Answer:
The answer is "239.62%".
Step-by-step explanation:
Given value:
[tex]\bold{\sin(x)=x- \frac{x^3}{3!}+\frac{x^5}{5!} - \frac{x^7}{7!}+....}[/tex]
Solve the first three values:
[tex]\sin(x)=x- \frac{x^3}{3!}+\frac{x^5}{5!}[/tex]
put the value of sin(4.1):
[tex]\to \sin(4.1)=(4.1)- \frac{(4.1)^3}{3!}+\frac{(4.1)^5}{5!} \\\\[/tex]
[tex]=(4.1)- \frac{(4.1)^3}{3!}+\frac{(4.1)^5}{5!} \\\\=(4.1)- \frac{68.92}{3 \times 2\times 1}+\frac{1158.56}{5\times 4 \times 3 \times 2 \times 1}\\\\[/tex]
[tex]=(4.1)- 11.48+9.65\\\\= 2.27[/tex]
The actual value of [tex]\sin(4.1) = -1.59[/tex]
Calculating the percentage relative approximate error value:
Formula:
[tex]=\frac{actual \ value - \ approx \ value }{actual \ value} \times 100\\\\[/tex]
[tex]=\frac{-1.59 - 2.27 }{-1.59} \times 100\\\\= \frac{-3.81}{-1.59} \times 100\\\\= \frac{3.81}{1.59} \times 100\\\\=239.62 \ \%[/tex]
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
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]
The segment with endpoints (-1,4) & (2,8) has a distance of
Answer:
5
Step-by-step explanation:
(X1,Y1) = (-1,4)
(X2,Y2) = (2,8)
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?
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
is 1 1/2 a rational number?
yes. It would be an irrational number if it didn't repeat in a pattern.
hope it helps comment if u have any questions
Answer:
Yes.
Step-by-step explanation:
Yes 1 [tex]\frac{1}{2}[/tex] is a rational number because because it can be converted to a decimal, which is 1.5
The area can be found by multiplying the side lengths that are 6 units & 4 units
Answer:squares area is. 24
Step-by-step explanation:
6×4 = 24
What is the sum?
−1.5+1.9
Enter your answer, as a decimal, in the box.
Answer:
0.4
Step-by-step explanation:
Answer: it's 0.4 as a decimal
Step-by-step explanation:
Determine if the following relations represent y as a function of x. x=y^4
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
What is the value of the expression below when y = 5?
4y2 – 7y - 6
Answer: 371
Step-by-step explanation:
Answer:59
Step-by-step explanation:
Help please TYSM IF YOU DO!
Answer:
I think it is mean
Step-by-step explanation:
because mean would be the average of the scores
Answer: The mean
Step-by-step explanation:
The mean will show the average of the teams scores.
Nathan is stocking bathrooms at the hotel where he works. he has 18 rolls of toilet paper and 9 bars of soap. if he wants all bathrooms to be stocked identically, with the same combination of supplies in each one and nothing left over, what is the greatest combination of bathrooms Nathan can stock
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.
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]
the sum of two numbers is 58. The larger number is 22 more than the smaller number. What are the numbers?
What is the domain in interval notation. do not include any spaces in your answers! Type in the word infinity if needed
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.
108 ÷ 9 x (-12) ÷ 6 - (100 ÷ 5)
Answer:
-44
Step-by-step explanation:
108 ÷ 9 x (-12) ÷ 6 - (100 ÷ 5)
= 108 ÷ 9 x (-12) ÷ 6 - (20)
= 12 x (-12) ÷ 6 - (20)
= -144÷ 6 - (20)
= -24 - (20)
= -44
During a sale, 20-cent candy bars were sold at 3 for 50 cents. How much is saved on 9 bars?
Answer:
Step-by-step explanation:
$0.30
Step-by-step explanation:
1 bar of candy = $0.20
3 bars of candy = $0.50
To solve, multiply for both:
If you pay for each candy bar individually, they each cost $0.20. Multiply 9 with 0.20:
9 x 0.20 = $1.80
If you pay for the candy bars by 3's, they cost $0.50 each pack. Divide 9 with 3, then multiply by 0.50:
9/3 = 3
3 x 0.50 = $1.50
Subtract the total cost of the individual from the pack:
$1.80 - $1.50 = $0.30
. $0.30 is your answer.
How do you write.09 in words?
Answer:
zero point 9
0 and nine tenths
Step-by-step explanation:
Seven is part of all of the following sets of numbers except
O irrational numbers
O integers
O rational numbers
natural numbers
Answer:
Seven isn't part of the set of irrational numbers.
Step-by-step explanation:
Seven and the Set of all Natural NumbersStart with the smallest set among the choices. The set of all natural numbers, [tex]\mathbb{N}[/tex], starts with [tex]0[/tex] (or [tex]1[/tex], for some people.) A number [tex]n[/tex] is in [tex]\mathbb{N}\!\!\![/tex] (write [tex]n \in \mathbb{N}[/tex]) if and only if [tex](n - 1)[/tex] is in [tex]\mathbb{N}\![/tex]. Conversely, if [tex]n\![/tex] is indeed in [tex]\mathbb{N}\!\!\!\!\![/tex], then [tex](n + 1)[/tex] would also be in [tex]\mathbb{N}\!\!\!\!\!\!\![/tex]. For [tex]7[/tex]:
[tex]1 \in \mathbb{N} \implies 2 \in \mathbb{N}[/tex].
[tex]\vdots[/tex].
[tex]6 \in \mathbb{N} \implies 7 \in \mathbb{N}[/tex].
Therefore, [tex]7[/tex] is indeed in the set of all natural numbers.
Seven and the Set of all IntegersSimilarly, a number [tex]n[/tex] is in the set of integers, [tex]\mathbb{Z}[/tex], if and only if either [tex](n - 1)[/tex] or [tex](n + 1)[/tex] is (or both are) in [tex]\mathbb{Z}\!\![/tex].
Conversely, if a number [tex]n[/tex] is in [tex]\mathbb{Z}[/tex], then both [tex](n - 1)[/tex] and [tex](n + 1)[/tex] will be in [tex]\mathbb{Z}\![/tex].
It can be shown in a similar iterative way that [tex]7 \in \mathbb{Z}[/tex].
Alternatively, consider the fact that the set of all natural numbers, [tex]\mathbb{N}[/tex], is a subset of the set of all integers, [tex]\mathbb{Z}[/tex]. Therefore, [tex]7 \in \mathbb{N}[/tex] implies that [tex]7 \in \mathbb{Z}[/tex].
Seven and the Set of all Rational NumbersA number [tex]m[/tex] is a member of the set of all rational numbers [tex]\mathbb{Q}[/tex] if and only if there exists two integers [tex]p[/tex] and [tex]q[/tex] such that:
[tex]\displaystyle m = \frac{p}{q}[/tex].
[tex]1[/tex] and [tex]7[/tex] are both integers. If [tex]p = 7[/tex] and [tex]q = 1[/tex], then [tex]\displaystyle 7 = \frac{7}{1} = \frac{p}{q}[/tex]. Hence,
Alternatively, note that the set of all integers, [tex]\mathbb{Z}[/tex], is a subset of the set of all rational numbers, [tex]\mathbb{Q}[/tex]. Therefore, the fact that [tex]7 \in \mathbb{Z}[/tex] would imply that [tex]7 \in \mathbb{Q}[/tex].
Seven and the Set of all Irrational NumbersA number is in the set of all irrational numbers if and only if:
this number is in the set of all real numbers, andthis number is not in the set of all rational numbers. (Hence "irrational.")Therefore, the fact that [tex]7[/tex] is a rational number implies that it is not an irrational number.
