Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.
4 0 x3 sin(x) dx, n = 8
Answers
Answer:
trapezoidal rule: -7.28midpoint rule: -4.82Simpson's rule: -5.61Step-by-step explanation:
The interval from 0 to 4 is divided into 8 equal parts, so each has a width of 0.5 units. For the trapezoidal and Simpson's rules, the function is evaluated at each end of each interval, and those results are combined in the manner specified by the rule.
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For the trapezoidal rule, the function values are taken as the "bases" of trapezoids, whose "height" is the interval width. The estimate of the integral is the sum of the areas of these trapezoids.
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For the midpoint rule, the function is evaluated at the midpoint of each interval, and that value is multiplied by the interval width to form an estimate of the integral over the interval. In the spreadsheet, midpoints and their function values are listed separately from those used for the other rules. The midpoint area is the rectangle area described here.
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For Simpson's rule, the function values at the ends of each interval are combined with weights of 1, 2, or 4 in a particular pattern. The sum of products is multiplied by 1/3 the interval width. In the spreadsheet, the weights are listed so the SUMPRODUCT function could be used to create the desired total.
We note the Simpson's rule estimate of the integral (-5.61) is very close, as the actual value rounds to -5.64.
___
A graph of the function and a computation of the integral is shown in the second attachment.
Related Questions
Find the volume of a right circular cone that has a height of 4.2m and a base with a radius of 3.4m
Answers
Answer:
about 50.8 cubic meters
Step-by-step explanation:
The formula for the volume of a cone is ...
V = (1/3)πr²h
Put the given values into the formula and do the arithmetic.
V = (1/3)π(3.4 m)²(4.2 m) = 16.194π m³
__
For π to calculator precision, this is ...
V ≈ 50.84 m³
For π = 3.14, this is ...
V ≈ 50.82 m³
When 1760 is divided into 14 equal parts, the remainder is 10. What is a correct way to write the quotient?
Answers
Answer:
125 r. 10
Step-by-step explanation:
If
f(x) = 13x + 1, then
f-1(x) =
Answers
Answer:
(x-1)/13
Step-by-step explanation:
y = 13x+1
To find the inverse, exchange x and y
x = 13y+1
Solve for y
Subtract 1 from each side
x-1 =13y+1-1
x-1 = 13y
Divide each side by 13
(x-1)/13 = y
The inverse is (x-1)/13
Answer:
f(x) = 13x + 1
To find the inverse let f(x) = y
y = 13x + 1
x = 13y + 1
13y = x - 1
y = (x-1)/13
The inverse is x-1/13.
The area of a triangle is 80cm² and its base is 8cm. If its height is (6+k) cm, find the value if k.
(3marks)
Answers
Answer:
K=14
Step-by-step explanation:
A=1/2*b*h
80=1/2*8*(6+k) multiply by 2 on both sides
160=8*(6+k) distribute by 8
160=48+8k subtract 48 from both sides
112=8k divide by 8
14=K
Question 2: The average price for a BMW 3 Series Coupe 335i is $39,368. Suppose these prices are also normally distributed with a standard deviation of $2,367. What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe? Round your answer to 3 decimal places.
Answers
Answer:
0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 39368, \sigma = 2367[/tex]
What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe?
This is 1 subtracted by the pvalue of Z when X = 44520. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{44520 - 39368}{2367}[/tex]
[tex]Z = 2.18[/tex]
[tex]Z = 2.18[/tex] has a pvalue of 0.985
1 - 0.985 = 0.015
0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe
The measures of two angles of a triangle are 105 and 31 degrees. Find the measure of the third angle.
Answers
Answer: 44°
Step-by-step explanation:
Measures of the angles of a triangle
= 180°
Therefore, 180 - 105 + 31 = 44°
The measure of the third angle is 44 degrees.
We have,
To find the measure of the third angle in a triangle, we can use the fact that the sum of the measures of all three angles in a triangle is always 180 degrees.
Let's denote the measure of the third angle as "x".
We are given that the measures of the other two angles are 105 degrees and 31 degrees.
Using the sum of angles in a triangle, we can set up the equation:
105 + 31 + x = 180
Simplifying the equation:
136 + x = 180
To isolate "x", we subtract 136 from both sides of the equation:
x = 180 - 136
x = 44
Therefore,
The measure of the third angle is 44 degrees.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ2
The promising alternative energy sources currently under development are fuel cell technology and large-scale solar energy power. The probabilities that these two sources will be successfully developed and commercially viable in the next 10 years are 0.70 and 0.85, respectively. The successful development of these two energy sources are statistically independent. Determine the following: a. The probability that there will be energy supplied by these two alternative sources in the next 10 years. b. The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years.
