Answer:
[tex]\mathbf{4 \lim \limits _{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n(n+4i)}{2n^3 +(n+4i)^3} \Big )}[/tex]
Step-by-step explanation:
Given integral:
[tex]\int ^5_1 \dfrac{x}{2+x^3} \ dx[/tex]
[tex]\mathbf{Using \ Riemann \ sums; \ we \ have: }[/tex]
[tex]\int ^b_a \ f(x) \ dx = \lim_{n \to \infty} \sum \limits ^n_{i =1} \ f( a + i \Delta x) \Delta x[/tex]
[tex]here; \ \Delta x = \dfrac{b-a}{n}[/tex]
∴
[tex]\int ^5_1 \dfrac{x}{2+x^3} \ dx = f(x) = \dfrac{x}{2+x^3}[/tex]
[tex]\implies \Delta x = \dfrac{5-1}{n} =\dfrac{4}{n}[/tex]
[tex]f(a + i \Delta x ) = f ( 1 + \dfrac{4i}{n})[/tex]
[tex]f( 1 + \dfrac{4i}{n}) = \dfrac{n^2 ( n+4i)}{2n^3 + (n + 4i)^3}[/tex]
[tex]\lim_{n \to \infty} \sum \limits ^n_{i=1} \ f(a + i \Delta x) \Delta x = \lim_{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n^2(n+4i)}{2n^3 +(n+4i)^3} \Big )\dfrac{4}{n}[/tex]
[tex]\mathbf{= 4 \lim \limits _{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n(n+4i)}{2n^3 +(n+4i)^3} \Big )}[/tex]
Dana surveyed students in her class. She found that 8 earned an A, 6 earned a B, 4 earned a C, and 2 earned a D on the last science test. If she randomly surveys one more student from the class, what is the experimental probability that the student would have earned an A on the test.
Answer:
0.4 or 2/5
Step-by-step explanation:
Dana surveyed 20 students in total and out of those 20 only 8 got an A
so:
[tex]\frac{8}{20}[/tex] now if you simplify it [tex]\frac{4}{10}[/tex] and if you simplify it again:
[tex]\frac{2}{5}[/tex] or 0.4 in decimal
Please answer quick!!! Will Mark BRAINLIEST!!!
Answer:
picture 1 : 360 cm2
picture 2: sorry I don't really know
picture 3: 11.25 cm2
Step-by-step explanation:
hope this helps
HELP ASAP! WILL GIVE BRAINLIEST!
Which statements below are ALWAYS TRUE about Rectangles? Choose ALL THAT APPLY.
- Diagonals are perpendicular
- Diagonals bisect each other in diagonals are equal in length
- Diagonals bisect each other, but they are NOT equal in length
- Opposite sides are congruent
- All four sides are congruent
- Diagonals bisect 90° angles
- Diagonals DO NOT bisect 90° angles
Helppppppppppppppppppppppp pleaseeeeeee
Answer:
12.57
Step-by-step explanation:
C=2πr
2π2
4π
12.57
12(x - 1) = - 4(3-X) + 8x
This equation has infinite solutions, any real number makes it true.
Andy and Jim are going to compete in the 100-meter dash against each other. Let AAA be the time it takes Andy to complete the race, and JJJ be the time it takes Jim to complete the race. Based on previous results, they know that \mu_A=11.5μ A =11.5mu, start subscript, A, end subscript, equals, 11, point, 5 seconds and \sigma_A=1σ A =1sigma, start subscript, A, end subscript, equals, 1 second. They also know that \mu_J=10.5μ J =10.5mu, start subscript, J, end subscript, equals, 10, point, 5 seconds and \sigma_J=0.5σ J =0.5sigma, start subscript, J, end subscript, equals, 0, point, 5 seconds.
Answer:
μd= 1 second
σd= square root (1.25) = √1.25 seconds= 1.1180 seconds
Step-by-step explanation:
Assume that their times are independent. Let DDD be the difference between their times in a random 100-meter dash (D=A-J)(D=A−J)left parenthesis, D, equals, A, minus, J, right parenthesis.
Find the standard deviation of DD
The mean difference is found out by subtracting the individual means.
The mean difference = μd= μA- μJ= 11.5- 10.5= 1 second
The difference standard deviation is given by the square root of sum of the individual variances divided by n. But here n1= n2= 1
σd = sqrt( σ1² / n1 + σ2 ²/ n2 )
First we calculate the variances.
Variance is the square of the standard deviation.
The variance of Andy =σA²= 1²= 1
The variance of Jim =σJ²= (0.5)²= 0.25
The standard deviation difference= σd= √σ²A+ σ²J/1= √1+ 0.25/1= √1.25/1 = √1.25 seconds = 1.1180 seconds
HELP HELP HELP
The function t relates the age of a plant fossil in years to the percentage c of carbon remaining in the fossil relative to when it was alive.
t(c)=-3970.9(ln c)
Use function t to complete the statements.
A fossil with 47% of its carbon remaining is approximately how old
1. 2998
2 11,910
3 7550
A fossil that is 7000 years old will have approximately
1. .2%
2. 57%
3 17%
Of its carbon remaining.
Select the correct answers
Answer:
2998 ; 17%
Step-by-step explanation:
Given the function:
t(c)=-3970.9(ln c)
c = % of carbon remaining ; t = time
1.) c = 47% = 47/100 = 0.47
t(0.47) = - 3970.9(In 0.47)
t = - 3970.9 * −0.755022
t = 2998.119
t = 2998
B.)
t = 7000
t(c)=-3970.9(ln c)
7000 = - 3970.9(In c)
7000 / - 3970.9 = In c
−1.762824 = In c
c = exp(−1.762824)
c = 0.1715596
c = 0.1715596 * 100%
c = 17.156% ; c = 17%
Answer: For plato family
The function t relates the age of a plant fossil, in years, to the percentage, c, of carbon-14 remaining in the fossil relative to when it was alive.
Use function t to complete the statements.
A fossil with 47% of its carbon-14 remaining is approximately
years old.
A fossil that is 7,000 years old will have approximately
17% of its carbon-14 remaining.
Step-by-step explanation:
The first box is 2,998
The second box is 17%
Given f(x) = -4x + 7 and g(x) = x3, choose
the expression for (fºg)(x).
Answer:
Solution,
Given,
f(x) = -4x + 7
g(x) = [tex]x^{3}[/tex]
Now,
fog(x) = f{g(x)} = f([tex]x^{3}[/tex]) = -4[tex]x^{3}[/tex]+7
the range of the quedractic function is {y|y
well I have no idea what that means but I hope you find your answer
Answer: The question is incomplete, Hope I could've helped.
A triangle with a base of 10 and side lengths of 13 is similar to what other kind of triangle
A. base of 100 and side lengths of 100
B. base of 20 and side lengths of 27.5
C. base of 25 and side lengths of 32.5
D. base of 5 and side lengths of 13
Answer:
Step-by-step explanation:
the only correct choice is C
= multiplied each side by 2.5
Help me! Which is the right correct answer?
Answer:
the way bottom one i think i dont rember planes anymore
Step-by-step explanation:
Answer:
(-4 1/2,3) is the final result.
Step-by-step explanation:
V(4 1/2, -3)
The order of the reflections do not matter.
So if I consider the x axis first, only the y value will change. Seems weird, but try doing this on a piece of scrap paper.
(4 1/2, 3 ) is the new point. The point is reflected an equal distance behind the mirror on the x axis.
Now do the y axis. Only the x value of the point is changed.
(-4 1/2, 3) is what happens.
===================================
Does the order matter?
V(4 1/2, - 3) goes across the y axis to become (-4 1/2 , - 3)
V'(-4 1/2, -3) goes across the x axis to become (-4 1/2, 3) which is exactly what we got before.
Order does not matter for these 2 transformations.
112 yards
R
Sand
15 yards
Trap
20 yards s
If RS is parallel to AB, what is the width of the sand trap?
149 yards
82 yards
107 yards
84 yards
Answer:
my teacher has cancer please help her at #snowmanchallenge
Step-by-step explanation:
try to spread the help every snowman is ten dollars for her
Answer:
84
Step-by-step explanation:
112/20= 5.6
5.6*15=84
brainly is easy
If 200 of the 550 reptiles in as you are on display what percent of the reptiles are on display
Answer:
200/550×100%
=20000/550
=36.37%
Find area of shaded. Exact answer of pi
please please help me
Answer:
-0.88
Step-by-step explanation:
(f/g)(9)=(x+7)/-2x and the 9 brackets is the value of x with which you have to substitute. after u do that you get (9+7)/-18=16/-18=-0.88(8)
help!!!!!!!!!!!!!!!!! due in 15min
Answer:
5
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
When you put the i out in place for x you multiply so
4x9=36
7x9=63
2x9=18
9x9=81
what is the equation of a line with a slope of -3 and a y-intercept of 9
Answer:
The answer to the question provided is y = -3x + 9.
Which of the following is NOT a level of measurement? nominal ratio qualitative ordinal
Answer:
Nominal.
Step-by-step explanation:
The option that is NOT a level of measurement is qualitative.
With qualitative, numbers are not assigned to the measurement.
A level of measurement classifies and relates values to variables. Four levels of measurement have been identified as nominal, ordinal, interval, and ratio.
Ordinal can be quantitative or qualitative, while interval and ratio are always quantitative, and nominal has non-quantitative values assigned as measurements.
Thus, qualitative is not a recognized level of measurement.
