Answer and Step-by-step explanation:
F(x) = x^3 (a)
then
compute f(x) dx for each of these, compute the corresponding absolute error.
Solution: f(x) = x3
F(x) d(x) = 3x2
The absolute error are ∆x= |x-ẋ|, ∆f=|f(x) – f(ẋ)|
(b) Compute the approximation L, and T, for n=4, 8, and 16 for an integral part.
The linear (L) approximation of function f(x) = x3, n= 4
f(4) = (4)3 = 64 and f”(4) = 3(4)2 = 48
The linear approximation is L4(x) = f (4) + f’(4)(x-4)
= 64 + 48 (x-4)
For n= 8,
f(8) = 512 and f,(8)= 3(8)2= 192
The linear approximate is L8(x) = f(8) + f’(8)(x-8)
Similarly for n= 16 the linear approximate is L16(x) = f (16) + f (16) (x-16)
The approximation for T, trapezoidal rule is:
a ʃb f(x)dx = Tn
for n = 4 the T approximation is:
T4 =a ʃb x3 dx
For n= 8 :
T8 = a ʃb x3 dx
For n= 16 : T16= a ʃb x3 dx.
2 of 6
Gavin & Henry share a lottery win of £8800 in the ratio 4: 1.
Gavin then shares his part between himself, his wife & their son in the ratio 1:6:3.
How much more does his wife get over their son?
Answer:
£2112
Step-by-step explanation:
To find Gavin's share, sum the parts of the ratio, 4 + 1 = 5 parts
Divide the win by 5 to find the value of one part of the ratio.
£8800 ÷ 5 = £1760 ← value of 1 part of ratio, thus
4 parts = 4 × £1760 = £7040 ← Gavin's share
Now repeat the process with the ratio for his family
1 + 6 + 3 = 10 parts
£7040 ÷ 10 = £704 ← value of 1 part of the ratio, thus
6 × £704 = £4224 ← wife's share
3 × £704 = £2112 ← son's share
Difference = £4224 - £2112 = £2112
Thus his wife gets £2112 more than the son
Can someone help me out in these 3 questions??
Answer:
I'm not completely sure about the first one, but #8 is 0.0419, and #9 is 30500.
Albert and John are partners in a Bakery store. They needed $70,000 to start the business. They
invested in the ratio 3:7, respectively. How much did Albert invest in the business? How much did John invest in the business?
Answer:
Albert invested 21,000 and John invested 49,000 :)
Answer:
A: $21,000J: $49,000Step-by-step explanation:
The number of "ratio units" in their investment ratio is 3+7 = 10. Albert's investment was 3/10 of the total, so was $21,000. John invested the remaining amount, $49,000.
Albert invested $21,000; John invested $49,000.
A research team conducts a survey to determine the area of land used for farming in Iowa. The team randomly selects house addresses and sends the survey by mail.
Which type of sampling method is the research team using?
Answer: simple random sampling
Step-by-step explanation:
From the question, we are informed that a research team conducts a survey to determine the area of land used for farming in Iowa and that the team randomly selects house addresses and sends the survey by mail.
The type of sampling method which the research team is using market is the simple random sampling method. A simple random sampling is a subset of a larger set whereby all the participants have an equal and fair chance of being selected in the survey participation.
what is the best estimate of the sum of the fractions?
Answer:
13
Step-by-step explanation:
P= $2000.00 A= $2160.00 t= 2 years
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r
Answer:
interest = Amount-Principal= 2160-2000=160
Rate = Interest*100/(P*T)= 160*100/(2000*2)=4%
Step-by-step explanation:
grtsdfgdfg.bshgfhysyugyudgyuf
Solve for x.
8
2x +7
I
.N
+
x + 12
Answer: 3x=-3 soooooo x= -1
Step-by-step explanation:
lmk for more info
Answer the questions in the picture please
Step-by-step explanation:
1) angle 2 and 4
2)angle 2 and 3
3)angle 1 and 4
Hope it helps
In the figure below, triangle ABC is similar to triangle PQR, as shown below:. PLEASE HELP ME!!!!!!!!!!
Answer:
35 i think
Step-by-step explanation:
a ball is kicked with an initial height of 0.75 meters and initial upward velocity of 22 meters/second. this inequality represents the time,t, in seconds, when the ball's height is greater than 10 meters. -4.9t^2+22t+0.75>10.
the ball's height is greater than 10 meters when t is approximately between blank and blank seconds
Answer:
t is between 0.47 seconds and 4.02 seconds
Step-by-step explanation:
Given
[tex]Inequality: -4.9t^2+22t+0.75>10[/tex]
Required
Determine the values of t
[tex]-4.9t^2+22t+0.75>10[/tex]
Subtract 10 from both sides
[tex]-4.9t^2+22t+0.75 - 10 >10 - 10[/tex]
[tex]-4.9t^2+22t-9.25 >0[/tex]
Multiply through y -1
[tex]4.9t^2-22t+9.25 <0[/tex]
Solve t using quadratic formula:
[tex]t = \frac{-b \±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 4.9[/tex]
[tex]b = -22[/tex]
[tex]c = 9.25[/tex]
So, we have:
[tex]t = \frac{-(-22) \±\sqrt{(-22)^2 - 4*4.9*9.25}}{2 * 4.9}[/tex]
[tex]t = \frac{22 \±\sqrt{484 - 181.3}}{9.8}[/tex]
[tex]t = \frac{22 \±\sqrt{302.7}}{9.8}[/tex]
[tex]t = \frac{22 \±17.40}{9.8}[/tex]
Split the equation
[tex]t = \frac{22 + 17.40}{9.8}[/tex] or [tex]t = \frac{22 - 17.40}{9.8}[/tex]
[tex]t = \frac{39.4}{9.8}[/tex] or [tex]t = \frac{4.6}{9.8}[/tex]
[tex]t = \frac{39.4}{9.8}[/tex] or [tex]t = \frac{4.6}{9.8}[/tex]
[tex]t = 4.02[/tex] or [tex]t = 0.47[/tex]
Hence; the range is
[tex]0.47 < t <4.02[/tex]
The table shows the distance, y, a cheetah can travel in feet in x seconds. Speed of a Cheetah Time, x (seconds) Distance, y (feet) 5 470 10 940 15 1,410 20 1,880 25 2,350 Based on the information in the table, which equation can be used to model the relationship between x and y? A. y = 5x B. y = x + 5 C. y = x + 470 D. y = 94x
Answer:D y=94x
Step-by-step explanation:
First dive y and x
Then you multiply the next x and the number that you got.
ALSO I GOT IT RIGHT
D. y = 94x. will be the equation that can be used to model the relationship between x and y.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given, a table is attached below.
Since The data in the table is showing the proportionality feature.
the property of having suitable proportions in terms of size, number, degree, harshness, etc. If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Thus,
The ratio of distance and time for the cheetah = 470/5 or 940/10 or 1410/15
Since the time is denoted by "x" (in seconds) and distance is denoted by "y".
So,
y/x = 470/5
y = 94x
therefore, the equation that can be used to model the relationship between x and y will be D. y = 94x.
Learn more about algebraic Expression here:
https://brainly.com/question/953809
#SPJ6
Need some help on my homework asap
Problem 9
List any three points that are on the same straight line.
So for example, you could say A, P and B. Or you could say C, P, and D. A third one you could do is J, D and K.
==============================
Problem 10
Now we're listing any three points that aren't on the same straight line.
One example of such triple is A, P and D. Another example is K, D, and C. There are many others as well.
==============================
Problem 11
List any four points that are in the same plane. So you'll pick four points from the set {A, B, C, D, P} to answer this question as these five points are all in the shaded plane R.
