Answers
a. The area on [0, 10] is that of a trapezoid with bases 5 and 15 and height 10, so
[tex]\displaystyle \int_0^{10} f(x) \, dx = \frac{5+15}2\cdot10 = \boxed{100}[/tex]
b. By linearity of the definite integral, we have
[tex]\displaystyle \int_0^{25} f(x)\,dx = \int_0^{10} f(x)\,dx + \int_{10}^{25} f(x)\,dx[/tex]
and the area on [10, 25] is another trapezoid with bases 15 and 7.5 and height 15, so that
[tex]\displaystyle \int_{10}^{25} f(x)\,dx = \frac{15+7.5}2\cdot15 = 168.75[/tex]
Then the total area on [0, 25] is
[tex]\displaystyle \int_0^{25} f(x)\,dx = \boxed{268.75}[/tex]
c. The area on [25, 35] is that of a triangle with base 10 and height 15. However, [tex]f(x)<0[/tex] on this interval, so we multiply this area by -1 to get
[tex]\displaystyle \int_{25}^{35} f(x)\,dx = -\frac{10\cdot15}2 = \boxed{-75}[/tex]
d. The area on [15, 25] is the same as the area on [25, 35] because it's another triangle with the same dimensions. But the area on [15, 25] lies above the horizontal axis, so
[tex]\displaystyle \int_{15}^{25} f(x)\,dx = \int_{15}^{25} f(x)\,dx + \int_{25}^{35} f(x)\,dx = \boxed{0}[/tex]
e. The plot of [tex]|f(x)|[/tex] lies above the horizontal axis. We know the area on [15, 25] is the same as the area on [25, 35], but now both areas are positive, so
[tex]\displaystyle \int_{15}^{35} |f(x)| \, dx = \int_{15}^{25} f(x)\,dx - \int_{25}^{35} f(x)\,dx = 2 \int_{15}^{25} f(x)\,dx = \boxed{150}[/tex]
f. Changing the order of the limits in the integral swaps the sign of the overall integral, so
[tex]\displaystyle \int_{10}^0 f(x)\,dx = -\int_0^{10} f(x)\,dx = \boxed{-100}[/tex]
Related Questions
Suppose you want to have $300,000 for retirement in 25 years. Your account earns 8% interest. How much would you need to deposit in the account each month?
Answers
Using the future value formula, it is found that you would need to deposit $272.95 in the account each month.
What is the future value formula?It is given by:
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
In which:
P is the payment.n is the number of payments.r is the interest rate.For this problem, considering that there are monthly compoundings, the parameters are:
r = 0.08/12 = 0.0067, V(n) = 300000, n = 25 x 12 = 300.
Hence we solve for P to find the monthly payment.
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
[tex]300000 = P\left[\frac{(1.0067)^{299}}{0.0067}\right][/tex]
1099.12P = 300000
P = 300000/1099.12
P = $272.95.
You would need to deposit $272.95 in the account each month.
More can be learned about the future value formula at https://brainly.com/question/24703884
#SPJ1
Amanda rented a bike from Ted's Bikes.
It costs $10 for the helmet plus $4.25 per hour.
If Amanda paid about $33.38, how many hours did she rent the bike?
a) Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answers
Answer:
5.5 hours
Step-by-step explanation:
I am going to assume that a helmet is necessary prerequisite for renting the bike.
I also am assuming that the hourly rate can be turned into a sub hourly rate if the full hour isn’t used.
10+4.25h=33.38
4.25h=23.38
h=23.38/4.25
h=5.5
If f(x) =
(3+x)
(x-3)
what is f(a + 2)?
Answers
We have f(x)=(3+x)(x-3)=3x-9+x²-3x=x²-9
So f(a+2)=(a+2)²-9=a²+4a+4-9=a²+4a-5
which statements are true
Answers
The true statements are;
-Both graphs are logarithmic functions
-Both graphs have been shifted and flipped (B and D).
What is a graph?A graph is a plot of information on the cartesian coordinates. The function is plotted on an x - y cartesian plane. Given the nature of function, we can understand the shape of the graph as shown.
In this case, the graph shows a flipped logarithmic function. As such, the following are true about the function;
-Both graphs are logarithmic functions
-Both graphs have been shifted and flipped
Learn more about graphs:https://brainly.com/question/16608196
#SPJ1
Drag the tiles to the correct boxes to complete the reasoning of the proof. Not all tiles will be used.
