[tex]5y^2+17y-84 / y^3+12y^2+36y[/tex] partial fraction decomposition is [tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]
What is partial fraction decomposition?Partially decomposing a rational fraction, also known as partially expanding it, in algebra includes expressing the fraction as the sum of a polynomial and one or more fractions with a lower common denominator.
One technique for breaking down rational expressions into smaller partial fractions is partial fraction decomposition. This method serves the integration process better.
In order to integrate a rational function, it is condensed to a valid rational function. The integrand can be expressed as the sum of more elementary rational functions through the use of partial fraction decomposition.
Therefore, starting with the simplified solution and proceeding backwards, the final expression is “decomposed” into the original polynomial fractions.
[tex]= -5y²+ 17y-84 / y³+12y²+36y[/tex]
[tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]
Learn more about fraction decomposition here:
https://brainly.com/question/30402740
#SPJ1
What is the value of In e4
Answer:
Pie heysgeusuwhueywgyssyywyw
HELP THANK YOU SO MUCH
Answer:
x = 3
Step-by-step explanation:
Since ∠CAT = ∠DOG, ∠CAT = ∠DGO
Therefore AC = DO
8x - 6 = 3x + 9
8x - 3x = 9 + 6
5x = 15
x = 15/5
x = 3
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Marta's family plans to sell their kitchen table and buy a new one. Marta originally wrote down the length of their old table as 1,602.5 centimeters. She realized she made a mistake and that the table has an actual length of 162.5 centimeters.
Which of the statements correctly compares the digits in the original measurement and the actual measurement?
A. The value of the digit 5 in the original measurement is 10 times the value of the digit 5 in the actual measurement.
B. Removing the digit 0 in the original measurement did not change the value of any digits in the actual measurement.
C. The value of the digit 1 in the actual measurement is 110 the value of the digit 1 in the original measurement.
D. The digit 6 has the same value in both the original measurement and the actual measurement.
The correct option is the value of the digit 1 in the actual measurement is 110 the value of the digit 1 in the original measurement. (option C)
What are the value of the digits in the measurement?Here is the place value of each of the digits in the wrong table length :
1 = thousand
6 = hundred
0 = tens
2 = units
5 = tenth
Here is the place value of each of the digits in the actual table length :
1 = hundred
6 = tens
2 = units
5 = tenth
5 has the same value in both the wrong length and the right length.
The value of 6 in the actual measurement is ten times that of the wrong measurement .
To learn more about measurement, please check: https://brainly.com/question/29405166
#SPJ1
Find the value of zα.
Z0.47
The critical probability of a critical value of α = 0.47 is [tex]Z_{0.47}[/tex] = 0.77.
What is the critical value?A crucial value is the test statistic's value that establishes a confidence interval's upper and lower boundaries, or the level of statistical significance for a given test.
Given:
The critical value, α = 0.47
Calculate the critical probability by the formula given below,
[tex]Z_\alpha = 1 - ( \alpha / 2)[/tex]
[tex]Z_{0.47}[/tex] = 1 - (0.47 / 2)
[tex]Z_{0.47}[/tex] = 1 - 0.235
[tex]Z_{0.47}[/tex] = 0.765 = 0.77
Therefore, the critical probability of a critical value of α = 0.47 is [tex]Z_{0.47}[/tex] = 0.77.
To know more about critical value:
https://brainly.com/question/14508634
#SPJ1
Music Company A charges a $ 15 membership fee and $ 0.75 each to download a song. Music Company B charges $ 0.90 each to
download a song with no membership fee.
a. For what number of songs will both companies charge the same amount? Justify your answer using mathematics.
____songs
You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of
money? Justify your answer using mathematics.
(i) At a total of 100 Songs the Charges for Company A and Company B will be Equal.
(ii) I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
What is Linear Equation in One Variable?
A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.
Solution:
Let, Songs Downloaded be x
Total Charges of Company A = 15 + 0.75*x
Total Charges of Company B = 0.9*x
(i) Total Charges by Company A = Total Charges by Company B
15 + 0.75*x = 0.9*x
15 = 0.15*x
x = 100 songs
(ii) Charges by Company A to Download 150 Songs = 15 + 0.75 * 150
= 15 + 112.5 = $127.5
Charges by Company B to Download 150 Somgs = 0.9 * 150 = $135
I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
To learn more about Linear Equation in One Varibale from the given link
brainly.com/question/85774
#SPJ4
There are 4 classrooms for fifth grade and 4 classrooms for sixth grade at a school. Each classroom has 20 students. A teacher is planning a field trip for some fifth and sixth grade students at this school. The teachers knows the following information:
90% of fifth and sixth grade students have permission to go on the trip.
