Answer:
35 students
And 8 tables
So you jsut divide
35/8 = 4.375
So you have 4.375 tables but you can’t have .375 of a table so
You really need 5 tables to seat all the students.
integral of x/(x + 1)²(x+2)²
I suppose you mean the integral
[tex]\displaystyle \int \frac{x}{(x+1)^2 (x+2)^2} \, dx[/tex]
Break up the integrand into partial fractions:
[tex]\dfrac{x}{(x+1)^2 (x+2)^2} = \dfrac{a}{x+1} + \dfrac{b}{(x+1)^2} + \dfrac{c}{x+2} + \dfrac{d}{(x+2)^2}[/tex]
[tex]\dfrac{x}{(x+1)^2 (x+2)^2} \\ = \dfrac{a(x+1)(x+2)^2 + b(x+2)^2 + c(x+1)^2(x+2) + d(x+1)^2}{(x+1)^2 (x+2)^2}[/tex]
[tex]\dfrac{x}{(x+1)^2 (x+2)^2} \\ = \dfrac{(a+c)x^3+(5a+b+4c+d)x^2+(8a+4b+5c+2d)x + 4a+4b+2c+d}{(x+1)^2(x+2)^2}[/tex]
[tex]x = (a+c)x^3+(5a+b+4c+d)x^2+(8a+4b+5c+2d)x + 4a+4b+2c+d[/tex]
Solve for the coefficients:
[tex]\begin{cases}a+c=0 \\ 5a+b+4c+d=0 \\ 8a+4b+5c+2d=1 \\ 4a+4b+2c+d=0\end{cases} \implies a=3,b=-1,c=-3,d=-2[/tex]
So we have
[tex]\displaystyle \int \frac{x}{(x+1)^2 (x+2)^2} \, dx= \int \left(\frac3{x+1} - \frac1{(x+1)^2} - \frac3{x+2} - \frac2{(x+2)^2}\right) \, dx[/tex]
[tex]\displaystyle \int \frac{x}{(x+1)^2 (x+2)^2} \, dx= 3\ln|x+1| + \frac1{x+1} - 3\ln|x+2| + \frac2{x+2} + C[/tex]
[tex]\displaystyle \int \frac{x}{(x+1)^2 (x+2)^2} \, dx= \ln|x+1|^3 - \ln|x+2|^3 + \frac{3x+4}{(x+1)(x+2)} + C[/tex]
[tex]\displaystyle \int \frac{x}{(x+1)^2 (x+2)^2} \, dx= \boxed{\ln\left|\frac{x+1}{x+2}\right|^3 + \frac{3x+4}{(x+1)(x+2)} + C}[/tex]
Find an equation for the line with slope m= -2/3
and which goes through the point (- 15,8).
Write your answer in the form y = mx + b. DO NOT use decimals as part of your answer... express all parts of
your equation in integer or reduced fraction form.
Answer:
y = -2/3x + 18
Step-by-step explanation:
to find the y intercept you should input the points 15,8
sooo
8 = -2/3(15) + b
8 = -10 + b
b = 18
Question 1
Which statement describes the basis for the proof that vertical angles are congruent?
А
Two adjacent angles are always supplementary
B.
Two adjacent angles that form a linear pair are congruent.
с
Two angles that are each supplementary to a third angle are congruent.
D
Two angles that are each complementary to a third angle are congruent.
Answer:
C
Step-by-step explanation:
On each linear pair, there is one of the Vertical angles and an angle shared between the two angles. This means we can use the fact that supplements of the same angle are congruent.
The basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".
What are vertical angles?Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.
In the provided figure.
∠1 + ∠2 = 180 degrees ( linear pair of angles)...(i)
∠ 1 + ∠4 = 180 degrees ( linear pair of angles)...(ii)
According to transitive property, if a = b and b = c then a = c
Therefore,
∠1 + ∠2 = ∠1 + ∠4...(iii)
⇒∠2 = ∠4
Similarly, we can prove that
∠1 = ∠3
Therefore, we conclude that vertically opposite angles are always equal.
Hence, the basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".
Thus, statement c is correct.
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On the tax bracket table, choose all the marginal tax rates that will apply to a single taxpayer with a taxable income of $75,000.
Single Taxpayers: Income Brackets
Tax Rate
Income Bracket
10%
O to 9,525
12%
9,526 to 38,700
22%
38,701 to 82,500
24%
82,501 to 157,500
32%
157,501 to 200,000
35%
200,001 to 500,000
37%
> 500,000
Reset
Next
The marginal tax rate that will apply to a single taxpayer with a taxable income of $75,000 is 22%.
What is tax?It should be noted that a tax simply means the compulsory levy that's paid by the individuals and businesses to the government.
In this case, the marginal tax rate that will apply to a single taxpayer with a taxable income of $75,000 is 22%. This is for people in the income bracket of $38701 to $82500.
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22% is the marginal tax rate that will apply to a single taxpayer with a taxable income of $75,000.
Tax is a mandatory financial charge or levy imposed by the government on individuals, businesses, or other entities in order to fund public expenditures and services.
It is a way for the government to generate revenue to finance various public goods and services, such as infrastructure, healthcare, education, defense, and social welfare programs.
The marginal tax rate that will apply to a single taxpayer with a taxable income of $75,000 is 22%.
This is for people in the income bracket of $38701 to $82500.
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Find the surface area of the prism. 12 in. 9 in. 3 in. The surface area is in . 2.
(p.s 366 is wrong)
Answer:
The answer is 342 in.^{2}.
which inequalities are true? Select four correct answers
A:square root of 5<2.3
B: square root of 5<2.4< square root of 6
C: square root of 4
D: square root of 8<3
E: square root of 8<2.9< square root of 9
F: square root of 4<4.5< square root of 5
Answer:
A, B, D and E are the correct answers because they are all true
Find the measure of the angle SYX
How many buses do you need for 850 people if each bus holds 200 people
Answer:
5 buses
Step-by-step explanation:
each bus will take 200 people except for and the fifth bus will take 50
[30 POINTS]
What is the amplitude of this function f(x) ?
f(x)=34cos(3x)+4
Enter your answer in the box.
The comparison between the standard form of the cosine and f(x)=34cos(3x)+4 shows that the amplitude of the function given is 34.
Cosine Functions
The standard form of the cosine is given by:
y=acos(bx+c)+d
where:
a= amplitude - half the distance between the maximum and minimum values of the function. The value of a will be |a|.
b= the number of cycles the function completes in an interval of from 0 to 2π. This parameter influences in the period since is [tex]\frac{2\pi }{b}[/tex].
c= horizontal shift
d= vertical shift
The question asks the value of amplitude. Therefore, you should compare the standard form with equation function given.
Thus, you have:
y=acos(bx+c)+d
f(x)=34cos(3x)+4
The comparison shows: a=34, b=3, c=0 and d=4
Hence, the amplitude of the function f(x)=34cos(3x)+4 is equal to 34.
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Answer:
3/4
Step-by-step explanation:
I took the teat K 12
[tex]0.5216 \div 0.08[/tex]
how to solve this problem
The area of a rectangle is its length times its width .
The area of a rectangle is 60 square centimeters.
its length is 7 cm longer than its width .find its width .
what is its length write an equation and solve it
Answer:
The length is 5cm.
Step-by-step explanation:
(x)(x+7) = 60
x^2 +7x = 60
x^2 +7x - 60 = 0
x^2 + 12x - 5x = 0
Answer:
[tex]lenght = 12cm \\ width = 5cm[/tex]
Step-by-step explanation:
[tex]area \: = lenght \times width \\ area = 60cm { }^{2} \\ let \: width = xcm \\ let \: lenght = (x + 7)cm \\ 60 = \: (x)(x + 7) \\ 60 = x ^{2} + 7x \\ x {}^{2} + 7x = 60 \\ x {}^{2} + 12x - 5x - 60 = 0\\ x(x + 12) - 5(x + 12) \\ (x + 5)(x + 12) \\ x = 5 \: or \: x =- 12 \\ since \: width \: cant \: be \: negative \\ width = 5cm \\ lenht = 5 + 7 = 12cm[/tex]
two number cubes are rolled. what is the probability of getting a 1 and a 4 in either order
Answer:
1/18
Step-by-step explanation:
Each cube can have 6 outcomes, from 1 to 6.
6 × 6 = 36
The total number of outcomes is 36.
The desired outcomes are only 1, 4 and 4, 1.
There are only 2 desired outcomes.
p(1, 4 or 4, 1) = 2/36 = 1/18
Answer: 1/18
Elisabeth reads 1/5 of her book in 1 1/2 hours. Elisabeth continues to read at this pace. How long does it take Elisabeth to read 3/4 of the book? Enter your answer as a mixed number in simplest form by filling in the boxes.
It will take her 5 5/8 hours to read 3/4 of the book
Ratio and proportions
Given that Elisabeth reads 1/5 of her book in 1 1/2 hours, this is expessed as:
0.2 of a book = 1.5 hours
In order to determine the time taken to read 0.75 part of the book, we will have:
0.75 of a book = x
Take the ratios
0.2/0.75 = 1.5/x
0.2x = 1.125
x = 1.125/0.2
x = 5.625
Hence it will take her 5 5/8 hours to read 3/4 of the book
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Bethany went to the dog park with her dog at 12:30 pm she arrived back home at 2:30 pm how long was she at the dog park with her dog?
Answer:
2 hours
Step-by-step explanation:
12:30 + 1 hour = 1:30
1:30 + 1 hour = 2:30
She was at the dog park with her dog for 2 hours.
The amounts spent by 5 students on back to school supplies are $28.50, $25.75, $23.60, $30.20, and $25.00. Jenny spends $41.13 for her supplies. If the amount Jenny spends is included in the data, how will the mean be affected?
A) The mean decreases by $3.55
B) The mean increases by $2.42.
C) The mean increases by $2.54.
D) The mean increases by $1.55.
(3y^3)^2 without exponents
[tex](3y^3)^2=(3^2)*(y^3)^2=9*y^6 = 9y^6[/tex]
Hope that helps!
What is blank + 1/16 equals 3/2
Answer:
1 7/16
Step-by-step explanation:
Let that blank be x
x + 1/16 =3/2
Then, find the common denominator:
3/2 - 1/16
LCM = 16
3/2 *8 = 24/16
24/16 - 1/16
Last, subtract:
23/16
OR
1 7/16
Hope this helps!
mark brainliest if possible!
Can someone help me with this problem please
Answer:
First blank: 11/9
Second blank: 20
Step-by-step explanation:
Hope this helps!
I need help with my homework
Answer:
1. x= 8√2
2. x = 14 y=14√2
3. x = 18√2 = 9√2
4. x= 18/√2 =9√2
5. x= 8/√2 = 4√2
6. x = 10/√2 i.e 5√√2
26= 7(g-9)+12 What is the value of g. A.g=11 B. g=12 C. g=13 D. g=14
Answer:
A.g=11
Step-by-step explanation:
26=7(g-9)+12
26=7g-63+12
7g=77
g=11
A ball is placed in a machine that throws the ball up in the air. The table represents some points on the graph of a function that models the ball’s distance from the ground with respect to the time since the ball has been thrown. What is the range for this situation? A. All real numbers less than or equal to 7.66 B. All real numbers less than or equal to 1.25 C. All real numbers greater than or equal to 0 and less than or equal to 7.66 D. All real numbers greater than or equal to 0 and less than or equal to 1.25
Using it's concept, it is found that the range for this situation is given by:
C. All real numbers greater than or equal to 0 and less than or equal to 7.66.
What is the range of a function?
The range of a function is the set that contains all possible output values.
In this problem, the output values are the height of the ball, which researching the problem on the internet, is represented by a table in which the minimum height is of 0(when it hits the ground) and the maximum height is of 7.66 feet, hence the correct option is:
C. All real numbers greater than or equal to 0 and less than or equal to 7.66.
More can be learned about the range of a function at https://brainly.com/question/24374080
anyone know the answer?