May this help other people in the near future!!!!!
Answers
The missing reasons for each of the given statements are respectively;
1) Substitution
2) Definition of a Straight angle because a straight angle is 180°.
3) Congruent Angles have equal measures
How to prove angles in a triangle?
We are given that;
m∠1 = 90°
m∠1 + m∠2 = m∠5
∠3 ≅ ∠4
Statement 1; 90° + m∠2 + m∠4 = 180°
Reason 1; Substitution
Statement 2; m∠1 + m∠2 + m∠3 = 180°
Reason 2; Definition of a Straight angle because a straight angle is 180°.
Statement 3; m∠3 = m∠4
Reason 3; Congruent Angles have equal measures
Thus, the missing reasons for each of the given statements are respectively;
1) Substitution
2) Definition of a Straight angle because a straight angle is 180°.
3) Congruent Angles have equal measures
Read more about angles in a triangle at; https://brainly.com/question/12852445
#SPJ1
The graph of a cosine function has an amplitude of 5, a vertical shift of −1, and a period of 4. These are the only transformations of the parent function.
Use the Sine tool to graph the function.
The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.
Answers
See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1
How to graph the cosine function?From the question, the given parameters are:
Amplitude, A = 5
Vertical shift, D = -1
Period, T = 4
A cosine function is represented as:
f(x) = A cos(B(x + C)) + D
Where
Amplitude = A
Period = T
Horizontal shift = C
Vertical shift = D
Since the horizontal shift is not stated in the question, we can assume that the horizontal shift is 0
i.e. C = 0
So, the equation of the cosine function becomes
f(x) = A cos(Bx) + D
Calculate the value of B using
B = 2π/T
So, we have:
B = 2π/4
Evaluate
B = π/2
So, we have:
f(x) = A cos(π/2x) + D
Substitute the known values of A and D in the above equation
f(x) = 5 cos(π/2x) - 1
Next, we plot the graph of the cosine function on a graphing tool
See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1
Read more about cosine function at
https://brainly.com/question/17075439
#SPJ1
Perdue Company purchased equipment on October 1 for $36,100. The equipment was expected to have a useful life of three years, or 4,900 operating hours, and a residual value of $1,800. The equipment was used for 900 hours during Year 1, 1,700 hours in Year 2, 1,500 hours in Year 3, and 800 hours in Year 4.
Required: Round up all final values
Straight line Method
Answers
Under the straight-line depreciation method, the depreciation expenses for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, for Perdue Company, are as follows:
Year Amount
Year 1 $2,858.33 ($11,4333.33 x 3/12)
Year 2 $11,433.33
Year 3 $11,433.33
Year 4 $8,575.01 ($11,433.34 - $2,858.33)
What is the straight-line depreciation method?The straight-line method is one of the depreciation methods in use by companies to allocate the cost of plants and equipment over their useful lives.
Under the straight-line method, the depreciable amount (cost less residual value) is divided by the estimated useful life.
Other depreciation methods include the unit-of-production, double-declining-balance, and the sum-of-the-years-digit methods.
Data and Calculations:Equipment cost = $36,100
Residual value = $1,800
Depreciable amount = $34,300 ($36,100 - $1,800)
Estimated useful life = 3 years
Annual depreciation = $11,433.33 ($34,300/3)
Learn more about the straight-line depreciation method at https://brainly.com/question/27258396
#SPJ1
Question Completion:Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by the straight-line method.
When the equation a-bx=cx
+d is solved for x, the result is
Answers
Answer:
x=a-d/c+b
Step-by-step explanation:
a-bx =cx+d
collect like terms
a-d=cx+bx
a-d=x(c+b)
x=a-d/c+b
Please solve this now. Everything is attached in the file. You need to provide a full solution. Thanks
Answers
Based on the requirements for FICA and Medicare tax, the amount to be withheld in March for FiCA is $685.10 and for Medicare is $160.23.
The amount to be withheld in December of FICA is $523.90 and for Medicare is $160.23.
How much is to be withheld for FICA?In March, the amount to be withheld is:
= 11,050 x 6.2%
= $685.10
To find out the amount withheld in December, find out the earnings up to that point:
= 11,050 x 12
= $132,600
FICA can only be withheld on the first $130,000 so the amount of FICA In December is:
= 6.2% x ( 11,050 - (132,600 - 130,000))
= $523.90
What amount will be withheld for Medicare?The amount will be the same for both March and December as Medicare is for all earnings:
= 11,050 x 1.45%
= $160.23
Find out more on Medicare taxes at https://brainly.com/question/1848671
#SPJ1
The volume of a sphere is 144π. What is its Surface Area to the nearest whole number?
Answers
144 PI = PI (r^2)
Divide both sides by pi
144 =radius ^2
Square root
Radius is 12
Surface area=4PI(radius^2)
4(144)
576
Express each of the following in metres.
(iii) 10,000cm
Answers
Answer:
100m
Step-by-step explanation:
How much are 10000 centimeters in meters?
10000 centimeters equal 100.0 meters (10000cm = 100.0m). Converting 10000 cm to m is easy. Simply use our calculator above, or apply the formula to change the length 10000 cm to m.
Answer:
100m
Because- 1m=100cm
10m=1000cm
100m=10,000cm
c. When we add together the PPV and the false discovery rate for any test, why is the sum always 100%? c. When we add together the PPV and the false discovery rate for any test, why is the sum always 100%?
Answers
The inference is that the sum of the PPV and the false discovery rate for any test is always 100% because they complement each other.
How to illustrate the information?When we add together the PPV and the false discovery rate for any test, the sum is always 100%.
It should be noted that the false discovery rate is the complement of the positive predicate value. The addition of their probability gives 100%.
Learn more about inference on:
brainly.com/question/25280941
#SPJ1
Calculate the volume of a sphere that has a diameter of 7 meters.
Answers
Answer:
1436.76
Step-by-step explanation:
use the formula 4piR^3 to solveAnswer:
538.57 m³
Step-by-step explanation:
The formula to find the volume of a sphere is:
V = 4 π r³
Given that,
diameter ⇒ 7 m
∴ radius = d / 2
radius ( r ) = 7 / 2 = 3.5 m
Let us find the volume now.
V = 4 π r³
V = 4 π × ( 3.5 )³
V = 4 π × ( 3.5 )³
V = 4 π × 42.875
V = 4 π × 42.88
V = 12.56 × 42.88
V = 538.57 m³
Colby needs to wash the windows on the second floor of a building.
He only has a 12 ft ladder and because of dense shrubbery, he hasto put the base of the ladder 5 feet from the building. How many feet above the ground would the windows need to be in order for Colby to reach them with his 12 ft ladder?
Answers
If the length of ladder is 12 feet then the height of windows from the ground is 10.91 feet.
Given that the length of ladder is 12 feet and the base is 5 feet.
We are required to find the height of the windows from the ground.
When we graph all the things like ladder and all that we will get a right angled triangle.
We can find the height of window by using pythagoras theorem.
Pythagoras theorem says that the square of the hypotenuse is equal to sum of squares of base and perpendicular of right angled triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex]
P=[tex]\sqrt{H^{2} -B^{2} }[/tex]
Height of wall=[tex]\sqrt{12^{2} -5^{2} }[/tex]
=[tex]\sqrt{144-25}[/tex]
=[tex]\sqrt{119}[/tex]
=10.908
After rounding off it will be 10.91 feet.
Hence if the length of ladder is 12 feet then the height of windows from the ground is 10.91 feet.
Learn more about pythagoras theorem at https://brainly.com/question/343682
#SPJ1
Graph the line y+3x=-3
Answers
Answer: y = -3x-3 (Choose values for x)
Step-by-step explanation:
1st change the equation to y = mx+b form
In order to change the equation to y = mx+b form subtract the 3x to both sides.
The equation now becomes y = -3x-3
2nd we can either choose values for x such has (-2,-1,0,1,2) and plug in those values into our equation y = -3x-3
For example, if we plug in x= -2 we get y= -3(-2)-3 which becomes y =3. We then plot the point (-2,3) because -2 is our x coordinate and 3 is our y coordinate.
Or we can plug the equation into a calculator that will graph the equation for you.
Find the area of rhombus JKLM given the coordinates of the vertices. Round to the nearest tenth if necessary.
J(-2, -4), K(2, 2), L(6, -4), M(2, -10)
Answers
Answer:
The area of rhombus JKLM is 48 units²=====================================
Given Rhombus JKLM,Vertices at J(-2, -4), K(2, 2), L(6, -4), M(2, -10).To find The area of rhombus JKLMSolutionWe know that diagonals of rhombus are perpendicular to each other.
Hence its area is half the product of diagonals.
The diagonals are JL and KM and one of them is vertical and the other one horizontal since x- or y-coordinates are equal in pairs.
Let's find the length of diagonals, using the difference of coordinates:
JL = 6 - (-2) = 8 units,KM = 2 - (-10) = 12 units.Now find the area:
A = JL*KM /2 = 8*12 / 2 = 48 units²Ama and her son Brandon's average age is currently 36 years. When Brandon was born, Ama was 34 years old. How old is Brandon now?
Answers
———— = 36
2
34 + x = 72
-34 -34
x = 38
He’s now 38!!
If Ama and her son Brandon's average age is currently 36 years. then
Brandon's age is 38 years.
What is Equation?Two or more expressions with an equal sign is called as Equation.
Let the Brandon age be x
Ama was 34 years old
Ama and her son Brandon's average age is currently 36 years
(34 + x)/2= 36
Use cross multiplication
34 + x = 72
x=72-34
x = 38
So Brandon's average age is 38.
Hence Brandon is 38 years old.
To learn more on Equation click:
https://brainly.com/question/10413253
#SPJ2
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answers
The required steps are
2x^2 + 12x – 3 = 0.
2x2 + 12x = 3
2(x^2+6x) = 3
2[(x+3)^2 - 9] = 3
Completing the square methodQuadratic equations are equations that has a leading degree of 2
Given the equation below;
2x^2 + 12x – 3 = 0.
Add 3 to both sides
2x2 + 12x = 3
Factor out 2
2(x^2+6x) = 3
Complete the square
2(x^2+6x+3^2-3^2) = 3
2[(x+3)^2 - 9] = 3
This gives the required steps to solve the equation
Learn more on completing the square here: https://brainly.com/question/13981588
#SPJ1
Karin has 13 coins (2 quarters, 6 dimes, 4 nickels, and 1 penny) in a piggy bank. She turns the bank
upside down and shakes the bank until a coin falls out, puts it aside, and the shakes until another coin
falls out.
What is the probability that the first coin is a nickel and the second coin is a quarter?
Select one:
OOO O
2 63 23
39
01/3
118
Answers
Using it's concept, the probability that the first coin is a nickel and the second coin is a quarter is: 2/39.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Hence:
For the first coin, out of 13 coins, 4 are nickels, hence the probability is 4/13.For the second coin, considering that a nickel was taken first, 2 out of 12 coins will be quarters, hence the probability is 2/12 = 1/6.Then the probability for both coins is:
p = 4/13 x 1/6 = 4/78 = 2/39
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
Select the correct answer.
Which equation represents the measure of the unknown angles?
C
E
D
Xº
A.
B.
50°
C.
(x+10)
F
x + x + 10 =
= 130°
x + 10 = 180°
x+10= 130°
D. x + x + 10 = 180°
Answers
Step-by-step explanation:
x+x+10+50=180
2x+60=180
2x=180-60
2x=120
x=120/2
x=60
Jen opened a savings account at the bank. The amounts of her first 3 deposits are shown below:
• Deposit 1: $325
• Deposit 2: $280
• Deposit 3: $480
• Deposit 4: ?
How much does she need in the fourth deposit so that her average deposit is $365?
Answers
Answer:$375
Step-by-step explanation: To find the average, we need to add all of the numbers up and divide by the number of numbers in the set. Since there are 4 deposits, to get an average of #365, Jen needs to have deposited 365x4 = $1460 in total. Now, it is pretty easy to find the answer. We add up her 3 deposits: 325+280+480 = $1085 and see that it is still $375(1460 - 1085) short. So, Jen needs to deposit $375 on her fourth deposit to have an average of $365.
11
A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3,-1), and (-6, 5), respectively. Which sentence about the points is true?
OA
A, B, C, and D lle on the same line.
OB.
AB and CD are perpendicular lines.
OC. AB and CD are parallel lines.
OD. AB and CD are intersecting lines but are not perpendicular.
OE. AC and BD are parallel lines.
Answers
For the given coordinates of A, B, C, and D as (-8, 1), (-2, 4), (-3,-1), and (-6, 5), respectively, OD, AB and CD are intersecting lines but are not perpendicular (third option) is the correct assertion.
