15. [-/1 Points] M4 DETAILS Use the Midpoint Rule with n = 4 to approximate the integral. 13 1²³×² = SCALCET9 5.2.009. x² dx
Answers
The approximate value of the integral ∫[1 to 5] x² dx using the Midpoint Rule with n = 4 is 41.
The Midpoint Rule is a numerical integration method used to approximate definite integrals. It divides the interval of integration into subintervals and approximates the area under the curve by summing the areas of rectangles. The formula for the Midpoint Rule is:
∫[a to b] f(x) dx ≈ Δx * (f(x₁) + f(x₂) + ... + f(xₙ)),
where Δx is the width of each subinterval and x₁, x₂, ..., xₙ are the midpoints of the subintervals.
In this case, the interval of integration is [1, 5], and we are using n = 4 subintervals. Therefore, the width of each subinterval, Δx, is (5 - 1) / 4 = 1.
The midpoints of the subintervals are x₁ = 1.5, x₂ = 2.5, x₃ = 3.5, and x₄ = 4.5.
Now we evaluate the function, f(x) = x², at these midpoints:
f(1.5) = (1.5)² = 2.25,
f(2.5) = (2.5)² = 6.25,
f(3.5) = (3.5)² = 12.25,
f(4.5) = (4.5)² = 20.25.
Finally, we calculate the approximate value of the integral using the Midpoint Rule formula:
∫[1 to 5] x² dx ≈ 1 * (2.25 + 6.25 + 12.25 + 20.25) = 41.
Therefore, the approximate value of the integral ∫[1 to 5] x² dx using the Midpoint Rule with n = 4 is 41.
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Related Questions
Solve the equation b/4 +2=-1
Answers
Answer:
b = -4
Step-by-step explanation:
\(\frac{b}{4} + 2 = 1\\\\\frac{b}{4} = -1\\\\b = -4\)
Find an equivalent ratio in simplest terms: 16 : 24
Answers
Answer:
2/3
Step-by-step explanation:
plz mrk brainliest
Atb xan
9. Factorise the expression (a + b)
A, (a + b + 2)(a-b+2)
B. (a-b-2)(a + b + 2)
C. (a + b + 2)2
D. (a - b + 2) (a + b-2)
E. (a + b + 2) (a + b -2)
10. Simplify: x2 - 2x
x² - 4
C. X-2 E. x2 - X
2
X +2
x + 2
21²-26
20-
A.
1 / 슬
B.
D.
х
x+2
х
X-2
A.
INSTRUCTION: Answer all questions.
1. Express 0.00562 in standard form
A. 5.62 x 103 8.5.62 x 10-2
C. 0.562 x 102 D. 5.62 x 10-3
E. 0:0562 X 10-3
2. Correct 0.04945 to two significant figures
A. 0.040 C. 0.050 E.0.0495
B. 0.049 D. 0.4950
3. One of the roots of the equation 6x2 = 5-7x is
A -X B. -1/3 C. D. 1/3 E. 2%
A rectangle polygon has each of its exterior
angle as 18º. How many sides has the polygon?
10 B. 11 C. 12 D. 20
20 E.2
E. 24
5. If five times a certain number is subtracted from
twice the square of the number the result is 63.
Find the number.
A. 21 B.9 0.8 0.7 E. 13
6. For what value of y is the expression undefined?
Y + 2
y2-3y - 10
A. y=0 B. y=-2 C. y=3 D.y=5 E. y=10
7. The first and seventh terms of a geometric
progression are 81/2 and 32/, respectively.
Find the common ratio.
A. 3/2 B. 3/4 c. 2²
2/3 D. 12 E. 1/3
11. What is the gradient of the straight line join
(3,0) and (2,-2)?
A.-2 B.
C.22 D.?/3
E.
12. Express the true bearing of 250° as a com
bearing.
A. N20°E
C. N20°W
S20°E
D. S700W
B.
13. If x2 + kx + 16 is a perfect square, then
A. 94
9/ B. %
B. C. 3/2 D. 3/8 E
14. Afiong got 58% in an examination, scort
marks. Her sister scored 330 marks in the
examination. Calculate her sister's per
Score.
A. 60%
C 64% E5%
Answers
Answer:
um i can't really understand what your trying to do here
Step-by-step explanation:
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1 less than the square of a number.
Don’t know the answer
Answers
Answer:
\(x<-1\quad \mathrm{or}\quad \:x>1\)
Step-by-step explanation:
Let the unknown number be x
\(1 < x^{2} \\\\Switch\:sides\\\\x^2>1\\\\\mathrm{For\:}u^n\:>\:a\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\:<\:-\sqrt[n]{a}\:or\:u\:>\:\sqrt[n]{a}\\\\x<-1\quad \mathrm{or}\quad \:x>1\)
Write the sentence as an equation.
