Using the Ratio Test the series ∑(n³ / [tex]4^n[/tex]) converges. Option A is the correct answer.
To determine the convergence or divergence of the series ∑(n³ / [tex]4^n[/tex]), we can apply the Ratio Test.
The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms in a series is less than 1, then the series converges. If the limit is greater than 1 or it does not exist, the series diverges.
Let's apply the Ratio Test to the given series:
lim n → ∞ |([tex]a_n[/tex] + 1) / [tex]a_n[/tex]| = lim n → ∞ |((n + 1)³ / [tex]4^{(n + 1)[/tex]) / (n³ / [tex]4^n[/tex])|
We simplify the expression by multiplying by the reciprocal:
lim n → ∞ |((n + 1)³ / [tex]4^{(n + 1)[/tex]) × ([tex]4^n[/tex] / n³)|
Next, we simplify the expression inside the absolute value:
lim n → ∞ |((n + 1)³ × [tex]4^n[/tex]) / ([tex]4^{(n + 1)[/tex] × n³)|
Now, we can cancel out the common factors:
lim n → ∞ |(n + 1)³ / (4 × n³)|
Simplifying further:
lim n → ∞ |(n + 1) / (4n)|³
Taking the limit as n approaches infinity:
lim n → ∞ |(1 + 1/n) / 4|³
Since the limit of the absolute value of the ratio is less than 1 (as n approaches infinity), the series converges.
Therefore, the answer is:
A. Converges
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The question is -
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
∑ n = 1 to ∞ (n³ / 4^n)
lim n → ∞ |(a_n + 1) / a_n| = _______
A. Converges
B. Diverges
Jeremiah and his children went into a bakery and he bought $20 worth of cupcakes and cookies. Each cupcake costs $5 and each cookie costs $1.25. He bought 4 times as many cookies as cupcakes. Graphically solve a system of equations in order to determine the number of cupcakes, x,x, and the number of cookies, y,y, that Jeremiah bought.
Answer: (2,8)
Step-by-step explanation:
5x+1.25=20
y=4x
5x+1.25y=20 y=4x
1.25y=-5x+20
1.25y/1.25=-5x+20/1.25
y=-4x+16
Jenny sleeps for 8 hours every day. How many days does she spend over the course
Answer:
56 Hours A Week... how long is the course though?
Step-by-step explanation:
Choose the best term from the box.
The ?
of an object is how heavy the object is.
?
weight
length
capacity
15
lily wants to put a bird food mix in her bird feeder.Her bird feeder can hold 8 cups of bird food.The bird food is a mix of 20% corn and the rest is sunflowers seeds how many cups of corn will lily need to fill the 8 cup bird feeder.If the rest of the mix is sunflower seed,what percent of the bird food is sunflower seed.
Answer:
80%
Step-by-step explanation:
100% is full so you do 100%-20%=80% so thats the answer
Need to help to find the slope pls helppp
Answer:
Step-by-step explanation:
easy
Answer:
it is 2
Step-by-step explanation:
rise over run
it goes up 2 points and
moves right 1 point
2/1 =2
What is the simple interest of $1500.00 for 4 months at 6 3/4%
annual interest?
A) $222.22
B)$101.25
C)$50.63
D)$33.75
The simple interest of $1500.00 for 4 months at 6 3/4% annual interest is $101.25. Thus, the correct answer is B) $101.25.
To calculate simple interest, we use the formula: Interest = Principal x Rate x Time. In this case, the principal (P) is $1500.00, the rate (R) is 6 3/4% (or 0.0675 as a decimal), and the time (T) is 4 months.
First, we need to convert the rate from a percentage to a decimal by dividing it by 100: 6 3/4% = 6.75/100 = 0.0675.
Next, we plug these values into the formula: Interest = $1500.00 x 0.0675 x 4 = $101.25.
Therefore, the simple interest on $1500.00 for 4 months at 6 3/4% annual interest is $101.25. Thus, the correct answer is B) $101.25.
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Anna owns a small business selling used books. She knows that in the last week 29 customers paid cash, 26 customers used a debit card, and 62 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number.
The probability that the next customer will pay with cash, expressed as a percent to the nearest whole number, is 25%.
To calculate the probability that the next customer will pay with cash, we need to use the total number of customers in the last week (29 + 26 + 62 = 117) and the number of customers who paid with cash (29).