==============================
Problem 12
Pick any four points such that they do not all exist in the same plane. It doesn't matter which points you pick as long as J or K are one of the points selected. This is because neither J nor K are in the plane R.
===============================
Problem 13
Line JK intersects CD at point D. The other line that crosses CD is line AB.
Line AB is in plane R, while line JK intersects the plane at point D only.
===============================
Problem 14
Intersecting line JK and plane R results in point D. This is where the line and plane meet, as mentioned in the previous problem.
If you were asked to intersect line AB and plane R, then you would get line AB as a result. All of line AB is inside the plane.
what is 75.25 - 7.94
Answer:
67.31
Step-by-step explanation:
ahhshshshahaha
Answer:
The answer is 67.31
Step-by-step explanation:
(-5, -6) and (6, – 4)
write in standard form
Answer: -5*10^0
-6*10^0
6*10^0
-4*10^0
I hope this helped there's also standard calculators so don't waste your points .
What is the value of x?
Enter your answer in the box
what is the mean of the data set rounded to the nearest tenth? 1.2, 1.8, 1.6, 1.4, 1.4, 2.2
Answer:
1.6
Step-by-step explanation:
1.2, 1.8, 1.6, 1.4, 1.4, 2.2's mean rounded to the nearest tenth is 1.6
I need help please
Answer:
part A 2.6+1.7+9.8-4.2=9.9
part B 6.7-9.9+22-28.46=9.66
Step-by-step explanation:
Part A
First find the square root.
the square root of 7 is 2.6
the square root of 3 is 1.7
the square root of 98 is 9.8
the square root of 18 is 4.2
Then: add and subtract them
2.6+1.7+9.8-4.2=9.9
Part B
I don't know how to explain the next part so I will just give you the answer
6.7-9.9+22-28.46=9.66
I hoped this helped
The two main components ofa stereo system are a radio and a speaker (ignore all other components). The lifetime of the radio is exponentially distributed with mean of 1000 hours and the lifetime of the speaker is exponentially distributed with mean of 500 hours, independent of theradio’s lifetime. What is the probability that system’s failure is due to the radio?
Answer:
the probability that system’s failure is due to the radio = [tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
From the question given;
Let the mean lifetime of the radio [tex]\dfrac{1}{\lambda_1} = 1000[/tex] and the mean lifetime of the speaker [tex]\dfrac{1}{\lambda_2} = 500[/tex]
we can re-write both expressions as:
[tex]\lambda_1= \dfrac{1}{1000}[/tex] and [tex]\lambda_2= \dfrac{1}{500}[/tex]
Let consider [tex]X_1 \ and \ X_2[/tex] to be the variables which are independent to the exponentially distributed mean of [tex]\dfrac{1}{\lambda _1} \ and \ \dfrac{1}{\lambda _2}[/tex]
∴
[tex]P(X_1< X_2) = \int ^{\infty}_{0} \ P (X_1<X_2|X_1 =x) \lambda_1 e^{-\lambda_1 \ x} \ dx[/tex]
[tex]P(X_1< X_2) = \int ^{\infty}_{0} \ P (X_1<X_2) \lambda_1 e^{-\lambda_1 \ x} \ dx[/tex]
[tex]P(X_1< X_2) = \int ^{\infty}_{0} \ e^{-\lambda_2 \ x} \lambda _1 \ e^{-\lambda_1 \ x} \ dx[/tex]
[tex]P(X_1< X_2) = \int ^{\infty}_{0} \lambda _1 \ e^{(-\lambda_1 +\lambda_2)} \ dx[/tex]
[tex]P(X_1< X_2) = \dfrac{\lambda_1}{\lambda_1 + \lambda_2}[/tex]
replace the values now; we have:
[tex]P(X_1< X_2) = \dfrac{\dfrac{1}{1000} }{\dfrac{1}{1000} + \dfrac{1}{500}}[/tex]
[tex]P(X_1< X_2) = \dfrac{\dfrac{1}{1000} }{\dfrac{1+2}{1000} }[/tex]
[tex]P(X_1< X_2) = \dfrac{\dfrac{1}{1000} }{\dfrac{3}{1000} }[/tex]
[tex]P(X_1< X_2) = {\dfrac{1}{1000} } \times {\dfrac{1000}{3}[/tex]
[tex]P(X_1< X_2) = {\dfrac{1}{3} }[/tex]
Thus, the probability that system’s failure is due to the radio = [tex]\dfrac{1}{3}[/tex]
If matherens bannanas cost $1.98 for 3lbs. At winn dixie bannanas cost $2.97 for 4lbs. Which store has the better price. Please give answer please
Answer: Matherens has the better price
Step-by-step explanation:
To find the better price, all we have to do is divide the price by the number of pounds to find how much one pound is for each store.
Matherens: 1.98 ÷ 3 = 0.66
That means 1 pound of bananas at Matherens is 66 cents.
Winn Dixie: 2.97 ÷ 4 = 0.74
That means 1 pound of bananas at Winn Dixie is 74 cents.
This means that Matherens is charging less per pound of banana.
An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is 15 cm/sec and the period is 628 milli-seconds. The amplitude of the motion in cm is:_______.
a. 3.
b. 2.
c. 1.5.
d. 1.0.
Answer:
The correct option is c: 1.5 cm.
Step-by-step explanation:
The amplitude of the motion can be calculated using the following equation:
[tex] A = \frac{v}{\omega} [/tex]
Where:
A: is the amplitude
v: is the speed = 15 cm/s
ω: is the angular speed
First, we need to find the angular speed:
[tex] \omega = \frac{2\pi}{T} [/tex]
Where:
T is the period = 628 ms
[tex] \omega = \frac{2\pi}{T} = \frac{2\pi}{0.628 s} = 10.01 rad/s [/tex]
Now we can find the amplitude:
[tex] A = \frac{v}{\omega} = \frac{15 cm/s}{10.01 s} = 1.5 cm [/tex]
Therefore, the correct option is c: 1.5 cm.
I hope it helps you!
Which equation has the solution x = -4?
3x + 6 - 2x = -2
2(2 - 4) = 16
(x + 6) 3 = -6
-x +4=3
Answer:
none of these have the solution of x = -4
Step-by-step explanation:
1 . 3x + 6 - 2x = -2 . (combine like terms)
x + 6 = -2 (isolate the variable)
-6 -6
x = -8 *x doesn't equal - 4*
2. 2(2 - 4) = 16 (distributive property)
2 - 8 = 16
-6 = 16
since theres no x in the equation its not a possible answer .
3 . (x + 6) 3 = - 6
this one also isn't a proper equation to find x
4. -x + 4 = 3 (isolate the variable)
-4 -4
-x = -1
/x . /x
x= -1
Kristy's yearly salary is $75,000. How do you express this number in
scientific notation?
Answer:
7.5000
Step-by-step explanation:
can you guys please help me. i don’t need the explanation i just need the answer
Answer:
36
Step-by-step explanation:
AOB + BOC = AOC
AOC = 90 since the lines are perpendicular
6x-12 + 3x+30 = 90
Combine like terms
9x + 18 = 90
Subtract 18 from each side
9x+18-18 = 90-18
9x = 72
divide by 9
9x/9 = 72/9
x = 8
AOB = 6x - 12
= 6*8 - 12
= 48 -12
= 36
Answer:
AOB = 36
Step-by-step explanation:
OA is perpendicular to OC
AOB + BOC = 90 ------------equation
where:
AOB = 6x - 12
BOC = 3x + 30
plugin values into the eq.
6x - 12 + 3x + 30 = 90
6x + 3x + 30 - 12 = 90
9x + 18 = 90
9x = 90 - 18
9x = 72
x = 72/9
x = 8
plugin values to AOB = 6x - 12
AOB = 6x - 12
AOB = 6(8) - 12
AOB = 36
......ssssssssssssssssssssssssssssssssssssshhhhhh
Hey there! I'm happy to help!
Step 2 is incorrect. She added 4 and 2 first, but you are supposed to multiply and divide first. Then she multiplied 6 and 6, which is 36. Then she divided 36 and 2, which is 18, and then she subtracted 7, giving her 11. Step 2 is what threw the whole thing off.
Here is what Sandy should have done.
STEP 1: 6·4+2÷2-7
STEP 2: 24+1-7
STEP 3: 25-7
STEP 4: 18
I hope that this helps! Have a wonderful day! :D
Steps to solve:
6 * 4 + 2 / 2 - 7
~Multiply
24 + 2 / 2 - 7
~Divide
24 + 1 - 7
~Add
25 - 7
~Subtract
18
In step one, she added instead of multiplied which caused her to get the wrong answer.
Best of Luck!
I will mark branliest for ever Andrews first and it’s also 40 points
1. Which number would divide the numerator and the denominator of the first fraction to yield the second fraction?
5/10 divide ?/?= 1/2
2. 12/15 divide ?/? = 4/5
3. 10/12divide ?/? = 5/6
4. 14/18 divide ?/? = 7/9
Answer:
3/3 12/15 divided 3/3 = 4/3
Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the p-value is
Answer:
The value is [tex]p- value = 0.041815[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 40 \ hours[/tex]
The sample size is [tex]n = 18[/tex]
The sample mean is [tex]\= x = 37.8 \ hours[/tex]
The standard deviation is [tex]\sigma = 5.4\ hours[/tex]
The null hypothesis is [tex]H_o : \mu = \ge 40[/tex]
The alternative hypothesis is [tex]H_a : \mu < 40 \ hour s[/tex]
Generally the test statistic is mathematically evaluated as
[tex]t= \frac{\= x - \mu}{ \frac{\sigma}{ \sqrt{n} } }[/tex]
[tex]t= \frac{37.8 - 40}{ \frac{5.4}{ \sqrt{18 } }[/tex]
[tex]t= -1.73[/tex]
From the z - table the p-value is obtained and the value is
[tex]p- value = P(Z < -1.73)[/tex]
[tex]p- value = 0.041815[/tex]
To test DullCo's hypothesis, the p-value is 0.041815 and this can be determined by using the given data.
Given :
DullCo Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours.The following steps can be used in order to determine the p-value for DullCo's hypothesis:
Step 1 - The formula for t-statistics can be used in order to determine the p-value for DullCo's hypothesis.
Step 2 - The formula for t-statistics is given below:
[tex]t = \dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n} }}[/tex]
where the sample size is 'n', the standard deviation is [tex]\sigma[/tex], and the mean is [tex]\mu[/tex].
Step 3 - Now, substitute the values of [tex]\sigma[/tex], [tex]\mu[/tex], [tex]\bar{x}[/tex], and n in the above formula.
[tex]t = \dfrac{37.8-40}{\dfrac{5.4}{\sqrt{18} }}[/tex]
Step 4 - SImplify the above expression.
[tex]t = \dfrac{-2.2}{1.2727}[/tex]
[tex]t = -1.73[/tex]
Step 5 - Now, with the help of the z-table the p-value is:
[tex]\rm p-value = P(Z<-1.73)[/tex]
[tex]\rm p-value = 0.041815[/tex]
To test DullCo's hypothesis, the p-value is 0.041815.
For more information, refer to the link given below:
https://brainly.com/question/14723549
Solve the following equation, and check your solution. Be sure to show all work in order to receive full credit.
Solve 24 - 3 x = -27.
PLS HURRY!!!!!!!! IM TIMED
Answer:
x=17
Step-by-step explanation:
Hope this helps
what is the cubed roof of 16? Help needed please
Which of the following pairs of functions are inverses of each other?
Answer:
i belive the answer is b but im not 100% sure
