Answer: The cube with side length of 12cm is alone in one plate, the other 3 cubes are in the other plate.
Step-by-step explanation:
We have 4 cubes with side lengths of:
6cm, 8cm, 10cm and 12cm.
Now, some things you need to know:
If we want a scale to be balanced, then the mass in both plates must be the same.
The volume of a cube of side length L is:
V = L^3
And the mass of an object of density D, and volume V is:
M = D*V.
As all the cubes are of the same material, all of them have the same density, so the fact that we do not know the value of D actually does not matter here.
Then we want to forms two groups of cubes in such a way that the total volume in each plate is the same (or about the same), the volumes of the cubes are:
Cube of 6cm:
V = (6cm)^3 = 216cm^3
Cube of 8cm:
V = (8cm)^3 = 512cm^3
Cube of 10cm:
V = (10cm)^3 = 1000cm^3
cube of 12cm
V = (12cm)^3 = 1728cm^3
First, if we add the volumes of the first two cubes, we have:
V1 = 216cm^3 + 512cm^3 = 728cm^3
Now we can see that we add 1000cm^3 the volume will be equal to the volume of the larger cube, so here we can also add the cube with side length of 10cm
Then the volume of the 3 smaller cubes together is:
V1 = 216cm^3 + 512cm^3 + 1000cm^3 = 1728cm^3.
Then, if we want to have the same volume in each plate, then we need to have the 3 smaller cubes in one plate, and the larger cube in the other plate.
Suppose 55 percent of the customers at Pizza Palooza order a square pizza, 72 percent order a soft drink, and 48 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza?
Answer: No, the orders are not independent.
Step-by-step explanation:
If event 1 has some possible outcomes, suppose that we choose a given outcome 1 with a probability P1, and event 2, also with different possible outcomes, we can select an outcome 2, that has a probability P2, and the two events are independent (meaning that the outcome in event 1 does not affect the outcome in event 2, and vice versa)
Then the probability of outcome 1 and outcome 2 happening at the same time is equal to the product of their individual probabilities.
P = P1*P2.
In this case, event 1 is the selection of the pizza, and outcome 1 is the selection of the square pizza, with a probability of 55%.
Event 2 is the selection of the drink, outcome 2 is the order of a soft drink, with a probability of 72%.
If those two events were independent, then the probability that a customer orders a square pizza and a soft drink would be:
P = 0.55*0.72 = 0.396 (or 39.6%)
But we know that the actual probability is 48%.
So this is larger, which means that the outcomes are not independent.
find the range. 83, 71, 62, 86, 90, 95, 61, 60, 87, 72, 95, 74, 82, 54, 99, 62, 78, 76, 84, 92
Answer: 45
Step-by-step explanation: The range is the difference between the greatest number in the data set and the least number in the data set which in this case is 99 - 54 or 45. So the range of this data set is 45.
Answer:
[tex] \boxed{45}[/tex]Step-by-step explanation:
Given data:
83 , 71 , 62 , 86 , 90 , 95 , 61 , 60 , 87 , 72 , 95 , 74 , 82 , 54 , 99 , 62 , 78 , 76 , 84 , 92
largest value = 99
Smallest value = 54
Let's find the range:
Range = Largest value - smallest value
= 99 - 54
= 45
Extra information:
Range
It is the simple method of measuring the variations. A range is defined as the difference between the largest and the smallest value of distribution. If the data are arranged in ascending or descending order, then the difference between the largest and smallest value is called the range.
The range is defined by
Range = Largest value - smallest value i.e ( highest value - lowest value )
= L - S
Range is the absolute measure of dispersion = L - S
Thus, if a₁ , a₂ , a₃ ...............aₙ are n term in a sequence arranged in ascending order, the range is given by
R = aₙ - a₁ where a₁ is the smallest value and aₙ is the highest value or R = L - S , where L is the largest value and S is the smallest value.
Hope I helped!
Best regards!
Suppose we want to choose 6 colors, without replacement, from 14 distinct colors. (a) How many ways can this be done, if the order of the choices matters? (b) How many ways can this be done, if the order of the choices does not matter?