The probability that the next customer will pay with cash can be expressed as: P(cash) = 29/117
To express this probability as a percentage, we can multiply by 100:
P(cash) = 29/117 × 100 ≈ 24.79%
Therefore, the probability that the next customer will pay with cash is approximately 24.79%. To round this to the nearest whole number, we need to look at the decimal part of the percentage. If it's less than 0.5, we round down, and if it's 0.5 or greater, we round up. In this case, the decimal part is 0.79, which is greater than 0.5, so we round up:
P(cash) ≈ 25%
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Finish the song:
Good little girl....
Always picking a fight with me~
You know that I'm bad!
But you're spending the night with me....
What do you want from my world?
You're a good little girl♪♪♪
Answer:
Bad little boy
That's what you're acting like
I really don't buy
That you're that kind of guy
And if you are
Why do you want to hang out with me?
Step-by-step explanation:
i had to look in the internet hehe click the ❤️
please
9. a) Why does every pair of whole
a
numbers have a GCF of 1 or greater?
Answer:
A whole number is any positive integer greater than zero and is not a fraction or a decimal. Any whole number can be divided by itself and one so therefor all pairs of whole numbers have a GCF of one. However the bigger the number the more factors it can have so the GCF of a pair of whole numbers may have a greater GCF than 1.
Step-by-step explanation:
Write the number in 2 equivalent forms as a fraction, decimal, or percent.
23%
Answer:
23%, 23/100, 0.23
Step-by-step explanation:
23%
= 23/100
= 0.23
Which angles!!! Need answers 40% of my grade please and thank you
Answer:
alternate interior angle
Omar rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 98 cents for each mile driven. Omar had to pay when he returned the truck. For how many mile did he drive the truck?
The given question is incomplete. The complete question is:
Omar rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 98 cents for each mile driven. Omar had to pay $23 when he returned the truck. For how many mile did he drive the truck?
Answer: Omar drove the truck for 5.15 miles
Step-by-step explanation:
Base fee = 17.95 $
Additional charge per mile = 98 cents = 0.98 $ ( 100cents = 1$)
Now Omar payed = 22 $
Let the miles he travelled = x
Now , [tex]17.95+0.98\times x=23[/tex]
Solvimg for x :
[tex]x=5.15miles[/tex]
Thus Omar drove the truck for 5.15 miles
Solve for v and put your answer in simplest radical form. Show steps plz!
r = stu/v^2
Answer:
V= √( r/Stu)
Step-by-step explanation:
r = stu/v^2
Let us cross multiply , we have
r. v^2 = (s. t. u)
Let us make v ^2 the subject of the formula, we have
v^2 = (s t u)/ r
Find the square of both sides we have
V= √( r/Stu)
PLS HELP ASAP
Eleri mows grass in her neighborhood. She charges $35 per yard. Eleri offers a discount to repeat customers, where she charges $3 less than the previous time to cut the grass. Suppose Eleri is cutting your grass for the 8th time. Which explicit formula describes how much she will charge you?
Abir walks four twelfths of a mile to school. Nadia walks two twelfths of a mile to school. How much farther does Abir walk than Nadia?
Answer:
SHe has walked 2 more miles more than the other person
Step-by-step explanation:
A cone has a volume of 100[tex]\pi[/tex] Cubic units and a diameter of 10 units. What is the height of the cone?
Answer:
12 units
Step-by-step explanation:
The formula for the volume of a cone is given as:
πr²h/3
The volume = 100π cubic units
Diameter = 10 units.
Radius = Diameter/2
= 10 units/2 = 5 units
Hence:
Formula to find the height of a cone
h = 3V/πr²
We substitute
h = 3 × 100π/π × 5²
h = 300π/25π
h = 12 units
The height = 12 units
Sombody please help ASAP!
Answer:
a translation down 9 unit
Step-by-step explanation:
Write an equation in point-slope form of the line that passes through the point(3,5) and has a slope of m=-1
which of the following angles is coterminal with 250°?
find the mean median mode, round to the neaerest tenth. 60,70,75,78,80,80,83,85,87,90.90,90,90,93,95,95,98,100.