341 is the same as the product of k and 273, minus 79
Answers
Answer:
341 = 273k - 79 or 273k - 79 = 341
For all of a and b, 3a (a + 2b)-b (2a-3b)
Answers
Answer:
3a^2 + 4ab + 3b^2
Step-by-step explanation:
just trust me bro :)
Find the value of ′x'
Answers
The value of x, which we get by using an exponent rule is x = 2.80259.
What is an exponent rule?
Exponent is defined as the method of expressing large numbers in terms of powers. That is, exponent refers to how many times a number is multiplied by itself. For example, 6 is multiplied by itself four times, resulting in 6 6 6 6. This can be written as 64. In this case, 4 is the exponent and 6 is the base.
We have,
\(\frac{2}{3} ^{x} . \frac{3}{2} ^{2x} = \frac{81}{16}\)
By applying the exponent rule:
\(\left(-1\cdot \:x+2x\right)\ln \left(\frac{3}{2}\right)=\ln \left(\frac{81}{26}\right)\)
By simplifying the equation:
\(x=\frac{\ln \left(\frac{81}{26}\right)}{\ln \left(\frac{3}{2}\right)}\)
x = 2.80259
Hence, the value of x = 2.80259
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Shane spent $15 on a shirt, 21.99 on a pair of pants, and 0.85 on a hat. Which is the best estimate for the amount of money in dollars Shane spent?
A) $23
B) $38
C) $70
D) $60
Answers
Answer:
B) $38
Step-by-step explanation:
Since the question asks for the amount of money in dollars that Shane has spent, we can add up all of her spendings to create this equation:
\(15+21.99+0.85\\=37.84\)
We are asked for the "best estimate", and according to our choices, $38 is closest to $37.84.
I have always been curious about this question.
What is 2+2 ???
Is it 22 or 4
Answers
Answer:
Step-by-step explanation:
both >:D
Answer: 4
Step-by-step explanation:
1. Hold up two fingers on both hands.
2. Then you count how many fingers are up on both hands.
3. Then you put your answer on your paper
4. Last is you turn it in
reduce 18/45 to simplest form
Answers
Answer:
2/5
Step-by-step explanation:
A circle with center (-1, 2) and radius of 8 has the equation
Answers
Answer:
c)
Step-by-step explanation:
The equation of the circle that has a center (-1, 2) and radius of 8 will be (x + 1)² + (y – 2)² = 64. Then the correct option is D.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x – h)² + (y – k)² = r²
A circle with center (-1, 2) and radius of 8.
Then the equation of the circle will be
(x – h)² + (y – k)² = r²
(x + 1)² + (y – 2)² = 8²
(x + 1)² + (y – 2)² = 64
Thus, the equation of the circle that has a center (-1, 2) and radius of 8 will be (x + 1)² + (y – 2)² = 64.
Then the correct option is D.
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What integer represents spending $100
Answers
Answer: <100
Step-by-step explanation:
An apartment complex rents an average of 2.3 new units per week. If the number of apartments rented each week has a Polsson distribution, then the probability of renting exactly three apartments in a week is ....
Answers
The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.
If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.
The probability of renting exactly three apartments in a week is given by the Poisson probability function:
\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)
Substituting the values, we get:
\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)
P(X = 3) = (0.09963 * 12.167) / 6
P(X = 3) = 0.2018
Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.
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These two triangles are similar. If the base of △ A B C is 3 cm and the base of △ D E F is 7 cm, and the area of △ A B C is 7 cm², calculate the area of △ D E F. Round your answer to two decimal places.
Answers
Answer:
38.11 cm^2
Step-by-step explanation:
DEF is larger than ABC
therefore find the height of ABC
7 = 1/2 * 3 * h
h = 7 * 2/3
h = 14/3
So, lets find height for DEF, 7/3 = H/ 14/3
H = 98/9
A = 1/2 * 7 * 98/9
A = 38.11 cm^2
Two turns contain vhite balls and yellow balls. The first urn contains 7 white balls and 10 yellowballs and the second turn contains 8 white balls and 2 yellow balls. A ball is drawn at randomfrom each turn. What is the probability that both balls are white?
Answers
Answer:
28/85
Explanation:
First Urn
Total number of balls = 7+10 =17
Number of white balls =7
P(White) = 7/17
SecondUrn
Total number of balls = 8+2=10
Number of white balls =8
P(White) = 8/10
Therefore, if a ball is drawn at random from each urn, the probability that both balls are white will be:
\(\begin{gathered} =\frac{7}{17}\times\frac{8}{10} \\ =\frac{56}{170} \\ =\frac{28}{85} \end{gathered}\)What is the missing numerator? (4 points)
blank over seven minus three eighths equals twenty seven fifty sixths
a. 4
Selected:b. 5This answer is incorrect.
c. 6
d. 7
Answers
Answer:
\(\frac{x}{7}\) - \(\frac{3}{8}\) = \(\frac{27\\}{56}\)
Step-by-step explanation:
C
6 x 8 = 32
7 x 3 = 21
32 - 21 = 27
Donna has boxes of doughnuts. Each box contains doughnuts. After eating one doughnut, Donna is able to rearrange the remaining doughnuts into bags so that each bag contains doughnuts, and none are left over. What is the smallest possible value of
Answers
The smallest possible value of doughnuts in each box is 2. The smallest possible value of doughnuts in each box is 2.
In order for Donna to rearrange the remaining doughnuts into bags so that each bag contains the same number of doughnuts and none are left over, the number of doughnuts in each box must be divisible by the number of bags. Since there are no doughnuts left over, this means that the number of doughnuts in each box must be a multiple of the number of bags.
To find the smallest possible value, we need to find the smallest common multiple of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 (since there are 9 possible numbers of bags). The smallest common multiple of these numbers is 2, so the smallest possible value of doughnuts in each box is 2.Therefore, the smallest possible value of doughnuts in each box is 2.
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5- For the regression equation 9 = 7 - 1.2x the predicted value y when x=4is? a) 0 b) 2.2√ c) 3.4 $1.6 6- If A and B make a partition of the sample space, (i. e AUB-S). Then the probability that at
Answers
For the regression equation 9 = 7 - 1.2x the predicted value y when x=4 is (b) 2.2√ is the predicted value of y.
The regression equation 9 = 7 - 1.2x is given. The task is to find the predicted value y when x = 4. Let's find out:
Putting x = 4 in the regression equation: 9 = 7 - 1.2x
⇒ y = 7 - 1.2(4)
⇒ y = 7 - 4.8
⇒ y = 2.2
Therefore, when x = 4, the predicted value of y is 2.2. Hence, the option (b) 2.2√ is correct.
Next, the second question is incomplete and the options are not provided. Please provide the complete question and options so that I can assist you better.
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5- For the regression equation 9 = 7 - 1.2x the predicted value y when x=4is? a) 0 b) 2.2√ c) 3.4 $1.6 6- If A and B make a partition of the sample space, (i. e AUB-S). Then the probability that at least one of the events occur is equal to a) 0 b) 0.25 c) 0.50 7- Let X be a continuous random variable and pdf f(x)=, 0sxs3 then P<X<D) is: a)- b) 8- If X is a discrete random variable with values (2, 3, 4, 5), which of the following functions is the probability mass function of X: C) IS
The predicted value of y when x=4 for the regression equation 9 = 7 - 1.2x is 2.2.
Explanation:
Given the regression equation: 9 = 7 - 1.2x, we need to find the predicted value of y when x=4.
To do this, we substitute x=4 into the equation and solve for y.
Substituting x=4 into the equation, we have:
9 = 7 - 1.2 × 4
9 = 7 - 4.8
9 = 2.2
Therefore, the predicted value of y when x=4 is 2.2.
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Please help, thank you!
Answers
Answer:
62.6
Step-by-step explanation:
The measure of variability easiest to compute, but seldom used as the only measure, is the _____
Answers
The measure of variability easiest to compute, but seldom used as the only measure, is the range.
What is the range of values?The range is the term that is used to refer to the difference that lies between the highest value and the lowest value in a data set while computing a statistical data.
The measures of variability are 4 in number. These are
The rangeThe interquartile rangethe standard deviationThe variance.Hence we can conclude that The measure of variability easiest to compute, but seldom used as the only measure, is the range.
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Please help and show work, will give lots of points!
Lourdes is reading a biography for her history class. She reads 30 pages each day. After 9 days, Lourdes has read 3/5 of the biography. Write a linear equation to represent the number of pages Lourdes still has to read after x days.
y = []x + []
(Use above format to write the equation.)
What does the y-intercept of this linear equation represent?
A. Pages already read
B. Pages in book
C. Pages read each day
D. Days to finish
Answers
Answer:
The linear equation is y = 450 - 30 x, where y is the number of pages
Lourdes has left to read after x days
Step-by-step explanation:
Each day, Lourdes reads 30 pages of a 450-page book
- We need to write a linear equation to represent the number of pages
Lourdes has left to read after x days
∵ Lourdes reads 30 pages each day
∵ Lourdes will read for x days
∴ The number of pages Lourdes will read in x day = 30 x
- The left pages will be the difference between the total pages of the
book and the pages Lourdes read
∵ The book has 450 pages
∵ Loured will read 30 x in x days
∴ The number of pages left = 450 - 30 x
- Assume that y represents the number of pages Lourdes has left
to read after x days
∴ y = 450 - 30 x
The linear equation is y = 450 - 30 x, where y is the number of
pages Lourdes has left to read after x days
7.
Find the smallest non-zero whole number which
can be multiplied by 112 to give a cube number.
Answers
Answer:
28 x 784
Step-by-step explanation:
Now 7 remains without a pair and therefore 7 should be multiplied to 112 to make it a perfect square. Similarly 28 should be multiplied to 784 to make it a perfect cube.
hope it helps, pls mark as brainliest and follow . thnx
Find the sum for the geometric series described as: a1=3125, 125, n=6, and r=1/5
Answers
The sum of the first 6 terms of the given geometric series is 3906.
Which statement is true regarding the graphed functions?
f(4) = g(4)
f(4) = g(-2)
f2) = g(-2)
f(-2) = g(-2)
Answer ASAP
Answers
Answer: f(2) = g(-2)
Step-by-step explanation: f(x) line if u go to the x axis you see that it’s 2 the x intercept.....
The g(x) line you go to the x axis and see it is -2, that is the x intercept
If two variables, x and y, have a strong linear relationship, then:
a. there may or may not be any causal relationship between x and y.
b. x causes y to happen.
c. y causes x to happen.
d. None of these alternatives is correct.
Answers
The cοrrect answer is a) There may οr may nοt be any causal relatiοnship between x and y.
What is Linear Relatiοnship?A linear relatiοnship is a relatiοnship which can be represented by a straight line.
When twο variables have a strοng linear relatiοnship, it indicates a strοng statistical assοciatiοn οr cοrrelatiοn between them. Hοwever, cοrrelatiοn dοes nοt imply causatiοn.
It means that changes in οne variable are accοmpanied by changes in the οther, but it dοes nοt establish a cause-and-effect relatiοnship between them.
There cοuld be οther factοrs οr variables at play that are respοnsible fοr the οbserved relatiοnship.
Therefοre, οptiοn a is the cοrrect answer.
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x2 + 4
Select all that apply
Answers
Answer:
The first three depending on what the first one says. 2 and three are definitely correct though. If the first one says x to the second power added by 4 then it is correct.
Step-by-step explanation:
Dallas has 5 fewer than 3 times as many marbles as Anthony. Anthony has x marbles. Enter an expression to represent the number of marbles Dallas has.
Answers
The expression that represent the number of marbles Dallas has is 3x - 5
How to determine the expression that represent the number of marbles Dallas has?From the question, we have the following parameters that can be used in our computation:
Dallas has 5 fewer than 3 times as many marbles as Anthony
Also from the question, we have
Anthony has x marbles
This means that
Anthony = x
So, we have
Dallas has 5 fewer than 3 times as many marbles as x
Express as equation
Dallas = 5 fewer than 3 times as many marbles as x
So, we have
Dallas = 5 fewer than 3x
Represent as equation
Dallas = 3x - 5
Hence, the expression is 3x - 5
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How much water will a cone hold that has a diameter of 6 inches and height of 21 inches. Use 3.15 pie and round your answer to the nearest whole number
Answers
Answer:
volume = 595 in³
Step-by-step explanation:
radius = 6/2 = 3
volume = 3.15(3²)(21) = 595.35 in³
Calculate the median, the range and identify the Q1 and Q3 for the following set: 5, 1, 6, 8, 1, 7, 4, 5, 6, 11, 3, 4, 4, 2, 5, 5 (hint draw a box and whisker plot)
Answers
Answer:
Arrange the data in ascending order
1,1,2,3,4,4,4,5,5,5,5,6,6,7,8,11
n=16
position of median = (n+1)/2 = 17/2 = 8.5 th item
8.5 th item is the average of 8 and 9th item
median = (5+5)/2 = 5
Range = largest value - smallest value
= 11 -1 = 10
position of Q1= (n+1)/4 = 17/4 = 4.25 th item
Q1 = 4 + 0.25(5th item - 4th item )
4 + 0.25(4-3)
= 4.25
position of Q3= (n+1)/4 = 3*17/4 = 12.75 th item
Q1 = 12 + 0.75(13th item - 12th item )
12 + 0.75(6-6)
= 12
Step-by-step explanation:
Martina bought a pair of
shoes for $39.90. The total cost for the
shoes was $41.50. What is the sales
tax rate in Martina's state?
Answers
Answer: 4% tax
Step-by-step explanation:
41.50- 39.90= 1.60 tax
1.60/ 39.90