We need a maximum enlargement of n = 18 terms in order to guarantee this level of accuracy for Simpon's Rule.
What is the estimation of the accuracy of Simpon's Rule?The estimation of Simpson's rule follows an approach where the value of the definite integral [tex]\int\limits^a_b f{x} \, dx[/tex] is approximated by using a parabolic method of approximation for each subinterval of the interval [a, b].
The formula for calculating Simpon's rule can be expressed as:
[tex]\mathbf{\int ^b_a f(x) d \simeq \dfrac{\Delta x}{3}[y_o+4y_1+2y_2+4y_3+2y_4+...+4{y_{n-1} +y_n}}[/tex]
Given that:
[tex]\mathbf{\int ^1_0 7ex^2 dx }[/tex],
where a = 0, b = 1, [tex]\mathbf{f(x) = 7 e^{x^2}}[/tex]We need to determine the fourth derivative; i.e.
[tex]\mathbf{f'(x) = 14xe^{x^2}}[/tex]
[tex]\mathbf{f''(x) = 14ex^2 +28x^2e^{x^2} = (14+28x^2)e^{x^2}}[/tex]
[tex]\mathbf{f'''(x) = 56xe^{x^2} +2(14+28x^2)e^{x^2} = (84x+48x^3)e^{x^2}}[/tex]
[tex]\mathbf{f^{iv}(x) = (84+144x^2)e^{x^2} +2x(84x+48x^3)e^{x^2} = (84x+312x^2+96x^4)e^{x^2}}[/tex]
The maximum value of the 4th derivative on the interval [0,1] is:
[tex]\mathbf{f^{iv}(1) = 624e}[/tex] and the error is bounded by:
[tex]\mathbf{\Bigg| \dfrac{f^{iv}(1) (1-0)^5}{180n^4} \Bigg| = \dfrac{624e}{180n^4}=\dfrac{52e}{15n^4}}[/tex]
Now for the error to be less than 0.0001; we have:
[tex]\mathbf{\dfrac{52e}{15n^4} < 0.0001}[/tex]
[tex]\mathbf{52e < 0.0015n^4}[/tex]
[tex]\mathbf{n^4 > \dfrac{52e}{0.0015}}[/tex]
[tex]\mathbf{n > \sqrt[4]{ \dfrac{52e}{0.0015}}}[/tex]
n ≅ 17.52.
Therefore, we can conclude that we need a maximum of n = 18 terms in order to guarantee this level of accuracy for Simpon's Rule.
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The factors of 52 and the first three factors of 130 are listed in the table below. Fill in the remaining five factors of 130 and then identify the greatest common factor, or GCF, of 52 and 130.
Type the multiples in the increasing order.
130: 1, 2, 5,
GCF of 52 and 130:
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
GCF of 52 and 130 is 26
I found a similar question here so that's what I can only tell you. I hope it will help you.
Suppose a normal distribution has a mean of 26 and a standard deviation of 4. What is the probability that a data value is between 28 and 35? Round your answer to the nearest tenth of a percent.
A. 29.6%
B. 23.6%
C. 27.6%
D. 25.6%
Using the normal distribution, it is found that the probability that a data value is between 28 and 35 is given by:
A. 29.6%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation are given by:
[tex]\mu = 26, \sigma = 4[/tex].
As a proportion, the probability that a data value is between 28 and 35 is the p-value of Z when X = 35 subtracted by the p-value of Z when X = 28, hence:
X = 35:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 26}{4}[/tex]
Z = 2.25
Z = 2.25 has a p-value of 0.988.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 26}{4}[/tex]
Z = 0.5
Z = 0.5 has a p-value of 0.692.
0.988 - 0.692 = 0.296 = 29.6%, which means that option A is correct.
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_30. Solve the following logarithmic equation: log8(x + 9) + 3 = 3
A) x = -8
B) x = 87
C) x = 12.5
D) x = 0
=
Answer:
A
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
[tex]log_{8}[/tex] (x + 9) + 3 = 3 ( subtract 3 from both sides )
[tex]log_{8}[/tex] (x + 9) = 0 , then
x + 9 = [tex]8^{0}[/tex] = 1 ( subtract 9 from both sides )
x = - 8
Alexa danced for 3 2/4 hours on Saturday. Sherlyn swam 1/5 of that time. How many
hours did Sherlyn swim on Saturday?