Answer:
Mean: 84.6
median:85
mode:90,80
range:40
minimum:60
maximum:100
Step-by-step explanation:
Answer:
mean = 85.5
median = 88.5
mode = 90
Step-by-step explanation:
Okay, so the mean is the sum of the terms divided by the total number of term so basically:
60 + 70 + 75 + 78 + 80 + 80 + 83 + 85 + 87 + 90 + 90 + 90 + 90 + 93 + 95 + 95 + 98 + 100 = 1,539
1,539 ÷ 17 = 85.5
Now, the median is just the number in the middle so we already have our numbers in order so the middle numbers are 87 and 90, so we just have to add them together and then divide by 2:
87 + 90 ÷ 2 = 88.5
and the mode is just the number that's repeated most, and that number is 90
hope this helps:)
The equation of line s is y = __13 x − 3. The equation of line t is y = –x + 5. The equations of lines s and t form a system of equations. The solution to the system of equations is located at point P. Draw a line to represent line s and another line to represent line t. Then plot point P.
Answer:
They cross at point (0.571, 4.429)
Step-by-step explanation:
I just did it and got it correct
Please mark me Brainliest
Use the reflection principle to find the number of paths for a simple random walk from So = 2 to S_15 = 5 that do not hit the line y = 2
The reflection principle is used to find the number of paths for a simple random walk from a starting point S0 to a destination point S15, without hitting a specific line.
In this scenario, we want to find the number of paths for a random walk from S0 = 2 to S15 = 5, without crossing the line y = 2. We can use the reflection principle to simplify the problem.
The reflection principle states that if a path hits a specific line and goes below it, we can reflect the portion of the path below the line to create a new path above the line. This new path is symmetric to the original path.
In our case, the line y = 2 acts as the reflecting line. We reflect the portion of the paths that hit the line y = 2 above the line. By doing so, we transform the problem into finding the number of paths from S0 = 2 to S15 = 5, without crossing or touching the line y = 2.
Using the principles of combinatorics and counting, we can calculate the number of valid paths without hitting the line y = 2. This involves considering the number of steps taken in the positive and negative y-directions, while ensuring that the path remains above the line y = 2. The specific calculations and details would require a more extensive analysis of the random walk and its possible movements.
By applying the reflection principle and counting the valid paths, we can determine the number of paths for the given scenario.
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Helpoopooo please !!!!!!
Answer:
I believe the answer is 2/3
Step-by-step explanation:
The expression 10,000(0.90)^t represents the population of a town t years after 2000. Select the value from each drop down menu that best completes the sentence. The population of the town____ by___ each year.
choices:
increase/decrease
1%, 10%, 90%, 9% or 10K%
Answer:
decrease by 10％ each year
A baseball team plays in a stadium that holds 60,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000. (a) Find a function that models the revenue in terms of ticket price. (Let x represent the price of a ticket and R represent the revenue.) R(x) = 63000x - 3000x2 R (b) Find the price that maximizes revenue from ticket sales. $ 33,000 (c) What ticket price is so high that no revenue is generated?
a) The revenue function in terms of ticket price is R(x) = 63000x - 3000x². b) The price that maximizes revenue from ticket sales is $10.50. c) The ticket price that is so high that no revenue is generated is $21.
(a) To model the revenue in terms of ticket price, we can use the given information. The revenue is calculated by multiplying the number of attendees by the ticket price.
Let x represent the price of a ticket and R represent the revenue. We know that the average attendance at recent games has been 33,000. With every dollar decrease in the ticket price, attendance increases by 3000. So, the attendance can be represented as 33,000 + 3000(10 - x) = 33,000 + 30000 - 3000x.
Therefore, the revenue function R(x) can be expressed as:
R(x) = x * (33,000 + 30000 - 3000x)
= 63000x - 3000x²
Hence, the revenue function in terms of ticket price is R(x) = 63000x - 3000x².
(b) To find the price that maximizes revenue from ticket sales, we need to find the maximum point of the revenue function. This can be determined by finding the vertex of the parabolic function, which represents the maximum point.
The revenue function is R(x) = 63000x - 3000x², which is in the form of a quadratic equation. The maximum point of the quadratic function occurs at x = -b / (2a), where a = -3000 and b = 63000.
Plugging in the values, we have:
x = -63000 / (2 * (-3000))
= -63000 / (-6000)
= 10.5
Therefore, the price that maximizes revenue from ticket sales is $10.50.
(c) To find the ticket price that generates no revenue, we need to consider the scenario where the revenue is equal to zero. From the revenue function R(x) = 63000x - 3000x², we can set R(x) = 0 and solve for x:
63000x - 3000x² = 0
Factoring out x, we have:
x(63000 - 3000x) = 0
This equation is satisfied when either x = 0 or 63000 - 3000x = 0.
For x = 0, it means that the ticket price is zero, which is not possible.
