Division yields
[tex]\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}[/tex]
Now for partial fractions: you're looking for constants a, b, and c such that
[tex]\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}[/tex]
[tex]\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a[/tex]
which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then
[tex]\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}[/tex]
Now, in the integral we get
[tex]\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx[/tex]
The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get
[tex]\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}[/tex]
Work out m and c for the line:
y – 37 = 5
Answer:
first thing is y - 35 = 5
then y = 35 + 5 because when = come here - will be + and
then we should do+ y=40 answer
Carin opened a money market account with a deposit of $3,000. This account earns 2% simple interest annually. How many years will it take for her $3,000 deposit to earn $420 in interest, assuming she does not withdraw any of the money?
Answer: 7 years
2% = 0.02
3000·0.02=60.00
1 year simple interest = $60.00
420/60=7
7 years
I need help with this problem.
Answer:
-4
Step-by-step explanation:
2t=-1-7
t=-8/2
t=-4
i am not sure also
Celia was a contestant on Jeopardy. At the
beginning of the round her score was -40.
Celia's score at the end of the round was -
35. How many points did Celia score (or
lose) during the round?
Answer:
75
Step-by-step explanation:
She is in the negatives right now so add 40 to get Celicia points equal to 0. Then add an extra 35 points (which is what she ended with). Overall, she gained 75 points to end with 35.
Peter is 8 years younger than Alex. In 9 years time, the sum of their ages will be 76 . How old is Alex now?
Answer:
Peter is a-8 in 9 years, (a-8)+ 9+ a+ 9= 76
Answer:
P = 25
A = 33
Step-by-step explanation:
P + 8 = A
P + 9 + A + 9 = 76
P + A = 58
~~~~~~~~~~~~~~
P = 58 - A
P = 58 - P - 8
2 P = 50
P = 25
A = 33
Simplify this algebraic expression y-3 over 3+12
Answer:
(Y-3)/(3+12)
(Y-3)/(15)
Y-1/5
so the answer is
(Y-1)
Answer:
[tex]y - 3 \: over \: 3 + 12 \\ y - 3.3 + 12 \\ y - 3.3 + 12 = y + 8.7 \\ y - 33 + 12 \\ y + 8.7[/tex]
calculate the value of X in the diagram
Answer:
[tex]EA = \frac{21 \times 15}{7} = 45 \\ { \tt{ \frac{21}{7} = \frac{x}{45} }} \\ x = 135[/tex]
My daughter had a quiz today and the 3 questions did not make sense to me. Can anyone decifer how you would solve for the variable on these? I am stumped!!
1) In 10 years, Sara will be 81 older than she is now. How old is Sara now?
2) In 8 years, Sara will be 49 years older than she is now. How old is Sara now?
3) In 11 years, Bob will be 100 years than he is now. How old is Bob now?
Answer:
1 71years
Step-by-step explanation:
x+10=81
x=71
2. x+8=49
x=41
3. x+11=100
x=99
9. What is the value of x if the quadrilateral is a rhombus? 15 5x 4x+3
Algebraically show that each of the given combinations are equivalent to the given functions.
h(x) + j(x) is equivalent to k(x) given:
h(x) = 2x – 3;j(x) = - 4x + 6; k(x) = – 2x + 3
h(x) + j(2) =
Is h(x) + j(x) equivalent to k(x)? yes
Answer:
YES, they are equal
Step-by-step explanation:
Given the expressions
h(x) = 2x – 3;j(x) = - 4x + 6; k(x) = – 2x + 3
h(x) + j(x) = 2x – 3 + (-4x + 6)
h(x) + j(x) = 2x - 3 -4x + 6
h(x) + j(x) = 2x - 4x -3 + 6
h(x) + j(x) = -2x + 3 = k(x)
This shows that h(x) + j(x) = k(x)
The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 8 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 8 golfers play a round of golf on his friend's course and records their scores again. The average difference in the scores (treated as the scores on his course - the scores on his friend's course) is 9.582 and the standard deviation of the differences is 15.9274. Calculate a 90% confidence interval to estimate the average difference in scores between the two courses.1) (13.73,-0.65).2) (-10.359,-4.021).3) (-9.259,-5.121).4) (-13.745,-0.635).5) (13.745, -0.635).
Answer:
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
Step-by-step explanation:
We have the standard deviation for the differences, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 8 - 1 = 7
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8946
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.8946\frac{15.9274}{\sqrt{8}} = 10.67[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.582 - 10.67 = -1.088
The upper end of the interval is the sample mean added to M. So it is 9.582 + 10.67 = 20.252
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
Write an algebraic expression for the situation. 28 divided by a number n An algebraic expression for the situation is
Answer:
[tex]\frac{28}{n}[/tex]
Step-by-step explanation:
A basketball player has a 0.498 probability of making a three-point shot. What is the probability that it takes the player 4 tries to make a three-point shot? (Round your answer to three decimals if necessary.)
Answer:
$1
Step-by-step explanation:
because of the dollar it makes sense to be a dollar
7. Calculate the Perimeter AND Area of triangle
ABC
B
24 m
40 m
14 m
А
с
20 m
37 m
9514 1404 393
Answer:
perimeter: 121 marea: 399 m²Step-by-step explanation:
The perimeter is the sum of the side lengths. Here, the bottom side is broken into two parts, so that side length is the sum of the parts. The area is given by the formula for the area of a triangle.
perimeter = 24 m +40 m + 37 m + 20 m = 121 m
area = 1/2bh = 1/2(20 m +37 m)(14 m) = 399 m²
the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths
Answer:length 30, width 18
Step-by-step explanation:
60% +100%=160%
160% × 2 = 320 %
96/320 = 0.3 ×100 =30 ( length)
30 × 0.6 =18 (width)
Check: (18 + 30) 2 = 96
If you multiply 0.47 × 3.2, then what is the answer?
Answer:
1.504
Step-by-step explanation:
0.47×100 = 47
3.2×100 = 320
47×320 = 15040
15040÷10000 = 1.504
Pls help! Answer the question
===============================================================
Explanation:
The given stem and leaf plot leads to this data set
68,68,69,69
71,72,77,77,78,78
80,81
I broke it up to have each tens digit get its own row. That way it's bit more readable.
Unfortunately, the term "average" in math is very vague. It could mean one of the following
meanmedianmodeTo get the mean (specifically the arithmetic mean), we will add up the values and then divide by n = 12 because there are 12 values in the list above. Adding said values gets us
68+68+69+69+71+72+77+77+78+78+80+81 = 888
Dividing that over 12 then leads to 888/12 = 74
The arithmetic mean is 74.
-------------
To get the median, we would first sort the data set. Though that is already done for us. From here, we locate the middle-most item.
Since there are n = 12 items here, the middle item is between slot n/2 = 12/2 = 6 and slot 7
The values in slots 6 and 7 are 72 and 77 respectively. The midpoint of those values is (72+77)/2 = 149/2 = 74.5
The median is 74.5
-------------
The mode is possibly the quickest measure of center or average we can compute. We simply look at the value that shows up the most. In this case, the following values show up twice (which is the most frequent of all the values)
68697778They are all tied for the title of "mode". It's possible to have more than one mode, so we say the mode is the set {68,69,77,78}.
Due to the nature of multiple modes, the mode is often not a good measure of center (but it's still a possibility; especially for categorical data).
In this case, I think the mean or median is a better measure of center.
Since there aren't any outliers, the mean is the best measure of center in this case. Luckily, the mean and median (74 and 74.5 respectively) are fairly close to one another.
-------------
To summarize everything, the term "average" is too vague and it could refer to the mean, median or mode. In this problem, the mean is possibly the best measure of center since there aren't any outliers and the mode isn't one single value.
We found the following:
mean = 74median = 74.5mode = {68,69,77,78}It's very likely your teacher is wanting the mean.
The triangles are similar by:
the ASA similarity theorem.
the SSS similarity theorem.
the AAS similarity theorem.
the AA similarity postulate.
the SAS similarity theorem.
Answer:
E. by the SAS similarity theorem.
Step-by-step explanation:
Included angle x° in ∆ ABC ≅ included angle x° in ∆EDC (vertical angles are equal)
DC/BC = 240/150 = 1.6
EC/AC = 320/200 = 1.6
This implies that the ratio of two corresponding sides of both triangles are the same.
Two triangles are considered similar to each other by the SAS similarity theorem of they have a corresponding included angle that is equal and two corresponding sides that are congruent to each other. Therefore, both triangles are similar by the SAS similarity theorem.
.What is the value of x if 2(x+1) = 16 ?
2(x +1) = 16
Use the distributive property ( multiply 2 by each term inside the parenthesis).
2x + 2 = 16
Subtract 2 from both sides:
2x = 14
Divide both sides by 2:
x = 7
Answer:
7
Step-by-step explanation:
2x+2=16
2x=16-2
x=16-2/2
x=14/2=7
A box contains 10 balls, of which 3 are red, 2 are yellow, and 5 are blue. Five balls are randomly selected with replacement. Calculate the probability that fewer than 2 of the selected balls are red.
Answer:
The required probability is 0.1.
Step-by-step explanation:
red balls = 3
yellow balls = 2
blue balls = 5
Selected balls = 5
Number of elemnets in sample space = 10 C 5 = 1260
Ways to choose 1 red ball and 4 other colours = (3 C 1 ) x (7 C 4) = 105
Ways to choose 5 balls of other colours = 7 C 5 = 21
So, the probability is
[tex]\frac{105}{1260} + \frac {21}{1260}\\\\\frac{126}{1260}=0.1[/tex]
When sales of a particular hybrid automobile reach 60,000 units, federal income tax credits begin to phase out. One year after reaching this threshold, buyers are still eligible for 25% of the original $3000 credit. What tax credit would buyers receive if they purchased the vehicle at this time.
Answer:
$750
Step-by-step explanation:
so, in short, we need to calculate 25% of $3000.
that is the amount of tax credit a buyer would get then.
direct and fast answer :
25% means 1/4 of the overall amount.
$3000 / 4 = $750
now, a little bit longer to explain % calculations in general.
let's say, we are talking 27%. now we have a problem to find a fast fraction as factor.
it always starts with the identification of 100%.
what is the full starting amount we are dealing with ? that is the 100%.
in our case $3000.
now, as a base for the calculation we determine 1%, which is 1/100 of 100%, of course.
1% = $3000 / 100 = $30
to get said 27% we have to multiply this by 27
27% = 1% × 27 = $30 × 27 = $810
or in general
x% = 100% × x / 100
that also works for more complex questions. e.g. calculate 1.5%
1.5% = $3000 × 1.5 / 100 = $30 × 1.5 = $45
and that is all there is to % calculations. all the questions are just some variations, where your are missing one of the 3 "ingredients" : 100% amount, x% amount and x itself.
and you need to transform the general equation above to get the missing piece of of the given information.
Find the surface area and volume of the solid given the figure below
Answer:
Volume - 582.8848178 cm cubed
Step-by-step explanation:
Volume - to fine the volume start with the cone...
The formula is 1/3 pi r^2h
so for this problem it would be
1/3 * 3.14 * 26.01 * 11.2
so your answer would be...
305.061213 cm cubed
Your next step is to find the volume of the dome. to do that the formula is (4/3 pi r^3)/2
so for this problem it would be
(4/3 * 3.14 * 132.651)/2
so your answer would be...
277.8236048 cm cubed
Finally you add together those 2 volumes and get 582.8848178 cm cubed as your final answer.
You and a friend were invited to a
party. You both were asked to bring
pizzas and chips. Your friend brought
three pizzas and four bags of chips
and spent $48.05. You brought five
pizzas and two bags of chips and
spent $67.25. What is the cost of
each? Answer should be in (Pizza, Chips)
Answer:
Pizza = 12.35
Chips = 2.75
Step-by-step explanation:
Let :
Pizza = x
chips = y
3x + 4y = 48.05 - - - (1)
5x + 2y = 67.25 - - - (2)
Multiply (1) by 5 and (2) by 3
15x + 20y = 240.25
15x + 6y = 201.75
Subtract :
20y - 6y = 240.25 - 201.75
14y = 38.50
y = 38.50/ 14
y = 2.75
Put y = 2.75 in (1)
3x + 4(2.75) = 48.05
3x + 11 = 48.05
3x = 48.05 - 11
3x = 37.05
x = 37.05 / 3
x = 12.35
Pizza = 12.35
Chips = 2.75
7. Draw an equilateral triangle of side 6.5 cm and after locating its circumcentre. Draw its circumcircle. send it with image
Answer:
Step-by-step explanation:
A circumcircle can be referred to as a circumscribed circle to a triangle. The steps to follow is stated below:
i. Since the triangle is equilateral, draw the triangle with sides 6.5 cm
ii. Bisect any of its two sides. The two bisecting lines would intersect at center, O, of the triangle.
iii. With the center and either radius OA, OB or OC, draw a circumscribed circle to the triangle.
The construction is attached to this answer for clarifications.
What is the prime factorization of 30?
O A. 2.2.3.5
O B. 5.6
O C. 3.10
O D. 2.3.5
D. 2.3.5 is the correct answer
Tom's graduation picnic costs $4 for every attendee. At most how many attendees can there be if Tom budgets a total of $36 for his graduation picnic?
For each of the following variables, identify the type of variable (categorical vs. numeric). (1) Temperature (in Fahrenheit) of an office building (11) Traffic congestion (e.g. light, medium, heavy)
1) (1) Numeric, and (II) Categorical
2) (1) Numeric, and (II) Numeric
3) (1) Categorical, and (II) Numeric
4) There is no correct match.
5) (1) Categorical, and (11) Categorical
Answer:
(a) Temperature: Numerical
(b) Traffic congestion: Categorical
Step-by-step explanation:
Required
Determine the variable type
(a) Temperature
Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.
Hence, the variable is numerical
(b) Traffic congestion
From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....
Hence, the variable is categorical
TIME REMAINING
49:02
What is the value of h?
The graph shows that f(x) = 3* is translated horizontally
and vertically to create the function g(x) = 3*- h + k.
81%
O-2
O-1
O 1
O 2
f(x)
001)
What is the answer to this photo
Answer:
h=2
Step-by-step explanation:
f is translated right 2 units (so h=2) and up 2 units (so k=2)
The value of h is 2.
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
A function f(x) when translated horizontally leads to the function g(x) which is equal to g(x) = f(x ± k) where k is the units to which the function is translated.
And the vertical translation leads to the function g(x) = f(x) ± k, where k is the units to which the function is translated.
Here the original function is, f(x) = 3ˣ.
The point corresponding to x = 0 in f(x) is x = 2 in g(x).
That is (0, 1) is translated to (2, 3).
f(x) is horizontally translated to the right.
3ˣ translates to 3ˣ⁻².
Hence the value of h is 2.
Learn more about Translations here :
https://brainly.com/question/29198392
#SPJ7
Find sin d, sin e, cos d, and cos e. Write each answer as a fraction in simplest form
Answer:
r= 17.73174
Step-by-step explanation:
calculations
A strawberry farmer in Poteet knows that 1/8 of his strawberries are typically not fit to sell at the market (either because they went bad or are too unusually shaped). The farmer takes a random sample of 156 strawberries to inspect for the upcoming farmer's market and finds that 24 are unfit to sell. If he were to go back and pick 1000 more strawberries to inspect for the market, how would the standard deviation of the sample proportion be affected
Answer:
It would be smaller.
Step-by-step explanation:
Given that :
The number of the strawberries that are unfit for sell, x = 24
The total number of the strawberries to inspect, n = 156
Total number of the strawberries to be picked = 1000 strawberries
Therefore,
[tex]$\widehat p =\frac{x}{n}$[/tex]
[tex]$=\frac{24}{156}$[/tex]
= 0.1538
[tex]$\widehat p =\frac{x}{n}$[/tex]
[tex]$=\frac{24}{1000}$[/tex]
= 0.024
Therefore, the standard deviation of the sample proportion would be smaller.
