The solution to the initial value problem y''' - y' = 0, with initial conditions y(0) = 2, y'(0) = 3, and y''(0) = -1, is [tex]y(x) = 2e^x + 3xe^x - e^x.[/tex].
To solve this differential equation, we can first find the characteristic equation by replacing y''' with [tex]r^3[/tex], y' with r, and rearranging the equation as [tex]r^3 - r = 0[/tex]. This equation can be factored as [tex]r(r^2 - 1)[/tex] = 0, giving us three roots: r = 0, r = 1, and r = -1.
For r = 0, the corresponding solution is y = [tex]C_1[/tex], where [tex]C_1[/tex] is a constant.
For r = 1, the corresponding solution is y = [tex]C_2\ e^x,[/tex], where [tex]C_2[/tex] is a constant.
For r = -1, the corresponding solution is y = [tex]C_3\ e^(^-^x^)[/tex], where [tex]C_3[/tex] is a constant.
Applying the initial conditions, we find that y(0) = 2, y'(0) = 3, and y''(0) = -1. Substituting these values into the general solution, we can determine the values of the constants [tex]C_1[/tex], [tex]C_2[/tex], and [tex]C_3[/tex].
By evaluating the initial conditions, we find [tex]C_1 = 2[/tex], [tex]C_2 = 3[/tex], and [tex]C_3 = -1[/tex]. Thus, the particular solution to the initial value problem is [tex]y(x) = 2e^x + 3xe^x - e^x[/tex].
In conclusion, the solution to the given initial value problem is [tex]y(x) = 2e^x + 3xe^x - e^x[/tex].
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Which expression is equivalent to 4n(6n + 2m)?
A 24n + 4n + 2m
B (4n + 2m) x 6n
C 24n2 + 8mn
D 10n2 + 6mn
Answer:
c maybe
Step-by-step explanation:
4n(6n+2m)
24n²+8mn
Answer: C, 24n²+8mn
Step-by-step explanation:
So because 4n is on the outside of the bracket, you have to times everything on the inside of the bracket by 4n.
So, you do:
4n×6n=24n² (4×6=24 and n×n=n²)
4n×2m=8mn (4×2=8 and n×m=mn)
Then you add 24n² to 8mn like this:
24n²+8mn
Hope this helps :)
A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32.What rule do you think the state park uses to decide the entrance fee for a vehicle?
Answer:
I think they charge a flat rate of $8 for a vehicle and $3 per person on top of that.
Step-by-step explanation:
There could be a multitude of rules, but let's try to find a simple one.
I would start by assuming that the park charges a fee for a vehicle and then for each person. Let's name those:
a - flat fee for a vehicle
b - fee per person
then a car with x people in it would be charged
a + bx
Let's see if the fees fit this assumption:
for x = 2
a + b*2 = $14
for x = 4
a + b*4 = $20
for x = 8
a + b*8 = $32
If so, we can subtract the second equation from the first and get
a + b*4 - a - b*2 = $20 - $14
b*2 = $6
b = 3$
a + b*2 = $14
a + $3*2 = a + $6 = $14
a = $8
so the first 2 equations gave us a = $8 and b = $3.
Let's see if these values fit the 3rd equation
a + b*8 = $32
$8 + $3*8 = $32
$8 + $24 = $32
$32 = $32
It fits!
That tells us that the rule is indeed very likely.
4x – 3y + 2 when x = 4 and y = -3
evaluate the expression, show work NO LINKS!
A social psychologist wants to assess whether there are geographical differences in how much people complain. The investigator gets a sample of 20 people who live in the Northeast and 20 people who live on the West Coast and asks them to estimate how many times they have complained in the past month. The mean estimated number of complaints from people living on the West Coast was 9.5, with a standard deviation of 2.8. The mean estimated number of complaints that people in the Northeast reported making was 15.5, with a standard deviation of 3.8. What can the researcher conclude? Use alpha of .05.
The researcher can conclude that there is a statistically significant difference in the mean number of complaints between people living on the West Coast and those living in the Northeast.
To determine if there are geographical differences in how much people complain between the Northeast and the West Coast, we can conduct a hypothesis test.
Null hypothesis (H0): There is no difference in the mean number of complaints between the Northeast and the West Coast.
Alternative hypothesis (H1): There is a difference in the mean number of complaints between the Northeast and the West Coast.
Given the sample statistics, we can perform a two-sample independent t-test to compare the means of the two groups.
Let's calculate the test statistic and compare it to the critical value at a significance level of α = 0.05.