Solving 63000 - 3000x = 0 for x, we get:
3000x = 63000
x = 21
Therefore, the ticket price that is so high that no revenue is generated is $21.
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Bamboo plants can grow 91 centimeters per day. what is the approximate growth of the plant inches per hour?
Answer:
roughly 1.5
Step-by-step explanation:
Select the correct answer.
If f(x) = 2x^2 - 4x - 3° and g(x) = 2x^2 - 16`, find "f(x) + g(x)
OA. 4x^2 - 4x + 13
OB.
* 4x^2 - 4x -13
OC -4x - 19
OD.
*4x^2 - 4x -19
Answer:
4x^2 - 4x - 19
Step-by-step explanation:
Given the following functions
f(x) = 2x^2 - 4x - 3
g(x) = 2x^2 - 16
f(x)+ g(x) =2x^2 - 4x - 3+ 2x^2 - 16
f(x)+ g(x) = 2x^2+2x^2 -4x - 3 - 16
f(x)+ g(x) =4x^2 - 4x - 19
Hence the required sum is 4x^2 - 4x - 19
Calculate Determine the amount of recoverable materials for an urban area in a recycling program if an MRF exists for separating and processing paper,cardboard,aluminum cans,metal tins,glass and mixed plastics.Assume the material distribution and percentage recoverable are as shown in example in class Component %MSW by weight Weight before recycling (suot) Food 46 5129 Paper ,cardboard 11 1226 Plastics 9 1003 Glass 7 780 Metals 5 558 Clothing/textiles 1 111 Ashes ,dust 19 2118 Unclassified 2 223
By considering the material distribution and recoverable percentages, we can calculate the amount of recoverable materials for the urban area's recycling program.
To determine the amount of recoverable materials in an urban area's recycling program, we need to consider the material distribution and the percentage of each component that is recoverable. Based on the provided data, let's calculate the recoverable weight for each component:
Food: 46% of municipal solid waste (MSW) weighs 5129 tons, so the recoverable weight is 46% of 5129 tons.
Paper and cardboard: 11% of MSW weighs 1226 tons, and assuming a certain percentage of paper and cardboard is recoverable, we multiply this percentage by 1226 tons to obtain the recoverable weight.
Plastics: 9% of MSW weighs 1003 tons, and the recoverable weight is determined similarly to paper and cardboard.
Glass: 7% of MSW weighs 780 tons, and the recoverable weight is calculated based on the recoverable percentage.
Metals: 5% of MSW weighs 558 tons, and the recoverable weight is determined using the recoverable percentage.
Clothing/textiles, ashes/dust, and unclassified materials: The recoverable weight for each component is calculated based on the respective percentages.
By summing up the recoverable weights of all components, we can determine the total amount of recoverable materials for the urban area's recycling program.
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write the answer in the simplest radical form
[tex] \sqrt{56} [/tex]
Classify the hypothesis test as left-tailed, right-tailed, or two-tailed. Circle your answer. Below your circle answer, state the null hypothesis, the alternative hypothesis, and label the claim. In the past, the mean running time for a certain type of manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result. A) Right-tailed B) Two-tailed C) Left-tailed
The appropriate classification for the hypothesis test in this scenario is a two-tailed test.
A two-tailed test is used when we are interested in determining whether the mean running time has changed as a result of the introduced change in the production method, without specifying a specific direction of the change. We want to consider the possibility of both an increase and a decrease in the mean running time.
The null hypothesis (H0) for a two-tailed test states that there is no change in the mean running time. In this case, it would be stated as: H0: μ = μ0, where μ represents the population mean running time and μ0 represents the hypothesized mean running time under the previous production method.
The alternative hypothesis (Ha) for a two-tailed test states that there is a change in the mean running time, either an increase or a decrease. In this case, it would be stated as: Ha: μ ≠ μ0, indicating that the mean running time is not equal to the hypothesized mean running time.
The claim being tested is that the mean running time has changed as a result of the introduced change in the production method. This claim is not specific to whether the mean running time has increased or decreased, but rather focuses on the existence of a change.
By classifying the hypothesis test as two-tailed, we are considering the possibility of both an increase and a decrease in the mean running time. This allows for a more comprehensive evaluation of the effects of the introduced change in the production method.
In summary, the hypothesis test is classified as a two-tailed test. The null hypothesis states that there is no change in the mean running time, while the alternative hypothesis states that there is a change, whether it is an increase or a decrease. The claim being tested is that the mean running time has changed as a result of the introduced change in the production method.
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