Answer:
Step-by-step explanation:
B.
nonlinear
Answer:
Step-by-step explanation:
The table shows a function. Is the function linear or nonlinear?
x y
17 8
18 10
19 12
The function shown in the given table is a linear function.
Given that, to determine whether the table shows a function is linear or non-linear.
What are functions?The connection between sets of values is what makes up a function. For instance, in the formula y=f(x), a set of y exists for each value of x. The independent variable is called x, while the dependent variable is called Y.
Here,
Table,
x = 17 18 19
y = 8 10 12
From the observation of the table, it is been observed that the value of x changes by 1 unit, and correspondingly the value of y changes by 2 units. So, the relationship arises is a linear function.
Thus, the function shown in the given table is a linear function.
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HELP MEE! 100 POINTS AND BRAINLY! GIVE ME THE STEPS, AND A GOOD ANSWER OR I WILL DELETE YOUR ANSWER AND GET MY POINTS BACK!
Example: solve √(2x−5) − √(x−1) = 1
Answer:
Solve the equation for
x by finding a , b , and c of the quadratic then applying the quadratic formula.
Exact Form:
x= 7 + 2 √ 5
Decimal Form:
x = 11.47213595 …
Step-by-step explanation:
Hi there! Hopefully this helps!
Answer: 11.47(to 2 decimal places).
Isolate one of the square roots: √(2x−5) = 1 + √(x−1)
Square both sides: 2x−5 = (1 + √(x−1))^2
We have removed one square root.
Expand right hand side: 2x−5 = 1 + 2√(x−1) + (x−1)
Simplify: 2x−5 = 2√(x−1) + x
Subtract x from both sides: x−5 = 2√(x−1)
Now do the "square root" thing again:
Isolate the square root: √(x−1) = (x−5)/2
Square both sides: x−1 = ((x−5)/2)^2
We have now successfully removed both square roots.
Let's continue with the solution.
Expand right hand side: x−1 = (x^2 − 10x + 25)/4
Since it is a Quadratic Equation! let's put it in standard form.
Multiply by 4 to remove division: 4x−4 = x^2 − 10x + 25
Bring all to left: 4x − 4 − x^2 + 10x − 25 = 0
Combine like terms: −x^2 + 14x − 29 = 0
Swap all signs: x^2 − 14x + 29 = 0
Using the Quadratic Formula (a=1, b=−14, c=29) gives the solutions:
2.53 and 11.47 (to 2 decimal places)
2.53: √(2×2.53−5) − √(2.53−1) ≈ −1 Oops! Should be plus 1. So it is not the solution.
11.47: √(2×11.47−5) − √(11.47−1) ≈ 1 Yes that one works.
Kendra needs 2 3/4 cups of flour for cookies, 4 1/2 cups of flour for bread, and cup of flour 2/3 for biscuits , How much flour does she need in all?
Answer:
7 11/12
Step-by-step explanation:
amount of the flour
= 2 3/4 + 4 1/2 + 2/3
= 11/4 + 9/2 + 2/3
= 33/12 + 54/12 + 8/12
= 95/12
= 7 11/12
make as the brainliest
Answer:
Wofford College
Step-by-step explanation:
Question Progress
Homework Progress
Sub
Describe fully the single transformation that maps triangle A onto triangle B.
-
।
Answer:
it is b
Step-by-step explanation:
6. 4ab + 13b
Can someone help me find the andwers
Answer:
You cannot simplify this. One has ab, and one has only b. So that is the most simplified it can get.
Answer: There are no like terms.
Step-by-step explanation:
A machine fills 75 bottles of water each minute. Write an equation to represent the number of bottles, B of water the machine can fill in m minutes.
Answer:
B x m
Step-by-step explanation:
Example: 75 x minutes
So no matter how much bottles you have, you just have to multiply the minutes.
Answer:I think it would be 75 divided by b = m
Step-by-step explanation:
A quantity with an initial value of 830 grows exponentially at a rate such that the quantity doubles every 2 weeks. What is the value of the quantity after 21 day, to the nearest hundredth?
Answer:
The value of the quantity after 21 days is 2,347.59.
Step-by-step explanation:
The exponential growth function is
[tex]A=A_0(1+r)^t[/tex]
A= The number of quantity after t days
[tex]A_0[/tex]= initial number of quantity
r= rate of growth
t= time in days.
