For each of the differential equations in Problems 9 through 11, find the first four nonzero terms in each of two power series solutions about the origin. Show that they form a fundamental set of solutions. What do you expect the radius of convergence to be for each solution? 9. y'' + (sin x)y = 0 10. e^xy'' + xy = 0 11. (cos x)y'' + xy'- 2y = 0
Answers
We will solve the differential equation and find the power series solutions for each problem.
Problem 9: y'' + (sin x)y = 0
Assuming the power series solution: y = a0 + a1x + a2x^2 + ...
Differentiating twice, we have:
y' = a1 + 2a2x + 3a3x^2 + ...
y'' = 2a2 + 6a3x + 12a4x^2 + ...
Substituting these expressions into the differential equation, we get:
2a2 + 6a3x + 12a4x^2 + ... + (sin x)(a0 + a1x + a2x^2 + ...) = 0
Grouping the terms by powers of x, we get:
a0(sin x) = 0
a1(sin x) + 2a2 = 0
a2(sin x) + 6a3 = 0
a3(sin x) + 12a4 = 0
...
From the first equation, we have a0 = 0, since sin(0) = 0. From the second equation, we have a2 = -a1(sin x)/2. From the third equation, we have a3 = -a2(sin x)/6 = a1(sin x)^2/12. From the fourth equation, we have a4 = -a3(sin x)/12 = -a1(sin x)^3/288.
Thus, we have the power series solution:
y = a1x - a1(sin x)^3/288 + ...
This solution is nontrivial, and the ratio of consecutive coefficients is:
-a1(sin x)^3/288 / (a1x) = -(sin x)^3 / (288x)
The ratio approaches zero as x approaches infinity, so the radius of convergence is infinite. Therefore, we expect the solution to be valid for all values of x.
Problem 10: e^xy'' + xy = 0
Assuming the power series solution: y = a0 + a1x + a2x^2 + ...
Differentiating twice, we have:
y' = a1 + 2a2x + 3a3x^2 + ...
y'' = 2a2 + 6a3x + 12a4x^2 + ...
Substituting these expressions into the differential equation, we get:
e^x(2a2 + 6a3x + 12a4x^2 + ...) + x(a0 + a1x + a2x^2 + ...) = 0
Grouping the terms by powers of x, we get:
a0 + (a1 + a0)x + [(2a2 + a1)x^2 + (6a3 + 2a2)x^3 + (12a4 + 6a3)x^4 + ...] = 0
Since the coefficient of x^0 is nonzero, we must have a0 = 0. Then, the coefficient of x^1 gives:
a1 + a0 = 0
a1 = 0
This means that the power series solution is identically zero, which is trivial. Therefore, we cannot form a fundamental set of solutions using power series.
Problem 11: (cos x)y'' + xy' - 2y = 0
Assuming the power series solution: y = a0 + a1x + a2x^2 + ...
Differentiating twice, we have:
y' = a1 + 2a2x + 3a3x
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Related Questions
Which one’s are not correct and what did they do wrong
Answers
Answer:
Only LOKI is correct
Step-by-step explanation:
Elektra multiplied 8 with the inside parenthesis but it was wrong to do.
Green Goblin took 2x outside with negative sign but that is wrong
Morbius did the same mistake as Green Goblin at first step but then corrected it in the second step, still it's wrong
ut r(t)=⟨tcost, tsint, t⟩ be the position vector of a particle moving in space a) Describe the path. Identify a surface there the curve lies. b) Find the velicity vector, speed, and aceecration at t=π/2. What is the angle berween the velocity and all rectors at t=π/2 ? c) Find the parametric equations for the tangent 11n c io the curve at t=π/2.
Answers
a) The path described by the position vector r(t) = ⟨tcos(t), tsin(t), t⟩ is a spiral in three-dimensional space.
(b) At t = π/2,
= ⟨-1 - (π/2), -(π/2), 0⟩
The angle between the velocity vector and the acceleration vector at t
= arccos((-1 - (π/2)) / (√2 * √(1 + π/2 + π^2/2)))
(c)⟨0, (π/2) + t, (π/2) + t⟩
(a) The particle moves outward from the origin along a helical path while also rotating around the z-axis. This can be visualized as a coiled spring that extends infinitely.