Reasons for the Choice
Because parallel lines never intersect, the fact that lines AB and CD come to a point proves that they are not parallel. It indicates that they are intersecting lines. (Refer to the attached figure)The location where lines AB and CD intersect is not at a straight angle. As a result, lines AB and CD are not parallel.Because the distances separating the two lines differ, AC and BD are not parallel. As a result, lines AB and CD do indeed intersect, but not at a straight angle. Consequently, despite not being perpendicular, both lines intersect.Therefore, the lines OD, AB, and CD are intersecting lines but are not perpendicular.
Learn more about intersecting lines here:
https://brainly.com/question/11297403
#SPJ1
Gia is participating in a jump-a-thon to raise money for her school. After completing
20 jumps, she raised $50. Gia wants to know how much money she raises per jump.
Which rate shows how much money Gia raises per jump?
50
20
20
50
jumps per dollar
dollars per jump
20
50
50
20
jumps per dollar
dollars per jump
Answers
Answer:
50/20
Step-by-step explanation:
Rate of money raised raises per jump is
money raised / jumps
$50/ 20 jumps
We can think that if we divide the $50 into 20 equal parts,
each part will represent 1 jump and will have 50/20 = $2.5 per 1 jump.
9e-6(-2e+7)= please help me solve this problem
Answers
[tex]\bold{Answer:} \small\boxed{21e-42}[/tex]
Step-by-step explanation:
[tex]To\ solve\ : \ 9e-6(-2e+7)[/tex]
we first must use the distributive property. You can think about solving this like this:
[tex]=9e-(6)(-2e+7)[/tex]
Notice how we are not distributing -6, but only 6. Now we can solve normally:
[tex]=9e-(-12e+42)[/tex]
Now we distribute the '-' sign to the terms in parenthesis.
[tex]=9e+12e-42[/tex]
[tex]\longrightarrow \large\boxed{21e-42}[/tex]
The decimal form is 15.08 rounded.
2×7×7-3×3×3×2+3×2×2-6×6
I need an answer
Answers
Answer:
98-54+12-36
110-54-36
56-36
20Ans
4/7=×/6 what does × =
Answers
Answer:
3.42857143
Step-by-step explanation:
You multiply 4/7 by 6 to isolate the variable
Answer:
3 3/7 or 24/7
As a decimal: 3.42857143
Step-by-step explanation:
Rewrite the proportion:
4/7 = x/6
Multiply both sides by 6 to isolate x:
(4/7) * 6 = x
Multiply 4 and 6, 7 is multiplied by 1 since 6 = 6/1:
x = 24/7
Rewrite as mixed number:
7 * 3 = 21
24 - 21 = 3
x = 3 3/7
Brainliest, please :) (Hoping to become a genius)
The test scores of 15 students are listed below. Find the third decile, D3.
41, 45, 51, 57,59, 62,66,69, 75,78, 85,87,90,94,95
Answers
The third decile is 58.
What is the third decile?Decile is a statistical term that divides the data into groups of ten. The third decile is the third group of the data set.
Third decile = 3/10 x (n + 1 )
3/10 x 16 = 4.8th term = 58
Which expression has a conflict of 10 and a constant of5
Answers
The expression that has a coefficient of 10 and constant of 5 is 10x + 5.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
A coefficient is a number or any symbol representing a constant value that is multiplied by a variable. A constant is a value or number that never changes in expression.
The expression that has a coefficient of 10 and constant of 5 is 10x + 5.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Becca polled the members of her volleyball team to see what their opinions were regarding the awards banquet. Her results were:
A total of 16 people wanted the steakhouse option.
• Seafood buffet but not bsteakhouse: 8
Steakhouse but not seafood buffet: 9
.neither 4
Answers
Based on the total number of people who want the steakhouse option, the probability that a student will not want the seafoodbuffet if they want the steakhouse option is 24%
What is the probability of the students' choice?The probability that a student does not want the seafood buffet given that they want the steakhouse option is:
= Number of people who want steakhouse but not seafood / Total surveyed
Solving gives:
= 9 / (16 + 8 + 9 + 4)
= 9 / 37
= 24%
Full question is:
If a student wants the steakhouse option, what is the probability that they will not want the seafoodbuffet?
Find out more on probability at https://brainly.com/question/27921932
#SPJ1
A random sample of 80 tires showed that the mean mileage per tire was 41,400mi, with a standard deviation of 4700mi
Answers
Question 14
Part (a)
[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]
Part (b)
[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]