4 teachers are going on the trip.
The school requires 1 parent volunteer for every 8 students going on the trip.
Part A
How many parent volunteers are needed to go on the trip? Show your work or explain your answer.
Enter your answer and your work or explanation in the space provided.
Answer:Żeby obliczyć ilu rodziców wolontariuszy potrzeba, najpierw trzeba obliczyć ile uczniów będzie brało udział w wycieczce. W klasie piątej jest 20 uczniów, z czego 90% ma pozwolenie na wyjazd, czyli 20 x 0,9 = 18 uczniów z piątej klasy pojedzie na wycieczkę. W klasie szóstej jest też 20 uczniów, z czego 90% ma pozwolenie na wyjazd, czyli 20 x 0,9 = 18 uczniów z szóstej klasy pojedzie na wycieczkę. Razem będzie 18 + 18 = 36 uczniów.
Szkoła wymaga 1 rodzica wolontariusza na każdych 8 uczniów, więc na 36 uczniów potrzeba 36/8 = <<36/8=4.5>>4,5 rodziców wolontariuszy. Ponieważ rodzice wolontariuszy trzeba wybrać całymi osobami, to potrzeba ich 5.
Odpowiedź: Potrzeba 5 rodziców wolontariuszy.
Step-by-step explanation:
A university has 25,000 students, of whom 10,000 are older than 25. The registrar draws a simple random sample of 400 students. a) Find the expected value and SE for the number of students in the sample who are older than 25. b) Find the expected value and SE for the percentage of students in the sample who are older than 25. c) The percentage of students in the sample who are older than 25 will be around _____, give or take _____ or so.
The expected value is 160 and SE for the number of students in the sample is 9.78
a)Given: students of which 25000 of which 10000 are older than 25 and 25000-10000=15000 are not older than 25.
we represent 400 students by drawing 400 tickets from a box that contains 15000 tickets labeled 0 and 10000 tickets labeled 1
Expected value and standard deviation of a box:
First, we determine the expected value of the box, which is the sum of all values on the tickets by the number of tickets.
[tex]expected value box=\frac{15000*0+10000*1}{25000}\\\\ =\frac{10000}{25000} =\frac{2}{5}[/tex]
expected value box=0.4
let us next determine the standard deviation using the shortcut formula:
SD=(big number-small number)*√fraction with small number*fraction with a small number.
[tex]SD=(1-0)*\sqrt{\frac{10000}{25000} *\frac{15000}{25000} \\\\SD=1*\sqrt{\frac{2}{5} *\frac{3}{5} } \\SD=1*\sqrt{\frac{6}{25} } =\frac{\sqrt{6} }{5}[/tex]
SD=0.4899.
Expected value sum=Number of draws*expected value box
=400*0.4
Expected value sum=160
standard error of the sum is the product of the square root of the number of draws and the standard deviation of the box.
SE Sum=√number of draws*SD box
SE Sum=√400*0.4899
=20*0.4899
SE Sum=9.78
b)EXpected value and standard error:
The expected value of the percentage is the expected value of the sum divided by the number of draws.
Expected value percentage=Expected value sum/Number of draws*100%
160/400*100
=0.4*100%
Expected value percentage=400%
The standard error of the percentage is the standard error for the sum divided by the sample size:
SE%=SE for number/Number of draws*100%
=9.798/400*100%
=0.0245*100%
SE% =2.45%
To learn more about Expected value:
https://brainly.com/question/24316739
#SPJ4
What is the variable in this expression?
4b + 2b + 1⁄4
Answer:
b
Step-by-step explanation:
a variable is an unknown number normally represented by a letter and in this case the variable is b
hopes this helps please mark brainliest
Find the missing number/s so that the equation has One solution.
Select all that apply.
__x + 3 = –4x + 17
a
2
b
5
c
7
d
-4
Answer: Choice A, Choice B, Choice C
In other words, it's nearly everything but choice D.
====================================================
Explanation:
Let's say we select "2" as the thing to fill the blank.
2x+3 = -4x+17
2x+4x = 17-3
6x = 14
x = 14/6
x = 7/3
We get one solution in this case.
The same applies for the values 5 and 7. I'll let you do those steps.
In contrast, if we filled the blank with -4, then,
-4x+3 = -4x+17
-4x+4x = 17-3
0x = 14
0 = 14
We get a contradiction which leads to "no solutions".
Visually, the equations y = -4x+3 and y = -4x+17 are parallel lines that never intersect. We need them to intersect if we want a solution. Recall that parallel lines have equal slopes but different y-intercepts. Both sides have a slope of -4 in this case.