Answer:
it’s A
Step-by-step explanation:
ur welcome
not sure how to solve this equation pls help out
Answer:
your answer is right
Step-by-step explanation:
I took the test
HELP ME OUT PLS!!!!!
x= 105°
y= 75°
z= 105°
Suppose you have a bag with 25 letter tiles in it and 7 of the tiles are the letter V. If you pick a letter tile at random from the bag, the probability that it is the letter V is 7/25
. Suppose another bag has 500 letter tiles in it and 250 of the tiles are the letter V. Write the probability of picking a tile that is the letter V as a fraction and as a percent. From which bag are you more likely to pick a tile that is the letter V?
So
[tex]\\ \rm\hookrightarrow P(E)=\dfrac{|E|}{|S|}[/tex]
[tex]\\ \rm\hookrightarrow P(E)=250/500=1/2=0.5[/tex]
7/25=0.3Second bag is more preferable
Answer:
Bag 1
Probability of picking a V = P(V) = 7/25 = 0.28
Bag 2
Probability of picking a V = P(V) = 250/500 = 1/2 = 0.5
You are more likely to pick a tile that is the letter V from Bag 2 since 0.5 > 0.28
Find the area of the shaded region, thank you!
Answer:
5.1 cm² (nearest tenth)
Step-by-step explanation:
[tex]\mathsf{area\ of \ sector=\dfrac{\theta\pi r^2}{360} \ (where\ \theta \ is \ measured \ in \ degrees)}[/tex]
Given:
r = 5[tex]\theta[/tex] = 80°[tex]\implies \mathsf{area\ of \ sector=\dfrac{80 \cdot\pi\cdot 5^2}{360}=\dfrac{50}{9}\pi \ cm^2}[/tex]
[tex]\mathsf{area\ of \ triangle=\dfrac12 ab\sin C}[/tex]
Given:
a = 5b = 5C = 80°[tex]\implies \mathsf{area\ of \ triangle=\dfrac12 \cdot 5 \cdot 5\sin (80)=\dfrac{25}{2}\sin(80) \ cm^2}[/tex]
Area of shaded area = area of sector - area of triangle
[tex]\implies \mathsf{area=\dfrac{50}{9}\pi-\dfrac{25}{2}\sin(80)}[/tex]
Therefore, area = 5.1 cm² (nearest tenth)
Urgent!!! Simplify the complex rational expression?
Step-by-step explanation:
[tex]( \frac{3}{w} + \frac{2}{x} ) \div ( \frac{2}{w} - \frac{3}{x} ) \\ ( \frac{3x}{xw} + \frac{2w}{xw} ) \div ( \frac{2x}{xw} - \frac{3w}{xw} ) \\ ( \frac{3x + 2w}{xw} ) \div ( \frac{2x - 3w}{xw} ) \\ \frac{3x + 2w}{xw} \times \frac{xw}{2x - 3w} \\ \frac{3x + 2w}{2x - 3w} [/tex]
hello help me with this question thanks in advance
Answer:
AD=25cm
Step-by-step explanation:
BC//AD
XY is also parallel to BC and AD as it bisects BA and CD.
BX=XA, CY=CD
so tge decreasing in length BC to XY is the same with XY to AD
29-27=2
27-2=25
That is why AD= 25cm
Find the volume of this rectangular
prism.
Answer:
36 in cubed
Step-by-step explanation:
3x2x6
3x2=6
6x6=36
Answer:
36 in
Step-by-step explanation:
First multiply 3 by 2 to get 6.
Then multiply the two 6s to gether to get 36.
Have an amazing day!
PLEASE RATE!
what are the algebraic expression,constant, variables, operations of 1.)3n+8, 2.)3x-2, 3.)4(N+5), 4.)2a+3b-c
Answer:
Step-by-step explanation:
Algebraic expression Constant Variables Operation
3n + 8 8 n addition
3x - 2 -2 x subtraction
4(N + 5) =4N + 20 20 N addition
2a + 3b - c 0 a,b,c addition & subtraction