Learn more about levels of measurement at https://brainly.com/question/24148016 and https://brainly.com/question/4823744
Solve this equation for a:
–5 + 4a = 27
Answer:
a=8
Step-by-step explanation:
solve for a by adding 5 on both sides
4a=32
Now divid 4 on both sides
a=8
Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to play as many games as they can before running out of tokens. Let m represent the number of games that require 2 tokens; n represent the number of games that require 3 tokens; and p represents the number of games that require 4 tokens.
Janie plays the 3-token game four times. Write two equivalent expressions to represent the number of tokens that Janie will need to play each of the three games at least one time.
12
3 + 3 + 3 + 3 = 12
3 x 4 = 12
Thanks!! <3
Calculus Problem shown in the attached image. I understand the concept of integrals but this particular question has me perplexed. I doubt its all that complex I just don't fully understand what its asking.
(a) For some given x, A(x) gives the signed area under f(t) on the interval [a, x]. Since f(t) is simple to integrate, and with a = 2, you can compute it exactly:
A(x) = ∫₂ˣ f(t) dt
A(x) = ∫₂ˣ (3t + 2) dt
A(x) = (3/2 t ² + 2t ) |₂ˣ
A(x) = 3/2 x ² + 2x - 10
which is parabolic and easy to graph.
(b) Differentiating A(x) is also easy if you use the "closed" form above:
A'(x) = (3/2 x ² + 2x - 10)'
A'(x) = 3x + 2
and this function tells you how the area under f(t) changes as you adjust the size of the integration interval.
You can get the same result using the fundamental theorem of calculus:
A'(x) = d/dx ∫₂ˣ f(t) dt = f(x) = 3x + 2
On Tuesday Bob, Larry, and Joe studied for their Algebra test. Bob
studied for 12 minutes less than Larry, and Joe studied twice as long
as Bob. How many minutes did each student study if they studied a
total of 96 minutes?
Answer:
Bob- 33, Larry- 21, Joe- 42
Step-by-step explanation:
Set up the equation with x=the amount of time Larry spent studying. x+(x-12)+2(x-12)=96. Distribute and combine: 4x-36=96. Add 36 to both sides (4x=132), and then divide by 4 (x=33). Larry studied 33 minutes, subtract 12 to find Bob, and then double Bob's time to get Joe's study time.
Which is a correct name for the angle shown?
Answer:
Angle CBA (the last one)
Step-by-step explanation:
Just look at the order of it. It could either be Angle ABC or Angle CBA.
(hope this helps!)
I will give brainiest to whoever answers correctly !!
Answer:
The number of units decreased by [tex]8.7\%[/tex].
Step-by-step explanation:
Initially, 470 units were sold. The following 429 units were sold, meaning this was [tex]470-429=41[/tex] less units than last year. Thus, the number of units sold decreased and the percent of decrease is:
[tex]\frac{41}{470}\approx 8.7\%[/tex]
HELP ASAP! Brainliest for correct answer!
Answer:
30
i hope it helps
Can someone write it on paper so I can copy
Answer:
453/ 2 = 226.5 rounds to 227
672/ 5 = 134.4 rounds to 134
1,294/ 4 = 323.5 rounds to 326
Step-by-step explanation:
Pls help extra points and mark brainlist easy reading
Answer:
A should be the answer pls brainliest
Step-by-step explanation:
anyone a J Balvin fan :)
Answer:
He Ll nah fam
Step-by-step explanation:
The tape diagram represents the ratio of your monthly allowance to your friend's monthly allowance. The monthly allowances total $90. How much is each allowance?
you [][][][][]
friend[][][][]
Your monthly allowance and your friend's monthly allowance is $50 and $40 respectively.
From the given tape diagram, the ratio of your monthly allowance to your friend's monthly allowance is 5:4.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, 5+4=9
Now, your monthly allowance = 5/9 × 90
= 50
So, your friend's monthly allowance = 90-50 = 40
Therefore, your monthly allowance and your friend's monthly allowance is $50 and $40 respectively.
To learn more about the ratio visit:
brainly.com/question/13419413.
#SPJ2
A researcher observes the level of aggression of six 5-year-old boys over the course of a school day. The number of incidents for the group of boys was 2, 4, 6, 12, 8, 10. What is the mean number of aggressive acts for this group of children?
a) 9
b) 5
c) 7
d) 4
Answer:
[tex]Mean = 7[/tex]
Step-by-step explanation:
Given
[tex]Data: 2, 4, 6, 12, 8, 10.[/tex]
Required
Determine the mean
The mean of a data is calculated as thus:
[tex]Mean = \frac{\sum x}{n}[/tex]
In this case:
[tex]n = 6[/tex]
So, the formula becomes:
[tex]Mean = \frac{2+4+6+12+8+10}{6}[/tex]
[tex]Mean = \frac{42}{6}[/tex]
[tex]Mean = 7[/tex]