Therefore, the quick rule of thumb is this: if the slopes are not equal, then the linear equation has exactly one solution.
Determine whether y varies directly with x If so, find the constant of variation and write the function rule.
Does y vary directly with x?
No
Yes
What is the constant of variation? Select the correct choice and fill in any answer boxes in your choice below.
A. k=__ (Simplify your answer. Type an integer or a fraction.)
B. There is no constant of variation.
What is the function rule? Select the correct choice and fill in any answer boxes in your choice below.
A. y=_____
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
B. There is no function rule.
The value of y varies directly with x, and the constant of variation is 3, and function rule y = 3x.
What is Direct Variation?When one value is dependent on another i.e if one value increases with respect to another or if one value decreases with respect to another then we can say that the two quantities are in direct variation.
In simple words, It is the relationship between two variables where one of the variables is a constant multiple of the other.
When two values a and b are varies directly then the relation between them can be shown as given below
=> a ∝ b
=> a = kb here 'k' constant of variation
Here we have
x values 57 63 66
y values 19 21 22
Let's assume that y varies directly with x
=> y ∝ x
=> y = kx ---- (1)
Where k is the proportionality constant
From (1)
We can write k = x/y
From the above calculations, if y varies directly with x then x/y must be a constant.
Now check whether the given value can give a constant
At x = 57 and y = 19
[tex]= > \frac{x}{y} = \frac{57}{19} = 3[/tex]
At x = 63 and y = 21
[tex]= > \frac{x}{y} = \frac{63}{21} = 3[/tex]
At x = 66 and y = 22
[tex]= > \frac{x}{y} = \frac{66}{22} = 3[/tex]
From the above calculation,
For given x and y values, x/y is always constant
Therefore,
It is true that y varies directly with x, and the constant of variation is 3
Here the function rule will be y = x × constant of variation
=> y = 3x
Therefore,
The value of y varies directly with x, and the constant of variation is 3, and function rule y = 3x
Learn more about Direct Variation at
https://brainly.com/question/15785278
#SPJ4
For the function f(x) = 5(x - 5)7, find f-¹(x).
Answer:
Step-by-step explanation:
What is the slope of 0,0 and 1/3, 7/3
To find the slope of a line that passes through two points, you can use the formula:
slope = (y2 - y1)/(x2 - x1)
In this case, the two points are (0,0) and (1/3, 7/3). Substituting these values into the formula, we get:
slope = (7/3 - 0)/(1/3 - 0)
slope = 7/3
Therefore, the slope of the line that passes through (0,0) and (1/3, 7/3) is 7/3.
The first four numbers in a pattern are 4,3.6,3.2 and 2.8. What is the next three next numbers in the pattern
Answer:
2.4 and 2
Step-by-step explanation:
x-0.4
Answer:
2.4, 2, 1.6
Explanation:
The sequence is counting down by 0.4.
One requirement can be met while the other fails. Show this by finding
(a) A set of vectors in R2 for which x+y stays in the set but 1/2x may be outside.
(b) A set of vectors in R2 (other than two quarter-planes) for which every cx stays in the set but x+y may be outside.
Forever c x stays in the set but x+y may be out side the set.
What is set?
A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.
a consider the set of vectors in [tex]$\mathbb{R}^2$[/tex]
[tex]A=\left\{\left(x_1, x_2\right) \in \mathbb{R}^2 \mid x_2 \geqslant 2\right\} .$$[/tex]
where[tex]$x=\left(x_1, x_2\right)$[/tex]
Then for any [tex]$x=\left(x_1, x_2\right), y=\left(y_1, y_2\right) \in A$[/tex]
ere that[tex]$x+y=\left(x_1+y_1, x_2+y_2\right) \in A\left(\right.$ Since $x_2+y_2 \geqslant 2+2$[/tex]
But take [tex](4,2) \in A$.[/tex]
Then [tex]\frac{1}{2}(4,2)=(2,1) \notin A$.[/tex]
ce. [tex]$\frac{1}{2}(4,2)$[/tex] belongs outside the set
i.. I some vectors in A such that[tex]\frac{1}{2} x \notin A$[/tex].
b Consider the set of vectors in [tex]$\mathbb{R}^2$[/tex]
[tex]A=\left\{\left(x_1, x_2\right) \in \mathbb{R}^2 \mid \begin{array}{ll}\frac{1}{2} x_1 \leq x_2 \leq \frac{3}{2} x_1 & \text { if } x_1 \geqslant 0 \\\frac{3}{2} x_1 \leq x_2 \leq \frac{1}{2} x_1 & \text { if } x_1 < 0\end{array}\right\}$$[/tex]
The geometrical representation of this set is
see that for any scalar [tex]$c, \quad c x=e\left(x_1, x_2\right) \in A$[/tex]. But if we take [tex](3,2) *(-2,3-3) \in A$ but $(3,2)+(-2,-3)=(1,-1) \& A$[/tex].
Thus forever c x stays in the set but x+y may be out side the set.
To learn more about set visit:https://brainly.com/question/8053622
#SPJ4
State whether each linear relationship is also a proportional correct box. Explain why or why not. If it does, writ form y=p x
Proportional relationship?
YES___
No___
Why?
y = p x is Proportional relationship.
What is proportional relationship?
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".
The answer depends on the equation given.
If the equation is in the form y=px, where p is a constant, then it is a proportional relationship. If the equation is in the form y=mx+b, where m and b are constants, then it is not a proportional relationship.To know more about proportional relationship check the given link
brainly.com/question/28777033
#SPJ4
Billing charges for Microsoft 365 Commercial licensing. When a customer purchases a subscription and changes the amount during the subscription period, a full refund is credited then prorated for what was used. For example, if a customer purchased 2 subscriptions for the month of June at $15 each, the total charge for the month would be $30. If they decide to return one subscription 5 days later, the full $30 would be credited then a prorated charge for what was used would be applied. Credit $30 Charge $15 Charge $0.5 * 5 = $2.50 $15 / 30 = $0.5 p/day Total Charge $17.50 Total Credit $12.50 If a customer purchases 10 Microsoft 365 Business Premium licenses at $22 each per month, for a full year then 6 months later decides they only need 5 licenses for the remainder of the year, what would be the total charge and credit for the year?
The customer who purchases 10 Microsoft 365 Business Premium licenses at $22 each per month, for a full year, then 6 months later decides they only need 5 licenses for the remainder of the year, would pay a total charge of $1,980 with a credit of $660 for the year.
How are the total charge and credit computed?The total charge the customer will pay is based on the difference between the total charge for the year and the prorated charge of credit for non-usage.
The charge per month for Microsoft 365 = $22
The charge per month for 10 Microsoft 365 = $220 ($22 x 10)
The charge for 1 year for one Microsoft 365 = $264 (22 x 12)
The charge for 6 months for 10 Microsoft 365 = $1,320 ($220 x 6)
The charge for 12 months for 10 Microsoft 365 = $2,640 (220 x 12)
The prorated charge for 6 months for 5 Microsoft 365 returned = $660 ($2,640 x 5/10 x 6/12)
The initial total charge for the year = $2,640
The total credit for the year = $660
The total charge for the year = $1,980 ($2,640 - $660)
Thus, the customer will pay $1,980 after receiving a prorated credit for 5 returned licenses worth $660.
Learn more about the total charge and proration at https://brainly.com/question/16028802
#SPJ1
Select all the expressions which are equivalent to 910x − 2.
A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is known as an algebraic expression.
What is an Algebraic Expression?A mathematical expression known as an algebraic expression is one that includes variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division.In most cases, something is said to be equivalent if two of them are the same. Similar to this, analogous expressions in mathematics are those that, despite their differences in appearance, have the same meaning. The two expressions, however, produce the identical outcome when the values are inserted into them.Example910x − 2
simplify | 910 x - 2
2 (455 x - 1).
To Learn more About Algebraic Expression, refer To:
https://brainly.com/question/4344214
#SPJ1
The functions S(t) = 1.0841t + 17.392 models the amount of money, S, in billions of dollars, the United States government spent on science, space, and technology for the time period 1999-2009, where t is the number of years since 1999.
a. Write the constraints for the variable t using set-builder notation.
b. Determine the value of S(7)
c. Interpret the value of S(7) in context
d. Name the key feature that is found when solving S(t) = 0. Then, label the key feature on the graph of S(t) = 1.084t + 17.392.
e. determine if the value for S(t) = 0 is reasonable for the context. Explain why or why not.
Hello,
I hope you and your family are doing well!
a. The variable t represents the number of years since 1999, so the constraints for t can be written as t ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
b. To find the value of S(7), we substitute t = 7 into the function: S(7) = 1.084(7) + 17.392 = 22.688.
c. In context, the value of S(7) represents the amount of money, in billions of dollars, that the US government spent on science, space, and technology 7 years after 1999.
d. The key feature that is found when solving S(t) = 0 is the y-intercept of the graph of S(t). The y-intercept is the point where the graph crosses the y-axis.
e. The value for S(t) = 0 is not reasonable for the context because it represents the amount of money spent on science, space, and technology in 1999, which would be a negative number of years after 1999.
-----
Please consider giving this 5 stars if you find it helpful.
Happy Holidays!
help meeeeeeeeeee pleaseee
(a) The population of the state was 18.5 million in 2000. (b) The population of the state reaches 26.6 million by 2002
What do you mean by Population?A population is a distinct collection of people, whether that group consists of a nation or a population that shares a particular trait. A population is the people from which a statistical sample is taken in statistics. As a result, a population can be defined as any group of people with something in common.
(a) The right response is 18.5
Given that
t = 0,
A = 18.5
(b) 2002.
Using the formula
18.5e 0.173 x t
Given,
A= 26.6
Then,
A = 18.5 x
[tex]e^{(0.1708t)} 26.6 = 18.5 x[/tex]
[tex]\frac{26.6}{18.5}= e^{(0.1708t)}[/tex]
[tex]1.437838 = e^{(0.1708t)}[/tex]
[tex]Ln \frac{1.437838}{0.1708}[/tex]
About
t = 2.126116
t =2
As a result, 2 represents the closest year when rounding down.
To learn more about the population visit here: https://brainly.com/question/25787521
#SPJ1
;oowgsvdsgg bss tr tbs
is that even a question bro?
24) Evaluate the expression with its given values.
x/4 + 3y; x = 12, y = 2
Answer:
9
Step-by-step explanation:
[tex]\frac{12}{4}+3(2) \\ \\ =3+6 \\ \\ =9[/tex]
Answer:
Answer is 9.
Step-by-step explanation:
If x is 12, then do 12 divided by 4, and you get 3. If y is 2, then di 3 times 2, which is 6. 3 plus 6 is 9.
What is the area of ΔOPQ if
a=18 b=17.5 and c=13.5
Answer:
Problem
Solution
Solve for the missing components of the triangle.
A
=
69.62591065
B
=
65.69947977
C
=
44.67460956
a
=
18
b
=
17.5
Please help a lot of points!! Will put bainliest answer!
Answer:
I haven't got a real clue
Step-by-step explanation:
I did some learning about it, I may be wrong(most likely)
but I think it might be SAS.
The shape can be proven congruent.
if you can find an angle which I think is H and K then most likely SAS. If this is a test and is very important then don't listen to this I am most likely wrong
what percentage of 64 is 16
Answer:
25%
Step-by-step explanation:
which of the following statements is correct? one-way anova is the same as correlation, but different from two-way anova dependent t-test is the same as one-way anova, but different from independent t-testone-way anova is the same as one sample z-test, but different from paired samples t-test paired samples t-test is the same as dependent t-test, but different from one sample z-test
Option D is the correct answer. Paired samples t-test is the same as the dependent t-test, but different from one sample z-test.
The dependent t-test also called the paired t-test or paired-samples t-test compares which means the two related groups to determine whether there is a statistically significant difference between these means.
The T-test is defined as a univariate hypothesis test that is based on a t-statistic, On the other side, Z-test is also a univariate test that is based on a standard normal distribution.
There is a small comparison between the t-test and z-test:
T-test refers to a type of parametric test that is applied to identify, how the means of two sets of data differ from one another when variance is not given. Z-test implies a hypothesis test that ascertains if the means of two datasets are different from each other when variance is given.The T-test is Based on Student-t distribution whereas z-Test depends on Normal distributionThe Population variance of the t-test is Unknown and for the z-test, it is known, and the Sample Size is Small for the t-test for the z-test size is Large.To know more about T-test and Z-test:
https://brainly.com/question/14018998
#SPJ4
Problem Situation: Ike has $126 in his bank account. He gets $20 for his birthday.
He also has a part-time job that pays $8 per hour. How many hours will he need to
work to have $250 in his bank account?
.
Answer: 13h
Step-by-step explanation:
126 + 20 = 146
250 - 146 = 104
104 : 8 = 13
He will need 13h
Answer:
13.5
126 plus 20 is $146
250 minus 146 is 108
108 divided by 8 is 13.5
0.2x + 2 = 0.2(4 - x)what is the solution of the equation?
show your work!!
Answer:
x = -3
Step-by-step explanation:
0.2x + 2 = 0.2(4 - x)
0.2x + 2 = 0.8 - 0.2x
0.4x = -1.2
x = -1.2/0.4
x = -3
i need helpp.....................
8. What value of g makes the equation true? g + 4.3 = 7.2 A) 3.5 B) 2.9 C) 11.5 D) 10.1