A quantity with an initial value of 830 grows at a rate such that the quantity doubles in 2 weeks = 14 days.
Now A= (2×830)= 1660
[tex]A_0[/tex] = 830
t = 14 days
r=?
Now plug all value in exponential growth function
[tex]1660=830(1+r)^{14}[/tex]
[tex]\Rightarrow \frac{1660}{830}= (1+r)^{14}[/tex]
[tex]\Rightarrow 2= (1+r)^{14}[/tex]
[tex]\Rightarrow (1+r) ^{14}=2[/tex]
[tex]\Rightarrow (1+r)=\sqrt[14]{2}[/tex]
[tex]\Rightarrow r=\sqrt[14]{2}-1[/tex]
Now, to find the quantity after 21 days, we plug [tex]A_0[/tex] = 830, t= 21 days in exponential function
[tex]A=830( 1+\sqrt[14]{2}-1)^{21}[/tex]
[tex]\Rightarrow A=830(\sqrt[14]2)^{21}[/tex]
[tex]\Rightarrow A=830(2)^\frac{21}{14}[/tex]
[tex]\Rightarrow A=830(2)^\frac{3}{2}[/tex]
[tex]\Rightarrow A=2,347.59[/tex]
The value of the quantity after 21 days is 2,347.59.
Final answer:
To calculate the value of a quantity after 21 days when it doubles every 2 weeks with an initial value of 830, use the exponential growth formula [tex]N(t) = N_0 \times 2^{t/T}[/tex]. Plugging in the values, the quantity after 21 days is 2347.14, to the nearest hundredth.
Explanation:
Calculating Exponential Growth
To find the value of a quantity after 21 days when it has an initial value of 830 and doubles every 2 weeks, we can use the formula for exponential growth:
N(t) = N_0 × 2^(t/T)
Where:
N(t) is the future value after time t,
N_0 is the initial value (830),
t is the time period in days (21 days),
T is the doubling period in days (2 weeks = 14 days).
First, we convert 21 days into weeks: 21 days / 7 days per week = 3 weeks.
Next, let's find the value after 3 weeks. We plug our values into the exponential growth formula:
[tex]N(3) = 830 \times 2^{3/2}[/tex]
To calculate 3/2 weeks in terms of doubling periods:
3 weeks / 2 weeks per doubling period = 1.5 doubling periods.
Now we can calculate the quantity:
N(21) = [tex]830 \times 2^{1.5}[/tex] = 830 × 2.828 = 2347.14
To the nearest hundredth, the value of the quantity after 21 days is 2347.14.
Carl bought 7 packs of pencils. He now has 42 pencils. He writes that 42 is 6 times as many as 7. Which comparison sentence below can he use to show the comparison?
Answer:
Option b
Step-by-step explanation:
Complete question is
Carl bought 7 packs of pencils. He now has 42 pencils. He writes that 42 is 6 times as many as 7. Which comparison sentence below can he use to
show the comparison?
A. 7 more than 6 is 42.
B. 7 is 6 times as many as 42.
C. 42 is 7 times as many as 6.
D. 6 is 7 times as many as 42
Solution -
It is given that Carl has 42 pencils.
It is not sure in which pack - the one with 6 pencils or the one with 7 pencils.
But when Carl wrote that "42 is 6 times as many as 7". By this he means that the present number of pencils i.e 42 is equal to 6 times the number of pencils in the pack of 7
Then, it becomes clear that Carl has 6 times the number of pencils in the pack of 7 pencils
Option B is correct
The number of absences for one week for all students at a high school were compiled, and the probability distribution below was created. What is the probability in any given week that a randomly selected student will be absent no more than one day? Probability Distribution Days Absent: X Probability: P(X) 0 0.78 1 0.14 2 0.03 3 0.01 4 0 5 0.04 0.08 0.14 0.78 0.92
Answer:
Option D) 0.92
Step-by-step explanation:
We are given the following probability distribution in the question:
x: 0 1 2 3 4 5
P(X): 0.78 0.14 0.03 0.01 0 0.04
We have to find the probability that a randomly selected student will be absent no more than one day.
Thus, we have to evaluate:
[tex]P(x\leq1)\\=P(X=0) + P(X = 1)\\=0.78 + 0.14\\=0.92[/tex]
0.92 is the probability that a randomly selected student will be absent no more than one day.
