Answers
Answer:
The average value of g is:
[tex]\displaystyle g_{ave}=\frac{1}{6}e^6-\frac{49}{6}\approx 59.071[/tex]
Step-by-step explanation:
The average value of a function is given by the formula:
[tex]\displaystyle f_{ave}=\frac{1}{b-a}\int_a^b f(x)\, dx[/tex]
We want to find the average value of the function:
[tex]g(x)=e^{3x-3}-4x[/tex]
On the interval [1, 3].
So, the average value will be given by:
[tex]g_{ave}=\displaystyle \frac{1}{3-1}\int_1^3 e^{3x-3}-4x\, dx[/tex]
Simplify. We will also split the integral:
[tex]\displaystyle g_{ave}=\frac{1}{2}\left(\int_1^3e^{3x-3}\, dx-\int _1^3 4x\, dx\right)[/tex]
We can use u-substitution for the first integral. Letting u = 3x - 3, we acquire:
[tex]\displaystyle u=3x-3\Rightarrow du = 3\, dx\Rightarrow \frac{1}{3} du=dx[/tex]
We will also change the limits of integration for our first integral. So:
[tex]u(1)=3(1)-3=0\text{ and } u(3)=3(3)-3=6[/tex]
Thus:
[tex]\displaystyle g_{ave}=\frac{1}{2}\left(\frac{1}{3}\int_0^6 e^{u}\, du-\int _1^3 4x\, dx\right)[/tex]
Integrate:
[tex]g_{ave}=\displaystyle \frac{1}{2}\left(\frac{1}{3}e^u\Big|_0^6-2x^2\Big|_1^3\right)[/tex]
Evaluate. So, the average value of g on the interval [1, 3] is:
[tex]\displaystyle g_{ave}=\frac{1}{2}\left(\frac{1}{3}\left[e^6-e^0\right]-\left[2(3)^2-2(1)^2\right]\right)[/tex]
Evaluate:
[tex]\displaystyle\begin{aligned} g_{ave}&=\frac{1}{2}\left(\frac{1}{3}(e^6-1)-16\right)\\&=\frac{1}{2}\left(\frac{1}{3}e^6-\frac{1}{3}-16\right)\\&=\frac{1}{6}e^6-\frac{49}{6}\approx59.071\end{aligned}[/tex]
Related Questions
After basketball practice, 8 players equally shared 3 large bottles of water. What fraction of a bottle did each player get?
Answers
Simplify and write answer in standard form.
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Step-by-step explanation:
2x^3 - 10x^2 + 8x -3
hope this helps
What is the opposite of -45?
Answers
Answer:
45 or positive 45
Step-by-step explanation:
Answer: 45
Step-by-step explanation:
Which statement about the net is true?
Answers
Answer:
A
Step-by-step explanation:
The net can be folded to form a pyramid
At a high school with over 500 students, a counselor wants to estimate the mean number of hours per week that students at the school spend in community service activities. The counselor will survey 20 students in the Environmental Club at the school. The mean number of hours for the 20 students will be used to estimate the population mean. Which of the following conditions for inference have not been met?
1. The data are collected using a random sampling method.
2. The sample size is large enough to assume normality of the distribution of sample means.
3. The sample size is less than 10 percent of the population size.
Answers
Complete option:
The sample size is less than 10 percent of the population size. A. II onlyB. III onlyC. II and III onlyD. I, II, and III
Answer:
D.) I, II, and III
Step-by-step explanation:
The sample are not well randomly selected as the samples were only selected from a single source, the environmental club in the school.
Similarly only 20 samples were chosen, these 20 samples are not enough to assume normality as the minimum number of samples required to assume normality according to the Central limit theorem is 30 samples or more.
10% of the population size is :
Population size = 5000
0.10 * 5000 = 500 samples
Hence, sample size used is less than 10% of population size.
[tex]if \: a = 3 + 2 \sqrt{2} .find \: a \times \frac{1}{a} [/tex]
Answers
Answer:
1
Step-by-step explanation:
Given that,
[tex]a=3+2\sqrt{2}[/tex]
We need to find the value of [tex]a\times \dfrac{1}{a}[/tex].
So,
[tex]=3+2\sqrt{2} \times \dfrac{1}{3+2\sqrt{2}}\\\\=\dfrac{3+2\sqrt{2}}{3+2\sqrt{2}}[/tex]
As numerator and dinominator is same. It means,
[tex]=\dfrac{3+2\sqrt{2}}{3+2\sqrt{2}}\\\\=1[/tex]
So, the value of the given expression is equal to 1.
The
Olympic time for men's 400-m hurdles
has been decreasing by about 0.09 seconds per
year since 1930, when the record was 52 seconds.
Predict what the time will be in 2010
Answers
Answer:
In 2010 the time will be 44.8 seconds.
Step-by-step explanation:
Given that the Olympic time for men's 400-m hurdles has been decreasing by about 0.09 seconds per year since 1930, when the record was 52 seconds, to predict what the time will be in 2010 the following calculation must be performed:
52 - ((2010 - 1930) x 0.09) = X
52 - (80 x 0.09) = X
52 - 7.2 = X
44.8 = X
Thus, in 2010 the time will be 44.8 seconds.
A group of children were asked if they like eating cupcakes or brownies.
The table shows the probabilities of the results.
Like cupcakes Do not like cupcakes Total
Like brownies 0.15 0.15 0.3
Do not like brownies 0.35 0.35 0.7
Total 0.5 0.5 1
What is the probability that a child likes brownies given that he likes cupcakes?
.70
.43
.50
.30
Answers
Answer:
It’s 0.30
Step-by-step explanation:
I took the test bro
calculate by rounding off and compensating 823-273
Answers
Not sure what exactly you want but the answer is 550.
You can compensate by subtracting 3 from 823 and subtracting 3 from 273 and after doing 820-270 you get 550.
Hope this helps!
if c and d vary inversely, and d=5/3 and c=5. write a function that models inverse variation and find d when c=10
Answers
9514 1404 393
Answer:
cd = 25/3d = 5/6Step-by-step explanation:
The inverse variation described can be either of ...
c = k/d
or
d = k/c
Either way, the equation can also be written as ...
cd = k
For the given values of c and d, the value of k is ...
(5)(5/3) = k = 25/3
So, the model can be written as ...
cd = 25/3
or
d = (25/3)/c
__
For c=10, the value of d is ...
d = (25/3)/10 = 25/30
d = 5/6
184 is what percent more than 148
Answers
a. find the area
b. find the perimeter
Answers
Answer:
Area= 4y^2 + 14y + 12
Perimeter = 10y + 16
Step-by-step explanation:
Area of a reactangle = length × width
= (4y+6) × (y+2)
= 4y^2 + 6y + 8y + 12
= 4y^2 + 14y + 12
Perimeter of a rectangle = 2 × (a +b)
= 2 × ( 4y + 6 + y+ 2)
= 2 × ( 5y + 8)
= 10y + 16
Suppose y varies directly with x. Write an equation relating x and y. y=-12 when x=20
Answers
Answer:
[tex]y = 8 - x[/tex]
when x=20 so y=-12
Find the range of the function
x) = 10- x
a 15.)
b. (2-1) U[0,
C. (10]
d (2-1) U. 10)
Please select the best answer from the choices provided
ОА
B
ос
OD
Answers
Please help is for now
Answers
the answer 16 im pretty sure
A wooden box has the shape of a rectangular prism. The inside of the box is also a rectangular prism. What is the volume of the solid part of the box? Enter your answer below.
Answers
ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE
Answers
Answer: the correct answer should be 160 but you said that didnt work so try 480
Step-by-step explanation:
I just did base times Hight 8*10 which is 80*6=480
hoped this helps:))
Answer:
80
Step-by-step explanation:
V= Bh/3
Area of base= (L × W) ÷2
(8×6)÷2 = 24
Multiply by height
24×10=240
Divide by 3 (since its a pyramid therefore has 3 sides)
240/3=80
80 is your answer
find the area of the shaded segment of the circle
Answers
9514 1404 393
Answer:
(3/2π -(9/4)√3) m² ≈ 0.8 m²
Step-by-step explanation:
The area of the segment is the difference between the area of the sector and the area of the triangle.
sector area = 1/2r²α . . . . where r is the radius and α is the central angle in radians
triangle area = 1/2r²·sin(α) . . . . same variable definitions
Then the area of the segment is ...
segment area = sector area - triangle area
segment area = (1/2)r²(α -sin(α))
The central angle subtended by the segment is 360° -300° = 60° = π/3 radians
Then the segment area is ...
A = (1/2)(3 m)²(π/3 -√3/2) = (3/2π -(9/4)√3) m² ≈ 0.8 m²
Kazi ran 1.2km how many centimeters did she run
Answers
9514 1404 393
Answer:
120,000 cm
Step-by-step explanation:
There are 100 cm in 1 m, and there are 1000 m in 1 km. So, there are 100,000 cm in 1 km.
1.2 km is 120,000 cm
A diagram shows the dimensions for a local botanical garden. Measure the parallelogram to the nearest 1/4 inch. What is the area of the botanical garden diagram in square inches?
Answers
Answer:
4.8 in2
Step-by-step explanation:
2.4 x 2 =4.8
tell me if I'm wrong
Answer:
Step-by-step explanation:
The sum of 4 consecutive integers is 354.
What is the second number in this sequence?
Answers
Answer:
87
Step-by-step explanation:
Step 1: X is the first number
Step 2: X + 1 is the second number
Step 3: X + 2 is the third number
Step 4: X +3 is the fourth number
Step 5: Take the sum of all of those:
4x+6=354
4x=348
x=87
The second number in the sequence is 88.
87,88,89,90 = 354
Answer: Second integer is 87
Step-by-step explanation:
Sum of four consecu. integers = 354
Let the integers be x, x+1, x+2 , x+3.
Sum = 354
x+x+1+x+2+x+3 = 354
4x+6 = 354
4x = 354 - 6
4x = 348
x = 348/4
x = 87
Therefore, first integer = x =87
Second integer = x+1 = 88
Third integer = x+2 = 89
Fourth integer = x+3 = 90
So, second integer is 88 .
a person invested $330 in an account growing at a rate allowing the money to double every 8 years. Write a function showing the amount of money in the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percent.
Answers
Answer:
The percentage of growth is of 9.05%.
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
Step-by-step explanation:
Amount of money after t years:
The amount of money in an account after t years is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial deposit and r is the growth rate, as a decimal.
Money doubles every 8 years.
This means that [tex]P(8) = 2P(0)[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]2P(0) = P(0)(1+r)^8[/tex]
[tex](1+r)^8 = 2[/tex]
[tex]\sqrt[8]{(1+r)^8} = \sqrt[8]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{8}}[/tex]
[tex]1 + r = 1.0905[/tex]
[tex]r = 1.0905 - 1[/tex]
[tex]r = 0.0905[/tex]
The percentage of growth is of 0.0905 = 9.05%.
Person invested $330
This means that [tex]P(0) = 330[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 330(1+0.0905)^t[/tex]
[tex]P(t) = 330(1.0905)^t[/tex]
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
Simone purchased a new car for $18,700. There
was also a 6% sales tax. What was the total
amount Simone paid for the car, including tax?
Answers
Answer:
19,822
Step-by-step explanation:
A normal distribution has a mean of 14 and a standard deviation of 4. What percent of values are from 14 to 22?
Answers
Answer:
80% of the values will occurs above 68.24.
Step-by-step explain
thinking this is right but im sorry if its wrong
please help will get brainliest
(the figure is not drawn to scale)
which one?
154 cm2
217 cm2
308 cm2
5488 cm2
Answers
V =14 V-6=8 - =22
K+K=14
22 x 14 =308
What is the Supplimentary angle of 21°?
Answers
Answer:
159 degrees
Step-by-step explanation:
Answer:
159°
Step-by-step explanation:
We can calculate supplementary angles by subtracting the given one angle from 180 degrees. To find the other angle, use the following formula: ∠x = 180° – ∠y or ∠y = 180° – ∠x where ∠x or ∠y is the given angle.
so 180° – ∠ 21= 159°
Simplify 16m6-15mn+m6+17mn
Answers
Answer:
[tex]17m^6 + 2mn[/tex]
Step-by-step explanation:
[tex]16m^6 -15mn +m^6 + 17mn[/tex]
Combine like terms, rewrite the equation and perform the operations between the coefficients,
[tex]16m^6 +m^6 -15mn+17mn[/tex]
[tex]17m^6 + 2mn[/tex]
2mn + 17m^6
Does anyone know what the answer is for the question???
Answers
A triangular garden has an area of 9 square yards. Which figure could represent the garden? 9 yd 9yd,
6 yd 6 yd , 6yd 3yd, 3yd 3yd
Answers
Answer:
3yds by 3yds
Step-by-step explanation:
3×3=9
A cooler contains 12 bottles of apple juice and 18 bottles of orange juice. You reach into the cooler without looking and pull out one bottle of apple juice. Then you reach into cooler and pull out another bottle of juice. What is the probability of pulling apple juice and then pulling another apple juice?
Answers
Answer:
P = 0.232
Step-by-step explanation:
In the cooler, we have 12 bottles of apple juice and 18 bottles of orange juice.
This adds up to a total of 30 bottles.
Now we want to find the probability of pulling a bottle of apple juice after you pulled one bottle of apple juice.
The probability of pulling a bottle of apple juice at the beginning is equal to the quotient between the number of apple juice bottles in the cooler and the total number of bottles in the cooler,
This means that 12 out of 30 are apple juice, then the probability of getting first a bottle of apple juice is:
p = 12/30
Now, we want to find the probability of getting another, we will do the same calculation than above, but now the number of bottles of apple juice is 11 (because we took one) and the total number of bottles is 29.
In this case, the probability is:
q = 11/29
The joint probability (the probability of both events happening) is equal to the product of the individual probabilities.
Then the probability of pulling apple juice and then pulling another apple juice is:
P = p*q = (12/30)*(11/29) = 0.232
