Answers
Answer:
9.29
Step-by-step explanation:
S₄ is the area using Simpson's rule and 4 intervals.
Simpson's rule can be calculated as:
Sᵢ = Δx/3 (f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + 4f(xᵢ₋₂) + 2f(xᵢ₋₁) + f(xᵢ))
Or, Simpson's rule can be calculated as a combination of midpoint and trapezoid sums:
S₂ᵢ = (2Mᵢ + Tᵢ) / 3
Using the first method:
Δx = (4−0)/4 = 1
S₄ = 1/3 (1.00 + 4(1.41) + 2(2.24) + 4(3.16) + 4.12)
S₄ = 1/3 (27.88)
S₄ ≈ 9.29
Using the second method:
S₄ = (2M₂ + T₂) / 3
The midpoint area for 2 intervals is:
M₂ = (2) (1.41) + (2) (3.16) = 9.14
The trapezoid area for 2 intervals is:
T₂ = ½ (1.00 + 2.24) (2) + ½ (2.24 + 4.12) (2) = 9.60
Therefore:
S₄ = (2 (9.14) + 9.60) / 3
S₄ ≈ 9.29
Related Questions
The data below were obtained from an experiment were participants were given drinks with or without caffeine and then asked to tap their fingers. The data for 20 participants are below. Assume the number of taps per minute is normally distributed. The variance is unknown. Find a 95% CI for μ number of taps. Identify the pivot function used. 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242
Answers
Answer:
The 95% confidence interval is [tex]244.26 < \mu < 246.95[/tex]
The pivot function used is
[tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]
Step-by-step explanation:
From the question we are told that
The data given is 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242
The sample size is [tex]n= 20[/tex]
Given that the confidence level is 95% then the level of significance is
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
The degree of freedom is mathematically represented as
[tex]df = 20 -1[/tex]
[tex]df = 19[/tex]
From the student t-distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]t_{\frac{\alpha }{2} , 19 } = 2.093[/tex]
The mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{ n}[/tex]
[tex]\= x = \frac{246+ 242 +248+245+ 250+ 244+252+ 248 +248 +247+ 250+ 248+ 246+ 242 +248 +244 +245 +246+ 250+ 242}{20}[/tex][tex]\= x = 246.6[/tex]
The standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum (x_i - \= x )^2)}{n} }[/tex]
[tex]\sigma = \sqrt{\frac{(246- 246.6)^2 +(242- 246.6)^2 +(248- 246.6)^2 + (248- 245)^2+}{20} } \ ..[/tex]
[tex]\ ...\sqrt{\frac{(250-246.6 )^2+ (244- 246.6)^2+(252- 246.6)^2+ (248- 246.6)^2+ (248- 246.6)^2+}{20} } \ ...[/tex]
[tex]\ ..\sqrt{\frac{(247- 246.6)^2+ (250- 246.6)^2+ (248-246.6)^2+ (246-246.6)^2+ (242-246.6)^2+ (248-246.6)^2+ (244-246.6)^2+}{20} } \ ...[/tex] [tex]\sqrt{\frac{ (245-246.6)^2+ (246-246.6)^2+ ( 246-246.6)^2 + ( 250-246.6)^2+ ( 242-246.6)^2 +( 246-246.6)^2+ ( 242-246.6)^2 }{20} }[/tex][tex]\sigma = 2.87411[/tex]
The margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , 19} * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.093 * \frac{2.87411 }{\sqrt{20} }[/tex]
[tex]E = 1.345[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]245.6 - 1.345 < \mu <245.6 + 1.345[/tex]
=> [tex]244.26 < \mu < 246.95[/tex]
The pivot function used is
[tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]
Write an equation in slope-intercept form (y = mx + b).
Passing through (2, -3) with a slope of 5/3.
Answers
Answer:
Step-by-step explanation:
y + 3 = 5/3(x - 2)
y + 9/3 = 5/3x - 10/3
y = 5/3x - 19/3
Findf '(3), where f(t) = u(t) · v(t), u(3) =1, 2, −2, u'(3) =8, 1, 4,andv(t) =t, t2, t3.
Answers
Answer:
[tex]f'(3)=100[/tex]
Step-by-step explanation:
Given:
[tex]f(t)=u(t)\cdot v(t)\\u(3)=\left ( 1,2,-2 \right )\\u'\left ( 3 \right )=\left ( 8,1,4 \right )\\v(t)=\left ( t,t^{2},t^{3} \right )[/tex]
To find: [tex]f'(3)[/tex]
Solution:
[tex]v(t)=\left ( t,t^{2},t^{3} \right )[/tex]
At [tex]t=3;[/tex]
[tex]v(3)=(3,3^{2},3^{3} )=(3,9,27)[/tex]
Differentiate with respect to t
[tex]v'(t)=\left ( 1,2t,3t^{2} \right )[/tex]
At [tex]t=3;[/tex]
[tex]v'(3)=\left ( 1,2(3),3(3)^{2} \right )=\left ( 1,6,27 \right )[/tex]
Using product rule, differentiate [tex]f(t)=u(t)\cdot v(t)[/tex] with respect to [tex]t[/tex]
[tex]f'(t)=u'(t)\cdot v(t)+u(t)\cdot v'(t)[/tex]
At [tex]t=3;[/tex]
[tex]f'(3)=u'(3)\cdot v(3)+u(3)\cdot v'(3)\\=\left ( 8,1,4 \right )\cdot \left ( 3,9,27 \right )+\left ( 1,2,-2 \right )\cdot \left ( 1,6,27 \right )\\=24+9+108+1+12-54\\=100[/tex]
PLEASE HELP
Consider the equation: 1/4x + 3y − 23 = 42
The variables are:
The coefficients are:
The constants are:
Answers
Answer:
The variables are x and y.The coefficients are 1/4 and 3.Lastly the constants are -23 and 42
Step-by-step explanation:
Variables are letters used to represent an unknown number.Coefficients are the numbers in front of the variables.Constants are numbers by themselves they can be positive and negative.
For the equation: 1/4x + 3y − 23 = 42 the variables are x, y the coefficients 1/4 , 3are the constants are -23 , 42
What is a variable?A quantity that may assume any one of a set of values or in simple words a quantity whose value changes may vary.
What is a coefficient?A numerical or constant quantity placed before and multiplying the variable in an algebraic expression
What is a constant?A constant is a value or number that never changes in expression
in the given equation: 1/4x + 3y − 23 = 42
x and y are variables as the changes for different set of values.
1/4 and 3 are coefficient as they are placed before and multiplying the variable.
-23, 42 is a constant as its value never changes in expression.
Thus for the equation: 1/4x + 3y − 23 = 42 the variables are x, y the coefficients 1/4 , 3are the constants are -23 , 42
To know more about variables , coefficients and constants click here
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Write the next 4 digits in the repeating decimal 4.715
Answers
Answer:
4.7157157
Step-by-step explanation:
because it is a repeating decimal, it will repeat the terms that come first such as 715.
Round 10.999244792948 to the nearest whole number
Answers
Answer:
11
Step-by-step explanation:
1. Listing Information
The number is 10.999244792948.
Simply put, numbers below 5 are rounded down and numbers that are greater than or equal to five are rounded up.
The tenths place value in 10.999244792948 is 9.
2. Solving the Problem
With the previous information in mind, 9 is greater than 5. Because of this, 10.999244792948 should be rounded to 11.
What is the value of the expression below when y = 5?
4y2 – 7y - 6
Answers
Answer: 371
Step-by-step explanation:
Answer:59
Step-by-step explanation:
Given the vectors shown, find the sum (P+Q+R).
Answers
Solve the equation –4 In(6x) = 2.
O A. 0.101
B. 0.275
C 3.639
D. 67.238
Answers
Isolate the variable using algebraic manipulation.
[tex]-4 ln(6x)=2[/tex]
[tex]ln(6x)=-\frac{1}{2}[/tex]
[tex]6x=e^{-\frac{1}{2}}[/tex]
[tex]x=\frac{e^-\frac{1}{2}}{6}[/tex]
[tex]x=0.101[/tex]
Hope this helps.
頑張って!
Answer:
A) 0.101
Step-by-step explanation:
[tex]ln(6x) = -1/2[/tex] [tex]6x = e^(^-^1^/^2^)[/tex] [tex]6x = 1/\sqrt{e}[/tex] [tex]x = 1/(6\times \sqrt{e})[/tex]Using the calculator [tex]x = 0.101[/tex]
Math 1 3/8 1/4 a c= 2 5/8 11/16 a c= 3 4/6 6/9 a c=
Answers
Wen can turn both fractions into decimals.
1 1/3 = 1.333...
1/4 = 0.25
As we can see 1 1/3 is greater than 0.25.
Therefore, the answer is [ 1 1/3 > 1/4 ]
Best of Luck!
Can someone explain this to me?
Answers
Answer:
120/7
Step-by-step explanation:
You cross multiply120=7xDivide both sides x= 120/7If f (x) = 3x − 4, Find f (−1) Helpp
Answers
Answer:
f(x) = 3x-4
f(-1)= 3(-1) -4
f(-1) = -3-4
= -7
hope this helps uh!
Answer:
f(-1)= -7
Step-by-step explanation:
We are given the function:
f(x)=3x-4
We want to find f(-1). We must plug -1 in for x and solve.
f(-1)= 3(-1)-4
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
Multiply 3 and -1.
f(-1)= -3 -4
Subtract 4 from -3.
f(-1)= -7
f(-1) is equal to -7.
PLEASEEE HELPPP
Solve for x:
Answers
Second option, just do Pemdas backwards.
c(a + b)- d = f, for a
Answers
Answer:
Step-by-step explanation:
C(a + b) = f + d
a + b = (f + d)/C
a = (f + d)/C - b
Find the midpoint of the segment with the following endpoints.
(-2, 1) and (6,-3)
Answers
Answer:
The midpoint is ( 2,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates and divide by 2
(-2+6)/2 =4/2 =2
To find the y coordinate of the midpoint, add the y coordinates and divide by 2
( 1+-3)/2 = -2/2 = -1
The midpoint is ( 2,-1)
Answer:
(2, -1)
Step-by-step explanation:
Let M is the midpoint of that segment with the endpoints A(-2,1) and B(6,-3)
x-coordinate of M:
xM = (xA + xB) / 2 = (-2 + 6) / 2 = 4 / 2 = 2
y-coordinate of M:
yM = (yA + yB) / 2 = ( 1 + -3) / 2 = -2 / 2 = -1
Answer: M(2, -1)
Determine if the following relations represent y as a function of x. x=y^4
Answers
Answer:
x = y⁴ does not represent y as a function of x
Step-by-step explanation:
Let's first isolate this equation for the 'y' value :
[tex]\mathrm{Switch\:sides} : y^4=x,\\\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)} : y=\sqrt[4]{x},\:y=-\sqrt[4]{x}[/tex]
So as you can tell, we have two functions. However, they can be rewritten as one function, y = ± ⁴√x. As we have two values of x that correspond to one value of y, this relation is not a function.
Solution: x = y⁴ does not represent y as a function of x
The sum of 2 composite numbers is never a prime number. Explain your answer.
Answers
Answer:
Step-by-step explanation:
Composite numbers are positive numbers that have factors, This means that they are divisible by numbers other than 1 and itself provided that number is a factor of the composite number. They possess at the bearest minimum level, a divisor other than 1 and itself. They are a natural number that is expressible as the product of two(or more) numbers other than 1 and itself.
For example:
4 is a composite number because its factors are 1, 2 and 4 which have another divisor apart from 1 and itself (4). That divisor is 2.
We all know that prime numbers are numbers that can be only be divided by 1 and itself.
Therefore, the sum of two composite number, for example:
4 + 6 = 10, We can now see that 10 is never a prime number.
What is the domain in interval notation. do not include any spaces in your answers! Type in the word infinity if needed
Answers
Answer:
(-6,5]
Step-by-step explanation:
Domain includes all of the x-values a function contains. In this case, it goes from -6 to 5. The open dot on the left indicates that this number is not included in the answer, and in interval notation you would use a parentheses. The filled in dot on the right coordinate indicates that this number is included, so you would use a bracket.
Plz help 7th grade math
Answers
Answer:
9feet
Step-by-step explanation:
B= -34 M=-25
-34-(-25)=-34+25=9
Answer:
9 feet
Step-by-step explanation:
Brett is -34 feet and Max is -25 feet from sea level.
In order to find how many feet Max is above Brett, we can change the numbers to be positive and subtract Brett's distance - Max's distance
34-25=9
Max is 9 feet above Brett
Identify the nonlinear graph A) B) C) D)
Answers
A linear function makes a straight line
A nonlinear graph is any curve that isn't a straight line. In this case, graph C is a parabola (from a quadratic function).
Graph A is a straight line.
Graph B is a straight line.
Graph C is not a straight line
Graph D is a straight line.
The non-linear graph is option D.
Option D is the correct answer.
What are coordin2ates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
Graph A
Graph B
Graph C
Graph D
A linear graph is a graph that is a straight line.
A non-linear graph is a graph that is not a straight line.
Now,
With the given coordinates on each graph, we see that,
Graph A is a straight line.
Graph B is a straight line.
Graph C is not a straight line
Graph D is a straight line.
Thus,
The non-linear graph is option D.
Option D is the correct answer.
Learn more about coordinates here:
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Compare the function ƒ(x) = –x2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maximum (vertex)? Question 16 options: A) There isn't enough information given. B) g(x) and ƒ(x) have equal absolute maximums. C) g(x) D) ƒ(x)
Answers
Answer:
Answer C: g(x)
Step-by-step explanation:
I used a graphing calculator to graph f(x) = -x^2 + 4x - 5, and by doing so I immedately saw that the vertex of f(x) is at (2, -1).
The absolute max of g(x) is approximately (3.25, 6.1).
The absolute max of f(x) is approximately (2, -1).
Since the y-coordinate of the absolute maximum of g(x) is greater than the y-coordinate of the absolute maximum of f(x), we conclude that Answer C is correct: g(x) has the greater absolute maximum
A bag contains 26 tiles, each with a different letter of the alphabet written on it. You choose 3 tiles from the bag without looking. What is the probability that you chose tiles with the letters A,B,C?
Answers
Answer:
1/26
Step-by-step explanation:
Total no. of tiles = 26
In each tile , a different alphabet is written.
And we need 3 tiles (in which A , B & C are written in it) in one try.
So the probability of choosing tiles with letters A , B & C ( in one try ) = 1/26
The area can be found by multiplying the side lengths that are 6 units & 4 units
Answers
Answer:squares area is. 24
Step-by-step explanation:
6×4 = 24
Perform row operations: The three elementary row operations can be performed in MATLAB using the following commands Type I: A([i,j], :)=([j,i],:) interchanges row i and row j Type II: A(i,:)=2*A(i,:) multiplies row i by a Type III: A(i, :)=A(i, :)+ q*A(j,:) multiplies row j by a and adds it to row i Enter the following matrix: [ 3 5 4 -12 -23 -14 6 4 14] Perform row operations in MATLAB that reduce the matrix A to Row Echelon Form. Use format rat.
Answers
Answer:
The solution and the calculation is shown on the first uploaded image
Step-by-step explanation:
Each day Tania decides to do something nice
for 2 strangers. What is the relationship
between the number people helped and days.
Write a Recursive and Explicit equation.
Answers
Answer:
Recursive:
[tex] a_1 = 2; a_n = a_{n-1} [/tex]
Explicit:
[tex] a_n = 2 [/tex]
Step-by-step explanation:
She helps the same number of people every day, 2.
Recursive:
[tex] a_1 = 2; a_n = a_{n-1} [/tex]
Explicit:
[tex] a_n = 2 [/tex]
34+987=what please help
Answers
Answer:
1021
Step-by-step explanation:
i added 34 +987 and got 1021
When a number is increased by 26, the result is tripled. Then the result is increased by 72. If the final result is 1/2 of the number, what is the value of this number?
Answers
Answer:
-60.
Step-by-step explanation:
Let the unknown number be x.
Number is increased by 26 = x+26
Then result is tripled = 3(x+26)
Then the result is increased by 72 = 3(x+26)+72
Final result is [tex]\dfrac{1}{2}[/tex] of the number = [tex]\dfrac{1}{2}x[/tex]
[tex]3(x+26)+72=\dfrac{x}{2}[/tex]
[tex]3x+78+72=\dfrac{x}{2}[/tex]
[tex]3x+150=\dfrac{x}{2}[/tex]
Isolate variable terms.
[tex]3x-\dfrac{x}{2}=-150[/tex]
[tex]\dfrac{6x-x}{2}=-150[/tex]
Multiply both sides by 2.
[tex]5x=-300[/tex]
Divide both sides by 5.
[tex]x=-\dfrac{300}{5}[/tex]
[tex]x=-60[/tex]
Therefore, the required number is -60.
What is the sum?
−1.5+1.9
Enter your answer, as a decimal, in the box.
Answers
Answer:
0.4
Step-by-step explanation:
Answer: it's 0.4 as a decimal
Step-by-step explanation:
The height off the ground, in feet, of a certain baseball that travels through the air is given by the equation h = 3.5 + 68t - 16t^2, where t is measured in seconds. Find the height off the baseball, to the nearest foot, when t = 4 seconds.
Answers
Answer:
20 feet
Step-by-step explanation:
Plug in 4 as t in the equation:
h = 3.5 + 68t - 16t^2
h = 3.5 + 68(4) - 16(4²)
h = 3.5 + 272 - 256
h = 19.5
So, the height of the basketball is 20 feet
Please help. I don’t understand this math problem.
Answers
Answer:
(7) The value of -j is 9.
(8) The value of -(-j) is -9.
(9) The value of (-j)(-j) is 81.
Step-by-step explanation :
Part 7:
Given algebraic expression is:
j = -9
Now we have to determine the value of (-j).
-j = - (-9) = 9
The value of -j is 9.
Part 8:
Given algebraic expression is:
j = -9
Now we have to determine the value of -(-j).
- (-j) = - [-(-9)] = -9
The value of -(-j) is -9.
Part 9:
Given algebraic expression is:
j = -9
Now we have to determine the value of (-j)(-j).
(-j)(-j) = [- (-9)] × [- (-9)] = 9 × 9 = 81
The value of (-j)(-j) is 81.