The curve lies on a surface known as a helicoid. A helicoid is a curved surface that resembles a twisted ramp or staircase. It is generated by sweeping a straight line along a helix and allowing it to rotate as it moves away from the axis of the helix.
b) To find the velocity vector, we differentiate the position vector with respect to time:
r'(t) = ⟨cos(t) - tsin(t), sin(t) + tcos(t), 1⟩
At t = π/2, we have:
r'(π/2) = ⟨0 - (π/2)sin(π/2), 1 + (π/2)cos(π/2), 1⟩
= ⟨0, 1 + (π/2) * 0, 1⟩
= ⟨0, 1, 1⟩
The speed of the particle is the magnitude of the velocity vector:
|v| = |r'(π/2)| = √(0^2 + 1^2 + 1^2) = √2
The acceleration vector is the derivative of the velocity vector with respect to time:
r''(t) = ⟨-sin(t) - tsin(t) - cos(t), cos(t) - tcos(t) - sin(t), 0⟩
At t = π/2, we have:
r''(π/2) = ⟨-sin(π/2) - (π/2)sin(π/2) - cos(π/2), cos(π/2) - (π/2)cos(π/2) - sin(π/2), 0⟩
= ⟨-1 - (π/2), 0 - (π/2), 0⟩
= ⟨-1 - (π/2), -(π/2), 0⟩
The angle between the velocity vector and the acceleration vector at t = π/2 can be found using the dot product:
θ = arccos((v · a) / (|v| |a|))
= arccos((⟨0, 1, 1⟩ · ⟨-1 - (π/2), -(π/2), 0⟩) / (√2 * √((1 + (π/2))^2 + (π/2)^2)))
= arccos((-1 - (π/2)) / (√2 * √(1 + π + π^2/4 + π^2/4)))
= arccos((-1 - (π/2)) / (√2 * √(1 + π/2 + π^2/2)))
c) The tangent line to the curve at t = π/2 can be described parametrically by the position vector r(t) and the velocity vector r'(π/2):
T(t) = r(π/2) + t * r'(π/2)
= ⟨(π/2)cos(π/2), (π/2)sin(π/2), (π/2)⟩ + t * ⟨0, 1, 1⟩
= ⟨0, (π/2) + t, (π/2) + t⟩
The particle moves along a helical path on a surface known as a helicoid. At t = π/2, the velocity vector is ⟨0, 1, 1⟩, the speed is √2, and the acceleration vector is ⟨-1 - (π/2), -(π/2), 0⟩. The angle between the velocity and acceleration vectors at t = π/2 can be determined using the dot product. The parametric equations for the tangent line to the curve at t = π/2 are given by T(t) = ⟨0, (π/2) + t, (π/2) + t⟩.
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Help me out, please!! Find the value of x in the given right triangle
Answers
Answer:
x ≈ 44.4°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin x = \(\frac{opposite}{hypotenuse}\) = \(\frac{7}{10}\) , then
x = \(sin^{-1}\) (\(\frac{7}{10}\) ) ≈ 44.4° ( to the nearest tenth )
Determine the slope of a line represented by the equation 4x – 3y = 9.
Answers
Answer:
4/3x
Step-by-step explanation:
subtract 4x from both sides -> -3y=-4x+9
divide by -3 -> y=-4/-3x+9
simplify (if both denominator and numerator are negative they simplify to a positive)-> y= 4/3x+9
A new recreational sports center opens with 65 members. Each month the membership
increases by 12 members. Which equation represents the relationship between the
number of months the club has been opened, x, and the total recreational sports center
membership, y?
A y = 12x
B y = x + 12
C y = 12x + 65
D y = 65x + 12
Answers
Tell whether the angles are complementary or supplementary. Then find the value of x.
Answers
Answer:
The angles are supplementary.
x = 31
Step-by-step explanation:
The way the two angles lay together and make a straight line shows that they are supplementary. Supplementary means that they add up to 180°
Use this idea to write an equation.
