For given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
For given question,
We have been given a power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex]
We need to find the radius of convergence of the power series.
We use ratio test to find the radius of convergence of the power series.
Let [tex]a_n=\frac{(-1)^nx^n}{2^n}[/tex]
[tex]\Rightarrow a_{n+1}=\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}[/tex]
Consider,
[tex]\lim_{n \to \infty}|\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}}{ \frac{(-1)^nx^n}{2^n} } |\\\\=\lim_{n \to \infty} |\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}\times \frac{2^n}{(-1)^nx^n} |\\\\=\lim_{n \to \infty} |\frac{(-1)x}{2} |\\\\=\lim_{n \to \infty}|\frac{-x}{2} |\\\\=\frac{x}{2}[/tex]
By Ratio test, given power series converges at [tex]|\frac{x}{2} | < 1[/tex]
⇒ |x| < 2
So, the radius of convergence is 2.
Therefore, for given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
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How many ways are there to get from (0, 0) to (7, 7) in the coordinate plane
with movements of only one unit right or one unit up? How many ways are there to do so that do not go above the line y = x?
The number of ways there are to move from (0, 0) to (7, 7) in the coordinate plane with movements of only one unit right or one unit up accordingly is; 49 while that such that y =x is; 7.
How many ways are there to get from (0, 0) to (7, 7) in the coordinate plane with pmovements of only one unit right or one unit up?It follows from the task content that the movement intended on the coordinate plane is; from (0, 0) to (7, 7).
The number of ways to move such that movements of only one unit right or one unit up is; 7 × 7 = 49.
The number of ways for which y= x is therefore is; 7 as the movement is diagonal.
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What is the measure of angle x and y in the diagram?
x
30°
YN
52°
Answer:
x = 30° and y = 52°
Step-by-step explanation:
angles on the circle subtended by the same arc are congruent
x and 30° are on the same arc, then x = 30°
y and 52° are on the same arc, then y = 52°
full of sand, the wagon weighs 100 pounds. If the wagon weighs 80 ounces when its empty, how much do the bags of sand weigh?
given,
wagon weight with sand = 100 pounds
wangon weight = 80 ounces ÷ 16 = 5 pounds
sand weight = 100 - 5 = 95 pounds//
A coin is flipped twice. What is the probability of getting heads on the first flip and tails on the second flip?
Answer: 0.25 or 25%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
Identify the two tables which represent quadratic relationships. x 0 1 2 3 y -4 -8 -10 -10 x 0 1 2 3 y 4 -4 -4 4 x 0 1 2 3 y -2 0 2 4 x 0 1 2 3 y 1 2 4 8 x 0 1 2 3 y -2 -4 -8 -16 x 0 1 2 3 y 3 4 5 6
To estimate that table given in Option (4) will define the quadratic relationship.
Therefore, the table of Option (5) will describe the quadratic relationship.
How to estimate the quadratic relationships between two tables?By estimating the second difference, if the second difference in a table exists equivalent, the table will define the quadratic relationship.
In the given option, we estimate that table given in Option (4) will define the quadratic relationship.
x y I st difference II nd difference
0 4 - -
1 -4 -4 - (4) = -8 -
2 -4 -4 - (-4) = 0 0 - (-8) = 8
3 4 4 - (-4) = 8 8 - 0 = 8
The second difference between the terms in y exists exactly as 8.
Therefore, the table of Option (4) means the quadratic relationship.
Similarly, in Option (5) we will estimate the second distinction of y terms.
x y I st difference II nd difference
0 -4 - -
1 -8 -8 - (-4) = -4 -
2 -10 -10 - (-8) = -2 -2 - (-4) = 2
3 -10 -10 - (-10) = 0 0 - (-2) = 2
Here the second difference exists identical to 2.
Therefore, the table of Option (5) will describe the quadratic relationship.
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For each graph below,state whether it represents a function
Answer:
1. No
2. No
3. Yes
4. No
5. Yes
6. No
Step-by-step explanation:
If you want to check if a graph is a function, do a vertical line test. For every vertical line, there should be only 1 point on the line if the graph is a function.
Find the value of z.
Applying the angle of intersecting chords theorem, the value of z is: D. 100.
What is the Angle of Intersecting Chords Theorem?According to the angle of intersecting chords theorem, in a circle like the one shown in the image above, where two chords intersect to form vertical angles, the theorem states that the angle formed equals half of the sum of the measures of the arcs intercepted by the angles.
Applying the angle of intersecting chords theorem, let's find x first:
73 = 1/2(96 + x)
Multiply both sides by 2
2 × (73) = 1/2(96 + x) × 2
146 = 96 + x
Subtract both sides by 96
146 - 96 = 96 + x - 96
50 = x
x = 50°
Therefore:
x + z + 96 + 114 = 360° [full circle measure]
Plug in the value of x
50 + z + 96 + 114 = 360
z + 260 = 360
Subtract both sides by 260
z + 260 - 260 = 360 - 260
z = 100°
The answer is: D. 100°.
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Quadilateral ABCD is similar to quadilateral EFGD. Which angle of quadilateral ABCD corresponds to F
Answer:
< B.
Step-by-step explanation:
B corresponds to F.
What are the zeros of the polynomial function: f(x) = x^3 - x^2 – 6x ?
Answer:
x=0, x=3, x=-2
Step-by-step explanation:
factor the equation
x(x^2-x-6)
factor more
x(x-3)(x+2)
set it equal to 0
x(x-3)(x+2)=0
plug in numbers for x that would result in the answer being 0
0(0-3)(0+2)=0
3(3-3)(3+2)=0
-2(-2-3)(-2+2)=0
(a+b)^2-2(a+b)
Factorise (please explain)
Answer:
(a + b)(a + b - 2)
Step-by-step explanation:
(a + b)² - 2(a + b) ← factor out (a + b) from each term
= (a + b)(a + b - 2)
an empty rectangular tank is 80 cm long and 60 cm wide. water flows into the tank at a rate of 24 liter per minute. how long will it take to fill the tank to a height of 50 cm?
By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.
How long will it take to fill the tank at constant rate?
Herein we find the case of a rectangular tank being filled with water at constant flow are, which is dimensionally speaking, volume by time. We know that dimensions of the tank are described in centimeters, whereas flow rate is described in liters per minute. Please notice that a liter is equal to 1000 cubic centimeters:
t = [(80 cm) · (60 cm) · (50 cm) · (1 L / 1000 cm³)] / (24 L / min)
t = 10 min
By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.
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Please help asap!!
Find the sum for the first 500 terms given the sequence -1,-3,-5,-7.....
Answer: -250000
Step-by-step explanation:
Sum of arithmetic terms = n/2[2a + (n - 1)d],
where 'a' is the first term,
'd' is the common difference between two numbers,
and 'n' is the number of terms.
'a' = -1
'd' = -2
'n' = 500
plug and chug
(500)/2[2(-1) + ((500)-1)*(-2)] =
250[-2 + -998] =
250[-1000] =
-250000
The point -2,5 is reflected across the y-axis. Which of these is the ordered pair of the image?
A) (-2,5)
B) (2,5)
C) (-2,-5)
D) (2, -5)
Answer:
B) (2,5)
Step-by-step explanation:
A class trip to a beach has been planned for your senior trip. the resort only allows swimming when the temperature is between 75 degrees and 110 degrees. there is room for 50 people on your trip. write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip. 0 < x ≤ 50 and 75 < y < 110 x > 75 and y < 110 75 < x < 110 and 0 < y ≤ 50 x < 110 and y > 75
This real-world problem has the limitations 75< x <110 and 0< y[tex]\leq[/tex] 50, hence:
option (C) is the best choice.
What is Inequality ?The term "inequality" refers to a mathematical expression in which both sides have mathematical signs that are either less than or greater than one another, and the expression is one where the two sides are not on equal footing.
We have:
Your senior vacation is scheduled to include a class trip to a beach. Only when it's between 75 and 110 degrees do guests at the resort get access to the pool. 50 passengers can go with you.
Let y be the number of passengers and x be the temperature
75 to 110 degrees are the range of the temperature.
75 < x < 110
50 passengers can go with you.
0 < y ≤ 50
In order to illustrate this real-world issue, the limitations are 75 <x <110 and 0< y [tex]\leq[/tex]50.
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pls answer this i will mark brainlest
Answer:
Answer is a
Step-by-step explanation:
it is the only answer that makes sense
50 points to whoever can answer!
Answer:
10724.29
Step-by-step explanation:
mean means average
so to find an average you add everything together then divide it by the amount of variables
m = (10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477)/7
m = 75070/7
m = 10724.2857143
m = 10724.29
Use interval notation to express the set of real numbers x that satisfies the inequality (x+2)(x-5) < 0.
The interval notation to express the set of real numbers x that satisfies the given inequality is -2<x<5. You also can represent it as (-2,5)
Inequality
It is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).
The solutions for inequalities can be given by: a graph in a number line or numbers.
For solving this exercise, it is necessary to find a number solution for the given inequality.
First, you should find the critical points of the inequality.
x+2=0
x = -2
and
x-5=0
x=5
Write, the intervals in between critical points. Therefore, -2<x<5.
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A school club has 5 members. From these 5 members, a 2-person team must be chosen to represent the club at a school carnival. How many different 2-person teams can be made from the 5 club members?
A 10 teams
B 15 teams
C 20 teams
D 25 teams
Answer:
20 teams can be made
Answer:
A. 10 teams
Step-by-step explanation:
a 2-person team is a combination of two elements out of 5.
Then
The number of possible teams is :
[tex]C^{2}_5 = \frac{5!}{2! \times (5-2)!} = \frac{5!}{2! \times 3!}=10[/tex]
simplify the expression 9^7/ 9^9 60 points
Answer:
1/9^2
Step-by-step explanation:
simplify
9^(7-9)
simplify further
9^-2
simplify even more
1/9^2
Answer:
9^16
Step-by-step explanation:
just took the test
Rearrange the formula to highlight time
Step-by-step explanation:
[tex]s = 2\pi(r)(r + h)[/tex]
[tex] \frac{s}{2\pi(r)} = r + h[/tex]
[tex] \frac{s}{2\pi(r) } - r = h[/tex]
two remaining of a right triangle have length of 4 and 5 units. what are two possible lengths for the remaining side?
Answer:
c^2 = a^2 + b^226^2 = 10^2 + b^2 676 = 100 + b^2 576 = b^2 shortest side length = 24 units
Step-by-step explanation:
9. Find the values of x and y.
Write answers in simplest radical form.
x=______ y=_____
Answer:
x = 3√3
y = 6
Step-by-step explanation:
The geometric mean relations between segments intersecting the long hypotenuse and its parts can be used to find the values of interest.
Altitudex = √(9·3) = 3√3
Short sidey = √((9+3)·3) = 6
__
Additional comment
These right triangles are all similar, so corresponding sides are proportional. When the proportions are solved for a missing side, a geometric mean relation results. (The geometric mean of 'a' and 'b' is √(ab).)
Identify the segments above the horizontal line as w, x, y. (x and y are already identified in this figure.)
The ratio of short side to long side is ...
x/9 = 3/x ⇒ x² = 9·3 ⇒ x = √(9·3)
The ratio of short side to hypotenuse is ...
y/(9+3) = 3/y ⇒ y² = (9+3)·3 ⇒ y = √((9+3)·3)
Likewise, the ratio of long side to hypotenuse is ...
w/(9+3) = 9/w ⇒ w² = (9+3)·9 w = √((9+3)·9) = 6√3
Suppose a group of 12 students consists of five freshmen and seven sophomores. how many six-student teams can be chosen that consist of three freshmen and three sophomores?
The number of six-student teams possible where a team consists of three freshmen and three sophomores, from a group of 12 students consisting of five freshmen and seven sophomores using combinations is computed to be 350.
The combination is a process of calculating the number of ways of selecting a smaller set, from a larger set, when the order of selection is irrelevant.
In selecting x number of items, from n number of items, when the order of selection is irrelevant, we use the combination, to calculate the number of possible ways as follows:
nCx = n!/{(x!)((n - x)!)}.
In the question, we are asked for the number of six-student teams possible where a team consists of three freshmen and three sophomores, from a group of 12 students consisting of five freshmen and seven sophomores.
The number of ways of selecting 3 freshmen from 5, using a combination is:
5C3 = 5!/{(3!)((5 - 3)!} = 120/{6*2} = 120/12 = 10.
The number of ways of selecting 3 sophomores from 7, using a combination is:
7C3 = 7!/{(3!)((7 - 3)!} = 5040/{6*24} = 5040/144 = 35.
The total number of teams possible is the product of each.
Thus, the total number of teams possible is 5C3 * 7C3 = 10*35 = 350.
Thus, the number of six-student teams possible where a team consists of three freshmen and three sophomores, from a group of 12 students consisting of five freshmen and seven sophomores using combinations is computed to be 350.
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g(a) = 4a + 5
f(a) = a² + 2a
Find: g(f(a))
Step-by-step explanation:
g(f(a))=4(a²+2a) + 5
= 4a²+8a+5
Krissy ran three miles one morning she ran the first mile in 11. 74 minutes the second mile in 11. 26 minutes in the third mile in 12.12 minute rounded to the nearest hundredth what is the total number of minutes that it took krissy to run these three miles?
Answer:
Step-by-step explanation:
Givens
Time 1 = 11.74
Time 2 = 11.26
Time 3 = 12.12 Add
Solution
11.74 + 11.26 + 12.12 =
Total Time = 35.12
35.12 miles is the total number of minutes that it took krissy to run these three miles.
What is a simple definition of time?
The measured or measurable period during which an action, process, or condition exists or continues : duration. b : a nonspatial continuum that is measured in terms of events which succeed one another from past through present to future.
Krissy ran three miles one morning she ran the first mile in time 1 = 11.74
Krissy ran three miles one morning she ran the first mile in time 2 = 11.26
Krissy ran three miles one morning she ran the first mile in time 3 = 12.12
To get total time , we have to add all the time 1,2,3
Total time = Time1 + Time2 + Time3
= 11.74 + 11.26 + 12.12
Total Time = 35.12 miles
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Which measurements of triangle BAC are correct
The measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
Trigonometrical ratiosFrom the question, we are to determine which of the given trigonometrical ratios for the given triangle are correct
The given triangle is a right angle triangle
Using SOH CAH TOA
sin C = 9/15
∴ The option sin C = 9/15 is correct
Also,
Using SOH CAH CAH
tan B = 12/9
∴ The option tan B = 9/12 is NOT correct
To determine the measure of angle B (m ∠B)
From tan B = 12/9
Then,
tan B = 1.33333
B = tan⁻¹(1.33333)
∴ B ≈ 53.13°
Thus, the option B ≈ 53.13° is correct
Hence, the measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
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Select the graph of the solution. Click until the correct graph appears. 3 x + 1 < 7
Answer:
Step-by-step explanation:
3x + 1 < 7...subtract 1 from both sides
3x < 7 - 1
3x < 6 ...divide both sides by 3
x < 6/3
x < 2
which means the second answer choice is correct!
Answer: Second Graph
Step-by-step explanation:
Given inequality
3x + 1 < 7
Subtract 1 on both sides
3x + 1 - 1 < 7 - 1
3x < 6
Divide 3 on both sides
3x / 3 < 6 / 3
x < 2
Apply the inequality to the graph
Since it is less than, the circle should be hollow
Since it is less than 2, the line should point to the left
Therefore, it should be the Second Graph
Multiply (x + 2)(3x² - 4x + 5).
a. 3x³ + 2x²-3x+10
b. 3x³-4x² + 5x+10
c. 3x³ - 2x²-3x+10
d.
3x² +10x² + 13x+10
Answer:
a. 3x^3 + 2x^2 - 3x +10
Step-by-step explanation:
(x+2)(3x^2-4x+5)
x(3x^2-4x+5) +2(3x^2-4x+5)
3x^3-4x^2+5x+6x^2-8x+10
3x^3-4^2+6x^2+5x-8x+10
3x^3+2x^2-3x+10
3x+5<6x+8
4x+3 is <7x+5
The solution to the inequalities 3x + 5 < 6x + 8 and 4x + 3 < 7x + 5 is x > -1 and x > -2/3 respectively
InequalityInequality signs are;
Greater than >Less than <Equal to =Less than equal to ≤Greater than equal to ≥3x + 5 < 6x + 8
collect like terms3x - 6x < 8 - 5
-3x < 3
divide both sides by -3x > 3/-3
The inequality sign is flipped from < to greater than because of the division with negative value.
x > -1
2. 4x + 3 < 7x + 5
collect like terms4x - 7x < 5 - 3
-3x < 2
divide both sides by -3The inequality sign is flipped from < to greater than because of the division with negative value.
x > -2/3
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What would be the coefficient of determination r2 if the total sum of squares (sst) is 90 and the sum of squares due to error (sse) is 0 (zero)?
The coefficient of determination is 1.
Given
Total Sum of squares (SST) = 90
Sum of squares due to error (SSE) = 0
We have to find coefficient of determination.
The correlation of determination is the ratio of the explained variation to the total variation.
The coefficient of determination is used to analyze how differences in one variable can be explained by a difference in a second variable.
The coefficient of determination is also called r-squared or r-square.
Its the percentage of variation in the y-variable(response) that can be explained by the least squares regression line of y on x.
Coefficient of determination can be found with the following formula:
Formula of coefficient of determination :
[tex]R^{2} = 1 - \frac{SSE}{SST}[/tex]
= 1 - [tex]\frac{0}{90}[/tex]
= 1 - 0
= 1
[tex]R^{2}[/tex] = 1
Therefore,
The coefficient of determination is 1.
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