Answer:
irrational numbers
Step-by-step explanation:
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.
Answer:
The solution and the calculation is shown on the first uploaded image
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.
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
PLEASEEE HELPPP
Solve for x:
Second option, just do Pemdas backwards.
34+987=what please help
Answer:
1021
Step-by-step explanation:
i added 34 +987 and got 1021
Round 10.999244792948 to the nearest whole number
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.
Write the next 4 digits in the repeating decimal 4.715
Answer:
4.7157157
Step-by-step explanation:
because it is a repeating decimal, it will repeat the terms that come first such as 715.
Answer to this PLEASE GOD BLESS YOU
Answer:
the answer to this question is b
Given the vectors shown, find the sum (P+Q+R).
Please help. I don’t understand this math problem.
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.
Solve the following equation: 3x - 7 = 9 + 2x.
A)12
B)16
c)20
d)24
Answer:
Option B
Step-by-step explanation:
[tex]3x - 7 = 9 + 2x\\\\3x-7+7=9+2x+7\\\\3x = 9 + 7 + 2x\\\\3x=16+2x\\\\3x-2x=16+2x-2x\\\\\boxed{x=16}[/tex]
Hope this helps!
solve this equation
3x+6=-2-2x
Answer:
x = -8/5
x = -1.6
Step-by-step explanation:
3x+6=-2-2x
Add 2x to each side
3x+2x+6=-2-2x+2x
5x+6 = -2x
Subtract 6 from each side
5x+6-6 = -2-6
5x= -8
Divide each side by 5
5x/5 = -8/5
x = -8/5
x = -1.6
5. Solve the following equations for the indicated variable.
a. 5(3x + 7)=20-2(x +1) for x
b. 2x - y= 24 for y
c. m(3 – 4m)= 7+4(8 – m2) for m
d. 5x(x + 3) =(x)(5x – 3) + 36 for x
Answer:a) x =−1
B) x=1/2y+12
C) m=13
D) x=2
Step-by-step explanation:a) Let's solve your equation step-by-step.
5(3x+7)=20−2(x+1)
Step 1: Simplify both sides of the equation.
5(3x+7)=20−2(x+1)
(5)(3x)+(5)(7)=20+(−2)(x)+(−2)(1)(Distribute)
15x+35=20+−2x+−2
15x+35=(−2x)+(20+−2)(Combine Like Terms)
15x+35=−2x+18
15x+35=−2x+18
Step 2: Add 2x to both sides.
15x+35+2x=−2x+18+2x
17x+35=18
Step 3: Subtract 35 from both sides.
17x+35−35=18−35
17x=−17
Step 4: Divide both sides by 17.
17x/17=−17/17
x=−1
B) Let's solve for x.
2x−y=24
Step 1: Add y to both sides.
2x−y+y=24+y
2x=y+24
Step 2: Divide both sides by 2.
2x/2=y+24/2
x=1/2y+12
C) Let's solve your equation step-by-step.
m(3−4m)=7+4(8−m2)
Step 1: Simplify both sides of the equation.
−4m2+3m=−4m2+39
Step 2: Add 4m^2 to both sides.
−4m2+3m+4m2=−4m2+39+4m2
3m=39
Step 3: Divide both sides by 3.
3m/3=39/3
m=13
D) Let's solve your equation step-by-step.
5x(x+3)=x(5x−3)+36
Step 1: Simplify both sides of the equation.
5x2+15x=5x2−3x+36
Step 2: Subtract 5x^2 from both sides.
5x2+15x−5x2=5x2−3x+36−5x2
15x=−3x+36
Step 3: Add 3x to both sides.
15x+3x=−3x+36+3x
18x=36
Step 4: Divide both sides by 18.
18x/18=36/18
x=2
K(h-j)+10’ if h= 7, j=-8, and k=5
Answer:
49
Step-by-step explanation:
5(7-8)+10
49
it's equals 49