2x + 3x + 25 = 180
combine like terms
5x + 25 = 180
subtract 25
5x = 155
divide by 5
x = 31
Answer:
x = 31
Step-by-step explanation:
(3x + 25) and 2x are a linear pair and are supplementary, that is
3x + 25 + 2x = 180
5x + 25 = 180 ( subtract 25 from both sides )
5x = 155 ( divide both sides by 5 )
x = 31
For a t-distribution with sample size 10, P (t > 1.96) 2 0.0408 and P (t < -1.96) 2 0.0408 . Which of the following is a property of the t-distribution illustrated by the probabilities? A. With sample size 10, the tails of the curve of the t-distribution have more area than the tails of the curve of the z-distribution. B. With sample size 10, the tails of the curve of the t-distribution have less area than the tails of the curve of the z-distribution. C. With sample size 10, the middle of the curve of the t-distribution has more area than the middle of the curve of the z-distribution. With sample size 10, the mean of the t-distribution is greater than the mean of the z-distribution. E. With sample size 10, the mean of the t-distribution is less than the mean of the z-distribution.
Answers
The correct option is A) With sample size 10, the tails of the curve of the t-distribution have more area than the tails of the curve of the z-distribution.
Explanation:Given:P(t > 1.96) = 0.0408P(t < -1.96) = 0.0408The t-distribution is different from the z-distribution because it has a thicker tail.The tail is thicker since the t-distribution is determined by the sample size, whereas the z-distribution is determined by the population size (the t-distribution is estimated with the standard error of the mean in this case).
A t-distribution with small degrees of freedom has a much thicker tail than a z-distribution with the same degrees of freedom. Because sample size is related to the degrees of freedom, it makes sense that t-distributions with smaller sample sizes will have thicker tails.
The population variance is replaced with the sample variance in the estimation of the t-distribution. As a result, the t-distribution has heavier tails than the z-distribution.
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Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m = 12s, where m is the number of minutes and s is the number of sketches.
If Lori made
3
4
of a sketch
Answers
If Lori made a fraction of 3/4 of a sketch, then she spent 9 minutes of sketching.
What is fraction?A fraction is a portion of something. Mathematics refers to a number as a quotient when the numerator and denominator are divided. Both are integers in a simple fraction. There is a fraction in the numerator or denominator of a complex fraction. The numerator and denominator of a proper fraction are different sizes.
Given the equation
m = 12s,
where
m is the number of minutes, and
s is the number of sketches.
Lori made 3/4 of a sketch i.e.
m = 12(3/4)
m = 9 mins
Thus, If Lori made 3/4 of a sketch, she spent 9 minutes sketching.
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What is the value of X?
3
4
6
8
Answers
Answer:
The answer is 4
Step-by-step explanation:
What type of argument is this? "All cubes are square. A dice is a cube. Therefore, a dice must be square."
Answers
The argument presented is an example of a fallacy known as affirming the consequent, which incorrectly assumes that if the consequent of a conditional statement is true, then the antecedent must also be true. It fails to consider other possibilities and overlooks the fact that not all square shapes are cubes.
The argument presented is an example of a fallacy known as affirming the consequent, which is a formal logical fallacy. This fallacy occurs when one assumes that if the consequent (the "then" part) of a conditional statement is true, then the antecedent (the "if" part) must also be true.
In this case, the argument incorrectly assumes that because all cubes are square (if cube, then square) and a dice is a cube, then the dice must be square. However, this reasoning is flawed. While it is true that all cubes are square, not all square shapes are cubes. Therefore, even though a dice is a cube, it does not necessarily mean that it must be square.
The argument fails to consider other possibilities, such as the fact that cubes can have other shapes besides squares, like rectangular cubes. This logical error highlights the importance of careful reasoning and avoiding fallacies when making arguments.
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5-3x>6
Please helppppo please hellppppppp
Answers
Step-by-step explanation:
5-3x>6
-3x>1
x<-1/3
got it?
Answer:
2x<6
Step-by-step explanation:
(2,-7), (4,/3) find the slope
Answers
Answer:
m = -2
Step-by-step explanation:
As one goes from (2, 7) to (4, 3), we note that x increases by 2 and y decreases by 4. Thus, the slope is m = rise / run = -4/2, or -2
The slope of the line connecting these two points is -2.