Answer:
Sherlyn swam 42 minutes on Saturday
Step-by-step explanation:
danced for 3 2/4 hours on Saturday
3 2/4 hours is equivalent to 3.5 hours
1 / 5 of (that time) 3.5 hours is (1 / 5) * 3.5 = 0.7 hours
Because one hour is equal to sixty minutes, in order to change the units you have to multiply the number of hours, 0.7, by 60.
0.7 x 60 = 42 minutes
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If P Is inversely proportional to the square of q and p is 22 when a is 8 determine p when Q is equal to 4
The value of p is equal to 76 when q is equal to 4
Given :
If p is inversely proportional to the square of q
when y is inversely proportional to x then [tex]y=\frac{k}{x}[/tex]
given that p is inversely proportional to the square of q. the equation becomes
[tex]p=\frac{k}{q^2}[/tex]
when p is 19 the value of a is 8
Replace the values and find out q
[tex]p=\frac{k}{q^2}[/tex]
[tex]22=\frac{k}{8^2}[/tex]
[tex]22=\frac{k}{64}[/tex]
Multiply both sides by 64
k=1216
Now we find out p when q is 4
Replace k value and q value to find out p
[tex]p=\frac{k}{q^2}[/tex]
[tex]p=\frac{1216}{4^2}[/tex][tex]p=76[/tex]
The value of p is equal to 76 when q is equal to 4
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Answer:
P = 88.
Step-by-step explanation:
P = k/q^2
22 = k/ 8^2
k = 22 * 64 = 1408.
So P = 1408/q^2
When q = 4:
P = 1408/4^2
q = 88
What is the volume of a sphere with a diameter of 9.1 m, rounded to the nearest tenth of a cubic meter?
Simplify.
- (u+5)+5 (2u-5)
Answer:
Step-by-step explanation:
-u-5+10u-25=9u-30
it was easy.
Solve y-8/3=-7 show work
Answer: y = -13
Step-by-step explanation:
Given:
[tex]\displaystyle \frac{y-8}{3} =-7[/tex]
Multiply both sides by 3:
[tex]\displaystyle y-8 = -21[/tex]
Add 8 to both sides:
[tex]\displaystyle y= -13[/tex]
Given equation,
y - 8 / 3 = -7Aim :
To find value of y.Cross multiplying them,
>> y - 8 = -7 × 3
>> y - 8 = -21
Transposing -8 from L.H.S. to R.H.S.,
>> y = -21 + 8
>> y = -13
Therefore :
Value of y is -13.does anyone know the width the length the height of this tissue box pls someone tell me Asap.
Answer:
Hey!
Well based on my knowledge it usually says that on the tissue box itself.... (in fine print)
i may be wrong.... but do check...
Which situation can be represented by the inequality 150 ≤ 15x + 55 ?
a. Thomas has 15 baseball cards in his collection. He will buy 55 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?
b. Thomas has 15 baseball cards in his collection. He will buy 55 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at least
150 baseball cards?
c. Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?
d. Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at least 150 baseball cards?
Inequalities help us to compare two unequal expressions. The correct option is C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The situation that can be represented by the inequality 150 ≤ 15x + 55 is Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?
Hence, the correct option is C.
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Use the stem-and-leaf plot below to match each term with the correct value. (Round to the nearest whole number.)
Answer:
Step-by-step explanation:
16, 18, 23, 25, 26, 34, 37, 37, 40, 41, 46
( 16 + 18 + 23 + 25 + 26 + 34 + 37 + 37 + 40 + 41 + 46 ) ÷ 11 = 31.181818...
mean ≈ 31
median = 34
mode = 37
help geometry ………ignore this i need 20 words
Answer:
The answer is 1
Step-by-step explanation:
To produce 10 shirts, the total cost is $80; to produce 11 shirts, the total cost is $99. The average total cost of the 11th shirt is equal to Group of answer choices $8. $9. $80. $99. $19.
Write (9,-4) and (1,6) in slope intercept form,
Answer:
y = -5/4x + 7 1/4
Step-by-step explanation:
The difference in y (10) over the difference in x (8)
3 added to twice a number
Answer:
The equation is n2 + 3
Step-by-step explanation:
The n represents the number.
for example the number 10
if you put it in the equation it becomes
(10)(2) +3
10x2=20
20+3=23
there are 18 sweets in a packet. 8 of the sweets are mint what fraction of the sweets are not mint
Answer:
10/18 of the sweets are not mint
you can also simplify this fraction and say 5/9
Find the equation of the line parallel to 6x+5y=1 and passing through (-4,-2)
Hi Student!
