Answer:
[tex]14x cos(\frac{1}{15}x^{2})=14 \sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]
Step-by-step explanation:
In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:
[tex]cos(x)=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{2k}}{(2k)!}[/tex]
So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: [tex]\frac{1}{15}x^{2}[/tex] so for
[tex]cos(\frac{1}{15}x^{2})[/tex]
the modified series will look like this:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15}x^{2})^{2k}}{(2k)!}[/tex]
So we can use some algebra to simplify the series:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15^{2k}}x^{4k})}{(2k)!}[/tex]
which can be rewritten like this:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]
So finally, we can multiply a 14x to the series so we get:
[tex]14xcos(\frac{1}{15}x^{2})=14x\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]
We can input the x into the series by using power rules so we get:
[tex]14xcos(\frac{1}{15}x^{2})=14\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]
And that will be our answer.
What iis 155 plus 33 minus 4 divided by 2
Answer:
155+33-4÷2155+33-2188-2186hope it is helpful to you
The simplified form of statement 155 plus 33 minus 4 divided by 2 is
186.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
The given statement is 155 plus 33 minus 4 divided by 2 which can be numerically expressed as,
155 + 33 - 4 ÷ 2.
PEMDAS rule states the correct order of simplifying an expression is as follows, Parenthesis, exponents, multiplications, divisions, additions, and, subtractions.
155 + 33 - 2.
= 188 - 2.
= 186.
learn more about numerical expressions here :
https://brainly.com/question/29199574
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Find the graph of the solution set of the following system of linear inequalities
Answer:
the graph looks like this:-
Step-by-step explanation:
for inequality 1
if we take x = 0 we get y = -4
and if we take y =0 we get x = 16
so we get 2 points (0, -4) and (16, 0) and the graph must pass thru these two.
now checking if the origin satisfies the inequality or not
take x and y = 0
0 + 0 is not greater than or equal to -16
so origin doesn't satisfy the inequality.
shade the graph on the side, of the line, opposite to where the origin is.
for inequality 2
if we take x = 0 we get y = 2
and if we take y =0 we get x = -⅔
so we get 2 points (0, 2) and (-⅔, 0) and the graph must pass thru these two.
the line should be a dotted line.
now checking if the origin satisfies the inequality or not
take x and y = 0
0 + 0 is less than 2
so origin satisfies the inequality.
shade the graph on that side of the line where the origin is.
[ red line shows graph 1 whereas the blue dotted line represents graph ]
2 starting terms of a diginacci sequence when the 2021st term is 11
Hello,
In a diginacci sequence, all term is the sum off digits of the 2 terms before.
Answer: 2,3
[tex]u_{-2}=1\\u_{-1}=1\\u_0=digit(u_{-2})+digit(u_{-1})=1+1=2\\u_1=1+2=3\\u_2=2+3=5\\u_3=3+5=8\\u_4=5+8=13\\u_5=8+1+3=12\\...\\u_{18}=11\\u_{19}=8\\u_{20}=10\\u_{21}=9\\u_{22}=10\\u_{23}=10\\u_{24}=2**********\\u_{25}=3**********\\2020=24*84+4\\u_{2020}=u_{4}=13\\[/tex]
We must begin with 13 , 10
Proof:
Dim a As Long, b As Long, c As Long, nb As Integer
a = 13
b = 10
nb = 1
Print nb, a
While nb < 2021
nb = nb + 1
c = somme&(a, b)
a = b
b = c
' Print nb, a
Wend
Print nb, a
End
Function somme& (a1 As Long, b1 As Long)
Dim strA As String, strB As String, n As Long
strA = LTrim$(Str$(a1))
strB = LTrim$(Str$(b1))
n = 0
For i = 1 To Len(strA)
n = n + Val(Mid$(strA, i, 1))
Next i
For i = 1 To Len(strB)
n = n + Val(Mid$(strB, i, 1))
Next i
somme& = n
End Function
giving brainiest Elinor solved this problem. Is her answer correct?
8.93 times 0.15 = 4465. 4465 + 8930 = 13.395
No, Elinor should have placed the decimal point between the 1 and the 3.
No, she should have placed the decimal point between the 3 and the 9.
No, she did not align the place values in the partial products correctly.
Yes. Elinor did not make an error. giving Branniest
Answer:
its a
Step-by-step explanation:
trust did test
Using each of the digits 2 through 5 only
once, write 2 two-digit whole numbers
whose product is as large as possible.
Answer:
52, 43
Step-by-step explanation:
the first instinct might be to make the first number as big as possible : 54
that leaves for the second number 2 and 3, and the largest combination here is 32 (larger than 23).