Thus, the correct answer is
Option D) 0.92
Answer:
Option D
Step-by-step explanation:
got it right on edg
You wonder if TV ads are more effective when they are longer or repeated more often or both. So you design an experiment. You prepare 30-second and 60-second ads for a camera. Your subjects all watch the same TV program, but you assign them at random to four groups. One group sees the 30-second ad once during the program; another sees it three times; the third group sees the 60-second ad once; and the last group sees the 60-second ad three times. You ask all subjects how likely they are to buy the camera. (a) This is a randomized block design, but not a matched pairs design. (b) This is a matched pairs design. (c) This is a completely randomized design with one explanatory variable (factor). (d) This is a completely randomized design with two explanatory variables (factors). (e) This is a completely randomized design with four explanatory variables (factors).
Answer:
d) This is a completely randomized design with two explanatory variables (factors).
Step-by-step explanation:
Explanatory variables are independent variables.
In this case, I prepared two explanatory variables, which are : (i)30-second ad
(ii) 60-second ad,
Then, the explanatory variables were assigned to 4 treatment groups, and each variable is done once or thrice.
All subjects are assigned randomly to all treatment groups, with each treatment group seeing one. We can conclude that this is a completely randomized design with two explanatory variables.
There are two peice pf gold and silver alloy. The ratio between the gold and silver in the first piece is 2:3, in the second peice 3:7. If we want to have 8 gram of gold and silver alloy with gold-silver ratio 5:11 how much of each peice of alloy is needed.
Answer:
1 grams of one of the alloy; and 7 grams of the other corresponding alloy.Step-by-step explanation:
The ratio between the gold and silver in the first piece = 2:3
The ratio between the gold and silver in the second piece =3:7
The ratio in the mixture = 5:11
We want to have 8 gram of the new mixture.
Let the gram of alloy taken from the first piece=x
Therefore: gram of alloy would be taken from the second piece=(8-x)
This gives:
[tex]\dfrac{2}{5}x+ \dfrac{3}{10}(8-x)=\dfrac{5}{16}*8[/tex]
We simplify the equation above for the value of x.
[tex]\dfrac{2x}{5}+ \dfrac{3(8-x)}{10}=\dfrac{5}{2} \\\dfrac{4x+24-3x}{10}=\dfrac{5}{2}\\\dfrac{x+24}{10}=\dfrac{5}{2}\\2x+48=50\\2x=50-48\\2x=2\\x=1[/tex]
Therefore to create 8 gram of gold and silver alloy with gold-silver ratio 5:11, we take 1 grams of one of the alloy and 7 grams of the other alloy.
The points A, B, C, and D are on a number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D ? (1) The distance between C and A is the same as the distance between C and B. (2) A is to the left of D on the number line.
Answer:
insufficient information
Step-by-step explanation:
If the order of the points is unknown, the distances AB and CD imply no particular distance for BD.
Mr. Padilla used similar triangles to make a design. Which statement about the triangles in the design must be true?
Answer:
They have corresponding angles that are congruent.
Step-by-step explanation:
The options of the question in the attached figure
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
therefore
The statement that must be true is
They have corresponding angles that are congruent.
Paul was thinking of a number. Paul halves the number and gets an answer of 6. Form an equation with
x
from the information.
The equation is x/2=6
What is an equation?A statement that the values of two mathematical expressions are equal (indicated by the sign =).
Given here: Paul was thinking of a number. Paul halves the number and gets an answer of 6. Let the number be x and this number is halved and it becomes equal to 6
thus we can construct an equation as follows:
x/2=6
Hence, The equation is x/2=6
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Final answer:
The equation formed based on the information that Paul halves the number to get 6 is x/2 = 6. Multiplying both sides by 2 gives us x = 12, which is the original number that Paul was thinking of.
Explanation:
The student question regarding forming an equation from a given word problem can be translated into: Paul halves the number and gets 6. To form an equation with x, we represent the unknown number as x, and then create an equation based on the information given. Since halving the number results in 6, the equation we form is x/2 = 6.
To find the value of x, we can multiply both sides of the equation by 2, which will give us x = 6 × 2. This simplifies to x = 12, which is the original number Paul was thinking of.
A basket full of 10 apples costs 23$, another basket full of 15 apples costs 33$. The prices of the baskets are the same. How much will a basket full of 25 apples cost? Write an equation that tells the price Y for the number of apples X. Fill in the chart.
Answer:
Equations:
y + 10x = 23
y + 15x = 33
cost of basket with 25 apples = $53
Step-by-step explanation:
A basket with 10 apples cost $23 and a basket with 15 apples cost $33. Note that these costs also include the cost of the basket, which is same in both case. Let the cost of empty basket with "y" and cost of each apple be "x"
Cost of basket and 10 apples is $23. We can transform this statement into an equation as:
y + 10x = 23 Equation 1
Similarly,
Cost of basket and 15 apples is $33. This gives us another equation:
y + 15x = 33 Equation 2
Subtracting Equation 1 from Equation 2 , we get:
y + 15x - (y +10x) = 33 - 23
5x = 10
x = 2
Using the value of x in equation 1, we get:
y + 10(2)= 23
y = 23 - 20
y = 3
This means, cost of basket is $3 and cost of each apple is $2.
Now we can calculate the cost of basket with 25 apples, which will be:
Cost of basket + Cost of 25 apples = Total Cost
3 + 25(2) = 3 + 50 = $53
Answer:
10=23
15=23
25=53
Step-by-step explanation:
Monique is an interior design student. As part of her internship, she is redesigning a small kitchen for a client. She would like to expand the kitchen and add a dining area. Before creating sketches for the client, she imagines the new layout in her mind, most likely using __________.A. tacit knowledge.
B. a proposition.
C. the method of loci.
D. a depictive representation.
2. What is the total outcome when picking a number from 1 to 30 and a
letter from the alphabet *
56
150
390
780
Answer: 780
Step-by-step explanation: 30 numbers times 26 letters.
30 x 26=780
Final answer:
To find the total number of outcomes for selecting a number between 1 and 30 and a letter from the alphabet, you multiply the outcomes of each event together, resulting in 30 numbers multiplied by 26 letters, which equals 780 total outcomes.
Explanation:
The question asks for the total number of outcomes when picking a number from 1 to 30 and a letter from the alphabet. In mathematics, to calculate the total number of outcomes for two independent events, you multiply the number of outcomes for each event. There are 30 different outcomes for picking a number from 1 to 30, and, assuming a standard English alphabet, there are 26 outcomes for picking a letter from A to Z.
To find the total number of outcomes when one event is selecting a number and another event is selecting a letter, you multiply the two: 30 (numbers) × 26 (letters) = 780 total outcomes.
Can you please help me find the area?
Answer:
40 in
Step-by-step explanation:
A= l x w
2 x 9 = 18
2 x 11 = 22
Then add together because the shape is together:
18 + 22 =
40
For this question please tell me if I'm right or wrong. If I'm wrong please correct me.
Please use the following image below in order to answer the question correctly:
Tell whether JL is best described as a radius, chord, diameter, secant, or tangent of ⊙P.
What can JL be best described as?
Please show all the work on how you got your answer. ( I'm not asking for an explanation. All I want is the work shown so I can understand how you got your answer)
Answer:
Your Wrong (Tangent)
Step-by-step explanation:
A tangent is a straight line that touches the curve, like the curve part of the circle. I posted an image so you could see an example.
Answer:
E) tangent
Step-by-step explanation:
JKL is a straight line which touches the circle at one point, so it's a tangent
There are 41 students in a Statistics class. The professor knows from experience that the time to grade one exam follows a normal distribution with average 8.8 minutes and standard deviation 3.2 minutes.
What is the average time and standard deviation to grade 41 exams
What is a tessalation
Answer:
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
Step-by-step explanation:
Scott is on his school's academic team. On average, it takes Scott 4 minutes, with a standard deviation of 0.25 minutes, to solve a problem at an academic bowl. How often will it take Scott more than 4.25 minutes to solve a problem at an academic bowl?
Answer:
15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 4 minutes
Standard Deviation, σ = 0.25 minutes
We standardize the given data.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(more than 4.25 minutes to solve a problem)
[tex]P( x > 4.25) = P( z > \displaystyle\frac{4.25 - 4}{0.25}) = P(z > 1)[/tex]
[tex]= 1 - P(z \leq 1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 4.25) = 1 - 0.8413 = 0.1587 = 15.87\%[/tex]
Thus,15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.
The correct answer is approximately 15.87%.
To solve this problem, we can use the properties of the normal distribution. Given that the average time Scott takes to solve a problem is 4 minutes with a standard deviation of 0.25 minutes, we can calculate the z-score for the time of 4.25 minutes to determine how many standard deviations away from the mean this time is.
The z-score formula is:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where[tex]\( X \)[/tex]is the value in question[tex](4.25 minutes), \( \mu \)[/tex] is the mean (4 minutes), and [tex]\( \sigma \)[/tex] is the standard deviation (0.25 minutes).
Plugging in the values, we get:
[tex]\[ z = \frac{4.25 - 4}{0.25} = \frac{0.25}{0.25} = 1 \][/tex]
Now, we look up the z-score of 1 in the standard normal distribution table or use a calculator to find the corresponding area to the left of this z-score. This area represents the probability that Scott will take 4.25 minutes or less to solve a problem.
The area to the left of a z-score of 1 is approximately 0.8413, or 84.13%. This is the cumulative probability up to 4.25 minutes.
To find the probability that it will take Scott more than 4.25 minutes, we subtract this value from 100% (since the total area under the normal distribution curve is 1, or 100%):
[tex]\[ P(X > 4.25) = 1 - 0.8413 = 0.1587 \][/tex]
Converting this to a percentage, we get:
[tex]\[ 0.1587 \times 100\% \approx 15.87\% \][/tex]
Therefore, it will take Scott more than 4.25 minutes to solve a problem approximately 15.87% of the time.
Penny is planning a baby shower for her daughter-in-law. The restaurant charges $950 for up to 25 guests, plus $31.95 for each additional guest. How many guests can attend if Penny wants the total cost to be no more than $1,500?
Answer:
42
Step-by-step explanation: I subtracted 950 from 1500 and that left me with 550 that i divided by 31.95 which left me with 17... but we keep it at 17 because we can't have half of a guest. Then you would add 17 to the 25 other guests you are paying for the answer of 42
Answer:
42
Step-by-step explanation:
1500-950=550
550÷32=17
17+25=42 guests
What is the volume of a cylinder with a base radius 3 and hight 8
Answer:
Solution
V=πr2h=π·32·8≈226.19467
Step-by-step explanation:
What is the slope between the points (4,–1) and (–4,3)?
The formula for slope is [tex]\frac{rise}{run} = \frac{y2-y1}{x2-x1}[/tex].
Subtract y1 from y2. (y1= -1, y2 = 3)
3 - -1 = 4
Now subtract x1 from x2. (x1 = 4, x2 = -4)
-4 -4 = -8
Divide the difference between the y coordinates by the difference between the x coordinates.
[tex]\frac{4}{-8}[/tex] or 4 ÷ -8 = -0.5
Answer:The slope between the two points is -0.5.
Hope this helpsss
The slope between the points (4, –1) and (–4, 3) is calculated using the slope formula and is found to be –0.5.
Explanation:The slope of the line passing through the points (4,–1) and (–4,3) is calculated using the slope formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. For the given points:
y2 = 3y1 = –1x2 = –4x1 = 4Plugging these into the formula gives:
m = (3 - (–1)) / (–4 - 4) = 4 / –8 = –0.5.
The slope between the points (4, –1) and (–4, 3) is –0.5.
A principal gathered data about the distance, in miles, that his teachers and bus drivers live from school. The box plots below show these data.
Answer:
We choose C
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo
Basically, interquartile range represents the width or "dispersion" of the set. [1] The interquartile range is determined by the difference between the top quartile (25% highest) and lower quartile (25% lowest) point of the data set.
From the picture, we can find that:
The interquartile range of the bus drivers is: 20 -10 = 10 The interquartile range of the teachers is: 30 -15 = 15So the interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.
We choose C
Answer:
Step-by-step explanation:
is 2 hours and 30 minuets more or less than 10%of a day. Explain your reasoning
Answer:
More
Step-by-step explanation:
because 2 hours and 30 min is 2.5 10 percent of a day is 2.4 so more
Helppppppppppp me please
Given:
The radius of the given diagram = 9 inches
The value of given angle = 120°
To find the length of the arc.
Formula:
The relation between arc (S), radius (r) and the angle ([tex]\theta[/tex]) is:
[tex]S[/tex]= [tex]2\pi r(\frac{\theta}{360})[/tex]
Now,
Putting, [tex]r = 9, \theta = 120 ^\circ[/tex] we get,
[tex]S = 2(\pi)(9)(\frac{120}{360} )[/tex]
[tex]S = 6\pi[/tex]
Hence,
The length of the arc is [tex]6\pi[/tex] inches.
