The average value of a continuous function f(x) over an interval [a, b] is
[tex]\displaystyle f_{\mathrm{ave}[a,b]} = \frac1{b-a}\int_a^b f(x)\,dx[/tex]
We're given that
[tex]\displaystyle f_{\rm ave[-1,2]} = \frac13 \int_{-1}^2 f(x) \, dx = -4[/tex]
[tex]\displaystyle f_{\rm ave[2,7]} = \frac15 \int_2^7 f(x) \, dx = 8[/tex]
and we want to determine
[tex]\displaystyle f_{\rm ave[-1,7]} = \frac18 \int_{-1}^7 f(x) \, dx[/tex]
By the additive property of definite integration, we have
[tex]\displaystyle \int_{-1}^7 f(x) \, dx = \int_{-1}^2 f(x)\,dx + \int_2^7 f(x)\,dx[/tex]
so it follows that
[tex]\displaystyle f_{\rm ave[-1,7]} = \frac18 \left(\int_{-1}^2 f(x)\,dx + \int_2^7 f(x)\,dx\right)[/tex]
[tex]\displaystyle f_{\rm ave[-1,7]} = \frac18 \left(3\times(-4) + 5\times8\right)[/tex]
[tex]\displaystyle f_{\rm ave[-1,7]} = \boxed{\frac72}[/tex]
solve for x please!!!!
Answer:
13.86
Step-by-step explanation:
Note m∠ADB = m∠ABC, and m∠A = m∠A, so
ΔABD ~ ΔABC
AD : x = x : AC
AD : x = x : (AD + DC)
12 : x = x : 16
x^2 = 12 * 16 = 192
[tex]x=\sqrt{192} = 13.86[/tex]
Rob is saving to buy a new MP3 player. For every $14 he earns babysitting, he saves $5. On Saturday, Rob earned $56 babysitting. How much money did he save?
Answer:
ok so from looking at this if he earns 14 dollars he saves 5 so he saves
5/14 so lets just multiply this by the 56
56*5/14=20
so he saves 20
20
Hope This Helps!!!
There are 15 students on the debate team. Of these, 3 are boys. Give the ratio of boys to girls on the debate team in simplest form.
Answer:
1:4
Step-by-step explanation:
15 - 3 = 12
3:12 = 1:4
Answer:
1:5
Step-by-step explanation:
hope this helps
what is the property of 3m x 1 =3m
Answer:
Assuming this is for a Conic Section. There is no property as it does not match a conic section.
Problem 3: Solve the differential equation
[tex]y' + 2y = 3[/tex]
Answer:
[tex]y=Ce^{2x}+\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]y'+2y=3\\\\\frac{dy}{dx}+2y=3\\ \\\frac{dy}{dx}=3-2y\\ \\dy=(3-2y)dx\\\\\frac{1}{3-2y}dy=dx\\ \\\int\limits {\frac{1}{3-2y}dy=\int dx}\\\\\frac{1}{2}ln(|3-2y|)=x+C\\\\ln(|3-2y|)=2x+C\\\\3-2y=e^{2x+C}\\\\3-2y=Ce^{2x}\\\\-2y=Ce^{2x}-3\\\\y=-\frac{Ce^{2x}}{2}+\frac{3}{2}\\ \\y=Ce^{2x}+\frac{3}{2}[/tex]
What is the highest common factor of 40 and 25?
Answer:
5 is the highest common factor of 40 and 25
Helped by QueenTLoveHave an nice day
HELP PLEASE!! a class must have fewer than 18 students due to the number of desks that can be placed in the classroom. write an inequality that represents this situation. use the variable n to represent the number of students
Answer:
n ≤ 18
Step-by-step explanation:
The students can be 18 but they can't be greater than 18 so the inequality must be n ≤ 18.
Solution (Part-A)
Note that:
Given clue: A class must have fewer than 18 studentsLet's reread the clue carefully.
{A class} must have {fewer} than {18 students}
↥ ↥ ↥
n < 18
The inequality formed: n < 18
This means that the solution of the inequality can be anything except 18 or above 18.
Solution (Part-B)
Note that:
Given clue: The class must have at least 15 studentsLet's reread the clue carefully.
{The class} must have {at least} {15 students}
n ≥ 15
The inequality formed: n ≥ 15
This means that the solution of the inequality can be 15 or less than 15.
Solution (Part-C)
The value of n that can be a solution of both inequalities can be 15, 16, and 17.
Hoped this helped!
Josef works in a factory and is paid £352 a week. He works 40 hours a week. What is his hourly rate?
An item is priced at $13.14. If the sales tax is 7%, what does the item cost including sales tax?
A.
$14.06
B.
$0.92
C.
$27.20
D.
$22.34
Answer:
A - $14.06
Step-by-step explanation:
1) Divide :
7 / 100 = 0.07
2) Multiply :
0.07 * 13.14 = $0.9198
3) Add :
0.9198 + 13.14 = $14.0598
4) Round to the nearest decimal :
So if you round you would get $14.06
Answer:
Option A
Step-by-step explanation:
Given the following question:
7% of $13.14
To find the answer we simply use the formula to calculate percentage.
[tex]\frac{t\times i}{100}[/tex]
[tex]\frac{7\times13.14}{100} =91.98\div100=0.9198[/tex]
[tex]0.9198[/tex]
Round to the nearest cent:
[tex]0.9198[/tex]
[tex]9>5[/tex]
[tex]0.92[/tex]
Add the initial cost and the sales tax:
[tex]13.14+0.92=14.06[/tex]
[tex]14.06[/tex]
The items after a 7% sales tax costs "$14.06 dollars" or option A.
Hope this helps.
How do i solve for number 3
Answer:
Part 2. Evaluate: C(-1).
Step-by-step explanation:
How do i solve for number 3.
Is the graph a linear function, nonlinear function, or relation?
Answer:
I think its a non linear graph
Jake buys a car for $1500 and sells it for $1800. What is Jake’s percentage profit?
step by step explanation:
Jake brought a car = 1500rs
Jake sell the car = 1800
profit = sp-cp
so profit = 1800-1500 = 300
profit percent = gain/cp×100
profit percent = 300/1500×100
profit percent = 20% (double zero are cancel and 300 divided by 15)
what is the range for 37, 40, 33, 45, 32, 34
Answer:
13
Step-by-step explanation:
The biggest number minus the smallest number.
Answer:
13
Step-by-step explanation:
the highest value is 45
the lowest value is 32
subtract them from each other and you get 13
100 points
help asap
Step-by-step explanation:
cars= 8, 24
trucks= 20
total ($)=
pounds=5
calories=
Answers and Step-by-step explanations:
(Answers are all bold-ed and underlined.)
For these problems, they are asking you to fill in the blanks by noticing and by trying to find a pattern. In order to determine what the values are, this will require multiplication and division.
Table 1:
For the cars side, we can notice that that side of the table is going by 4's. Because 4, 12 and 16 are all multiples of 4. So, let's fill in this side.
Cars:
4
8
12
16
20
And, if we look at the trucks side, we can also notice a pattern of 5's. The numbers 5, 10, 15, and 25 are all multiples of 5. Now we can fill in the trucks side.
Trucks:
5
10
15
20
25
We can notice a pattern that both sides of the equation are being multiplied by 1, 2, 3, and so on (4x1=4, 4x2=8, 4x3=12...).
Table 2:
This table requires a little bit more work. We are going to need to do division for this problem. First, let's pick a value on the "Total ($)" side. From there, we can then take the "Pounds" side and use that to find the rest of the answers. Because 1.50 is the number below the first column, it will be the easiest to use to find what goes in that first column. And because we are using this column, we also have to use the "Pounds" side as well. So our equation will look something like this:
1.50 ÷ 2 = 0.75
So we can now place this in the first column. We can now use this to fill out the rest of the table. Because 0.75 x 2 = 1.50, then we can conclude that those pounds represent what we are multiplying the 0.75 by.