The first step that we need to take before trying to solve the problem is that we need to take out important information from the problem. The first important piece of information that is given to us is that we are trying to find an equation of a line that is parallel to a different line. This means that our slope is going to be the same as the initial line given. The second piece of information that is given is a point through which our line passes through which will help us greatly when solving for our line.
The next step that we must take is to solve for y in the given equation so we can see what the slope is.
Subtract 6x from both sides
[tex]6x + 5y = 1[/tex][tex]6x - 6x + 5y = 1 - 6x[/tex][tex]5y = 1 - 6x[/tex]Divide both sides by 5
[tex]\frac{5y}{5} = \frac{1 - 6x}{5}[/tex][tex]y= \frac{1}{5} - \frac{6x}{5}[/tex][tex]y=- 1.2x+ 0.2[/tex]Now that we have completely solved for y, we can see that the slope is -1.2 using the y = mx + b formula which states that m is the slope.
Moving onto the next step, we must use the point-slope formula to determine what the new equation is that has the same slope and passes through (-4, -2).
Insert the Values
[tex](y-y_1)=m(x-x_1)[/tex][tex](y-(-2))=-1.2(x-(-4))[/tex]Simplify the Equation
[tex]y+2=-1.2(x+4)[/tex]Distribute the Equation
[tex]y+2=(-1.2*x)+(-1.2*4)[/tex][tex]y+2=-1.2x-4.8[/tex]Subtract 2 from both sides (to isolate y)
[tex]y+2 - 2=-1.2x-4.8- 2[/tex][tex]y=-1.2x-6.8[/tex]Therefore, our final answer for the equation of the line parallel to 6x + 5y = 1 and that passes through (-4, -2) is y = -1.2x - 6.8.
How do I find the function rule???
x: 0, 1, 2, 3
y: 5, 4, 3, 2
Answer: y=-1x+5
Step-by-step explanation:
1. Use slope-intercept formula (y = mx + b) to find the slope which is represented by the variable 'b'.
m = ∆y / ∆x
m = -1 / 1
m = -1
y= -1x + b
2. Use any cooresponding x and y values to substitute into the formula. Ex: (x,y) → (1,4)
y = mx + b
4 = -1(1) + b
4 = -1 + b
5 = b
3. Plug in the values found into the formula.
y = -1x + 5
What are the coordinates of the image of (-3, -7) after the translation (x, y) - > (x-9, y + 9)? F (-6, 16) H (12, -2) G (6, -16) J (-12, 2)
The coordinates of the image of (-3, -7) after the translation will be equal to .(-12,2)
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation. Here the image is translated as (x-9,y+9).
The given coordinate of the point is:- (-3,-7)
So the translation will be calculated as:-
=(x-9,y+9 )
=(-3-9,-7+9
=(-12,2)
Hence coordinates of the image of (-3, -7) after the translation will be equal to (-12,7)
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7). John had 9 pieces of gum at the
beginning of the day. He now has 8
pieces of gum. How much gum did
he eat during the day? Write the
equation and the solution.
Answer:
9-1=8
Step-by-step explanation:
he started with 9 but at the end of the day he had 8. meaning he ate 1 peice
My son would like to know what is the solution to Pi and i don't even know so I someone to help me with this!
Answer:
3.14285714Step-by-step explanation:
[tex] \frac{22}{7} = 3.14285714[/tex]Stay safe, stay healthy and blessed.Stay safe, stay healthy and blessed.Have a good day !Stay safe, stay healthy and blessed.Have a good day !Thank youhow to solve to |12(16−63)|
Step-by-step explanation:
simply do the calculations :
|12 × (16 - 63)|
|12 × - 47|
|-564| = 564
that's it.
remember, the absolute value is always the positive value of a number.
|-x| = x
and also
|x| = x
Find the statement Pk + 1 for the given statement Pk
Step-by-step explanation:
k has to be replaced by k+1.
so,
4 / ((k+1)(k+1 + 3)) = 4 / ((k+1)(k+4))
I am not sure how far your teacher expects you to go with this.
just in case, I will do also the full multiplications
4 / ((k+1)(k+4)) = 4 / (k² + 4k + k + 4) = 4 / (k² + 5k + 4)
and if you need the factor to go from Pk to Pk+1 :
Pk+1 / Pk = (4/((k+1)(k+4))) / (4/(k(k+3)) =
= (4/((k+1)(k+4))) × (k(k+3))/4 =
= (k(k+3)) / ((k+1)(k+4))
Answers this any links will be reported
Hey there!
ASSUMING
(3x)° + 45° = 180°
3x + 45 = 180°
SUBTRACT 45 to BOTH SIDES
3x + 45 - 45 = 180 - 45
SIMPLIFY IT!
3x = 180 - 45
3x = 135
DIVIDE 3 to BOTH SIDES
3x/3 = 135/3
SIMPLIFY IT!
x = 45°
Therefore, the answer should be:
x = 45
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
[tex]\large\boxed{\sf{x=45}}[/tex]Step-by-step explanation:
Given:
Complementary angles of 180 degrees.To solve:
For x, to isolate it one side of the equation.(3x)°+45°=180°
3x+45=180First, subtract by 45 from both sides.
3x+45-45=180-45
Solve.
Subtract these numbers goes from left to right.
180-45=135
3x=135
Divide by 3 from both sides.
3x/3=135/3
Solve.
Divide these numbers from left to right.
135/3=45
[tex]\Longrightarrow: \boxed{\sf{x=45}}[/tex]
Therefore, the final answer is x=45.I hope this helps, let me know if you have any questions.
help help help help help
Answer:
mPS = 80°
Step-by-step explanation:
angles on a circle subtended by the same arc are congruent
∠ PQS and ∠ PRS are both subtended by arc PS , then
10 + 3x = 110 - 7x ( add 7x to both sides )
10 + 10x = 110 ( subtract 10 from both sides )
10x = 100 ( divide both sides by 10 )
x = 10
then
∠ PQS = 110 - 7x = 110 - 7(10) = 110 - 70 = 40°
the inscribed angle PQS is half the measure of its intercepted arc PS , then
PS = 2 × 40° = 80°
A stone pyramid in Egypt has a square base that measures 154 m on each side. The height is 91 m. What is
the volume of the pyramid?
Answer:
14014
Step-by-step explanation:
base of stone pyramid=154
height=91
b×h
154×91=4014
Options
3 - 2n
3 + 2n
2 + 3n
2 - 3n
Answer:
3 - 2n
Explanation:
Difference means we have to subtract integers.
Let the number be n. Twice of this number: 2n
Difference of 3 and twice this number: 3 - 2n
A transport company needs to deliver 500,000 pounds of rocks to a construction site. The company owns a set of dump trucks- each with a container in the shape of a rectangular prism (figure A). If each pound of rock has a volume of 0.01 cubic feet, how many dump trucks will it take to transport the rock? Calculate the total volume of rock that the transport company is responsible for. Calculate the maximum volume of each dump truck. How many trucks are needed to deliver the rock in one trip?
The number of trucks needed to deliver the rock in one trip will be 6.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
V = a x b x c
A transport company needs to deliver 500,000 pounds of rocks to a construction site.
The company owns a set of dump trucks- each with a container in the shape of a rectangular prism (figure A).
If each pound of rock has a volume of 0.01 cubic feet.
Then the total volume of rock that the transport company is responsible for.
Volume of rocks = 0.01 x 500,000
Volume of rocks = 5,000 ft³
Then the maximum volume of each dump truck will be
Volume of truck = 12 x 9 x 8
Volume of truck = 864 ft³
Then the number of the trucks are needed to deliver the rock in one trip will be
Number of trucks = 5000 / 864
Number of trucks = 5.787
Number of trucks ≅ 6
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What is the greatest common factor of
21xy^3 6x^4y^2
A. 42x^4 y^3
B. 42x^5 y^5
C. 3x^4 y^3
D. 3xy^2
The sum of 7.2 and a number is 10
Someone help?
Answer:
2.8
Step-by-step explanation:
Just substract 7.2 from 10
You get: 2.8
Answer:
2.8
Step-by-step explanation:
because 7.2 plus 2.8 equals