Consider the series
\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}.
Find the interval of convergence of this power series by first using the ratio test to find its radius of convergence and then testing the series' behavior at the endpoints of the interval specified by the radius of convergence.
interval of convergence =
Answer:
(-\infty,-1/2) U (1/2,+\infty)
Step-by-step explanation:
You have the following series:
[tex]\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}[/tex]
You calculate the radius of convergence by using the formula:
[tex]R= \lim_{n \to \infty} |\frac{a(x)_n}{a(x)_{n+1}}|= \lim_{n \to \infty} |\frac{\frac{(2x)^n}{n}}{\frac{(2x)^{n+1}}{n+1}}|\\\\=\lim_{n \to \infty} |\frac{\frac{(2x)^n}{n}}{\frac{(2x)^n(2x)}{n+1}}|=\lim_{n \to \infty}|\frac{n+1}{2xn}|=|\frac{1}{2x}|\lim_{n \to \infty}|1+\frac{1}{n}|=|\frac{1}{2x}|[/tex]
The radius of convergence is R=1/2x.
Hence, the interval of convergence is
|2x| < 1
|x| < 1/2
By evaluating in the extrems of the interval:
[tex]\sum_{n=1}^{\infty} \frac{(2 (\frac{1}{2}))^n}{n}=\sum_{n=1}^{\infty} \frac{(1)^n}{n}=0\\\\\sum_{n=1}^{\infty} \frac{(2 (-\frac{1}{2}))^n}{n}=\sum_{n=1}^{\infty} \frac{(-1)^n}{n}[/tex]
for x=-1/2 we obtain an Alternating Harmonic Series, for x=1/2 we obtain the divergent harmonic series. Thus the interval is:
(-\infty,-1/2) U [1/2,+\infty)
Answer:
Step-by-step explanation:
Recall the ratio test. Given a series [tex]\sum_{n=1}^{\infty}a_n[/tex] if
[tex] \lim_{n\to \infty} \left|\frac{a_{n+1}}{a_n}\right|<1[/tex]
Then, the series is absolutely convergent.
We will use this to the given series [tex]\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}[/tex], where [tex] a_n = \frac{(2 x)^n}{n}[/tex]. Then, we want to find the values for which the series converges.
So
[tex] \lim_{n\to \infty} \left|\frac{(2x)^{n+1}}{n+1}\cdot \frac{n}{(2x)^n}\right|<1[/tex], which gives us that
[tex] |2x|\cdot\lim_{n\to \infty} \frac{n}{n+1}<1[/tex]
We have that [tex]\lim_{n\to \infty} \frac{n}{n+1}=1[/tex]. Then, we have that
[tex]|2x|<1[/tex],
which implies that |x|<1/2. So for [tex]x \in (-1/2,1/2)[/tex] the series converges absolutely.
We will replace x by the endpoints to check convergence.
Case 1, x=1/2:
In this case we have the following series:
[tex]\sum_{n=1}^{\infty} \frac{1}{n}[/tex] which is the harmonic series, which is know to diverge.
Case 2, x=-1/2:
In this case we have the following series:
[tex]\sum_{n=1}^{\infty} \frac{(-1)^n}{n}[/tex]
This is an alternating series with [tex]b_n = \frac{1}{n}[/tex]. Recall the alternating series test. If we have the following
[tex]\sum_{n=1}^\infty (-1)^nb_n [/tex] and[tex] b_n[/tex] meets the following criteria : bn is positive, bn is a decreasing sequence and it tends to zero as n tends to infinity, then the series converge.
Note that in this case, [tex]b_n = \frac{1}{n}[/tex] si always positive, its' limit is zero as n tends to infinity and it is decreasing, hence the series converge.
So, the final interval of convergence is
[tex] [\frac{-1}{2}, \frac{1}{2})[/tex]
Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month. Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month. Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? (1 point)
Answer:
B) Victoria's method is linear because the number of minutes increased by an equal number every month.
Step-by-step explanation:
Zach reading time written in sequence form is given as:
10,20,40,80,...Each succeeding term is a product of the previous term by 2Victoria reading time written in sequence form is given as
35,50,65,80...Each succeeding term is an addition of 15 Minutes to the previous term.The statement that best describes the methods used by Zach and Victoria to increase the time they spent reading a book is therefore:
B) Victoria's method is linear because the number of minutes increased by an equal number every month.
Answer:
B
Step-by-step explanation: