Answer:
One-way ANOVA
Step-by-step explanation:
One-way ANOVA(analysis of variance) a testing method in statistics that is used to compare the means of two or more independent samples, to check if the differences are statistically significant.
In this case, we have three groups which their various reaction time to caffeine is to be tested using the same testing method (amount of caffeine). Hence the appropriate test to use here is the one-way ANOVA
A study of women’s weights found that a randomly selected sample of 234 women had a mean weight of 157.3 lb. Assuming that the population standard deviation is 15.6 lb., construct a 95% confidence interval estimate of the mean weight of all women.
A. (145.3, 160.5)
B. (155.3, 159,3)
C. (165.5, 173.5)
D. (185.7, 199.3)
Answer:
[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]
[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]
So on this case the 95% confidence interval would be given by (155.301;159.299)
And the best option would be:
B. (155.3, 159,3)
Step-by-step explanation:
Information given
[tex]\bar X=157.3[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma =15.6[/tex] represent the population standard deviation
n=234 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence level is is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]
[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]
So on this case the 95% confidence interval would be given by (155.301;159.299)
And the best option would be:
B. (155.3, 159,3)
The average lifetime of a set of tires is 3.4 years. The manufacturer will replace any set of tires failing within three years of the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that the tires will fail within three years of the date of purchase?
Answer: the probability that the tires will fail within three years of the date of purchase is 0.12
Step-by-step explanation:
The average lifetime of a set of tires is 3.4 years. It means that μ = 3.4
Decay parameter, m = 1/3.4 = 0.294
The probability density function is
f(x) = me^-mx
Where x is a continuous random variable representing the time interval of interest(the reliability period that we are testing)
Since x = 3 years,
Therefore, the probability that the tires will fail within three years of the date of purchase is
f(3) = 0.294e^-(0.294 × 3)
f(3) = 0.294e^- 0.882
f(3) = 0.12
g In a large midwestern university (the class of entering freshmen is 6000 or more students) respectively, who graduated in the bottom third of their high school class. A 99% confidence interval for p1 – p2 is:
Answer:
–0.029 to 0.229.
Step-by-step explanation:
So, we are given the following data or information or values/parameters which are going to help us in solving this particular equation:
=>" A class of entering freshmen = 6000 or more students) respectively"
=> "The class of entering freshmen graduated in the bottom third of their high school class."
=>" 99% confidence interval for p1 – p2"
Let p1 = k1 and p2 = k2
Here, we can deduce that p1 > p2; k1 > k2. Hence,
a = (1 - 0.99)/2 = 0.005.
b = 513 × 0.005 = 2.6.
c = standard deviation = ✓ [ k1 (1 - k1) / j1 + k2 (1 - k2) / j2] = 0.05.
99% confidence interval for p1 – p2 =
k1 - k2 - b × c = –0.029
Also, k1 - k2 + b × c = 0.029.
Which are the lower and upper boundaries respectively.
someone pls help me! ❤️❤️❤️
Answer:
(x-1) ( x -i) (x+i)
Step-by-step explanation:
x^3 -2x^2 +x-2
Factor by grouping
x^3 -2x^2 +x-2
x^2(x-2) +1(x-2)
Factor out (x-2)
(x-2) (x^2+1)
Rewriting
(x-1) ( x^2 - (-1)^2)
(x-1) ( x -i) (x+i)
Answer:
Should be b
Step-by-step explanation:
Since it's a multiple choice question you know that -2 or 2 has to be a root for the cubic.
You can test both -2 and 2 and see that replacing x for 2 has the expression evaluate to 0.
Then, since you know the imaginary roots have to be conjugates, you get B.
Find the solutions to x^2 = 8
Answer:
x=2√2 is the answer
Step-by-step explanation:
x²=8
TAKING SQUARE ROOT ON BOTH SIDES
√x²=√8
x=√2×2×2
x=√2²×√2
x=2√2
i hope this will help you
Answer:
The value of x is -2.828 or 2.828
Step-by-step explanation:
In order to eliminate of square of x, you have to square root both sides :
[tex] {x}^{2} = 8[/tex]
[tex] \sqrt{ {x}^{2} } = ± \sqrt{8} [/tex]
[tex]x = \sqrt{8} \\ x = 2 \sqrt{2} \: or \: 2.828[/tex]
[tex]x = - \sqrt{8} \\ x = - 2 \sqrt{2} \: or \: - 2.828[/tex]
i need help on this. anyone ?
Answer:
Read below
Step-by-step explanation:
To copy a segment, you have to open your compass to the length of the given segment. The instructions say to have an endpoint at R, so, with the compass open to the length of the given line segment, place one end of the compass at R and draw an arc that intersects the line that R lies on. This new segment is congruent to the given segment.
I hope this helps!
Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. AIB Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance policy holders is
A. (76.87, 80.33)
B. (72.5, 82.9)
C. (77.1, 78.3)
D. (74.1, 81.3)
E. (74.5, 80)
Answer:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.102[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Step-by-step explanation:
Information given
[tex]\bar X=77.7[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.6 represent the sample standard deviation
n=100 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=100-1=99[/tex]
Since the Confidence is 0.90 or 90%, the significance would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value for this case would be [tex]t_{\alpha/2}=1.66[/tex]
And replacing we got:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.10[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
2x^2+8x = x^2-16
Solve for x
Answer:
x=-4
Step-by-step explanation:
[tex]2x^2+8x=x^2-16[/tex]
Move everything to one side:
[tex]x^2+8x+16=0[/tex]
Factor:
[tex](x+4)^2=0[/tex]
By the zero product rule, x=-4. Hope this helps!
Answer:
x=-4
Step-by-step explanation:
Move everything to one side and combine like-terms
x²+8x+16
Factor
(x+4)²
x=-4
A college surveys 300 graduates and finds 98 graduated with honors and 207 had one or both parents graduate from college. Of the 98 students with honors, 79 had one or both parents graduate from college. Find the probability that a randomly chosen graduate from these 300 graduated with honors given that neither parent graduated from college.
Answer:
20.43% probability that a randomly chosen graduate from these 300 graduated with honors given that neither parent graduated from college.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Graduated with honors:
98 students graduated with honors. Of those, 79 had at least one parent graduating from college. So 98 - 79 = 19 did not.
Of 300 students, 207 had one or both parents graduate from college. So 300 - 207 = 93 did not have at least one parent graduating.
Find the probability that a randomly chosen graduate from these 300 graduated with honors given that neither parent graduated from college.
Of the 93 with no graduated parent, 19 earned honors
19/93 = 0.2043
20.43% probability that a randomly chosen graduate from these 300 graduated with honors given that neither parent graduated from college.
Which of the following is the equation of the function below?
Answer:
Step-by-step explanation:
its B
Answer:
the answer is B
Step-by-step explanation:
Find the volume of the cone.
Diameter: 20 m, Slant Height: 26 m
Round to the nearest whole number.
Volume
=
[?] m3
Answer:
2513the step-by-step explanation for height first :
[tex]h=\sqrt{h^{2} } +r^{2} =26[/tex]
[tex]h=\sqrt{h^{2} } +10^{2} =676[/tex]
[tex]h=\sqrt{h^{2} } + 100 = 676[/tex]
[tex]100-100 = 0[/tex]
[tex]676-100=576[/tex]
[tex]\sqrt{576}[/tex]
[tex]height =[/tex] 24 m
________________
step-by-step explanation for the problem :
FORMULA : [tex]v = \frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]
v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]10^{2}[/tex] · [tex]24[/tex] = [tex]800\pi[/tex] = [tex]2513.27412[/tex] = 2513
$5.60 is what perecentage of $17.50?
Answer:
To find it's percentage divide $5.60 by
$17.50 and multiply it by 100%
That is
5.60/ 17.50 × 100%
= 32%
Hope this helps you
Need help ASAP!! thank you sorry if u can’t see it good :(
Answer/Step-by-step explanation:
==>Given:
=>Rectangular Pyramid:
L = 5mm
W = 3mm
H = 4mm
=>Rectangular prism:
L = 5mm
W = 3mm
H = 4mm
==>Required:
a. Volume of pyramid:
Formula for calculating volume of a rectangular pyramid us given as L*W*H
V = 5*3*4
V = 60 mm³
b. Volume of prism = ⅓*L*W*H
thus,
Volume of rectangular prism given = ⅓*5*3*4
= ⅓*60
= 20mm³
c. Volume of the prism = ⅓ x volume of the pyramid
Thus, 20 = ⅓ × 60
As we can observe from our calculation of the solid shapes given, the equation written above is true for all rectangular prism and rectangular pyramid of the same length, width and height.
1/5divided by (-5/7)
Answer:
-0.28
Step-by-step explanation:
(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28
Answer:
[tex]-7/25[/tex]
Step-by-step explanation:
[tex]1/5 \div -5/7[/tex]
Do the reciprocal of the second fraction.
[tex]1/5 \times 7/-5[/tex]
Multiply the first fraction by the reciprocal of the second fraction.
[tex]7/-25=-0.28[/tex]
The answer in decimal form is -0.28.
A homogeneous second-order linear differential equation, two functions y 1y1 and y 2y2, and a pair of initial conditions are given. First verify that y 1y1 and y 2y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x.
y'' + 49y = 0; y1 = cos(7x) y2 = sin(7x); y(0) = 10 y(0)=-4
1.Why is the function y, = e * a solution to the differential equation?
A. The function y1 =e 4X is a solution because when the function and its indefinite integral, , are substituted into the equation, the result is a true statement.
B. The function y1 = e 4X is a solution because when the function and its second derivative, y1" = 16 e 4x, are substituted into the equation, the result is a true statement.
2. Why is the function y2 solution the differential equation?
A. The function y2 = e 4x is a solution because when the function and its indefinite integral, are substituted into the equation, the result a true statement. The function y2 = e 4X is a solution because when the function and its second derivative, y2" = 16 e -4x are substituted into the equation, the result is a true statement. The particular solution of the form y = c, y, +c,y2 that satisfies the initial conditions y(0) 2 and y'(0) = 9 is y =.
Answer:
[tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex]
B.
B.
[tex]y = \frac{17}{8}e^4^x - \frac{1}{8}e^-^4^x[/tex]
Step-by-step explanation:
Question 1:
- We are given a homogeneous second order linear ODE as follows:
[tex]y'' + 49y = 0[/tex]
- A pair of independent functions are given as ( y1 ) and ( y2 ):
[tex]y_1 = cos ( 7x )\\\\y_2 = sin ( 7x )[/tex]
- The given ODE is subjected to following initial conditions as follows:
[tex]y ( 0 ) = 10\\\\y ' ( 0 ) = -4[/tex]
- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:
[tex]y = c_1y_1 + c_2y_2[/tex]
Solution:-
- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.
- Formulate the second derivatives of both functions y1 and y2 as follows:
[tex]y'_1 = -7sin(7x) , y''_1 = -49cos(7x)\\\\y'_2 = -7cos(7x) , y''_2 = -49sin(7x)\[/tex]
- Now plug the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.
[tex]y''_1 + 49y_1 = 0\\\\-49cos(7x) + 49cos ( 7x ) = 0\\0 = 0\\\\y''_2 + 49y_2 = 0\\\\-49sin(7x) + 49sin ( 7x ) = 0\\0 = 0\\\\[/tex]
- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.
- The complete solution to a homogeneous ODE is given in the form as follows:
[tex]y = c_1y_1 + c_2y_2\\\\y = c_1*cos(7x) + c_2*sin(7x)\\[/tex]
- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,
[tex]y (0) = c_1cos ( 0 ) + c_2sin ( 0 ) = 10\\\\y'(0) = -7c_1*sin(0) + 7c_2*cos(0) = -4\\\\c_1 ( 1 ) + c_2 ( 0 ) = 10, c_1 = 10\\\\-7c_1(0) + 7c_2( 1 ) = -4 , c_2 = -\frac{4}{7}[/tex]
- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:
[tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex] .... Answer
Question 2
- We are given a homogeneous second order linear ODE as follows:
[tex]y'' -16y =0[/tex]
- A pair of independent functions are given as ( y1 ) and ( y2 ):
[tex]y_1 = e^4^x\\\\y_2 = e^-^4^x[/tex]
- The given ODE is subjected to following initial conditions as follows:
[tex]y( 0 ) = 2\\y'( 0 ) = 9[/tex]
- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:
[tex]y = c_1y_1 + c_2y_2[/tex]
Solution:-
- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.
