangle
Solving (a): The tangent of S
Using tan formula:
[tex]tan\theta = \frac{Opposite}{Adjacent}[/tex]
So:
[tex]tan(S) = \frac{RT}{ST}[/tex]
[tex]tan(S)= \frac{28}{45}[/tex]
Solving (b): The tangent of R
Using tan formula:
[tex]tan\theta = \frac{Opposite}{Adjacent}[/tex]
So:
[tex]tan(R) = \frac{ST}{RT}[/tex]
[tex]tan(R) = \frac{45}{28}[/tex]
Solve the unit rate
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
See the thing on the left?
▢ unknown
- = -
▢ 1
Fraction lines that look like minus signs, missing units, poor formatting—it’s ridiculously unclear!
::::;
Julius’s walking rate is
(12 miles)/(3 hours) = (4 miles)/(1 hour)
time walked in 1 hour = 1 hour × (4 miles)/(1 hour) = 4 miles
time walked in 2.5 hours = 2.5 hours × (4 miles)/(1 hour) = 10 miles
time walked in 13 hours = 13 hours × (4 miles)/(1 hour) = 52 miles
time required to walk 27 miles = 27 miles × (1 hour)/(4 miles) = 6.75 hours
time required to walk 106 miles = 106 miles × (1 hour)/(4 miles) = 26.5 hours
A driveway measures 1.25 miles.
What does the driveway measure in feet?
Answer:
If you have a conversion table that would be 6600 feet.
Step-by-step explanation:
brainliest? >.<
Answer:
I think it's 3,960 ft!
Please give brainliest!
Simplify:
64 ÷ 8 + 6 (2)
A. 23
B. 20
C. 17
Answer:
B. 20
Step-by-step explanation:
64 ÷ 8 + 6(2)
64 ÷ 8 + 12
8 + 12
20
Answer:
B) 20
Step-by-step explanation:
64/8+6(2)
8+6(2)
8+12
20
(X/36) and (x+20) please help!
Answer:
x=98
Step-by-step explanation:
(x-36)+(x+20)=180 <--- that's how you would set it up.
Gary is 4 years less than three times his brothers age, b. The sum of Gary and his brothers' age is 52. Write an equation to represent this relationship. Please need ASAP. 10 POINTS!
Answer:
52 = b + (3b - 4)
What is the volume of the prism below
Answer:
B. 196 units squared
Step-by-step explanation:
The formula of a prism is V = Bh
= (1/2 bh) h
=(1/2 x 7 x 14) x 4
= (3.5 x 14) x 4
=49 x 4
= 196 units squared
I haven't did these type of questions in a while, but i think my answer is correct. Hope it helps :)
The table shows the amount of rainfall above or below average for big town in 2015 and 2016.How much more rainfall did big town receive in 2015 than 2016?
2015: -3.17
2016: +3.95
7.12 more
Step-by-step explanation:
Just add the two number together ❤
Answer:
lol
Step-by-step explanation: