y" +2y' +17y=0; y(0)=3, y'(0)=17
Answer:
The solution is [tex]y(t)=e^{-t}(\cos 32t + (\frac{5}{8}) \sin 32t)[/tex]
Step-by-step explanation:
We need to find the solution of [tex]y''+2y'+17y=0[/tex] with
condition [tex]y(0)=3,\ y'(0)=17[/tex]
This is a homogeneous equation with characteristic polynomial
[tex]r^{2}+2r+17=0[/tex]
using quadratic formula [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]r=\frac{-2\pm \sqrt{2^{2}-4(1)(17)}}{2(1)}[/tex]
[tex]r=\frac{-2\pm \sqrt{4-68}}{2}[/tex]
[tex]r=\frac{-2\pm \sqrt{-64}}{2}[/tex]
[tex]r=\frac{-2\pm 64i}{2}[/tex]
[tex]r=-1 \pm 32i[/tex]
The general solution for eigen value [tex]a \pm ib[/tex] is
[tex]y(t)=e^{at}(A \cos bt + B \sin bt)[/tex]
[tex]y(t)=e^{-t}(A \cos 32t + B \sin 32t)[/tex]
Differentiate above with respect to 't'
[tex]y'(t)=-e^{-t}(A \cos 32t + B \sin 32t) + e^{-t}(-32A \sin 32t + 32B \cos 32t)[/tex]
Since, y(0)=3
[tex]y(0)=e^{0}(A \cos(0) + B \sin(0))[/tex]
[tex]3=(A \cos(0) +0)[/tex]
so, A=1
Since, y'(0)=17
[tex]y'(0)=-e^{0}(3 \cos(0) + B \sin(0)) + e^{0}(-32(3) \sin(0) + 32B \cos (0))[/tex]
[tex]17=-(3 \cos(0)) + (0 + 32B \cos (0))[/tex]
[tex]17=-3 + 32B[/tex]
add both the sides by 3,
[tex]17+3 = 32B[/tex]
[tex]20= 32B[/tex]
divide both the sides, by 32,
[tex]\frac{20}{32}= B[/tex]
[tex]\frac{5}{8}= B[/tex]
Put the value of constants in [tex]y(t)=e^{-t}(A \cos 32t + B \sin 32t)[/tex]
[tex]y(t)=e^{-t}((1) \cos 32t + (\frac{5}{8}) \sin 32t)[/tex]
Therefore, the solution is [tex]y(t)=e^{-t}(\cos 32t + (\frac{5}{8}) \sin 32t)[/tex]
hi i’m not sure how to do question 20 if u could explain how to do it that’d b great !!
Answer:
A) -2
Step-by-step explanation:
The form is indeterminate at x=0, so L'Hopital's rule applies. The resulting form is also indeterminate at x=0, so a second application is required.
Let f(x) = x·sin(x); g(x) = cos(x) -1
Then f'(x) = sin(x) +x·cos(x), and g'(x) = -sin(x).
We still have f'(0)/g'(0) = 0/0 . . . . . indeterminate.
__
Differentiating numerator and denominator a second time gives ...
f''(x) = 2cos(x) -sin(x)
g''(x) = -cos(x)
Then f''(0)/g''(0) = 2/-1 = -2
_____
I like to start by graphing the expression to see if that is informative as to what the limit should be. The graph suggests the limit is -2, as we found.
Maria needs to know How much Money $ to have with her when She Goes to her favorite Show Store ... How Much money Should Bring to buy a pair of Shoes ?? ? If, the Original price is $ 80 and there is a discount of 20% and the Sale will only last for one week ...
Answer: $64
Step-by-step explanation:
Set up is/of ratio. See photo attached. (:
A ball is thrown at an initial height of 7 feet with an initial upward velocity at 27 ft/s. The balls height h (in feet) after t seconds is give by the following. h- 7 27t -16t^2 Find the values of t if the balls height is 17ft. Round your answer(s) to the nearest hundredth
Answer:
The height of ball is 17 ft at t=0.55 and t=1.14.
Step-by-step explanation:
The general projectile motion is defined as
[tex]y=-16t^2+vt+y_0[/tex]
Where, v is initial velocity and y₀ is initial height.
It is given that the initial height is 7 and the initial upward velocity is 27.
Substitute v=27 and y₀=7 in the above equation to find the model for height of the ball.
[tex]h(t)=-16t^2+27t+7[/tex]
The height of ball is 17 ft. Put h(t)=17.
[tex]17=-16t^2+27t+7[/tex]
[tex]0=-16t^2+27t-10[/tex]
On solving this equation using graphing calculator we get
[tex]t=0.549,1.139[/tex]
[tex]t\approx 0.55,1.14[/tex]
Therefore the height of ball is 17 ft at t=0.55 and t=1.14.
The number of typing errors made by a typist has a Poisson distribution with an average of two errors per page. If more than two errors appear on a given page, the typist must retype the whole page. What is the probability that a randomly selected page does not need to be retyped? (Round your answer to three decimal places.)
Answer: 0.6767
Step-by-step explanation:
Given : Mean =[tex]\lambda=2[/tex] errors per page
Let X be the number of errors in a particular page.
The formula to calculate the Poisson distribution is given by :_
[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]
Now, the probability that a randomly selected page does not need to be retyped is given by :-
[tex]P(X\leq2)=P(0)+P(1)+P(2)\\\\=(\dfrac{e^{-2}2^0}{0!}+\dfrac{e^{-2}2^1}{1!}+\dfrac{e^{-2}2^2}{2!})\\\\=0.135335283237+0.270670566473+0.270670566473\\\\=0.676676416183\approx0.6767[/tex]
Hence, the required probability :- 0.6767
A sample is selected from a population with a mean of μ = 40 and a standard deviation of σ = 8. a. If the sample has n = 4 scores, what is the expected value of M and the standard error of M? b. If the sample has n = 16 scores, what is the expected value of M and the standard error of M? Gravetter, Frederick J. Statistics for The Behavioral Sciences (p. 221). Cengage Learning. Kindle Edition.
Answer:
a) The expected value of M = 40
The standard error for M = 4
b) The expected value of M = 40
The standard error for M = 2
Step-by-step explanation:
* Lets revise some definition to solve the problem
- The mean of the distribution of sample means is called the expected
value of M
- It is equal to the population mean μ
- The standard deviation of the distribution of sample means is called
the standard error of M
- The rule of standard error is σM = σ/√n , where σ is the standard
deviation and n is the size of the sample
* lets solve the problem
- A sample is selected from a population
∵ The mean of the population μ = 40
∵ The standard deviation σ = 8
a) The sample has n = 4 scores
∵ The expected value of M = μ
∵ μ = 40
∴ The expected value of M = 40
∵ The standard error of M = σ/√n
∵ σ = 8 and n = 4
∴ σM = 8/√4 = 8/2 = 4
∴ The standard error for M = 4
b) The sample has n = 16 scores
∵ The expected value of M = μ
∵ μ = 40
∴ The expected value of M = 40
∵ The standard error of M = σ/√n
∵ σ = 8 and n = 16
∴ σM = 8/√16 = 8/4 = 2
∴ The standard error for M = 2
When the sample has n = 4 scores then the expected value of M is 40 and the standard error of M is 4.
When the sample has n = 16 scores then the expected value of M is 40 and the standard error of M is 2.
Given
A sample is selected from a population with a mean of μ = 40 and a standard deviation of σ = 8. a. If the sample has n = 4 scores.
What is the expected value of M?The mean of the distribution of sample means is called the expected value of M.
The standard deviation of the distribution of sample means is called the standard error of M.
1. The sample has n = 4 scores
The expected value of M = μ
The expected value of M = 40
The standard error of M is;
[tex]\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }\\\\ \sigma = 8 \ and \ n = 4}\\\\ Standard \ error=\dfrac{8}{\sqrt{4}}\\\\ Standard \ error=\dfrac{8}{2}\\\\ Standard \ error=4[/tex]
The standard error for M = 4
2. 1. The sample has n = 16 scores
The expected value of M = μ
The expected value of M = 40
The standard error of M is;
[tex]\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }\\\\ \sigma = 8 \ and \ n = 16}\\\\ Standard \ error=\dfrac{8}{\sqrt{16}}\\\\ Standard \ error=\dfrac{8}{4}\\\\ Standard \ error=2[/tex]
The standard error for M = 2
To know more about standard deviation click the link given below.
https://brainly.com/question/10984586
You are given three white balls, one red ball, and two identical boxes. You are asked to distribute the balls in the boxes in any way you like. You then are asked to select a box (after the boxes have been shuffled) and to pick a ball at random from that box. If the ball is red you win a prize. How should you distribute the balls in the boxes to maximize your chances of winning? Justify your reasoning.
The diagram represents the polynomial 4x2 + 23x – 72.
What is the factored form of 4x2 + 23x – 72?
(4x + 8)(x – 9)
(4x – 8)(x + 9)
(4x + 9)(x – 8)
(4x – 9)(x + 8)
For this case we must factor the following expression:
[tex]4x ^ 2 + 23x-72[/tex]
We rewrite the middle term as a sum of two terms whose product is [tex]4 * (- 72) = - 288[/tex] and whose sum is 23. These numbers are -9 and +32. So:
[tex]4x ^ 2 + (- 9 + 32) x-72\\4x ^ 2-9x + 32x-72[/tex]
We factor the highest common denominator of each group.
[tex]x (4x-9) +8 (4x-9)[/tex]
We factor taking into account the common term [tex](4x-9):[/tex]
[tex](4x-9) (x + 8)[/tex]
Finally, the factored expression is:
[tex](4x-9) (x + 8)[/tex]
Answer:
Option D
Answer:
The correct answer option is D. (4x – 9)(x + 8).
Step-by-step explanation:
We are given the following polynomial and we are to find its factored form:
[tex]4x^2+23x-72[/tex]
Finding factors of (-72 * 4 = ) -288 such that when added they give a result of 23 and when multiplied it gives a product of -288.
[tex] 4 x ^ 2 + 3 2 x - 9 x - 7 2[/tex]
[tex] 4 x ( x + 8 ) - 9 ( x + 8 ) [/tex]
[tex] ( 4 x - 9 ) ( x + 8 )[/tex]
At a certain school, intro to economics and intro to calculus meet at the same time, so it is impossible for a student take both classes. If the probability that a student takes intro to economics is 0.57, and the probability that a student takes intro to calculus 0.17, what is the probability that a student takes intro to economics or into to calculus?
Answer:
0.74
Step-by-step explanation:
P(A∪B) = P(A) + P(B) - P(A∩B) = 0.57 + 0.17 - 0
P(A∪B) = 0.74
The probability of A∩B is zero because the classes are mutually exclusive.
A computer system uses passwords that contain exactly 7 characters, and each character is 1 of the 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the probability that a password contains all lowercase letters given that it contains only letters. Report the answer to 3 decimal places.
Answer:
0,008 or 0,8%
Step-by-step explanation:
To calculate the probability the selected password is made out only of lower-case letters, if it's only letters, we have first to find out how many passwords could be formed with only letters and with only lower-case letters.
For lowercase letters, we can make this many passwords, since for each of the 7 characters, we can pick among 26 lowercase letters:
NLL = 26 * 26 * 26 * 26 * 26 * 26 * 26
In the same fashion, for the number of passwords consisting only of letters, we can pick among 52 letters for each each character (26 lower-case, 26 upper-case):
NOL = 52 * 52 * 52 * 52 * 52 * 52 * 52
We can rewrite NOL differently to ease our calculations:
NOL = (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26)
or
NOL = 26 * 26 * 26 * 26 * 26 * 26 * 26 * 2 * 2 * 2 * 2 * 2 * 2 * 2
Now we have to find out the probability a password containing only letters (NOL) is a password containing only lowercase letters (NLL). So, we divide NLL by NOL:
[tex]\frac{NLL}{NOL} = \frac{26 * 26 * 26 * 26 * 26 * 26 * 26}{26 * 26 * 26 * 26 * 26 * 26 * 26 * 2 * 2 * 2 * 2 * 2 * 2 * 2} = \frac{1}{2 * 2 * 2 * 2 * 2 * 2 * 2} = \frac{1}{2^{7} }[/tex]
The probability is thus 1/2^7 or 1/128 or 0,0078125
Which we are asked to round to 3 decimals... so 0,008 or 0,8%
A student's course grade is based on one midterm that counts as 15% of his final grade, one class project that counts as 15% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 35% of his final grade. His midterm score is 83, his project score is 97, his homework score is 82, and his final exam score is 63. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but < 90 is a B, and so on.
Answer:
Overall final score = 77.75% ; Grade = C.
Step-by-step explanation:
The approach to solve this question is to realize that the marks have to be converted into the respective percentages of the whole course. This means that the marks of all the components have to be normalized according to the grading breakdown.
Project Marks = 97/100. Weightage = 15%. So 97*15/100 = 14.55/15.
This means that the student received 14.55 marks in the project out of 15.
Similarly for other components:
Mid-Term Marks = 83/100. Weightage = 15%. So 83*15/100 = 12.45/15.
Homework Marks = 82/100. Weightage = 35%. So 82*35/100 = 28.7/35.
Finals Marks = 63/100. Weightage = 35%. So 63*35/100 = 22.05/35.
After the conversion process, add up the normalized marks, which are now acting as the percentages earned in all the components.
Aggregate Percentage = 14.55 + 12.45 + 28.7 + 22.05 = 77.75%.
According to the grade scale, the student receives a C because 70 is less than 77.75 and 77.75 is less than 80.
Summarizing, the student receives a C at 77.75%!!!
The student gets the Grade 'C' because the aggregate percentage is greater than 70 and less than 80 and this can be determined by using the given data.
Given :
A student's course grade is based on one midterm that counts as 15% of his final grade.One class project counts as 15% of his final grade.A set of homework assignments that counts as 35% of his final grade.A final exam that counts as 35% of his final grade. His midterm score is 83, his project score is 97, his homework score is 82, and his final exam score is 63.A student's project marks are 97 out of 100 but the weightage of the project marks is 15%. That is:
[tex]=\dfrac{97\times 15}{100}[/tex]
[tex]=14.55[/tex]
So, the project marks are 14.55 out of 15.
A student's homework assignments marks are 82 out of 100 but the weightage of the project marks is 35%. That is:
[tex]=\dfrac{82\times 35}{100}[/tex]
= 28.7
So, homework assignments marks are 28.7 out of 35.
A student's midterm marks are 83 out of 100 but the weightage of the project marks is 15%. That is:
[tex]=\dfrac{83\times 15}{100}[/tex]
= 12.45
So, midterm marks are 12.45 out of 15.
A student's final exam marks are 63 out of 100 but the weightage of the project marks is 35%. That is:
[tex]=\dfrac{63\times 35}{100}[/tex]
= 22.05
So, final exam marks are 22.05 out of 35.
So, the aggregate percentage is given by:
Aggregate Percentage = 14.55 + 12.45 + 28.7 + 22.05 = 77.75%
The student gets the Grade 'C' because the aggregate percentage is greater than 70 and less than 80.
For more information, refer to the link given below:
https://brainly.com/question/22687297
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting aa clubclub or spadespade. (b) Compute the probability of randomly selecting aa clubclub or spadespade or heartheart. (c) Compute the probability of randomly selecting aa twotwo or diamonddiamond.
Answer:
a) 1/2 = 50%
b) 3/4 = 75%
c) 1 / 52 or 1,9%
Step-by-step explanation:
In a standard deck of cards, there are 52 cards in total:
13 are hearts, 13 are diamonds, 13 are clubs and 13 are spades.
(a) Compute the probability of randomly selecting a club or spade
How many cards are a club or a spade?
C = 13 clubs + 13 spades = 26 cards
Out of the 52 total, that means that:
P (club or spade) = 26/52 = 1/2 = 50%
(b) Compute the probability of randomly selecting a club or spade or heart.
How many cards are a club or a spade?
C = 13 clubs + 13 spades + 13 hearts = 39 cards
Out of the 52 total, that means that:
P (club or spade or heart) = 39/52 = 3/4 = 75%
(c) Compute the probability of randomly selecting a two or diamond.
There's only ONE two of diamond in regular deck of cards, so...
P(2 of diamond) = 1 / 52 or 1,9%
From a survey taken several years ago, the starting salaries of individuals with an undergraduate degree from Business Schools are normally distributed with a mean of $40,500 and a standard deviation of $4,500.What is the probability that a randomly selected individual with an undergraduate business degree will get a starting salary of at least $36,000.00? (Round your answer to 4 decimal places.)
Answer: 0.8413
Step-by-step explanation:
Given: Mean : [tex]\mu=\$40,500[/tex]
Standard deviation : [tex]\sigma = \$4,500[/tex]
The formula to calculate z-score is given by :_
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= $36,000.00, we have
[tex]z=\dfrac{36000-40500}{4500}=-1[/tex]
The P-value = [tex]P(z\geq-1)=1-P(z<-1)=1-0.1586553=0.8413447\approx0.8413[/tex]
Hence, the probability that a randomly selected individual with an undergraduate business degree will get a starting salary of at least $36,000.00 = 0.8413
The probability of a randomly selected individual with an undergraduate business degree having a starting salary of at least $36,000, based on the given normal distribution with a mean of $40,500 and a standard deviation of $4,500, is approximately 0.8413 or 84.13%.
The question asks us to find the probability that a randomly selected individual with an undergraduate business degree will have a starting salary of at least $36,000.00, given that the mean starting salary is $40,500 with a standard deviation of $4,500. This problem can be solved using the properties of the normal distribution.
First, we calculate the z-score, which is the number of standard deviations away from the mean:
Z = (X - μ) / σ
Where X is the salary in question ($36,000), μ is the mean ($40,500), and σ is the standard deviation ($4,500). Plugging in the values:
Z = ($36,000 - $40,500) / $4,500 = -1
The next step is to look up this z-score in a standard normal distribution table or use a calculator with a standard normal distribution function to find the area to the right of this z-score. This area represents the probability we are looking for. Let's assume we found this area to be approximately 0.8413.
Therefore, the probability that a randomly selected individual with an undergraduate business degree will have a starting salary of at least $36,000 is about 0.8413 or 84.13%.
What is the average rate of change of the function over the interval x=0 to x=4?
f(x)=2x-1/3x+5
Enter your answer, as a fraction, in the box.
(To whoever is looking for the answer)
Step-by-step explanation:
The average rate of change of a function f(x) over an interval [a, b] is:
(f(b) − f(a)) / (b − a)
(f(4) − f(0)) / (4 − 0)
(7/17 − -1/5) / 4
(52/85) / 4
13/85
Answer:
yes thank you so much i was struggling so much with this tysm
Step-by-step explanation:
F(x)=3x+4. Determine the value of F (X) when X equals -1
ANSWER
The value of this function at x=-1 is 1
EXPLANATION
The given function is
[tex]f(x) = 3x + 4[/tex]
We want to find the value of this function at x=-1.
We substitute x=-1 into the function to obtain:
[tex]f( - 1) = 3( - 1)+ 4[/tex]
We multiply out to obtain:
[tex]f( - 1) = - 3+ 4[/tex]
[tex]f( - 1) = 1[/tex]
Therefore the value of this function at x=-1 is 1.
Answer: [tex]f(-1)=1[/tex]
Step-by-step explanation:
Given the linear function f(x):
[tex]f(x)=3x+4[/tex]
By definition. a relation is a function if each input value has only one output value. In this case you need to find the output value for the input value [tex]x=-1[/tex]. In order to do this, you need to substitute this value of the variable "x" into the linear function given.
Then:
When [tex]x=-1[/tex]:
[tex]f(-1)=3(-1)+4[/tex]
Remember the multiplication of signs:
[tex](+)(-)=-\\(+)(+)=+\\(-)(-)=+[/tex]
Then, the value of f(x) when [tex]x=-1[/tex] is:
[tex]f(-1)=-3+4[/tex]
[tex]f(-1)=1[/tex]
Twenty switches in an office computer network are to be connected so that each switch has a direct connection to exactly three other switches. How many connections will be necessary?
Answer:
30 connections
Step-by-step explanation:
20 switches with 3 connections each will have a total of 20×3 = 60 connections. That counts each connecting link twice, so only 30 connecting links are required.
Answer:
30 Connections!
Step-by-step explanation:
I did this on AoPs :)
What is the area of this composite figure?
Answer:
88 ft²
Step-by-step explanation:
Area of larger square
10 × 8 = 80
10 × 8 because 10 is the length and 8 because the 6 and 2 rectangle is missing so it wouldn't be 10 × 10
4 × 2 = 8
4 × 2 = 8 because we need to work out the area of the smaller rectangle
80 + 8 = 88
Fill in the blank with a digit such that the resulting number is divisible by 11.
(a) 362,375,__35
(b) 82,919,__21
(c) 57,13__,473
Answer: Hence, a) 0, b) 2, and c) 0
Step-by-step explanation:
As we know that If the difference of sum of odd places values and sum of even places value is divisible by 11, then the number is itself divisible by 11.
(a) 362,375,__35
Sum of odd places values : 3+2+7+5+x=17+x
Sum of even places values : 6+3+5+3=17
Difference between them is 17+x-17=x
So, x should be 0 to get divisible by 11 as 0 is divisible by 11.
(b) 82,919,__21
Sum of odd places values : 8+9+9+2=28
Sum of even places values : 2+1+x+1=4+x
Difference between them is 28-(4-x)=24-x
So, x should be 2 so, that it becomes 24-2=22 which is divisible by 11.
(c) 57,13__,473
Sum of odd places values : 5+1+x+7=13+x
Sum of even places values : 7+3+4+3=17
Difference between them is 17-(13+x)=4-x
So, x should be 4 so that it becomes 4-4=0 which is divisible by 11.
Hence, a) 0, b) 2, and c) 0
Harry operates a coffee shop. One of her customers wants to buy two kinds of beans. Arabian mocha and Columbian decaf. If she wants twice as much Arabian mocha as Columbian decaf how much of each can she buy for a total of $181.50?
The customer can buy ____ lbs of arabian mocha
And ______ lbs of Columbian decaf
Answer:
11 lbs of Arabian Mocha5.5 lbs of Columbian DecafStep-by-step explanation:
Since we want twice as much Mocha as Decaf, we can create a "bag" that contains 2 lbs of Mocha (at 11.50 each) and 1 lb of Decaf (at 10). The value of this "bag" is then 2×11.50 +10.00 = 33.00. For 181.50, we can buy ...
181.50/33.00 = 5.5
"bags". This amount is ...
11 lbs of Arabian Mocha and 5.5 lbs of Columbian Decaf
HELP PLEASEEE, I REALLY DO NOT UNDERSTAND THESE QUESTIONS. THANK YOU HELP IS VERY MUCH APPRECIATED!!!
5) The mean salary of 5 employees is $40300. The median is $38500. The lowest paid employee's salary is $32000. If the lowest paid employee gets a $3100 raise, then ...
a) What is the new mean?
New Mean = $
b) What is the new median?
New Median = $
Answer:
a) $40920
b) $38500
Step-by-step explanation:
Given:
5 employees,
Mean = $40300
Median = $38500
Min = $32000
If he lowest paid employee gets a $3100 raise, then his salary becomes
$32000+$3100=$35100
a) If the mean was $40300, then the sum of 5 salaries is
[tex]\$40300\cdot 5=\$201500[/tex]
After raising the lowest salary the sum becomes
[tex]\$201500+\$3100=\$204600[/tex]
and new mean is
[tex]\dfrac{\$204600}{5}=\$40920[/tex]
b) The lowest salary becomes $35100. It is still smaller than the median, so the new median is the same as the old one.
New median = $38500
Find the interest rate needed for an investment of $10,000 to grow to an amount of $11,000 in 4 years if interest is compounded quarterly. (Round your answer to the nearest hundredth of a percent.) %
Answer:
[tex]2.39\%[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=4\ years\\ P=\$10,000\\A=\$11,000\\ r=?\\n=4[/tex]
substitute in the formula above
[tex]11,000=10,000(1+\frac{r}{4})^{4*4}[/tex]
[tex]1.1=(1+\frac{r}{4})^{16}[/tex]
Elevated both sides to (1/16)
[tex]1.005975=(1+\frac{r}{4})[/tex]
[tex]0.005975=\frac{r}{4}[/tex]
[tex]r=0.005975*4=0.0239[/tex]
Convert to percent
[tex]0.0239*100=2.39\%[/tex]
The sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. After identifying the sample space for a couple having four children, find the probability of getting (one girl and three boys) in any order right parenthesis.
[tex]|\Omega|=2^4=16\\|A|=4\\\\P(A)=\dfrac{4}{16}=\dfrac{1}{4}[/tex]
Line m is parallel to line n. The measure of angle 4 is 109°. What is the
measure of angle 6?
A) 71°
B) 109°
C) 95°
D 101°
The answer is A, 71°.
180-109=71
Since m and n are parallel, angles 4 and 6 will add up to 180 degrees - just like angles 4 and 2. Remember that 180 degrees is a straight line: if angles 4 and 6 are put together, they will make a straight line.
The average age of doctors in a certain hospital is 45.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 8.0 years. If 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 46.9 years. Assume that the variable is normally distributed.
Answer: 0.7619
Step-by-step explanation:
Given : Mean : [tex]\mu=45.0 [/tex]
Standard deviation : [tex]\sigma =8.0[/tex]
Sample size : [tex]n=9[/tex]
We assume that the variable is normally distributed.
The value of z-score is given by :-
[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
a) For x= 46.9 years
[tex]z=\dfrac{46.9-45.0}{\dfrac{8}{\sqrt{9}}}=0.7125[/tex]
The p-value : [tex]P(z<0.7125)=0.7619224\approx0.7619[/tex]
Hence, the probability that the average age of those doctors is less than 46.9 years =0.7619
The question relates to probability in a normally distributed population. We calculated the standard error and z-score, then used the z-table to find that there is approximately a 76.11% chance that the average age of 9 randomly chosen doctors from this hospital will be less than 46.9 years.
Explanation:The subject of this question pertains to Probability and Statistics, specifically the application of the Normal Distribution in the context of calculating the probability of a particular outcome in a real-world scenario. We'll apply the rule for the Central Limit Theorem (CLT) since the sample size is reasonably large (n = 9).
The first step is to calculate the standard error (SE). The SE of the mean can be calculated by dividing the standard deviation by the square root of the number of doctors:
SE = 8.0/sqrt(9) = 8.0/3 = 2.67.
Next, you would calculate the z-score. The z-score of 46.9 is obtained by subtracting the population mean from 46.9 and then dividing by the SE:
Z = (46.9 - 45.0)/2.67 = 0.71.
To determine the probability that the average age is less than 46.9 years, you will want to look up the z-score of 0.71 in a z-table, which gives a value of 0.7611, or 76.11%. So there is approximately a 76.11% chance that the mean age of the 9 doctors chosen will be less than 46.9 years old.
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y is 4 less than the product of 5 and x
y is (replace "is" with an equal sign) 4 less (replace with subtraction sign) than the product (multiply 5 and x) of 5 and x
y = 5x - 4
The reason the answer is like this ^^^ instead of y = 4 - 5x is because for this to be true it would have to say y is 5x less then 4
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
y=5x-4
Step-by-step explanation:
Question about: ⇒ algebraic expression
Y: ⇒ Symbol into letters
is: ⇒ equal sign
less than: ⇒ <
product: ⇒ multiply
y=5x-4 is the correct answer.
I hope this helps you, and have a wonderful day!
Help Algebra!!
10. To solve a system of equations using the matrix method, use elementary row operations to transform the augmented matrix into one with _______. Then, proceed back to substitute.
A. zeros in its final column
B. an inverse
C. zeros below the diagonal
D. Gaussian elimination
Answer:
C. zeros below the diagonal
Step-by-step explanation:
Upper echelon form (zeros below the diagonal) corresponds to a system of equations that has one equation in one variable, one equation in two variables, and additional equations in additional variables adding one variable at a time.
The single equation in a single variable is easily solved, and that result can be substituted into the equation with two variables (one of which is the one just found) to find one more variable's value. This back-substitution proceeds until all variable values have been found.
The process of producing such a matrix is called Gaussian Elimination.
__
The back-substitution process effectively makes the matrix be an identity matrix (diagonal = ones; zeros elsewhere) and the added column be the solution to the system of equations.
To solve a system of equations using the matrix method, you transform the augmented matrix to have zeros below the diagonal through Gaussian elimination. Then, you substitute back into the equations to find the solution.