- Formulate the second derivatives of both functions y1 and y2 as follows:
[tex]y'_1 = 4e^4^x , y''_1 = 16e^4^x\\\\y'_2 = -4e^-^4^x , y''_2 = 16e^-^4^x[/tex]
- Now substitute the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.
[tex]y''_1 - 16y_1 = 0\\\\16e^4^x - 16e^4^x = 0\\\\0 = 0\\\\y''_2 - 16y_2 = 0\\\\16e^-^4^x - 16e^-^4^x = 0\\\\0 = 0[/tex]
- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.
- The complete solution to a homogeneous ODE is given in the form as follows:
[tex]y = c_1y_1 + c_2y_2\\\\y = c_1*e^4^x + c_2*e^-^4^x[/tex]
- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,
[tex]y ( 0 ) = c_1 * e^0 + c_2 * e^0 = 2\\\\y' ( 0 ) = 4 c_1 * e^0 - 4c_2 * e^0 = 9\\\\c_1 + c_2 = 2 , 4c_1 - 4c_2 = 9\\\\c_1 = \frac{17}{8} , c_2 = -\frac{1}{8}[/tex]
- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:
[tex]y = \frac{17}{8} e^4^x - \frac{1}{8}e^-^4^x[/tex] .... Answer
Find the LCM of the set of algebraic expressions.
28x2,49xy, 28y
Answer
Answer:
196x^2y
Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
In a certainâ state, the recent average critical reading standardized test score was 514. Assume that the standard deviation is 50 and that standardized test scores are Normally distributed. Complete partsâ (a) andâ (b) below. Include a Normal curve for each part.
Required:
a. What percentage of standardized test takers scored 550 or less?
b. What percentage of standardized test takers scored 524?
Answer:
a) Percentage of standardized test takers that scored 550 or less = 76.4%
b) Percentage of standardized test takers that scored 524 = 0.782%
Step-by-step explanation:
This is a normal distribution problem with
Mean = μ = 514
Standard deviation = σ = 50
a) Percentage of standardized test takers scored 550 or less = P(x ≤ 550)
We first normalize or standardize 550
The standardized score for any is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (550 - 514)/50 = 0.72
To determine the required probability
P(x ≤ 550) = P(z ≤ 0.72)
We'll use data from the normal distribution table for these probabilities
P(x ≤ 550) = P(z ≤ 0.72) = 0.76424 = 76.424%
The normal curve for this question and the b part are sketched in the first attached image to this solution.
b) Percentage of standardized test takers that scored 524 = P(x = 524)
On standardizing,
z = (x - μ)/σ = (524 - 514)/50 = 0.20
For this part, since it's an exact probability, we will use the normal distribution formula
P(z = Z) = [1/(σ√2π)] × e^(-z²/2)
Since z = (x - μ)/σ
It can be written properly as presented in the second attached image to this question.
Putting x = 524 or z = 0.20 in this expression, we get
P(x = 524) = P(z = 0.20) = 0.0078208539 = 0.782%
Hope this Helps!!!
Find the diagonal of a square whose sides measure 3x square root of 2
Answer:
that means each side equals 8
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line 2y – 3x = 8?
Answer:
[tex] = \frac{3}{2} [/tex]
Step-by-step explanation:
[tex]y = mx + c[/tex]
Here,
m => slopec => interceptIn this equation ,
[tex]2y - 3x = 8[/tex]
to find the value of m or the value of slope we have to solve for y
Let's solve,
[tex]2y - 3x = 8 \\ 2y = 8 + 3x \\ \frac{2y}{2} = \frac{8 + 3x}{2} \\ y = 4 + \frac{3x}{2} \\ y = \frac{3x}{2} + 4[/tex]
So, the slope is,
[tex] = \frac{3}{2}[/tex]
Which lists the ratios in order from least to greatest 2:9,1:6,7:36
Answer:
1:6, 7:36, 2:9
Step-by-step explanation:
2 : 9 → 8 : 36
1 : 6 → 6 : 36
7 : 36
Least → Greatest
1:6, 7:36, 2:9
Can someone please help
Use the In key on your calculator to estimate
the logarithm.