Answers
Answer:
Step-by-step explanation:
a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S
Write the probability of energy supplied by these energy sources in the next 10 years
P(energy supplied) = P(S ∪ F) -----(1)
Rewrite eqn (1)
P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)
substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources
P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)
= 0.85 + 0.7 - (0.595)
= 1.55 - 0.595
= 0.955
Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955
B) write the probability of only one source of energy available
P(only one source of energy available) = [tex]P(\bar F S)[/tex] ∪ [tex]P( \bar S F)[/tex] ---(3)
Rewrite the equation (3)
P(only one source of energy available) =
[tex]=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)[/tex]
[tex]=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36[/tex]
Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36
answer this please ????
Answers
Answer:
a. x = 4
b. x = 17.5
Step-by-step explanation:
a. 5x/2 + 1 = 11
5x/2 = 10
5x = 20
x = 4
b. 2x/7 - 3 = 2
2x/7 = 5
2x = 35
x = 35/2
Answer:
a) x = 4
b) x = 17.5
Step-by-step explanation:
a)
(5x)/2 + 1 = 11
(5x)/2 = 10
5x = 20
x = 4
b)
(2x)/7 - 3 = 2
(2x)/7 = 5
2x = 35
x = 17.5
Which theoretical probabilities are equal to 1/3? Check all that apply.
Answers
Answer:
2/6, 4/12, 8/24, 16/48, 32/96 ect....
Step-by-step explanation:
I hope this helps I really didnt know if this is what you were asking about
−10x+3y=5 x=y−4 Need X and Y pleaseee men :(
Answers
Answer:
x= 1
y = 5
Step-by-step explanation:
-10x+3y=5
x = y−4
-10(y-4)+3y=5
-10y+40+3y=5
-7y=5-45
-7y=-35
y=5
x = 5−4
x = 1
Answer:
[tex] x = 1 \\ y = 5 \\ [/tex]
[tex] - 10x + 3y = 5nd10x - 10( - 1)y = - 10( - 4) \\ - 10x + 3y = 5nd10x + 10y = 40 \\ - 10x10x + 3y - 10 = 5 - 40 \\ 3y - 10y = 5 - 40 \\ - 7y = 5 - 40 \\ - 7y = 35 \\ y = 5 \\ x - 5 = - 4 \\ x = 1[/tex]
paulina plays both volleyball and soccer .the probability of her getting injured playing soccer is 0.10 and the probability of her getting injured playing soccer is 0.20 .which of the event is more likely
Answers
Step-by-step explanation:
While playing volleyball, probability of getting hurt is
P(A) = 0.1 = 1/10
and in the case of soccer, it is
P(B) = 0.2 = 2/10 = 1/5
Here we see, P(A) < P(B)
Answer: We can conclude that the probability of getting injured while playing soccer is more likely.
Any help would be great
Answers
Answer:
15
Step-by-step explanation:
38=10+13+c
c=38-10-13=15
Hope this helps!
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope intercept form.
Answers
Answer:
y = x-2
Step-by-step explanation:
Pick two points on the line
(0,-2) and (2,0)
We can find the slope
m = (y2-y1)/(x2-x1)
= (0--2)/(2-0)
= (0+2)/(2-0)
2/2
=
We know the y intercept is -2 ( where it crosses the y axis)
y = mx +b is the slope intercept form of the equation where m is the slope and b is the y intercept
y = 1x -2
y = x-2
Answer: [tex]y=x-2[/tex]
Step-by-step explanation:
I explained the other problem you asked, why couldnt you apply that info to this one? Either way, Ill explain it again.
We can see the slope intercept is -2, so b = -2
To get the slope, just from visualization. Look at the y value and x value direction for which you gotta take to get to the next coords. From the y-intercept, you go up 1 and then right 1. 1/1 = 1
Assume that the population proportion is 0.56. Compute the standard error of the proportion, σp, for sample sizes of 100, 200, 500, and 1,000. (Round your answers to four decimal places.)
Answers
Answer:
Standard errors are 0.049, 0.035, 0.022, and 0.016.
Step-by-step explanation:
The given value of population proportion (P) = 0.56
Given sample sizes (n ) 100, 200, 500, and 1000.
Now standard error is required to calculate.
Use the below formula to find standard error.
When sample size is n = 100
[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{100}} =0.049[/tex]
When sample size is n = 200
[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{200}} = 0.035[/tex]
When sample size is n = 500
[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{500}} =0.022[/tex]
When sample size is n = 1000
[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{1000}} = 0.016[/tex]
Suppose you have a dataset with m = 50m=50 examples and n = 200000n=200000 features for each example. You want to use multivariate linear regression to fit the parameters \thetaθ to our data. Should you prefer gradient descent or the normal equation?
Answers
Answer:
Step-by-step explanation:
Consider X to be the matrix whose columns are the values for our 50 examples. The normal equation gives us the values of [tex]\theta[/tex] in the following way
[tex] \theta = (X^{T}X)^{-1}X^{T}y[/tex]
The matrix [tex]X^{T}X[/tex] however, might not be invertible when [tex]m\leq n[/tex]. So we must use the pseudo inverse to solve the problem. For a big number of features, calculating the pseudoinverse might be computational expensive. So, gradient descent should be prefered.
Stealers, study components: In a study of the relationship between socio-economic class and unethical behavior, 129 University of California undergraduates at Berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. They were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. After completing some unrelated tasks, participants reported the number of candies they had taken. It was found that those who were identified as upper-class took more candy than others (Piff, 2012). Identify the following about this study.
a) What are the cases?_____
b) What are the variables and their types?_____
c) What is the main research question?_____
Answers
Answer:
a) 129 University of California undergraduates at Berkeley.
b) (i) social-class (ordinal), (ii) money (continuous), (iii) education (ordinal) , (iv) respected job (ordinal), (v) number of candies (continuous)
c) The main question is to find the relationship between socio-economic class and unethical behaviour
Step-by-step explanation:
a) 129 University of California undergraduates at Berkeley.
b)
i) social-class (ordinal)
ii) money (continuous)
iii) education (ordinal)
iv) respected job (ordinal)
v) number of candies (continuous)
c) The main question is to find the relationship between socio-economic class and unethical behaviour
Help solve attached question.
Answers
Answer:
[tex]\mathrm{12\sqrt{5} \: \: inches}[/tex]
Step-by-step explanation:
Use Pythagorean theorem, where:
[tex]a^2+b^2=c^2[/tex]
Substitute in the values.
[tex]24^2+12^2=c^2[/tex]
[tex]c^2=576+144[/tex]
[tex]c^2=720[/tex]
[tex]c=\sqrt{720}[/tex]
[tex]c=12\sqrt{5}[/tex]
[tex]c=26.83281[/tex]
4(4x - 2) = x + 4
asnwerplsssssssss
Answers
Answer:
4(4x - 2) = x + 4
16x - 8 = x + 4
15x = 12
x = 12/15 = 4/5
Answer:
x = 0.8
Step-by-step explanation:
4(4x - 2) = x + 4
16x - 8 = x + 4
16x - x = 4 + 8
15x = 12
x = 0.8
2)
Which of these objects are two-dimensional? Check all that apply.
A.Point
B.Segment
C.Square
D. Line
E. Solid
F. Plane
Answers
Answer:
Option C and F
Step-by-step explanation:
=> Square and Plane a two-dimensional objects.
Rest of the objects are either 1 - dimensional or 3- dimensional.
Suppose tossing a coin 8 times represents the 8 cups of tea, heads represents a correct identification of what was poured first, tea or milk, and tails represents an incorrect identification of what was poured first. Select the best conclusion you would draw about whether the woman was just guessing.
A. Repeat the process many times (1000). If 6 correct out of 8 cups rarely occurs, then it is most likely that the woman was just guessing as to what was poured first.
B. Repeat the process many times (1000). If 8 correct out of 8 cups rarely occurs, then it is unlikely that the woman was just guessing as to what was poured first.
C. Repeat the process many times (1000). If 8 correct out of 8 cups rarely occurs, then it is likely that the woman was just guessing as to what was poured first.
D. Repeat the process many times (1000). If 4 correct out of 8 cups rarely occurs, then it is unlikely that the woman was just guessing as to what was poured first.
Answers
Answer:
A. Repeat the process many times (1000). If 6 correct out of 8 cups rarely occurs, then it is most likely that the woman was just guessing as to what was poured first.
Step-by-step explanation:
Since tossing a coin 8 times implies 8 cups of tea, with the given conditions.
The sample space = 1000
Then;
[tex]\frac{6}{8}[/tex] × 1000 = 750
If 6 correct out of 8 cups occurs (750 out of 1000), the woman got 750 correctly. Thus it can be inferred that it is likely that she knew what was poured first, either the tea or milk.
But, if 6 correct out of 8 cups rarely occurs (i.e 250 out of 1000), then it is most likely that the woman was just guessing as to what was poured first.
A polynomial is factorable, but it is not a perfect square trinomial or a
difference of two squares. Can you factor the polynomial without finding the GCF?
Answers
Answer:
So in this problem, we're told that a polynomial is fact herbal and it's not a perfect square. Try no meal or a difference of two squares. Can you factor the pie? Nomi bite or polynomial without finding the G C F. So no Jacey after is allowed. So if it's not a perfect squared, try no meal. So not a perfect square. We know it's not this, and we also know it's not a difference of two squirt if it's not any of these or if it's not either of these, but we can't find the G. C F. There are three different ways we could find the factored form. You could do it by grouping where you separating the polynomial into two parts and factor them individually before combining. You could also use the sum or a difference of cubes. This is for a cubic or a um, polynomial of third degree, and you could also use fractional or negative exponents. So even if you can't find the G c f or use these methods, there are still three ways you can factor the
Step-by-step explanation:
Glad i could help!
