Write the first five terms of the sequence defined by the explicit formula.
Answers
Answer:
(a) 112, 28, 7, (7/4), (7/16)
Step-by-step explanation:
The sequence is given by the explicit formula
[tex]a_{n} = 112 (\frac{1}{4} )^{n-1}[/tex]
The terms of the sequence are :
[tex]a_{1} = 112 (\frac{1}{4} )^{1-1} = 112 (\frac{1}{4} )^{0} =112 [/tex]
[tex]a_{2} = 112 (\frac{1}{4} )^{2-1} = 112(\frac{1}{4} ) =28 [/tex]
[tex]a_{3} = 112 (\frac{1}{4} )^{3-1} = 112(\frac{1}{4} )^{2} = 7 [/tex]
[tex]a_{4} = 112 (\frac{1}{4} )^{4-1}=112(\frac{1}{4} )^{3} = \frac{7}{4}[/tex]
[tex]a_{5} = 112 (\frac{1}{4} )^{5-1}=112 (\frac{1}{4} )^{4} = \frac{7}{16}[/tex]
Related Questions
which graph shows rotation?
Answers
Please help me, ASAP! Algebraic equation needed.
A candy mixture is made from 6 pounds of sugar sticks of $10 per pound and 14 pounds of jelly beans of $8 per pound. Find the price of the candy mixture per pound.
Answers
14 × 8 = 112$ per 14 pounds
you'll get 20 pounds of the candy mixture and will cost 172
172/20
8.6$ per pound
Final answer:
The price of the candy mixture per pound is $8.60.
Explanation:
To find the price of the candy mixture per pound, we need to calculate the total cost of the sugar sticks and jelly beans, and then divide it by the total weight of the candy mixture.
Let's start by calculating the total cost of the sugar sticks. The cost per pound of sugar sticks is $10, and we have 6 pounds of sugar sticks, so the total cost of the sugar sticks is 6 x $10 = $60.
Next, let's calculate the total cost of the jelly beans. The cost per pound of jelly beans is $8, and we have 14 pounds of jelly beans, so the total cost of the jelly beans is 14 x $8 = $112.
Now, let's calculate the total weight of the candy mixture. We have 6 pounds of sugar sticks and 14 pounds of jelly beans, so the total weight of the candy mixture is 6 + 14 = 20 pounds.
Finally, let's calculate the price of the candy mixture per pound. We divide the total cost of the candy mixture by the total weight of the candy mixture: ($60 + $112) / 20 = $172 / 20 = $8.60.
Therefore, the price of the candy mixture per pound is $8.60.
Which expression is equivalent to 36x^2-25
Answers
Answer
The answer is the fourth one or D.
Step-by-step explanation:
Answer:
THE ANSWER IS D
Step-by-step explanation:
I DID TEST GOT 100
Jasmine borrowed $15,000 for 8 years and she paid $6,600 in interest. What was the interest rate for Jasmine's loan?
A) .055%
B) 6%
C) 3.25%
D) 5.5%
Answers
Answer:
D) 5.5%
Step-by-step explanation:
To find the interest rate, use the equation: I = prt
I = Interest = $6,600
p = principal = $15,000
r = rate = unknown
t = time = 8 years
Now plug the numbers into the equation.
6,600 = 15,000 * r * 8
6,600 = 120,000 * r
Now isolate the variable by dividing both sides of the equation by 120,000.
0.055 = r
Now change the rate to a percent by moving the decimal point 2 digits to the right.
5.5% = r OR r = 5.5%
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Given the regular decagon (10-sided polygon), which statements are true?
Choose all that apply
A. The polygon has 90° rotational symmetry
B. The polygon has 36° rotational symmetry
C. The polygon has 144° rotational symmetry
D. The polygon has point symmetry
Answers
The regular decagon has 36° rotational symmetry and point symmetry because it can map onto itself by rotating 36° and when flipped 180° around its center.
Explanation:The subject of the question is a regular decagon, which is a 10-sided polygon.
To find out which statements are true regarding its symmetry, consider that rotational symmetry of a polygon is determined by the angle of rotation that maps the polygon back onto itself without altering its general outline.
For a regular decagon, the angle of rotation that achieves this is 360 degrees divided by the number of sides, which is 10 in this case.
Therefore, the correct angle of rotational symmetry is 360/10 = 36 degrees.
Thus, the correct answer from the provided options is:
B. The polygon has 36° rotational symmetryD. The polygon has point symmetryHelp me please it due today.
Answers
20 PTS!
Which situation is best modeled with a division expression?
finding the number of equal-sized parts into which a number can be split
finding the combined value of several different number
finding the distance between two numbers on a number line
finding the total value when several of the same number are grouped together
Answers
Answer:
finding the number of equal-sized parts into which a number can be split
Step-by-step explanation:
Let us split the number 80 into 10 equal parts.
80 = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8
= 8 + 8 + 8 +...to 10 times
= 8(10)
or [tex]\frac{80}{10} =8[/tex]
So, if N is any number and p is one of its equal part, then the number of parts into which N is split by p is [tex]\frac{N}{p}[/tex].
Hence, finding the number of equal-sized parts is best modeled with a division expression.
Answer:
Finding the number of equal-sized parts into which a number can be split
Step-by-step explanation:
The correct answer is - finding the number of equal-sized parts into which a number can be split.
Division is defined as the action of splitting something in equal parts.
So, here the first option states this definition.
Taking an example of: Lets divide 100 in 5 equal parts. So, this becomes
[tex]\frac{100}{5}=20[/tex]
This can be also written like : [tex]20+20+20+20+20=100[/tex]
So, division is where you split something equally.
How do you solve this? r^2+32=12r
Answers
Answer:
r = {-8, -4}
Step-by-step explanation:
Simplifying
r2 = -32 + -12r
Solving
r2 = -32 + -12r
Solving for variable 'r'.
Reorder the terms:
32 + 12r + r2 = -32 + -12r + 32 + 12r
Reorder the terms:
32 + 12r + r2 = -32 + 32 + -12r + 12r
Combine like terms: -32 + 32 = 0
32 + 12r + r2 = 0 + -12r + 12r
32 + 12r + r2 = -12r + 12r
Combine like terms: -12r + 12r = 0
32 + 12r + r2 = 0
Factor a trinomial.
(8 + r)(4 + r) = 0
Subproblem 1
Set the factor '(8 + r)' equal to zero and attempt to solve:
Simplifying
8 + r = 0
Solving
8 + r = 0
Move all terms containing r to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + r = 0 + -8
Combine like terms: 8 + -8 = 0
0 + r = 0 + -8
r = 0 + -8
Combine like terms: 0 + -8 = -8
r = -8
Simplifying
r = -8
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:
Simplifying
4 + r = 0
Solving
4 + r = 0
Move all terms containing r to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4
Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4
Combine like terms: 0 + -4 = -4
r = -4
Simplifying
r = -4
Solution
r = {-8, -4}
HELP NOW Which table shows a proportional relationship between x and y? x 1 2 3 6 y 1.5 3 6 9 x 1 3 4 5 y 50 150 200 250 x 3 5 7 8 y 1.5 2.5 3 4.5 x 2 4 5 6 y 6 12 18 21
Answers
Answer: B - x 1 3 4 5 y 50 150 200 250
Step-by-step explanation: The equation is y = 50x
Answer:
b
Step-by-step explanation:
plz mark brainlyest
School started at 8:05 a.m. and ended at 2:40 p.m. The work below shows Erica’s calculation of the length of the school day.
Answers
Erica made errors by failing to borrow 1 hour when subtracting the hours and misrepresenting the final duration of the school day as 5 hours and 25 minutes instead of the correct 6 hours and 45 minutes.
Erica's calculation:
7hr 65
8 hr 5 min -
2hr 40 min
---------------
5hr 25 minutes
1. **Subtraction of minutes:**
Erica correctly subtracted the minutes: 5 minutes - 40 minutes = 25 minutes.
2. **Subtraction of hours:**
Here's where the error lies. Erica attempted to subtract the hours directly without borrowing. Let's correct this step:
Borrow 1 hour from the 7 hours:
[tex]\[7 \text{ hours} - 1 \text{ hour} = 6 \text{ hours}\][/tex]
Now subtract the remaining hours:
[tex]\[6 \text{ hours} - 2 \text{ hours} = 4 \text{ hours}\][/tex]
So, the corrected calculation is:
6 hr 65
4 hr 25 min -
2hr 40 min
---------------
1hr 45 minutes
```
Therefore, the correct length of the school day is 6 hours and 45 minutes, not 5 hours and 25 minutes.
Complete correct question:
School started at 8:05 a.m. and ended at 2:40 p.m. The work below shows Erica’s calculation of the length of the school day.
7hr 65
8 hr 5 min -
2hr 40 min
---------------
5hr 25 minutes
Which two errors did Erica make?
For the function y=3x, what is the output when the input is -4?
Answers
Answer:
x is the input, y is the output
Step-by-step explanation:
Answer:
I believe the answer is -12.
Step-by-step explanation:
If the input if the x value, then y would be equal to -12.
what is the measure of a base angle of an isosceles triangle if its vertex angle measure 80
Answers
Knowing base angles theorem, we know that if the triangle is isosceles, then the bottom base angles and congruent. That means that, we must subtract 80 from 180 and then divide the number by 2, since we must find 1 base angle. This brings us to the answer, 50 degrees.
Hope this helps! <3
Alana earnerd money doing chores. Her grandmother agreed to add $4.00 to the amount Alana earned and then give her half of that sum. Alana's grandmother gave her gave her $4.25. Write and solve an equation to find the amount of Alana's donation
Answers
Answer:
Hence amount of Alana's donation is $4.5.
Step-by-step explanation:
Amount of Alana's donation = x
Her grandmother agreed to add $4.00 to the amount Alana earned.
So new amount of money = (x+4)
She gives only half of the sum which is (x+4)/2.
She gave her $4.25 so both values must be equal.
[tex]\frac{\left(x+4\right)}{2}=4.25[/tex]
[tex]x+4=4.25*2[/tex]
[tex]x+4=8.5[/tex]
[tex]x=8.5-4[/tex]
[tex]x=4.5[/tex]
Hence amount of Alana's donation is $4.5.
Alana earned $4.50 from doing chores before her grandmother added an additional $4.00 and then gave her half of the total, which was $4.25.
The question relates to finding out how much money Alana earned by doing chores before her grandmother added $4.00 and then gave her half. In this scenario, we let x represent the amount of money that Alana earned from doing chores. According to the information provided, Alana's grandmother agreed to add $4.00 to Alana's earnings and then give her half of the total sum. This can be expressed as:
(x + 4.00) / 2 = 4.25
To solve for x, we first multiply both sides of the equation by 2 to get rid of the denominator:
x + 4.00 = 4.25 * 2
x + 4.00 = 8.50
Next, we subtract $4.00 from both sides of the equation to solve for x:
x = 8.50 - 4.00
x = 4.50
Therefore, the amount of money Alana earned from doing chores is $4.50.
The value of a stock increases 14 2/3 points twice in one week.the other 3 days the value decreases by 10 points,8 1/3 points and 12 2/3 points.By how many points did the value of the stock change that week? A 2/3 points. B 1/3 points C -1 1/3 points D -1 2/3 points
Answers
Answer:
D
Step-by-step explanation:
The number of points the stock changed in a week will be equal to -1 2/3. Hence, option D is correct.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the given information in the question,
Value of a stock increased 14 2/3 twice in one week.
Then, its value will be.
= 2 × 14 2/3
= 2 × 44/3
= 88/3
Then, the other 3 days it decreased by 10, 8 1/3, and 12 2/3 points.
So, the total decrease will be,
10 + 25/3 + 38/3
= (30 + 25 + 38)/3
= 93/3
So, the value of stock change will be,
88/3 - 93/3
= - 5/3 or,
In mixed fraction form, it can be written as -1 2/3.
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Which values of s are solutions to the inequality?
s>−10
Select each correct answer.
s=−2
s=−8
s=−18
s=−108
s=−180
Answers
Answer:
the answers are s = -2 and s = -8
Step-by-step explanation:
To paint a sunset Tran and makes a shade of orange paint using five drops of red paint for every eight drops of yellow paint if tranny uses 15 drops of red paint how many drops of yellow paint would you need
Answers
Answer:
24 drops of yellow paint
Step-by-step explanation:
We have a ratio of red paint to yellow paint
red:yellow
5: 8
We need red to be 15 drops, so we multiply by 3
What we do to one side we do to the other
red:yellow
5*3 8*3
15 : 24
We need 24 drops of yellow paint
Daniel wants to buy a tv that’s cost 732.98 If the sales tax is 732.98 If the sales tax is 75% how much does he spend all together total cost
Answers
Answer:
Step-by-step explanation:My answer I would say is 1,282.735.I got that by multiplying 732.98 by .75 since the sales tax is 75% of 732.98 which is 549.735.Then you just add those 2 together.Hope this helps!!! Please mark brainliest!!!!
Diet cola was on sale last week, it cost $10 for every 4 pack. How much do 2 packs of diet cola cost
Answers
Answer:
Step-by-step explanation: Your answer to this question is 5$. Reason is because for 4 packs is 10$. You are trying to figure out how much it will be for 2 packs. The only thing you have to do is divide 10$ by 2 which should give you 5. Hope this helps!!!!
Please mark brainliest!!!!☺
if i clock out at 11:53 and i have 30 Minutes what time do i get in?
Answers
Answer:
you get in at 11:23
Step-by-step explanation:
53-30=30
so 11:23
Answer:
11:27
Step-by-step explanation:
which of the following expressions are equivalent to 2/x^8-y^8? choose all that applyA.2/(x^4-y^4)*1/(x^4+y^4)B.2/(x^4)^2-(y^4)^2C.2/(x4-y^4)*1/(x^4-y^4)D.1/(x^4-y^4)*1/(x^4+y^4)
Answers
Answer: option a and b are correct :)
Step-by-step explanation:
which equation and ordered pair represent the correct vertex form and vertex for j(x) = x^2 - 12 x +7?
Answers
Answer:
see explanation
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given the equation in standard form : ax² + bx + c : a ≠ 0
then the x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
j(x) = x² - 12x + 7 is in standard form
with a = 1, b = - 12 and c = 7, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{-12}{2}[/tex] = 6
substitute x = 6 into j(x) for y- coordinate
y = 6² - 12(6) + 7 = 36 - 72 + 7 = - 29
vertex = (6, - 29 ) and
j(x) = (x - 6)² - 29 ← equation in vertex form
The wall in the family room is exactly 12 feet long. Your couch is 10 feet and 6 inches long. Once the couch is placed, how much room is left for your end table?
Answers
Answer:
1 foot 6 inches
Step-by-step explanation:
That would be the difference between 12 feet and 10 feet 6 inches.
Answer:
the answer is 18 inches (:
Step-by-step explanation:
Evaluate. Round your answer to the nearest hundredth (precalculus)
Answers
Answer:
-1.83
Step-by-step explanation:
To find sum of geometric series we use formula
[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex]
In the question , given i=1 so a= 11* -1/5 = -11/5
Here a= 11
r= -1/5, n=10
Plug in the values in the formula
[tex]S_10 = \frac{-11}{5}*\frac{(1-(\frac{-1}{5})^{10}}{1-(\frac{-1}{5})}[/tex]
S_10 = -1.83
The correct option is c.
To evaluate ∑(i=1 to 10) 11(-1/5)^i, we substitute each value of i into the formula and sum the results. Rounding the answer to the nearest hundredth gives -0.01.
Explanation:To evaluate the given expression, we need to substitute each value of i from 1 to 10 into the formula 11(-1/5)^i and then sum up the results:
i = 1: 11(-1/5)^1 = -11/5i = 2: 11(-1/5)^2 = 11/25i = 3: 11(-1/5)^3 = -11/125i = 4: 11(-1/5)^4 = 11/625i = 5: 11(-1/5)^5 = -11/3125i = 6: 11(-1/5)^6 = 11/15625i = 7: 11(-1/5)^7 = -11/78125i = 8: 11(-1/5)^8 = 11/390625i = 9: 11(-1/5)^9 = -11/1953125i = 10: 11(-1/5)^10 = 11/9765625Summing up all these values, we get:
-11/5 + 11/25 - 11/125 + 11/625 - 11/3125 + 11/15625 - 11/78125 + 11/390625 - 11/1953125 + 11/9765625 ≈ -0.00001
Therefore, the rounded answer to the nearest hundredth is C. -0.01.
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The complete question is here:
Evaluate \sum_{i=1}^{10} 11\left(-\frac{1}{5}\right)^i. Round your answer to the nearest hundredth.