In 44
Round your answer to the nearest thousandth.
Answer:
3.784
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down,drag into the correct position in the answer box.Release your mouse button when the item is place. If you change your mind,drag the item to the trash can,click the trash and to clear all your answers. Divide the following polynomials,then place the answer in the proper location on the grid. Write the answer in descending powers of x. 9x^2-18x-7 divided by (3x+1)
Answer:
[tex]\boxed{\sf \ \ 9x^2-18x-7 \ \ divided \ by \ (3x+1) \ is \ (3x-7) \ }[/tex]
Step-by-step explanation:
Hello,
let's find a and b reals so that
[tex]9x^2-18x-7=(3x+1)(ax+b)[/tex]
[tex](3x+1)(ax+b)=3ax^2+(3b+a)x+b[/tex]
we identify the terms in [tex]x^2[/tex]
9 = 3a
we identify the terms in x
-18 = 3b + a
we identify the constant terms
-7 = b
so ti goes with a = 9/3 = 3, b = -7
so we can write
[tex]9x^2-18x-7=(3x+1)(3x-7)[/tex]
so [tex]9x^2-18x-7 \ divided \ by \ (3x+1) \ is \ (3x-7)[/tex]
hope this helps
A real estate agent has 1313 properties that she shows. She feels that there is a 40%40% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling at least 11 property in one week. Round your answer to four decimal places.
Answer:
0.0013
Step-by-step explanation:
The probability of selling a property is 40%, so the probability of not selling it is 60%.
To find the probability of selling at least 11 properties, we can calculate the following cases:
Selling 11:
P(11) = C(13,11) * P(sell)^11 * P(not sell)^2
P(11) = (13! / (11! * 2!)) * 0.4^11 * 0.6^2
P(11) = 13*12/2 * 0.4^11 * 0.6^2 = 0.001178
Selling 12:
P(12) = C(13,12) * P(sell)^12 * P(not sell)^1
P(11) = (13! / (12! * 1!)) * 0.4^12 * 0.6^1
P(11) = 13 * 0.4^12 * 0.6 = 0.000131
Selling 13:
P(13) = C(13,13) * P(sell)^13 * P(not sell)^0
P(11) = 1 * 0.4^13 * 0.6^0
P(11) = 1 * 0.4^13 * 1 = 0.000007
Final probability:
P(at least 11) = P(11) + P(12) + P(13)
P(at least 11) = 0.001178 + 0.000131 + 0.000007 = 0.001316
P(at least 11) = 0.0013
Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2? (6 points) Question 7 options: 1) x3 − 2x2 − 3x + 6 2) x3 − 3x2 − 5x + 15 3) x3 + 2x2 − 3x − 6 4) x3 + 3x2 − 5x − 15
Answer:
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
Step-by-step explanation:
A nth order polynomial f(x) has roots [tex]x_{1}, x_{2}, ..., x_{n}[/tex] such that [tex]f(x) = (x - x_{1})*(x - x_{2})*...*(x - x_{n}}[/tex],
Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2?
So
[tex]x_{1} = x_{2} = \sqrt{3}[/tex]
[tex]x_{3} = -2[/tex]
Then
[tex](x - \sqrt{3})^{2}*(x - (-2)) = (x - \sqrt{3})^{2}*(x + 2) = (x^{2} -2x\sqrt{3} + 3)*(x + 2) = x^{3} + 2x^{2} - 2x^{2}\sqrt{3} - 4x\sqrt{3} + 3x + 6[/tex]
Since [tex]\sqrt{3} = 1.73[/tex]
[tex]x^{3} + 2x^{2} - 3.46x^{2} - 6.93x + 3x + 6 = x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
Find the general solution to 3y′′+12y=0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2.
Answer:
[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]
Step-by-step explanation:
You have the following differential equation:
[tex]3y''+12y=0[/tex] (1)
In order to find the solution to the equation, you can use the method of the characteristic polynomial.