The West Coast sample has a mean (x1) of 9.5 and a standard deviation (s1) of 2.8, with a sample size (n1) of 20.
The Northeast sample has a mean (x2) of 15.5 and a standard deviation (s2) of 3.8, with a sample size (n2) of 20.
Using the formula for the pooled standard deviation (sp), we can calculate the test statistic (t):
sp = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))
t = (x1 - x2) / (sp * sqrt(1/n1 + 1/n2))
Calculating the test statistic:
sp = sqrt(((19 * 2.8^2) + (19 * 3.8^2)) / (20 + 20 - 2)) ≈ 3.273
t = (9.5 - 15.5) / (3.273 * sqrt(1/20 + 1/20)) ≈ -4.63
Using a t-table or a statistical calculator, we can find the critical value for a two-tailed t-test with α = 0.05 and degrees of freedom (df) = n1 + n2 - 2 = 38. The critical value is approximately ±2.024.
Since the absolute value of the test statistic (4.63) is greater than the critical value (2.024), we reject the null hypothesis.
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True or False The sample variance may not be always greater than the sample standard deviation
This statement is false because the sample variance is always greater than or equal to the sample standard deviation.
Variance and standard deviation are both measures of variability or dispersion within a dataset. The sample variance is defined as the average of the squared differences between each data point and the mean of the dataset. On the other hand, the sample standard deviation is the square root of the variance.
Since variance involves squaring the differences, it accounts for the spread of the dataset more effectively than the standard deviation. As a result, the sample variance tends to be larger than or equal to the sample standard deviation.
Mathematically, this relationship can be expressed as follows:
Sample Variance = [tex]\[\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}\][/tex]
Sample Standard Deviation = [tex]\[\sqrt{\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}}\][/tex]
Where x represents each data point, [tex]\(\overline{x}\)[/tex] represents the mean, and n is the sample size.
Therefore, it is not possible for the sample variance to be smaller than the sample standard deviation.
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IMPORTANT QUESTION!!!!! CORRECT = BRAINLIEST!!!!
Answer: V = 891 feet cubed
Step-by-step explanation:
Answer: R = 12*9 = 108*7.5 = 810ft
T = 12*9*1.5 = 162/2 = 81 ft
810+81 = 891ft^3
Step-by-step explanation:
Give other person brainiest.
A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 98.3°F. Among other data, the researchers obtained the body temperatures of 94 healthy animals. Suppose you
want to use those data to decide whether the mean body temperature of healthy animals is less than 98.3°F. Complete parts (a) through (c) below.
a. Determine the null hypothesis.
H_o: μ _____
(Type an integer or a decimal. Do not round.)
b. Determine the alternative hypothesis.
H_a: μ_____
(Type an integer or a decimal. Do not round.)
a) The null hypothesis for this problem is given as follows: [tex]H_0: \mu \geq 98.3[/tex]
b) The alternative hypothesis for this problem is given as follows: [tex]H_0: \mu < 98.3[/tex]
How to identify the null and the alternative hypothesis?The claim for this problem is given as follows:
"The mean body temperature of healthy animals is less than 98.3°F.".
At the null hypothesis, we consider that there is not enough evidence to conclude that the mean is true, that is:
[tex]H_0: \mu \geq 98.3[/tex]
At the alternative hypothesis, we test if there is enough evidence to conclude that the mean is true, that is:
[tex]H_0: \mu < 98.3[/tex]
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Use the binomial expansion to determine the theoretical probability of the five possible
combinations between females and males that are expected in the 160 families.
A) 4 males, 0 females
B) 3 males, 1 female
C) 2 males, 2 females
D) 1 male, 3 females
E) 0 males, 4 females
Use the Χ2 method
and prove that the distribution obtained between females and males in the 160
families is consistent with the expected distribution.
5. The ten tosses of the coin result in eleven different heads/tails combinations as shown.
points out in the following table. Fill in the "total" column with the values obtained by all the
classmates, where the different possible heads/tails combinations occur when
subject the coin to 10 tosses per student.
The probabilities using Binomial Expansion is
A) P(X = 4) = C(160, 4) p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾
B) P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾
C) P(X = 2) = C(160, 2) p² (1 - p)⁽¹⁶⁰⁻²⁾
D) P(X = 1) = C(160, 1) p¹ (1 - p)⁽¹⁶⁰⁻¹⁾
E) P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾
To determine the theoretical probability of the five possible combinations between females and males in the 160 families, we can use the binomial expansion formula:
P(X = k) = C(n, k) [tex]p^k(1-p)^{n-k}[/tex]
Where:
C(n, k) is the binomial coefficient, calculated as n! / (k! * (n - k)!).
p is the probability of success
(1 - p) is the probability of failure.