Total ($):
0.75
1.50
2.25
3.00
6.00
For the pounds side all we have to do is divide the Total ($) sides by the 0.75 to get our answer.
Pounds:
1
2
3
4
8
Table 3:
This table shouldn't be very hard since it already gives us the first value. All we do is just multiply the cookies by the calories to get our answers for the Calories side.
Second column: 35 x 2 = 70, and so onto the rest of the columns.
Calories:
35
70
140
280
350
____________________________________
I hope that this helps.
Solve for y.
x+y=7
x=5
Simplify your answer as much as possible.
Answer:
y = 2
Step-by-step explanation:
Given equations:
x+y=7
x = 5 .........given that x is 5
--------------------------------------------------------------------
5 + y = 7 ...............replace x as 5 here.
y = 7 - 5
y = 2
Saleh rented a truck for one day. There was a base fee of 16.95, and there was an additional charge of 79 cents for each kilometer driven. Saleh had to pay 234.99 when he returned the truck. For how many kilometers did he drive the truck?
8 1/2 = 7 ?/2
Need help asap:)
a) What is the equation of line A?
B
b) What is the equation of line B?
y
10
9
8
7
6
5
4
3
2
1
А
O' 1 2 3 4 5 6 7 8 9 10
gg
Step-by-step explanation:
Divide the following
Answer:
69/61+-34/61i
Step-by-step explanation:
i think this is correct, hope this helped!
If you make a yearly income of $76,923.54 and are taxed 23% of your income, how much do you owe in taxes?
Hey there! Your answer is:
17692.4142
Hope this helps! :D
At what point does the graph of y=9x(x is exponent) cross the y-axis?
A. (0,9)
B. (9,0)
C. (0,1)
D. (1,0)
Answer:
-The graph crosses the y-axis at the point (0,0)
None of the given options is correct
A graph crosses the y-axis at the point (0,y).This means that the graph will cross the y-axis when x-=0
To find the point where the graph crosses the y-axis,substitute x=0 into the given equation y-9x
substitute x=0 into the equation y-9x to find the corresponding value of y
That is,
y=9(0)
y=0
therefore the graph crosses the y-axis at the point (0,0)
Step-by-step explanation:
hope it hlps
Evaluate The Following Expression
136
-----
-10-7
Answer:
-8
Step-by-step explanation:
136/-17 when simplified because -10-7=-17 then plug into a calculator and you get -8
Hope this helps! :)
Answer:
Step-by-step explanation:
What is the equation of a line with a slope of -1 and a y-intercept of -5?
[tex]\huge\boxed{\boxed{Hello\:there!}}[/tex]
We are given the slope of the line and its y-intercept, so we can easily determine its equation.
Since we have the slope and the y-intercept, we can write the equation in slope-intercept form.
Slope-Intercept form looks like so:
y=mx+b
Where m is the slope and b is the y-intercept.
Slope: -1
Y-intercept: -5
Equation: y=-1x-5
y=-x-5 (Answer)
Hope it helps! Enjoy your day!
Please feel free to ask if you have any doubts.
-Sparkles-
Help me with this question please
please help this is for my son
Answer:
8 cookies left to be baked
Step-by-step explanation:
Len
Len bakes 1/3 of 30 cookies
To find 1/3 of 30, divide 30 by 3 then multiply by 1:
[tex]\implies \frac{30}{3} \times1=10 \times 1=10[/tex]
Therefore, Len bakes 10 cookies
Sallesh
Sallesh bakes 2/5 of 30 cookies
To find 2/5 of 30, divide 30 by 5 then multiply by 2:
[tex]\implies \frac{30}{5} \times2=6 \times 2=12[/tex]
Therefore, Sallesh bakes 12 cookies
Cookies left to bake
To calculate how many cookies are left to bake, subtract the found number of cookies Len and Sallesh have baked from 30:
30 - 10 - 12 = 8
So there are 8 cookies left to be baked.
Total cookies both baked
[tex]\\ \tt\longmapsto \dfrac{1}{3}+\dfrac{2}{5}[/tex]
[tex]\\ \tt\longmapsto \dfrac{5+6}{15}=\dfrac{11}{15}[/tex]
Cookies left:-
[tex]\\ \tt\longmapsto 30-11/15(30)=30-22=8[/tex]
y
3+
2+
1
т
-4 -3
-2
1
1
3
N
-3
-4
What is the slope of the line?
Calculate the median of the data set below.
15, 19, 24, 12, 9, 24, 19, 16, 21, 12
Answer:
17.5
Step-by-step explanation:
9, 12, 12, 15, 16, 19, 19, 21, 24, 24
16 + 19 = 35 divided by 2 = 17.5
mr dlamini transport people between butterworth and east london using a bus which has a capacity of 100 people. the transport charge starts with a minimum charge of r8 and end of dig king muscle contr thereafter it was increased by r2 for each kilometre. peces eces and urine fo ine (ur. where small inte on a particular day the bus was full with passengers from butterworth. in each and every kilometre there was a passenger getting off while no new passenger entered in the bus. mr dlamini was calculating total money in his hand after each passenger was getting out. the total amount he has after each stop can be written as a series as follows: sn=8+10+12+14+...
From the computation regarding the series, it can be deduced that the sum of the first two terms will be 18.
How to calculate the seriesFrom the information given, it was stated that the transport charge starts with a minimum charge of R8, and thereafter it was increased by R2 for each kilometer.
The series is also given as S. = 8 + 10 + 12 + 14 +... Therefore, the sum of the first two terms will be:
= 8 + 10
= 18
Also, expressing T2 in terms of S, and S2 will be T2 = S + S2.
Learn more about arithmetic series on:
brainly.com/question/24295771
A boat costs $92,000.00 and depreciates in value by 15% per year. How much will the boat be worth after 10 years?
Answer:
$18,112.45 (nearest cent)
Step-by-step explanation:
Let y = value of the boat
Let x = the number of years
If the boat depreciates in value by 15% each year, then each year that goes by, it is worth 85% of the previous year's value (since 100 - 15 = 85)
85% = 85/100 = 0.85
Therefore, the equation is: [tex]y = 92000 \times 0.85^x[/tex]
So, when x = 10:
[tex]\implies y = 92000 \times 0.85^{10}=18112.45[/tex]
I have tried it for multiple times but it still doesn’t work TvT! Please help me eight this question
Answer:
a) x = -2
b) 8 integer values
Step-by-step explanation:
Matthew's solution is correct as far as it goes. However, he failed to take into account the possibility of negative square roots.
His solution might rightly look like ...
3 < 3x² ≤ 75
1 < x² ≤ 25 . . . . . divide by 3
1 < ±x ≤ 5 . . . . . . take the square root
Separating the results:
1 < x ≤ 5
-1 > x ≥ -5 . . . . . . multiply by -1
a)The value x=-2 shows Matthew's solution is incorrect:
3 < 3(-2)² ≤ 25 ⇒ 3 < 12 ≤ 25 . . . true
__
b)x can have the integer values {-5, -4, -3, -2, 2, 3, 4, 5}, a total of 8 values.
__
In the attached, the white space (and dashed line) are the solution set. The shaded areas (and solid line) are excluded from the solution set.
_____
Additional comment
It can be helpful to remember that ...
[tex]\sqrt{x^2}=|\,x|\ne x[/tex]
That is, values of x may be negative, but the positive square root will only show you a positive value.