The characteristic polynomial of the given differential equation is:
[tex]3m^2+12=0\\\\m^2=-\frac{12}{3}=-4\\\\m_{1,2}=\pm2\sqrt{-1}=\pm2i[/tex]
The solution of the differential equation is:
[tex]y(x)=c_1e^{m_1x}+c_2e^{m_2x}[/tex] (2)
where m1 and m2 are the roots of the characteristic polynomial.
You replace the values obtained for m1 and m2 in the equation (2). Then, the solution to the differential equation is:
[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]
Please answer this correctly
Answer:
13 students
Step-by-step explanation:
At least 30 and fewer than 67 makes it 30-66
So,
30-66 => 13 students
Answer:
16
Step-by-step explanation:
There are two columns in the diagram.
The column headed stem represents tens while the column headed leaf represents units. e.g. 2 3 = 23
So we just have to count how many of the numbers are less than 8 in the 6th Stem column and all the numbers below it, which are:
20, 23, 28, 31, 31, 34, 38, 40, 44, 50, 51, 53, 54, 65, 65, 66
State whether the data described below are discrete or continuous, and explain why.
The exact lengths (in kilometers) of the ocean coastlines of different countries.
a. The data are continuous because the data can only take on specific values.
b. The data are discrete because the data can only take on specific values.
c. The data are continuous because the data can take on any value in an interval.
d. The data are discrete because the data can take on any value in an interval.
Answer:
c. The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
A variable is said to be continuous if it can take on any value in an interval. Examples are lengths, temperature, etc
A discrete variable, on the other hand, can only take on specific values. Examples of discrete variables are the number of students and age.
The exact lengths (in kilometers) of the ocean coastlines of different countries is a continuous variable because it can take on any value in an interval.
A stated earlier, Lengths are in general, continuous variables.
Kaya figured out that she will need $47,592 to attend college. What is the amount rounded to the nearest ten thousand? Help meeee
Answer:
50,000
Step-by-step explanation:
ten thousand thousand hundreds tens ones
4 7 5 9 2
When rounding to the ten thousands, we look at the thousands place
If it is 5 or higher we round the ten thousands place up
7 is five or higher so we round the 4 up one place 4 becomes 5 and the rest becomes 0
5 0 0 0 0
Answer:
$50,000
Step-by-step explanation:
=> $47,592
While rounding off to the nearest thousand, we check the thousands place. If the digit in the thousands place is greater than 5, 1 will be added to the T. Th. place while if its less than 5, there will be no change and The digits except the ten thousands place will all become zero.
So,
=> $50,000
A robotic machine fills containers with an acid solution at the rate of 50 + 5 t milliliters (mL) per second, where t is in seconds and 0 ≤ t ≤ 60 . How many mL are put into a container in 60 seconds? Evaluate your answer to a whole number.
Answer:
12,000
Step-by-step explanation:
The machine fills the containers at a rate of 50+5t milliliters (mL) per second.
Therefore, the rate of change of the number of containers, N is:
[tex]\dfrac{dN}{dt}=50+5t, 0\leq t\leq 60[/tex]
[tex]dN=(50+5t)dt\\$Taking integrals of both sides\\\int dN=\int (50+5t)dt\\N(t)=50t+\frac{5t^2}{2}+C $(C a constant of integration)\\\\When t=0, , No containers are filled, therefore:$ N(t)=0\\0=50(0)+\frac{5(0)^2}{2}+C\\C=0\\$Therefore, N(t)=50t+2.5t^2[/tex]
When t=60 seconds
[tex]N(60)=50(60)+2.5(60)^2\\N(60)=12000$ mL[/tex]
Therefore, 12,000 milliliters of acid solution are put into a container in 60 seconds.
Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation Can the method of undetermined coefficients together with superposition be applied to find a particular solution of the given equation?
A. No, because the right side of the given equation is not the correct type of function
B, Yes °
C. No, because the differential equation is not linear.
D. No, because the differential equation does not have constant coefficients.
Answer:
D. No, because the differential equation does not have constant coefficients.
Step-by-step explanation:
The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.