How is the vertex related to the maximum or minimum of a parabola?
Answers
Answer:
Vertical parabolas give an important piece of information: When the parabola opens up, the vertex is the lowest point on the graph — called the minimum, or min. When the parabola opens down, the vertex is the highest point on the graph — called the maximum, or max.
Step-by-step explanation:
The y coordinate of the vertex tells you the highest or lowest point, depending on whether the parabola opens downward or upward.
For something like y = -2(x-5)^2 + 10, it opens downward and has the vertex at (5,10). The highest point is (5,10) so the largest y value or output is y = 10. This is the maximum of the function. Note the value of 'a' is a = -2 which is negative. Also note the vertex form y = a(x-h)^2 + k with vertex (h,k).
For an example like y = 7(x+2)^2 - 8 we have a = 7 so the parabola opens upward meaning we'll have a minimum this time. The lowest point is the vertex (h,k) = (-2,-8). The minimum of the function is y = -8.
State the domain of f(a,b) = e^ab
Answers
Answer:
a2+b2=c2
Step-by-step explanation:
find the saqure roof of two
Answer:
(∞,∞), (a /a∉R)
Step-by-step explanation:
Sixteen of 80 dogs in a rescue kennel are puppies.what percent of the dogs in the kennel are puppies?
Answers
Answer:
20%
Step-by-step explanation:
Answer:
20%
Step-by-step explanation: All you have to do is 16 divided by 80 which is 0.2. 0.2 as a decimal is 20%.
A kite is flying 85 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 52degrees. Find the length of the string. Round your answer to the nearest tenth.
Answers
Answer:
107.9 ft
Step-by-step explanation:
Imagine Kite is a point A. The person ,who keeps the string is point B.
The height of flying is AC=85 ft. So we have right triangle ABC :angle C=90 degrees, angle B is 52 degrees. Length of AB (triangle ABC hypotenuse) is the length of the string.
AB=AC/sinB=85/sin52=107.8665...=approx 107.9 ft
What transformations to the linear parent function, f(x) = x, give the function
g(x) = 4x - 2? Select all that apply.
A. Shift down 2 units.
B. Vertically stretch by a factor of 4.
O c. Horizontally stretch by a factor of 4.
O D. Shift left 2 units.
Answers
Answer:
A. Shift down 2 units.
B. Vertically stretch by a factor of 4.
Step-by-step explanation:
Given the function
f(x)=x
If we stretch y vertically by a factor of m, we have: y=m·f (x)
Therefore:
Vertically stretching f(x) by a factor of 4, we have: 4x.
Next, if we take down f(x) by k units we have: y= f(x)-k
Therefore: Taking down 4x by 2 units, we obtain:
g(x)=4x-2
Therefore, Options A and B applies.
For the following situations, state which type of sampling plan was used. In order to find out how its employees felt about higher student fees imposed by the legislature, a university divided employees in three categories: staff, faculty, and student employees. A random sample was selected from each group and they were telephoned and asked for their opinions. A. Cluster sampling B. Systematic sampling C. Stratified sampling D. Convenience sampling
Answers
Answer:
I think sample B is better.
Step-by-step explanation:
Its more careful and better
According to a milk carton, 2% milk contains 70 % less fat than whole milk. The nutrition label on the other side of the carton states that one serving of this milk contains 2.5 grams of fat. How many grams of fat are in an
equivalent serving of whole milk?
Answers
Answer:
8.33 grams of fat
Step-by-step explanation:
One serving of the milk contains 2.5 grams of fat.
2% milk has 70% less fat than whole milk.
This means 2% milk has 30% of the fat that whole milk has.
Let W = amount of fat in whole milk
30% of the fat that whole milk has
=30% × w
=30/100×w
=0.30×w
=0.30w
How many grams of fat are in an equivalent gram of whole milk
2.5g=0.30w
w=2.5g/0.30
=8.33 grams of fat
The mean of 10 positive numbers is 16. when another number is added, the mean becomes 18. Find the number added
Answers
Answer:
The number added was 38.
Step-by-step explanation:
(16x10+x)/11 = 18
160+x = 198
x = 38
Best Regards!
Please answer this correctly
Answers
Answer:
3| 4 4 7
4| 0 3 4
5| 5 5 5
6| 0 1 3 8 9
7| 9
8| 1 4 6 8
hope it helps!
Step-by-step explanation:
Check the numbers and list out the tens digit in stem (that is 3-8) and then write the corresponding leaf values