54×32 = 1728
but, the area of a rectangle (and that is what we are calculating here) is the larger, the closer the lengths of its side are.
so, a bigger difference between length and width creates a smaller area, than a smaller difference between length and width for similar lengths.
so, what if we sacrifice just a little bit of the length, and make it 53 ? that opens up 4 for the second number, giving us 42 as width. they are much closer to each other with still very similar length.
53×42 = 2226
you see ? much bigger.
let's experiment further and pick 52 as length.
that gives us 43 as width.
52×43 = 2236
and again a little bit closer and with bigger result.
you see, in the previous case we "added" comparably to this last case a 42 (53×42 instead of 52×42), and in the last case we added a 52 (52×43 instead of 52×42) creating the difference of 10.
but of course, this only works, if we don't decrease the length too much.
Answer:
Using each of the digits 2 through 5 only once, write 2 two-digit whole numbers whose product is as large as possible.
What do the chi-square test for independence, the Pearson correlation, and simple linear regressions all have in common
Answer:
They all test relationship when it involves two variables
Explanation:
All of the statistical methods listed above all measure the relationship between two variables.
The Chi Square test tests the relationship between two nominal/categorical variable groups.
The Pearson correlation test tests relationship between two continuous variables using the Pearson correlation coefficient to determine statistical relationship between them.
The simple linear regression measures relationship between two variables: dependent/response variable and independent/explanatory variable, to see if a relationship exists between by way of influence of the independent variable on the dependent variable.
The list shows the ages of first-year teachers in one school system. What is the mode of the ages? 23, 42, 21, 25, 23, 24, 23, 24, 37, 23, 39, 51, 63, 24, 55
Answer:
La moda es 23
Step-by-step explanation:
23 es el numero que mas se repite es decir la moda
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
Y
p(x,y) 0 1 2
x 0 0.10 0.04 0.02
1 0.08 0.20 0.06
2 0.06 0.14 0.30
a. What is P(X = 1 and Y = 1)?
b. Compute P(X ≤ 1 and Y ≤ 1).
c. Give a word description of the event {X ≠ 0 and Y ≠ 0}, and compute the probability of this event.
d. Compute the marginal pmf of X and of Y. Using pX(x), what is P(X ≤ 1)?
e. Are X and Y independent rv’s? Explain.
Answer:
a. 0.2
b. 0.42
c. 0.7
d. the solution is in the explanation
e. x and y are not independent
Step-by-step explanation:
a. from the joint probability mass function table,
p(x=1) and p(Y= 1)
= p(1,1) = 0.2
b. prob(0,0)+prob(0,1)+prob(1,0)+prob(1,1)
= 0.10 + 0.04 + 0.08 + 0.20
= 0.42
P(X ≤ 1 and Y ≤ 1) = 0.42
c. prob {X ≠ 0 and Y ≠ 0}
= prob(1,1) + prob(1,2) + prob(2,1) + prob(2,2)
= 0.20 + 0.06 + 0.14 + 0.30
= 0.7
d. we have to calculate the marginal pmf of x and y here.
we have the x values as 0,1,2
prob(x=0) = 0.1 + 0.04 + 0.02
= 0.16
prob(x=1) = 0.08 + 0.2 + 0.06
= 0.34
prob(x=2) = 0.06+0.14+0.3
= 0.50
we have y values as 0,1,2
prob(y=0) = .1+.08+.06
= 0.24
prob(y=1) = .04+.2+.14
= 0.38
prob(y = 2) = 0.02+0.06+0.3
= 0.38
P(X ≤ 1) = prob(x=0)+prob(x=1)
= 0.34+0.16
= 0.50
e. from the joint table we have this,
prob(1,1) = 0.2
prob(x=1) = 0.34
prob(y=1) = 0.38
then prob(x=1)*prob(y=1)
= 0.34*0.38
= 0.1292
therefore prob(1,1) is not equal to prob(x=1)*prob(y=1)
0.2≠0.1292
x and y are not independent
A Sociology instructor gives students points for each discussion-board post and points for each reply to a post. Ana wrote 6 posts and 8 replies and received 114 points. Jae wrote 5 posts and 4 replies and received 79 points. Determine how many points a discussion post is worth and how many points a reply is worth?
Answer:
5 points per post and 2 points per replies
Suppose f(x)=x^2 and g(x)=(1/2x)^2. Which statement best compares the graph of g(x) with the graph of f(x)?
Answer:
"A"
Step-by-step explanation:
in an examination 30% of the candidates failed in English and 35% failed in general studies and 27% failed in both subjects.if310 candidates passed in both how many candidates appeared in the examination
Answer:
500
Step-by-step explanation:
in a class of 50 student,35 are boys.what is the ratio of girls to boys in the class?
Answer:
15:35
Step-by-step explanation:
50-35=Girls
50-35=15
38. The ______ is also not convenient to use because the process of working for it produces large numbers due to squaring. 39. The ______ is the most reliable measure of variability. 40. The lesser the variability, the ______ is the mean.
Answer:
This Question Is From The Novel Of The Fantastic Mr.Fox
Q. Boggis , Bunce and Bean are Offering a reward for Mr.Fox , They are tired of Losing Chickens Geese and Cider , Create a Description And Drawing of Mr.Fox to allow him to be captured , use the word bank....
________________________________
Swift | Slay | Ginger | Rough | Fast
Thief. | Clever | Fur | Tail | Wife | Night
Cunning | Bushy | wiry | bush | Den | trick
________________________________
Help ASAP!! A triangle has side lengths of 11in, 15in, and 20in. Find the angle measures of the triangle. Round decimal answers to the nearest tenth. Someone help pls.
Answer:
<A = 47.7°
<B = 99.4°
<C = 32.9
Step-by-step explanation:
When given the measurements of all three sides, you can calculate the angles using the Cosine Law.
c² = a² + b² - 2ab cos C
(based on Pythagorean Theorem)
If we say: a = 15
b = 20
c = 11
11² = 15² + 20² - 2(15)(20) cos C
121 = 625 - 2(15)(20) cos C
121 = 625 - 600 cos C
⁻504 = ⁻600 cos C
cos⁻¹ (504 ÷ 600) = C
< C = 32.9°
a² = b² + c² - 2bc cos A
15² = 20² + 11² - 2(20)(11) cos A
225 = 521 - 2(20)(11) cos A
225 = 521 - 440 cos A
⁻296 = ⁻440 cos A
cos⁻¹ (296 ÷ 440) = A
<A = 47.7°
Then, since we know the sum of all three angles of a triangle equals 180°:
180° - 32.9° - 47.7° = 99.4°
<B = 99.4°
What is 5.071 in words?
Answer:
Step-by-step explanation:
The number 5.071 written in english words is "five and seventy-one thousandths
8/9 - 1/3
Very easy question for 10 pts
Answer:
answer is 5/9
Step-by-step explanation:
Answer:
The answer is 5/9 or 0.555 (the 5 is repeated)
Find the domain.
p(x) = x^2+ 2
Answer:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
( − ∞ , ∞ )
Set-Builder Notation:
{ x | x ∈ R }
Step-by-step explanation:
hope that helps bigger terms
An investor puts $1,200 into an account that pays 5.5% interest compounded annually. The total amount A in the account after t years is given by which function below?
A = 1200(1.55) t
A = 1200(1.055) t
A = 1200(1.055) t
A = 1200 + (1.055) t
Let's see
[tex]\\ \tt\leadsto A=P(1+r/n)^{nt}[/tex]
n=1[tex]\\ \tt\leadsto A=1200(1+0.055)^t[/tex]
[tex]\\ \tt\leadsto A=1200(1.055)^t[/tex]
Answer:
[tex]\sf A=1200(1.055)^t[/tex]
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
P = $1,200r = 5.5% = 0.055t = t yearsSubstitute the given values into the equation:
[tex]\implies \sf A=1200(1+0.055)^t[/tex]
[tex]\implies \sf A=1200(1.055)^t[/tex]
Learn more about compound interest here:
https://brainly.com/question/27222595
https://brainly.com/question/26865309
Find the value of x. Round to the nearest tenth.
a construction company built a scale
Answer:
There are no shortcuts to scaling successfully. It takes just as much — or more — work as it did to start the company in the first place. Take control of the transition. Get organized with tools that support your employees in their day-to-day roles, making it easier for them to get more done as the company grows.
The lebgth of a rrctangle is 3 inches more than its width.The perimeter of the rectangle is 34 inches.
Step-by-step explanation:
there is the answer. good luck
Identify the level of measurement (nominal, ordinal, or interval-ratio) of each of the following variables: (1) How satisfied a person is with his or her employment benefits, measured as very satisfied, somewhat satisfied, neither satisfied nor dissatisfied, somewhat dissatisfied, or very dissatisfied. (2) The number of times someone has shoplifted in her or his life. (3) The number of times someone has voted in a public election measured as 0-1 times, 2-3 times, or 4 or more times. (4) The type of attomey a criminal defendant has attrial, measured as privately retained or publicly funded.
Solution :
Nominal variable
A nominal variable is defined as a variable which is used to [tex]\text{nam}e \text{ or label or categorize some particular attributes }[/tex] which are being measured.
An ordinal variable is the one in which the order matters, but the difference between any two orders does not matter.