Answer:
(a) 2,162,160
(b) 3,003
Step-by-step explanation:
(a) order matters
You can choose from 14 for the first pick. Then you have 13 left for the second pick. Then you have 12 left for the third pick. Keep going until you have 9 left for the 6th pick. The number when order matters is:
total = 14 * 13 * 12 * 11 * 10 * 9 = 2,162,160
(b) Order does not matter
Start with the same number as above for picking 6 out of 14. Since order does not matter, we divide by the number of ways you can arrange 6 items.
Since there are 6! ways of arranging 6 items,
total = 2,162,160/6! = 3,003
The number of ways when the order matters are 121080960.
The number of ways when order does not matters are 3003.
Given,
Choose 6 colors, without replacement, from 14 distinct colors.
We have to find:
- How many ways can this be done, if the order of the choices matters.
- How many ways can this be done if the order of the choices does not matter.
What are permutation and combination?We use permutation when the order of the arrangements matters.
It is given by:
[tex]^ nP_r[/tex] = n! / r!
We use combination when order does not matter.
It is given by:
[tex]^nC_{r}[/tex] = n! / r! (n-r)!
Find the number of ways when order matters.
We have,
n = 14 and r = 6
[tex]^{14}P_{6}[/tex]
= 14! / 6!
= (14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6!) / 6!
= 4 x 13 x 12 x 11 x 10 x 9 x 8 x 7
= 121080960
Find the number of ways when order does not matter.
We have,
n = 14 and r = 6
[tex]^{14}C_{6}[/tex]
= 14! / 6! 8!
= 14 x 13 x 12 x 11 x 10 x 9 / 6 x 5 x 4 x 3 x 2
= 7 x 13 x 11 x 3
= 3003
Thus,
The number of ways when the order matters are 121080960.
The number of ways when order does not matters are 3003.
Learn more about combination here:
https://brainly.com/question/28134115
#SPJ2
nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?
Using concepts of circles, it is found that the angle measure of each slice is of 72º.
--------------------------------------------
The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.--------------------------------------------
5 equal slices, thus:
[tex]\frac{360}{5} = 72[/tex]
The angle measure of each slice is of 72º.
A similar problem is given at https://brainly.com/question/16746988
Which of the following is not a way of generating random numbers? A. random number tables B. using phone numbers selected at random in a local phone book C. using the internet D. books of random numbers
Answer:
well all of these look like a way so we have to use elimination method
A : random number tables : well it has random numbers so X out
B: PHONE NUMBERS: well phone numbers are random so X out
C: USing the internet : totally X out
D: books of random numbers: X out
so none of the above i guess
The only way that might not be used in generating random numbers is : (B). using phone numbers selected at random in a local phone book
Meaning of random numbersRandom numbers are numbers that occurs randomly without prediction. these numbers are impossible to predict using past values.
Random numbers are important for computer encryption and lotteries.
In conclusion, The only way that might not be used in generating random numbers is using phone numbers selected at random in a local phone book
Learn more about random numbers: https://brainly.com/question/10352102
#SPJ2
Adam’s house is 2 centimeters from Juan’s house on a map. If each centimeter on the map represents 6 kilometers, how far apart are the two houses?
Answer:
Since 1 cm represents 6 km
2 cm will represent 12 km
Hence Adam's house is 12 km away
Answer:
The answer is C. 3
Step-by-step explanation:
If u divide 6 divided by 2 it will get you 3
i also got it right bc i took the quiz.
the square of a number is 3 less than four times the number. which values could be the number?
Answer:
x could be 3 or 1
Step-by-step explanation:
x²+3=4x
x²-4x+3=0
(x-3)(x-1)
x could be 3 or 1
The values could be 1 or 3.
Let the number be n.In this exercise, you're required to write a mathematical (algebraic) expression for the given word problem and determine which values could be the unknown number.
Translating the word problem into an algebraic expression, we have;
[tex]n^{2} = 4n - 3\\\\n^{2} - 4n + 3 = 0[/tex]
We would solve the quadratic equation by using the factorization method;
[tex]n^{2} - 3n -n + 3 = 0\\\\n(n - 3) - 1(n - 3) = 0\\\\(n - 1)(n - 3) = 0[/tex]
Therefore, the values could be 1 or 3.
Find more information: https://brainly.com/question/17215161
NEED ASAP I WILL GIVE BRAINLEYEST What is the value of the expression 22 + 82 ÷ 22? 8 10 17 20
Answer:
Exact Form:
283 /11
Decimal Form:
25. 72
Mixed Number Form:
25 8 /11
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
A sport jacket is on sale for 35% off, if the originsl price is $140, what is the sale price?
Answer:
$91
Step-by-step explanation:
If a jacket is on sale for 35% off, that means that the price of the jacket is [tex]100-35=65[/tex]% of its original price.
We can find 65% of 140 by making 65% into a decimal - 0.65, then multiply it by 140.
[tex]140\cdot0.65=91[/tex]
Hope this helped!
Answer:
$91.00
Step-by-step explanation:
The jacket is on sale for 35%. Usually, you pay for 100% of the jacket's price. Since it is on sale, we can subtract 35% from 100%.
100%-35%=65%
With the sale, you only pay for 65% of the price.
Now, we can multiply 65% and 140.
65% * 140
Convert 65% to a decimal. Divide 65 by 100 or move the decimal place 2 spots to the left.
65/100=0.65
65.0 --> 6.5 --> 0.65
0.65 * 140
Multiply
91
$91
The sale price for the sports jacket is $91.00
Find the equation with the given slope through the given point. Write the equation in the given form AX+BY=C m=1/9 (-6,2)
Answer:
x - 3y = 12
Step-by-step explanation:
Find the point-slope form of this equation and then convert the point-slope form into standard form (ax + by = c):
y - k = m(x - h) becomes y - 2 = (1/9)(x + 6).
Multiplying all three terms by 9 removes the fraction:
3y - 6 = x + 6, or x - 3y = 12
Hey guys! I have this problem and I dont really understand how to solve it, could you guys help me? :' )
Answer:
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
Aiko and Kendra arrive at the Texas
State Fair with $60. What is the total
number of rides they can go on if
they each pay the entrance fee of
$17 and rides cost $3 each?
Answer:
They can go on 14 rides the maximum.
Step-by-step explanation:
First, you have to set up the equation. Basically, Aiko and Kendra only carry $60 with them. They cannot go over that limit. Furthermore, the entrance free is $17. Each ride is $3.
(x = the amount of rides)
17 + 3x ≤ 60
17 represents the entrance fee which only has to be paid one time. 3x represents the cost of each ride (x equals to the amount of rides).
Now you solve.
Isolate the variable, which is 3x.
3x ≤ 60 - 17
3x ≤ 43
Now, divide 43 by 3 to find the value of x.
x ≤ 43 ÷ 3
x ≤ 14.3333333333
They can go on a max of 14 rides. Anymore, and they will go over budget. Normally, with problems like this one, if you have a decimal, you should round down unless your instructor says otherwise.
After all, who would you be able to go on a third of a ride? It isn't possible, so generally, they just have you round down.
Factor the expression.
p^2 - 10pq + 16q^2
[tex]p^2 - 10pq + 16q^2=\\p^2-2pq-8pq+16q^2=\\p(p-2q)-8q(p-2q)=\\(p-8q)(p-2q)[/tex]
SOMEONE PLEASE HELP.............
Select the type of equations.
consistent
equivalent
inconsistent
Answer:
this is an inconsistent because no solutions
musah stands at the center of a rectangular field . He first takes 50 steps north, then 25 step west and finally 50 steps on a bearing of 315°. How far west and how far north is Musah final point from the center?
Answer:
85.36 far north from the center
10.36 far east from the center
Step-by-step explanation:
The extra direction taken in the north side is x
X/sin(360-315)=50/sin 90
Sin 90= 1
X/sin 45= 50
X= sin45 *50
X= 0.7071*50
X= 35.355 steps
X= 35.36
Then the west direction traveled
West =√(50² - 35.355²)
West = √(2500-1249.6225)
West= √1250.3775
West= 35.36 steps
But this was taken in an opposite west direction
From the center
He is 35.36 +50
= 85.36 far north from the center
And
25-35.36=-10.36
10.36 far east from the center
Mark each of the following as true or false and explain how you know.
true false false true...is the quick answer
Remember that negatives are always less than positive numbers.
The paper usage at a small copy center is normally distributed with a mean of 5 boxes of paper per week, and a standard deviation of 0.5 boxes. It takes 2 weeks for an order of paper to be filled by its supplier. What is the safety stock to maintain a 99% service level?
Answer:
1.649 approximately 2
Step-by-step explanation:
S.d = standard deviation = 0.5
Time taken = lead time = 2 weeks
Mean = demand for week = 5 boxes
We are required to find the safety stock to maintain at 99% service level.
At 99% level, the Z value is equal to 2.326.
Therefore,
Safety stock = z × s.d × √Lt
= 2.326 × 0.5 x √2
= 1.649
Which is approximately 2.
log 7 (x^2 + 11) = log 7 15
Answer:
x = ±2
Step-by-step explanation:
log 7 (x^2 + 11) = log 7 15
We know that log a ( b) = log a(c) means b =c
x^2 + 11 = 15
Subtract 11 from each side
x^2 = 15-11
x^2 =4
Take the square root of each side
sqrt(x^2) =±sqrt(4)
x = ±2
A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed below. 20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27 It is known that the population standard deviation is 7. The instructor has recommended that students devote 2 hours per week for the duration of the 12-week semester, for a total of 24 hours. Test to determine whether there is evidence at the 0.07 significance level that the average student spent less than the recommended amount of time. Fill in the requested information below.A. The value of the standardized test statistic:Note: For the next part, your answer should use interval notation. An answer of the form (−[infinity],a) is expressed (-infty, a), an answer of the form (b,[infinity]) is expressed (b, infty), and an answer of the form (−[infinity],a)∪(b,[infinity]) is expressed (-infty, a)U(b, infty). B. The rejection region for the standardized test statistic:C. The p-value isD. Your decision for the hypothesis test: A. Reject H0. B. Do Not Reject H1. C. Do Not Reject H0. D. Reject H1.
Answer:
Reject H₀.
Step-by-step explanation:
In this case, we need to test whether the average student spent less than the recommended amount of time doing homework in statistics.
The provided data is:
S = {20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27}
Compute the sample mean:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{12}\cdot [20+29+...+27]=23.167[/tex]
The population standard deviation is σ = 7.
The hypothesis for the test is:
H₀: The average student does not spent less than the recommended amount of time doing homework, i.e. μ ≥ 24.
Hₐ: The average student spent less than the recommended amount of time doing homework, i.e. μ < 24.
(A)
Compute the standardized test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{23.167-24}{7/\sqrt{12}}\\\\=-0.412[/tex]
Thus, the standardized test statistic value is -0.412.
(B)
The significance level of the test is:
α = 0.07
The critical value of z is:
z₀.₀₇ = -1.476
The rejection region is:
(-∞, -0.1476)
(C)
Compute the p-value as follows:
[tex]p-value=P(Z<-0.412)=0.34[/tex]
*Use a z-table.
Thus, the p-value is 0.34.
(D)
Since, p-value = 0.34 > α = 0.07, the null hypothesis was failed to be rejected at 7% level of significance.
Thus, the correct option is (A).
A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds.
Clothes Food Toys
27 44 61
22 49 64
46 37 57
35 56 48
28 47 63
31 42 53
17 34 48
31 43 58
20 57 47
47 51
44 51
54
1. Find the values of mean and standard deviation.
2. Is there a difference in mean attention span of the children for various commercials?
3. Are there significance differences between pair of means?
Answer: Find answers in the attachment files
Step-by-step explanation:
There are 8 books needing re-shelving in a library where 65% of the library's collection consists of reference books. Let X be the number of reference books a student helper re-shelves out of the 8 on her cart. a) What is the probability that all 8 of them are reference books
Answer:
0.0319
Step-by-step explanation:
To approximate this probability, we shall be using the Bernoulli approximation of the Binomial distribution.
Let p = probability of selecting a reference book = 65% = 0.65
Let q = probability of selecting other books= 1-p = 1-0.65 = 0.35
Now, we want to find the probability that all of these 8 books to be re-shelved are reference book.
We set up the probability as follows;
P(X = 8) = 8C8 •p^8•q^0
P(X = 8) = 1 * (0.65)^8 * (0.35)^0
P(X = 8) = 0.031864481289 which is 0.0319 to 4 decimal places
A recent survey asked 1200 randomly selected U.S. adults if they believe that the U.S. federal government is doing enough to keep U.S. elections safe from outside interference. After analyzing the results, the researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe. Which statement BEST describes how to interpret these results
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is D
Step-by-step explanation:
From the question the question we are told that
The researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe.
Generally a confidence interval states to what extent the chances of the true population is within the a given range
So the 95% confidence interval given in the question as 52.5% and 59.5% means that the chances of the true population mean being with this given range is 95%
So given that the the true population mean is within this range then it means that the population mean will be greater than 50%
So the statement that best describe and interprets this result is
The results show significant statistical support that most U.S. adults (over 50%) believe that the U. S. Federal government is not doing enough to keep U.S. election safe.
The table shows the results of a survey in which 10th-grade students were asked how many siblings (brothers and/or sisters) they have. A 2-column table has 4 rows. The first column is labeled Number of siblings with entries 0, 1, 2, 3. The second column is labeled number of students with entries 4, 18, 10, 8. What is the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings? Round to the nearest whole percent. 65% 70% 75% 80%
Answer:
70%
Step-by-step explanation:
Given
Number of Siblings: || 0 || 1 || 2 || 3
Number of Students: || 4 || 18 || 10 || 8
Required
Determine the probability of a student having at least one but not more than 2 siblings
First, we have to determine the total number of 10th grade students
[tex]Total = 4 + 18 + 10 + 8[/tex]
[tex]Total = 40[/tex]
The probability of a student having at least one but not more than 2 siblings = P(1) + P(2)
Solving for P(1)
P(1) = number of students with 1 sibling / total number of students
From the given parameters, we have that:
Number of students with 1 sibling = 18
So:
[tex]P(1) = \frac{18}{40}[/tex]
Solving for P(2)
P(2) = number of students with 2 siblings / total number of students
From the given parameters, we have that:
Number of students with 2 siblings = 10
So:
[tex]P(2) = \frac{10}{40}[/tex]
[tex]P(1) + P(2) = \frac{18}{40} + \frac{10}{40}[/tex]
Take LCM
[tex]P(1) + P(2) = \frac{18 + 10}{40}[/tex]
[tex]P(1) + P(2) = \frac{28}{40}[/tex]
Divide numerator and denominator by 4
[tex]P(1) + P(2) = \frac{7}{10}[/tex]
[tex]P(1) + P(2) = 0.7[/tex]
Convert to percentage
[tex]P(1) + P(2) = 70\%[/tex]
Hence, the required probability is 70%
Answer:
Step-by-step explanation:
bB
how do you figure out ratios? the problem is 12 quarters to 34 dollars. thanks
Step-by-step explanation:
When you have a ratio, you put one number as the numerator and than one number as the denominator.
so it would be (12/34)=(x/68)
In this example I made the ratio you are comparing it to have 68 dollars, so when you solve for the amount of quarters you need it should be 24, since all of the numbers in this example are just being doubled.
To solve for x, you multiply 68 on both sides of the equation, 68×(12/34)=x
24=x
So this proves that this is how ratios, are used. It also does not matter what number you place on the numerator or denominator.
Name one real-world object that suggests A. Points B. Lines and C. Planes
There are many examples to pick from, one is
point = location on map
line = straight road between two locations (aka two points)
plane = flat ground (the ground cannot have any hills or valleys)
First, let's write some useful definitions:
Point: it is an entity that has a location in a given space or plane, and do not have any surface nor measure.
Line: if we have two points, we can define a line as a straight, infinite ray that connects them. Still does not have a surface
Plane: We can define a plane as a line and a point outside of it, here appears the concept of the surface.
So, the easier one is a plane, a sheet of paper could be a good representation of a plane. And in the same way that a sheet of paper can bend in different ways, also do the planes.
For the line, we could use a really straight wire.
Finally, the point, which is the hardest one to describe (notice that we used points to describe the other two, lines, and planes) so here we could choose something small, that has near to no surface and that also has a location in the space. An example of this could be an electron or any other elemental particle.
If you want to learn more, you can read:
https://brainly.com/question/17213603
Finding Slope On a coordinate plane, a line goes through points (0, 1) and (4, 2). What is the slope of the line? m =
Answer:
slope = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (4, 2)
m = [tex]\frac{2-1}{4-0}[/tex] = [tex]\frac{1}{4}[/tex]
Answer:
the answer would be 1/4
Step-by-step explanation:
Help and show work plz
Answer:
30
Step-by-step explanation:
If we have 4 integers that have an average of 9, then all the numbers will add up to [tex]9\cdot4=36[/tex].
If we want the greatest number possible, the other 3 need to be the lowest possible.
Since they are all different, the lowest possible values of the first 3 numbers are 1, 2, and 3.
[tex]1 + 2 + 3 = 6[/tex]
[tex]36 - 6 = 30[/tex]
So 30 is the greatest value of one of the integers.
Hope this helped!
two ratios equivalent to 27:9
Answer:
Those ratios could be 3:1
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 4 cos(x), a = 7π
Answer:
The Taylor series of f(x) around the point a, can be written as:
[tex]f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....[/tex]
Here we have:
f(x) = 4*cos(x)
a = 7*pi
then, let's calculate each part:
f(a) = 4*cos(7*pi) = -4
df/dx = -4*sin(x)
(df/dx)(a) = -4*sin(7*pi) = 0
(d^2f)/(dx^2) = -4*cos(x)
(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4
Here we already can see two things:
the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.
so we only will work with the even powers of the series:
f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....
So we can write it as:
f(x) = ∑fₙ
Such that the n-th term can written as:
[tex]fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}[/tex]
In this exercise we must calculate the Taylor series for the given function in this way;
[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]
The Taylor series of f(x) around the point a, can be written as:
[tex]f(x) = f(a) + f'(a)(x-a)+\frac{1}{2!} f''(a)(x-a)^2+....[/tex]
Here we have:
[tex]f(x) = 4cos(x)\\a = 7\pi[/tex]
Then, let's calculate each part:
[tex]f(a) = 4cos(7\pi) = -4\\df/dx = -4sin(x)\\(df/dx)(a) = -4sin(7\pi) = 0\\(d^2f)/(dx^2) = -4cos(x)\\(d^2f)/(dx^2)(a) = -4cos(7\pi) = 4[/tex]
Here we already can see two things:
1) The odd derivatives will have a sin(x) function that is zero when evaluated in [tex]x=7\pi[/tex].
2) We also can see that the sign will alternate between consecutive terms.
So we only will work with the even powers of the series:
[tex]f(x) = -4 + (1/2!)*4*(x - 7\pi)^2 - (1/4!)*4*(x - 7\pi)^4 + ....[/tex]
So we can write it as:
[tex]f(x)=\sum f_n[/tex]
Such that the n-th term can written as:
[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]
See more abour Taylor series at: brainly.com/question/6953942
A methods and measurements analyst for Timepiece, Inc., needs to develop a time standard for the task of attaching a watch to a wristband. How many observations should be made if he wants to be 95.44 percent confident that the maximum error in the observed time is one second
In a preliminary study, he observed one of his workers perform this task five times, with the following results:
Observation: Time (secs):
1 27
2 19
3 20
4 21
5 13
Answer:
100 Observations
Step-by-step explanation:
Z value = 2 (due to confidence percentage of 95.44)
S = 5
A = 1
N equals to square of (ZxS/A)
N = (ZxS/A)^2
N = (2x5/1)^2
N = 10^2 = 100