Let's calculate the probabilities for each combination:
A) 4 males, 0 females:
P(X = 4) = C(160, 4) p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾
B) 3 males, 1 female:
P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾
C) 2 males, 2 females:
P(X = 2) = C(160, 2) p² (1 - p)⁽¹⁶⁰⁻²⁾
D) 1 male, 3 females:
P(X = 1) = C(160, 1) p¹ (1 - p)⁽¹⁶⁰⁻¹⁾
E) 0 males, 4 females:
P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾
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The shaded sector above covers 1/3 of the circle. If the radius of the circle above is 3 cm, what is the area of the sector in terms of ?
Given:
The shaded sector above covers [tex]\dfrac{1}{3}[/tex] of the circle.
Radius of the circle = 3 cm
To find:
The area of the sector in terms of π.
Solution:
The area of a circle is
[tex]A=\pi r^2[/tex]
Substituting [tex]r=3[/tex], we get
[tex]A=\pi (3)^2[/tex]
[tex]A=9\pi[/tex]
It is given that the shaded sector above covers [tex]\dfrac{1}{3}[/tex] of the circle.
The area of shaded sector [tex]=\dfrac{1}{3}A[/tex]
[tex]=\dfrac{1}{3}(9\pi)[/tex]
[tex]=3\pi[/tex]
Therefore, the area of shaded sector is 3π sq. cm.
If 1 inch on a map equals 4 miles and there are 3 inches on the map from
where you at school and home then you need to travel how many miles
from school to home?
*
Answer:
12 miles
tep-by-step explanation:
1 inch is 4 miles 4 times 3 inches ls 12
A bag contains 7 red, 3 yellow, and 4 blue marbles. What is the probability of pulling out a blue marble, followed by a red marble, without replacing the blue marble first?
Answer:
2/13
Step-by-step explanation:
P(Red,Blue) = 4/14 × 7/13
simplified it becomes 2/13
Find the value of x. Round to the
nearest tenth.
12
Х
2597
X = ?
Enter
Answer:
x ≈ 5.1
Step-by-step explanation:
Using the sine ratio in the right triangle
sin25° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{12}[/tex] ( multiply both sides by 12 )
12 × sin25° = x , that is
x≈ 5.1 ( to the nearest tenth )
33.6
25
27
68.4
8
[4 * (4 + 3)] - 3
[17 – 5) = 3] x 2
(5.4 + 3) * (6-2)
[9= 3 +6] * 3
DDDDD.
0
(4 +3.2) * [(9 - 2) + 2.5]
Step-by-step explanation:
1
A student made 6 bows from 12 yards of ribbon. How many bows can be made from 3
2
yards of ribbon?
2
D A bag of almonds weighs 1-pounds.
Help slove this problems
Answer: k= 10,-3 j=10,-8 L=5,-9 please give me the brainliest if you want to
Step-by-step explanation:
A quadratic function is given. f(x) = 3r-x+6 What is f(2)?
F 40
28
16
Answer:
answer is 16
good day mate
Choose the equation and the slope of the line that passes through (5, -3) and is perpendicular to the x-axis. A. Equation: x= -3 B. Slope: undefined C. Slope: 0 D. Equation: y = -3 E. Equation: x = 5 E Equation: y = 5
The sum of two numbers is 19 and their difference is 1.
What are the two numbers ?
Smaller number
Larger number
if x+y=19
and
x-y=1
now solve it by adding the equations together
x+x , y+[-y] and 19+1
2x=20
x=10, y=9
You have 15 red marbles, 18 yellow marbles, and 12 blue marbles. If you put
them all in a bag and choose 1 marble at random, what is the probability that
the marble is red? Answer in lowest terms.
Answer:
1/3
Step-by-step explanation:
15/(15+18+12)=15/45=1/3
Three sisters are saving for a special trip. The ratio of Helga's savings to Gertrude's savings is 9:2
and the ratio of Gertrude's savings to Maurice's savings is 2:5. Together all 3 sisters have saved $64.
How much has each girl saved? Answer questions 3–4.
? How can you use a diagram to make sense of the problem?
Answer:
Solution in photo
PLSSSS HELP I'LL GIVE YOU BRAINLIEST
A university class has 10 students enrolled, 4 of whom are juniors.
What is the probability that a randomly chosen student will be a junior?
Write your answer as a fraction or whole number and explain how you solve the problem.
Answer:
2/5
Step-by-step explanation:
Since 4 out of 10 students are juniors, you can express this with the fraction 4/10. 4/10 can then be simplified to 2/5.
Use the Chain Rule to find dw/dt.
w = xey/z, x = t7, y = 6 − t, z = 4 + 9t
dw/dt =
The value of dw/dt is [tex]e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]
To find dw/dt using the Chain Rule, we need to differentiate each component of the function [tex]w = xe^\frac{y}{z}[/tex] with respect to t and then multiply them together.
Given:
[tex]w = xe^\frac{y}{z}[/tex]
x = t⁷
y = 6 - t
z = 4 + 9t
Let's find dw/dt step by step:
x = t⁷
Taking the derivative of x with respect to t:
dx/dt = 7t⁶
y = 6 - t
Taking the derivative of y with respect to t:
dy/dt = -1
z = 4 + 9t
Taking the derivative of z with respect to t:
dz/dt = 9
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to x:
[tex]\frac{dw}{dx} =e^\frac{y}{z}[/tex]
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to y:
[tex]\frac{dw}{dy} = (\frac{x}{z} )e^\frac{y}{z}[/tex]
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to z:
[tex]\frac{dw}{dz} = (\frac{-xy}{z^2} )e^\frac{y}{z}[/tex]
Apply the Chain Rule to find dw/dt:
dw/dt = (dw/dx)(dx/dt) + (dw/dy)(dy/dt) + (dw/dz)(dz/dt)
Substituting the derivatives we found earlier:
dw/dt [tex]= (e^\frac{y}{z})(7t^6) + (\frac{x}{z} )e^\frac{y}{z}(-1) + (\frac{-xy}{z^2} )e^\frac{y}{z}(9)[/tex]
dw/dt [tex]= e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]
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В чемпионате мира по футболу участвуют 32 команды. С помощью жребия их делят
на восемь групп, по четыре команды в каждой. Группы называют латинскими буквами от А
до Н. Какова вероятность того, что команда Франции, участвующая в чемпионате, окажется
в одной из групп А, В, С или D?
Ответ:
Ответ:
P = 1/4Объяснение:
Probability of an event happening = Number of ways it can happen / Total number of outcomes
Number of ways it can happen: 1 (there is only 1 group with french team in it)
Total number of outcomes: 4 (there are 4 groups)
So the probability = 1/4
------------------------------------------------------------------------------------
Вероятность возникновения события = Количество способов которыми это может произойти / Общее количество исходов
Количество способов которыми это может произойти: 1 (есть только 1 группа с французской командой в ней)
Общее количество исходов: 4 (есть 4 группы)
Таким образом вероятность = 1/4
Я надеюсь, что это было полезно ^^
A ladder that is 18 ft. long is leaning
against the side of a building. If the angle
formed between the ladder and the ground
is 30°, how far is the bottom of the ladder
from the base of the building?
(Please help im desperate)
3. What is the perimeter of the figure graphed below?
What is the solution to this system
Answer:
Sorry, I was on my phone. Its (2,3)
Step-by-step explanation:
Answer:
(2,3) is the answer
Step-by-step explanation:
The radius of a circle is 4 feet. What is the area?
r=4ft
Give the exact answer in simplest form.
PLEASE ANSWER FAST!
Complete the square. Fill in the number that makes the polynomial a perfect square quadratic. m² - 16m + c. Find the value of c.
Step-by-step explanation:
mmmmmmmmmmmmmmmmmmmmmmmmmmm
True/False Questions: For statements that are true, give a very short expla- nation. For statements that are false, give an example. (a) If A is an invertible matrix, then A is an invertible matrix. (b) If A is an invertible matrix, then A+ A is an invertible matrix. (c) If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. (d) If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix.
(a) If A is an invertible matrix, then A is an invertible matrix. - True
Explanation:
If A is invertible, then A has an inverse matrix A^(-1).
(b) If A is an invertible matrix, then A+ A is an invertible matrix. - False
Explanation:
A+ A = 2A is invertible if and only if A is invertible.
Therefore, this statement is false.
(c)
If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. - False
Explanation:
Even if AB is invertible, it is not always true that B is invertible.
For instance, if A = [1 0], B = [0 1],
then AB = [0 1] which is invertible, but B is not invertible.
(d)
If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix. - False
Explanation:
If A = [2 0], B = [0 1], then both A and B are invertible, but A - B = [2 -1] is not invertible.
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Help me with the please
Answer:
32 degrees.
Step-by-step explanation:
A rectangular dining room has a perimeter of 28 meters and an area of 49 square meters.
What are the dimensions of the dining room?