In interval ratio variable is defined as the variable where the difference between any two values is meaningful.
The level of measurement for each of the following are :
1) Variables that are categorized in categories so that it is ordinal data.
2) Data scaled with the two categories her or his, so it is a nominal data.
3) Number of votes categorized in the intervals so it is Interval type data.
4) nominal data.
On a coordinate plane, a line goes through points (negative 1, 0), (0, 1), and (1, 2). Which table goes with the graph?
Answer:
Table B
Step-by-step explanation:
correct on edge :)
A company decides to drain the water heater to flush out sediments. The water heater has a capacity of 500 gallons. It drains 100 gallons in 20 minutes. After 20 minutes, they open another drain valve and it drains 200 gallons in the next 20 minutes. The drain valves are closed for 10 minutes, while the workers take a break and then the water heater is drained until the water heater is completely empty.
What are the domain and the range of this relation?
Answer:
≤ y ≤ 70 and 0 ≤ x ≤ 500
Step-by-step explanation:
In this relation we have two things to analyze, the number of gallons of water in the heater, that is 500 gallons, and the time that it took to empty the heater.
Let's count the time.
First, there are 20 minutes in wich 100 gallons are drained.
then, another drain valve is opened, so in 20 minutes they drain 200 gallons of water.
now, the wait for 10 minutes.
Now there are 200 gallons remaining, so the workers must wait for the other 20 minutes to drain the 200 gallons remaining.
The total amount of time is 70 minutes.
So if we have a relationship of water in the heater vs time, where X is the water remaining and Y is the time, the correct domains are:
Y from 0 minutes to 70 minutes
X from 0 gallons to 500 gallons
So the correct options are C and E.
0 ≤ y ≤ 70 and 0 ≤ x ≤ 500
Ryan spent 1/3 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill. If $759 was left, what was his monthly salary?
Step-by-step explanation:
Given Information :Ryan spent 1/3 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill. Remaining money = $759To calculate :His monthly salary.Calculation :Let us assume his monthly salary as x. According to the question,
➝ Money spent on rent + Money spent for utility bill + Remaining money = His salary
[tex]\longrightarrow\sf {\dfrac{1}{3}x + \dfrac{1}{7}x + 759 = x} \\ [/tex]
[tex]\longrightarrow\sf {\dfrac{7x + 3x + 15939}{21}= x} \\ [/tex]
[tex]\longrightarrow\sf {\dfrac{10x+ 15939}{21}= x} \\ [/tex]
[tex]\longrightarrow\sf {10x+ 15939= 21x} \\ [/tex]
[tex]\longrightarrow\sf {15939= 21x - 10x} \\ [/tex]
[tex]\longrightarrow\sf {15939= 11x} \\ [/tex]
[tex]\longrightarrow\sf {\cancel{\dfrac{15939}{11}}= x} \\ [/tex]
[tex]\longrightarrow\underline{\boxed{\bf {1449= x}}} \\ [/tex]
Therefore, his monthly income is $1449.
Need help
Identify the domain of the function shown in the graph
Answer:
B
Step-by-step explanation:
When f(x) is divided by x + 4 the quotient is x2+5x−3+2x+4. What is f(−4)?
You and Michael have a total of $19.75. If Michael has $8.25, how much
money do you have?
$27.00
$28.00
$11.50
$12.00
Answer:
You have a total of $11.50
Step-by-step explanation:
We first subtract $19.75 by $8.25 and the result will be $11.50
Answer:
11.50
Step-by-step explanation:
19.75-8.35= 11.50
May I have the brainiest?
what is the value of the expression 5²5
Answer:
5^2×5
=25×5
=125
hope this will help you
Answer:
125
Step-by-step explanation:
hope this helps you
=25×5
=125
95, 86, 78, 71, 65, 60 _____
Answer:
hello there here is your answer
51 is your next term.
Step-by-step explanation:
you are subtracting 9 from each number
95-9= 86
86-9=78
78-9=65
65-9=60
60-9=51
so on and so on
Hope this help
have a good day
bye
Step-by-step explanation:
[tex]here \: is \: your \: solution: - \\ \\ given \: number \: = 95.86.78.71.65.60 \\ \\ = > 95 - 9 = 86 \\ \\ = > 86 - 8 = 78 \\ \\ = > 78 - 7 = 71 \\ \\ = > 71 - 6 = 65 \\ \\ = > 65 - 5 = 60 \\ \\ \: now \: follow \: the \: sequence \: \\ \\ subtract \: 4 \: from \: 60 \\ \\ = > 60 - 4 = 56 \\ \\ = > \: \: 56 \: \:( ANSWER✓✓✓)[/tex]