A. 13.75
B. 9.17
C. -0.01
D. -1.83
If a,b,c,d are replaced by four different digits from 1 to 9, inclusive, then what's the largest possible value for a.bc + 0.d ?
Answers
Answer:
Step-by-step explanation:
I'm not sure but I would nominate 9 8 7 6 written this way.
9.86
0.7
10.56
Answer:
9.86 plus 0.7 is 10.56
Step
I NEED HELP PLEASE I AM BEGGING YOU PLEASE HELP ME !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A factory that manufactures basketballs spends $6 on each basketball that it produces.
Which of the following describes the rate of cost growth at the factory?
A.
both linear and nonlinear
B.
nonlinear
C.
neither linear nor nonlinear
D.
linear
Answers
Answer:
D.) Linear
Step-by-step explanation:
There are no exponents
also I had the same question
The rate of cost growth can be seen as the cost of adding 1 unit of basketball to the output. This cost as we know is $6, given for each basketball produced. Since this is constant, the rate of cost growth is seen as linear. Hence option D is the right choice.
What does linear growth mean?A quantity grows linearly if it increases by the same amount per unit of time.
What does non-linear growth mean?A quantity grows non-linearly if the increase in the amount is not the same per unit of time.
How to solve the question?In the question, we are informed that a factory that manufactures basketballs spends $6 on each basketball that it produces.
We are asked to describe the rate of cost growth at the factory.
The rate of cost growth can be seen as the cost of adding 1 unit of basketball to the output. This cost as we know is $6, given for each basketball produced. Since this is constant, the rate of cost growth is seen as linear. Hence option D is the right choice.
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An author has 18 pages to send to a publisher. The author has only small envelopes and can't fit all the pages into a single envelope. It ends up taking 6 envelopes to hold all the pages. If each envelope has the same number of pages in it, how many pages are there in each envelope? A) 2 pages B) 3 pages C) 4 pages D) 5 pages
Answers
[tex]6 \times 3 = 18[/tex]
What is the additive inverse of the complex number –8 + 3i?
Answers
Additive inverse is what you add to a number to get zero.
So, by definition, the additive inverse of (-8 + 3i) would be (8 - 3i).
Julie designs gardens for a living. For a year she kept track of the amount of time she spent designing the garden and whether or not the customer returned. She recorded the time and probability that a customer returned.
To have the greatest probability of a returning customer, what amount of time should Julie spend per customer?
TIME DESIGNING PROBABILITY OF RETURN
1-2 Hours 5/8
2-3 Hours 5/9
3-4 Hours 7/8
4-5 Hours 3/4
5-6 Hours 1/2
6-7 Hours 3/7
7-8 Hours 2/9
A. 1-2 Hours
B. 2-3 Hours
C. 3-4 Hours
D. 4-5 Hours
Answers
Answer:
To have the greatest probability of a returning customer, Julie should 3-4 Hours per customer
Step-by-step explanation:
==> To compare the Time Designing Probability of Return, we need to convert the Probabilities into Percentage form by multiplying them with 100.
1-2 Hour = (5÷8) × 100 = 62.5%
2-3 Hours = (5÷9) × 100 = 55.55%
3-4 Hours = (7÷8) × 100 = 87.5%
4-5 Hours = (3÷4) × 100 = 75%
5-6 Hours = (1÷2) × 100 = 50%
6-7 Hours = (3÷7) × 100 = 42.85%
7-8 Hours = (2÷9) × 100 = 22.22%
To have the greatest probability of a returning customer, Julie should 3-4 Hours per customer
Answer:C)3-4 hours
Step-by-step explanation:
need help turning this improper fraction into mixed number, it's super easy.
Answers
Answer:
2 3/4
Step-by-step explanation:
22/8 = 2 6/8 = 2 3/4
Hope that helps and feel free to ask me more questions :)Brainliest??
Common denominator for 9/15 and 4/9
Answers
Answer:
45 and 36
Step-by-step explanation:
The common denominator for the two proper fractions is 45
What are proper fractions?A proper fraction is a fraction which has its numerator value less than the denominator. For example, ⅔, 6/7, 8/9, etc. are proper fractions.
Given here: The proper fractions 9/15 and 4/9
now LCM(9,15) = 45
Thus, 9×3/45=27/45 , 4×5/45=20/45
Hence, The common denominator for the two proper fractions is 45
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