Explanation:To solve a system of equations using the matrix method, you use elementary row operations to transform the augmented matrix into one with zeros below the diagonal. This is achieved through a method called Gaussian elimination. The goal is to reduce the matrix to its row-echelon form, which leaves zeros below the diagonal. After this reduction, you can then proceed to substitute back into the equations to find the solution.
For example, let's take the system of equations:
x+2y=7
3x-4y=11
This can be represented as an augmented matrix:
[1 2 | 7]
[3 -4 | 11]
Using Gaussian elimination, we can eliminate the '3' below the diagonal by subtracting 3x the first row from the second, getting you:
[1 2 | 7]
[0 -10 | -10]
By substituting, we then find the solutions for the system of equations.
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Which number is rational?
Answer:
5.(3)
Step-by-step explanation:
5.(3)=16/3
Answer:
d
Step-by-step explanation:
[tex]\text{I was eating cookies and had some thoughts. If I wanted to cut out exactly }[/tex][tex] \frac{1}{3} [/tex]of the cookie to share with someone, how far from one side would I have to make a straight cut to get that exact amount? How far would I have to cut if I wanted to cut off[tex] \frac{1}{n} [/tex][tex]\text{ of the cookie?}[/tex]
[tex]\text{Basically, the question is, find the value of }a\text{ given only n, and r}[/tex]
[tex]\text{One way of finding this, is by finding the area of the shaded reigon, Q in terms of}[/tex]
[tex]\text{r, a, and b, and equating it to the area of the fraction of the cookie then solving for a.}[/tex]
[tex]\text{In math, this means solving } \frac{1}{n}\pi r^2=Q \text{ for }f(r,n)=a.[/tex]
[tex]\text{From the diagram, we can see that }r=a+b[/tex]
[tex]\text{Eventually, by 2 different means, I found 2 equations that, if solved, would give the}[/tex][tex]\text{ relationship between r, n, and a.}[/tex][tex]\text{They are as follows:}[/tex]
[tex]\text{1. }\frac{1}{n}\pi r=r\theta-bsin(\theta) \text{ where }\theta=cos^{-1}(\frac{b}{r})[/tex]
[tex]\text{2. }\frac{1}{n}\pi=\theta-sin(2\theta)\text{ where }\theta=cos^{-1}(\frac{b}{r})[/tex]
[tex]\text{These 2 equations are equivalent, but annoying to solve.}[/tex]
[tex]\text{To claim these points, please solve for a in terms of r and n, showing all work.}[/tex]
[tex]\text{I would like an analytic solution if possible.}[\tex]
[tex]\text{All incorrect, spam, or no-work solutions will be reported.}[/tex]
In the attachement, there is what I came up with so far. I think that finding 'a' is non-trivial, if possible at all.
[tex]A_c[/tex] - the area of a circle
[tex]A_{cs}[/tex] - the area of a circular segment
Answer:
- the area of a circle
- the area of a circular segment
Consider the following sets of sample data: A: $29,400, $30,900, $21,000, $33,200, $21,300, $24,600, $29,500, $22,500, $35,200, $20,800, $39,800, $22,300, $35,700, $25,100 B: 4.53, 4.17, 4.48, 3.73, 3.83, 2.91, 2.99, 4.67, 4.21, 4.68, 3.38 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
The coefficient of variation (CV) is calculated as the standard deviation divided by the mean, expressed as a percentage. Calculate the mean and standard deviation for each set of data, then use these to calculate the CV. Round to one decimal place.
Explanation:The coefficient of variation (CV) is a measure of relative variability. It's calculated as the ratio of the standard deviation to the mean, and it's often expressed as a percentage. We first need to calculate the mean and standard deviation for both sets of data, A and B.
Let's take Set A as an example: Add all the values together and divide by the count (the total number of values) to get the mean. Next, subtract each value by the mean and squared it, then sum all those squared differences. Divide that by the count minus one to get the variance. The standard deviation is the square root of the variance. Finally, the CV is (standard deviation / mean) x 100.
Repeat these steps for Set B.
Remember to always round to one decimal place as requested in the question.
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Solve the following system of equations, 3x +5y+2-0
Answer:
3x+5y+2
Step-by-step explanation:
remove the 0