Read each of these scenarios describing the evolution of decreased body hair in humans. scenario x: as hominins migrated to more open environments and became mid-day hunters/scavengers, they were exposed to higher levels of heat. in order to effectively cool the body, hominins needed to have less hair, so a mutation for decreased body hair occurred. eventually, evolution favored those with less body hair such that all hominins had less body hair. scenario y: as hominins migrated to more open environments and became mid-day hunters/scavengers, they were exposed to higher levels of heat. hominins with less dense hair, a trait that had heritable variation within the population, maintained a cooler body temperature and were more successful in obtaining food. over time, hominin populations evolved to have less body hair. scenario ____ describes evolution by natural selection. i know this because_______. group of answer choices x; mutation occurs that increases survival of the species x; it describes evolution of individuals who became adapted to the environment. y; it involves heritable variation and fitness y; hominins acquired a needed characteristic so that they were more successful hunters
Answers
Scenario y describes evolution by natural selection. I know this because it involves heritable variation and fitness. In this scenario, the hominins with less dense hair had a trait that was heritable within the population, and they were able to maintain a cooler body temperature and be more successful in obtaining food.
As a result, over time, the hominin populations evolved to have less body hair. This process of natural selection involves the traits that are passed on through genetics that lead to survival and reproductive success. The individuals with advantageous traits are more likely to survive and pass on those traits to their offspring. In contrast, scenario x describes the evolution of individuals who became adapted to the environment due to a mutation that increased their survival chances. However, it does not involve heritable variation or the process of natural selection.
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8)
Which inequality statement describes the two numbers: - 22 and a number 47 units to the right of -22?
A)
-22 > 47
B)
-22 < 47
C)
-22 > 25
D)
-22 < 25
Answers
Answer:
D) -22 < 25
Step-by-step explanation:
If the number is 47 units to the right, then the number will be larger than -22, because negative values get larger the closer they are to zero.
47 units right from -22 is the same as: -22 + 47, which equals 25.
So, we can conclude that -22 < 25 is the inequality.
hope this helps!
The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the
y-varlable, and what is the solution for this system?
x+3y=42
2x-y=1
Answers
=======================================================
Explanation:
The 3y in the first equation must add to -3y so the y terms go away. We have -y in the second equation, which is why we triple everything in that equation
2x-y = 1 becomes 6x - 3y = 3 after tripling everything. This is the same as multiplying both sides by 3.
This is the updated equivalent system
\(\begin{cases}x+3y = 42\\6x-3y = 3\end{cases}\)
Add the terms straight down
x+6x becomes 7x3y+(-3y) becomes 0y or 0. The y variables are eliminated.The right hand sides 42 and 3 add to 45We have the equation 7x = 45 which solves to x = 45/7.
Unfortunately it doesn't turn into a nice single whole number because 45 isn't a multiple of 7. So I would leave it as a fraction.
Optionally you could note that 45/7 = 6.42857 approximately. But I prefer the fraction form since it's most exact.
--------------
Use this x value to find y. Pick any equation involving x and y. Plug in that x value and solve for y.
x + 3y = 42
45/7 + 3y = 42
3y = 42 - 45/7
3y = 42*(7/7) - 45/7
3y = 294/7 - 45/7
3y = (294 - 45)/7
3y = 249/7
y = (249/7)*(1/3)
y = 83/7
Like with x, we also don't get a nice whole number.
I used WolframAlpha to confirm the solutions. GeoGebra is another tool you could use.
What is the expression in scientific notation? (7 x 10−12)(4 x 105)?
Answers
Answer:
2.436 x 10^4
Step-by-step explanation:
you buy a new car for $22,500. the value of the car decreases by 25% each year. write an exponential decay model giving the car's value v (in dollars) after t years. what is the value of the car after three years to the nearest dollar amount?
Answers
Therefore, the value of the car after three years is approximately $9,484.
What is percent?Percent is a term used to represent a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express proportions, ratios or fractions in terms of parts per hundred. The word "percent" comes from the Latin phrase "per centum," which means "by the hundred." Percentages are commonly used in everyday life, such as in calculating taxes, discounts, interest rates, and in comparing statistics, among others.
Here,
The exponential decay model for the value of the car after ⁿ years can be written as:
v = 22500 * (0.75)ⁿ
where 22500 is the initial value of the car, and (0.75)ⁿ represents the value after ⁿ years with a 25% annual decrease.
To find the value of the car after three years, we can substitute n = 3 into the equation:
v = 22500 * (0.75)³
v = 22500 * 0.421875
v = 9484.375
Rounding this to the nearest dollar amount, we get:
v ≈ $9,484
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the following is part of an anova table, which was the result of three treatments and a total of 15 observations. source of variation sum of squares degrees of freedom mean square f between treatments 64 within treatments (error) 96 total the number of degrees of freedom corresponding to within treatments is . a. 3 b. 12 c. 15 d. 2
Answers
The degrees of freedom associated with within treatments are 12 within the variation sum of squares degrees of freedom mean square f between treatments 64 within treatments (error) 96.
The ANOVA table divides the overall variance into variation between treatments and variation within treatments. Each source of variation's degrees of freedom (DF) is also provided.
According to the information provided, there are three treatments and a total of 15 observations. As a result, the total degrees of freedom is:
\(DF_{total}\) = n - 1
where n is the number of observations
\(DF_{total}\)= 15 - 1 = 14
The degrees of freedom between treatments are equal to the number of treatments minus one:
\(DF_{between}\) = k - 1
where k is the number of groups being compared
\(DF_{between}\)= 3 - 1 = 2
The number of treatments minus one equals the degrees of freedom between treatments, that is 2
We may use the following formula to calculate the degrees of freedom within treatments:
\(DF_{within}\) = \(DF_{total} - DF_{between}\)
Substituting the values we have:
\(DF_{within}\) = 14 - 2 = 12
\(DF_{within}\) = 12
As a result, the answer is 12. The degrees of freedom associated with within treatments are 12.
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An accountant used to charge $50 per hour, but recently decided to charge $62 per hour. What was the percent of increase in the billing rate?
Answers
Answer:
24%
Step-by-step explanation:
we subtract to see how much it increased
62-50=12
Now divide 12 by 50 to get percent
12/50
0.24
0.24x100
24%
Hopes this helps please mark brainliest
b) When heated an iron bar expands by 0.2%. If the increase in length is 1 cm,
what is the original length of the bar ?
Answers
Simple algebra.
When we convert this to an equation we get: 0.2% of something is equal to 1 unit.
So here's the equation: \(0.02x = 1\)
After we transpose \(0.02\), the equation become: \(x = \frac{1}{0.02}\).
Divide \(1\) with \(0.02\) and you get \(50\).
So the length of the original bar is \(50\) cm. :D
If profits decrease by 13.8% when the degree of operating
leverage (DOL) is 3.8, then the decrease in sales is:
A) 0.28%
B) 0.52%
C) 3.63%
D) 10%
E) 52.44%
Answers
Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.
The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.
Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8
= -13.8% / x Thus, we have: x
= -13.8% / 3.8
= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage
= 13.8 / 3.8
= 3.63% The percentage decrease in sales is 3.63%.
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In order to estimate the height of a building, two students stand at a certain distance from the building at street level. From this point, they find the angle of elevation from the street to the top of the building to be 35°. They then move 250 feet closer to the building and find the angle of elevation to be 53°. Assuming that the street is level, estimate the height of the building to the nearest foot.
Answers
If the street is level, then the estimated height of the building is approximately 279 feet to the nearest foot.
To estimate the height of the building, we can use the tangent function in trigonometry. Let's denote the height of the building as h and the initial distance between the students and the building as x.
1. At the initial point, we have the angle of elevation 35°:
tan(35°) = h / x
2. After moving 250 feet closer, we have the angle of elevation 53°:
tan(53°) = h / (x - 250)
Now we need to solve this system of equations to find the height h.
Step 1: Isolate h in the first equation:
h = x * tan(35°)
Step 2: Substitute the expression for h from Step 1 into the second equation:
tan(53°) = (x * tan(35°)) / (x - 250)
Step 3: Solve for x:
x * tan(53°) = x * tan(35°) - 250 * tan(35°)
x * (tan(53°) - tan(35°)) = 250 * tan(35°)
x = (250 * tan(35°)) / (tan(53°) - tan(35°))
Step 4: Calculate the value of x:
x ≈ (250 * 0.7002) / (1.3270 - 0.7002) ≈ 394.74 feet
Step 5: Substitute the value of x back into the expression for h:
h ≈ 394.74 * tan(35°) ≈ 278.84 feet
So, the estimated height of the building is approximately 279 feet to the nearest foot.
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Help I WILL MARK BRAINLEST PLZZZZ 20 POINTS PLZZ ANSWER I REALLY NEED IT
Answers
Answer:
35
Step-by-step explanation:
The sampling distribution is based on the assumption that the _____ hypothesis is _____.
Answers
The sampling distribution is based on the assumption that the null hypothesis is true.
What is a null hypothesis?A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
What is a two-tailed test?A two-tailed test can be defined as a type of hypothesis test in which a rejection of the null hypothesis occurs for values of the point estimator in either tail of the sampling distribution.
In this context, we can infer and logically deduce that the sampling distribution is based on the assumption that the null hypothesis is true.
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Evaluate yz + x² x=3.2, y=6.1, z=0.2
Answers
Answer:
Step-by-step explanation:
To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:
yz + x²
Substituting the given values, we get:
(6.1 * 0.2) + (3.2^2)
This simplifies to:
1.22 + 10.24
Therefore, the value of the expression is approximately 11.46.
11.46
gimme brainlyest gang
What is the wall height for H??
Answers
Answer:
Step-by-step explanation:
Side "h" ( wall height ) is 35
The height of the wall "h".
Solution:-\({\boxed{\mathcal{\red{The\:height\:of\:the\:wall\:"h"\:is\:35.71\:ft.}}}}\)
Step-by-step explanation:\(\sf\purple{Using\:Pythagoras \:theorem, \:we\:have}\)
\(( {Perpendicular})^{2} + ( {Base})^{2} = ( {Hypotenuse})^{2} \\ ➡ \: {h}^{2} + ({35 \: ft})^{2} = ({50 \: ft})^{2} \\ ➡ \: {h}^{2} + 1225 \: {ft}^{2} = 2500 \: {ft}^{2} \\ ➡ \: {h}^{2} = 2500 {ft}^{2} - 1225 \: {ft}^{2} \\ ➡ \: {h}^{2} = 1275 \: {ft}^{2} \\ ➡ \: h \: = \sqrt{1275 \: {ft}^{2} } \\ ➡ \: h = 35.707\: ft \: \\ ➡ \: h = 35.71\: ft\)
\(\sf\red{Therefore\:the\:height\:of\:the\:wall\:"h"\:is\:35.71\:ft.}\)
To verify :-\(( {35.71 \: ft})^{2} + ( {35 \: ft})^{2} = ({50 \: ft})^{2} \\ ✒ \: 1275 \: {ft}^{2} + 1225 \: {ft}^{2} \: = 2500 \: {ft}^{2} \\ ✒ \: 2500 \: {ft}^{2} = 2500 \: {ft}^{2} \\ ✒ \: L.H.S.=R. H. S\)
Hence verified.
\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)
who is the prime minister of India ?
Answers
Answer: Narendra Modi (Since 2014)
I. Direction: Write the following statement as equations. Write your answers
on a sheet of paper.
1. Four times a number minus twenty-nine is eleven.
2. The product of four less than thrice a number and two will result to forty-
six.
be
3. Three-fifths of a number plus eight is fifty.
II. Direction: Translate the following Algebraic expressions to word phrases.
Write your answers on a sheet of paper.
4.) 51 - (x+5)
5.) 3(y-8)
Answers
Answer:
1. 4x - 29=11
2. (3x - 4) (2) = 46
3. 3/5x + 8 = 50
4. The difference of 51 and the sum of x and 5.
5. The product of 3 and y minus eight.
Step-by-step explanation:
Random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. calculate the p-value. t.test(a2:a31,b2:b31,2,3)
Answers
The p-value is 0.0064
Given that a random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. Let us first understand the t-test(a2:a31, b2:b31, 2, 3) formula:
t-test stands for student's t-test.
a2:a31 is the first range or dataset.
b2:b31 is the second range or dataset.
2 represents the type of test (i.e., two-sample equal variance).
3 represents the type of t-test (i.e., two-tailed).
Now, let's solve the problem at hand using the formula given by putting the values into the formula:
P-value = 0.0064
The p-value calculated using the t.test(a2:a31, b2:b31, 2, 3) formula is 0.0064.
Learn more about t-test:
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When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?
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Answer:
When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?
https://www.louisianabelieves.com/docs/default-source/assessment/grade-7-answer-key.pdf
Step-by-step explanation: