Answer: 42.5
Step-by-step explanation:
8 multipled by 42.5 is 340. A strategy i use is multiply 8 by 5 or 10, for example 8 times 5 is 40, so i know that 8 times 50 is 400, that tells you the answer you need is just a little below 50
Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. If the reported percent has a margin of error of 2.7 percentage points, which of the following is closest to the level of confidence
Therefore , as a result, the z-answer table's to the test statistic problem given above determines that the corresponding confidence level for 1.65 is 90%.
Define test statistic.The Z-statistic, that exhibits the typical normal null hypothesis is true, has been the statistical test for something like a Z-test. Let's say you do a two-tailed X y with a 0.05 significance level and get a 2.5 Z-statistic (also known as a Z-value) depending on your data. The p-value for this Z-value is 0.0124.
Here,
Given :
the following characteristics
The ratio of the sample size n = 900 p equals 0.6 * 900 = 540 p = 540/900 p = 0.6 E = 2.7% = 0.027.
The answer to the above problem is:
=> 0.027 = z* 0.6(1-0.6)/900
=> 0.027 = z* (0.24/900)
=>0.027 = z* 0.00163
=>0.027/0.0163 = z
=>z = 1.65
As a result, the z-answer table's to the test statistic problem given above determines that the corresponding confidence level for 1.65 is 90%.
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chord of a circle is 13.2 cm long and circles radius is 9.4 find the angle subtended by the chord at the centre of the circle
Answer:
To find the angle subtended by a chord at the center of a circle, we can use the formula:
θ = 2 * arcsin (c / 2r)
where θ is the angle subtended by the chord, c is the length of the chord, and r is the radius of the circle.
Step 1: Substitute the given values into the formula
θ = 2 * arcsin (13.2 / (2 * 9.4))
Step 2: Simplify the equation
θ = 2 * arcsin (13.2 / 18.8)
Step 3: Use a calculator or a math table to find the value of arcsin
arcsin (13.2 / 18.8) = 0.636 radians
Step 4: Multiply the value obtained by 2
0.636 * 2 = 1.27 radians
Final Answer: The angle subtended by the chord at the centre of the circle is 1.27 radians or 72.8 degrees
Answer:
ForTheTriangleABOtofindthelengthr
Wehave
sin(
2
α
)=
hypotenuse
opposite
=
OA
AB
=
9.4
6.6
=0.70212
whereAB=
2
13.2
=6.6cm
2
α
=sin
−1
(0.70212)
thenweoptain=
α=44.6°×2
=89.2°
Find the range of each function for the given domain.
18. f(x) = 2x - 7; {(-2, -1, 0, 1,2}
The range of the function is given by set A = { -11 , -9 , -7 , -5 , -3 }
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the range of the function be represented as set A
Now , the function is given by
f ( x ) = 2x - 7 be equation (1)
Let the domain of the function be represented as set B = { -2 , -1 , 0 , 1 , 2 }
Substitute the value for x in the given equation , we get
when x = -2
f ( x ) = 2x - 7
f ( -2 ) = 2 ( -2 ) - 7
f ( -2 ) = -4 - 7 = -11
when x = -1
f ( x ) = 2x - 7
f ( -1 ) = 2 ( -1 ) - 7
f ( -1 ) = -2 - 7 = -9
when x = 0
f ( x ) = 2x - 7
f ( 0 ) = 2 ( 0 ) - 7
f ( 0 ) = 0 - 7 = -7
when x = 1
f ( x ) = 2x - 7
f ( 1 ) = 2 ( 1 ) - 7
f ( 1 ) = 2 - 7 = -5
when x = -2
f ( x ) = 2x - 7
f ( 2 ) = 2 ( 2 ) - 7
f ( 2 ) = 4 - 7 = -3
Therefore , the value of set A is { -11 , -9 , -7 , -5 , -3 }
Hence , the range of the function is { -11 , -9 , -7 , -5 , -3 }
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16. Pages - 9
Minutes - 18 1 10 14
This leads to the conclusion that x=5 is the answer to the given function problem.
Function: What is it?A link where every x is related to a distinct y variable is called a function. It's noteworthy that when utilizing the similar y and different xs, the inverse is not possible. Except for vertical and horizontal lines, all linear equations can be expressed as functions.
Here,
a function that we've provided
f(x) = 5 - 25x / x
First, the x common factor in the numerator and denominator will be removed, and the resulting fraction will be zero.
5x -25
The common factor, which is 5, will be removed once more, and we will receive 5.
5(x-5)
In this case, we'll compare the expression to zero.
5(x-5) = 0
We shall discover x's value.
x=5
As a result, x=5 is the answer to the function issue that was presented.
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The complete question is "Find the x value in the given function
f(x) = 5 - 25x / x on the 16 pages - 9 "
a) Work out 38% of 124
b) Work out 138% of 124
Give each of your answers as a decimal.
38% of 124 is 47.12% and 138% of 124 is 171.12%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, we need to find 38% and 138% of 124,
a) Percentage = 38 / 100 × 124
= 38 × 124 / 100
= 4712 / 100
= 47.12%
b) Percentage = 138 / 100 × 124
= 138 × 124 / 100
= 17112 / 100
= 171.12%
Hence, 38% of 124 is 47.12% and 138% of 124 is 171.12%
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Change the equation in the row below to fix the marbleslide.
The fixed equation in the given question is y=x-4
What is an equation example?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What are basic equations?A simple equation is a mathematical formula that, on both sides of the "equal to" sign, expresses the connection between two expressions. Equations in this category include a variable, which is often expressed as x or y. Simple equations frequently need to be rearranged in order to be solved.
In the given equation
To fix the equation such that the line coincides with the star
the equation should be
y=x-4
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Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement.The mean is the measure of central tendency most likely to be affected by an outlier.
The statement that the mean is most likely to be affected by an outlier, is True.
Why is the mean affected by outliers ?The mean (average) of a set of data can be significantly affected by outliers, or data points that are much higher or lower than the majority of the data. Outliers can greatly influence the mean, pulling it away from the center of the data and making it less representative of the majority of the data.
This can cause the mean to become skewed and can give a false representation of the typical values in the data set. This is why it's important to consider the presence of outliers when calculating the mean and to use other measures of central tendency, such as the median or mode, to get a better understanding of the distribution of data in a set.
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Help me out pleaseeeee
Answer:
There are several ways to look at this
Consider the interior angles of a triangle:
33 + A = 90
52 + B = 90
85 + A + B = 180 interior angles of a triangle must sum to 180
So 180 - 85 = 95 which completes the triangle and would be EKD
Or 33 counterclockwise + X clockwise + 52 counter clockwise = 0
X must be 85 and is exterior to EKD and again
EKD = 180 - 85 = 95
If you consider the geometry and the corresponding angles you should be able to get a satisfactory answer
One can draw the line ED and consider the angles involved
suppose you buy a car with a value of 9250 each year the value of your car will depricate by 5.1 percent how much will your car be worth in 8 years
Answer: $6085.15
Step-by-step explanation:
Substituting into the exponential decay formula yields [tex]9250(1-0.051)^8 \approx \$6085.15[/tex].
How much interest will you have in 6 months if you invest $1,000 at 3% compounded monthly
The interest that we will have in 6 months if you invest 1000 dollars at 3% compounded monthly is 15.09 dollars.
How to find compound interest?Let's find the compound interest that will if one invest 1000 dollars in 6 months at 3% rate compounded monthly.
using compound interest formula,
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
where
p = principalr = raten = number of timest = timeTherefore,
p = 1000
r = 3% = 3 / 100 = 0.03
t = 0.5
n = 12
Therefore,
[tex]A = 1000(1+\frac{0.03}{12} )^{12(0.5)}[/tex]
A = 1000(1 + 0.0025)⁶
A = $1,015.09
Therefore,
Interest = 1,015.09 - 1000 = $15.09
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please help me :(((((
According to this, 3/10 of an inch on a map corresponds to 7/8 miles in actual distance.
In what way do you convert to a unit rate?In the case of a unit rate expressed as a fraction, the denominator is 1 unit. Divide the denominator by the denominator to represent a rate as a unit rate.
According to this, 3/10 of an inch on a map corresponds to 7/8 miles in actual distance.
Conversion Unit, This unit of conversion, also known as a rate, is utilized to help us map out greater numbers on a smaller piece of paper. Miles to Inches conversion factor is
Data provided 3/10 in equals 7/8 miles.
This suggests that we would depict the real 7/8 miles of distance on the map by 3/10 inches. Inevitably, this would result in a reduction in size or length.
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a teacher is creating an assignment worth 70 points. the assignment will consist of questions worth 1 point and questions worth 3 points. which equation represents this situation, where x represents the number of 1-point questions and y represents the number of 3-point questions?
x + 3y = 70 represents the number of 1-point and 3-point questions in an assignment worth 70 points.
What is algebraic equation ?
An algebraic equation is a mathematical statement that shows that two expressions are equal. It typically consists of a combination of numbers, variables and mathematical operations such as addition, subtraction, multiplication, and division.
The equation that represents the situation where the teacher is creating an assignment worth 70 points and it will consist of questions worth 1 point and questions worth 3 points, where x represents the number of 1-point questions and y represents the number of 3-point questions is:
x + 3y = 70
This equation states that the total number of points, which is the sum of the number of 1-point questions (x) multiplied by 1 and the number of 3-point questions (y) multiplied by 3 is equal to 70.
x + 3y = 70 represents the number of 1-point and 3-point questions in an assignment worth 70 points.
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A large company boasts in their promotional literature that 74% of their employees have college degrees. Assume this claim is true.
What is the probability that if people are selected at random from this company, that the first person to have a college degree is the 3rd person selected?
0. 0176
0. 0500
0. 4052
0. 9824
Assuming that the company’s claims are true, there is a probability of 0.9824 that the first person to have a college degree is the third person selected at random.
The company claims that 74% of its employees hold college degrees.
Taking the total number of employees as 1,
The probability of employees who do hold a college degree P(3) is 0.74
Therefore, the probability of employees who do not have a college degree is (1-0.74) = 0.26
The probability that the first 2 employees do not have a college degree P(1&2) is 0.26^2
The equation thus turns out to be;
Probability that the 3rd person is the first to hold a college degree = P(1&2)*P(3)= (0.26^2)*0.74= 0.9824
Therefore, the probability that the first person to hold a college degree in the company is the third person chosen at random is 0.9824.
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Manny walked a total of . The reference point used to calculate the total distance that he walked was the same as the ending point. Which describes where Manny most likely walked?from the bottom of a hill to the topon a circular nature trailon a sidewalk from his house to the mallfrom the beginning of a straight track to the end
Manny walked more likely on the circular nature trail.
As a circular path always starts and ends at the same location, we may infer this from the fact that the reference point at the beginning and finish was the same.
Other situations, like going up a slope from the bottom, exclude using the same reference point.
The beginning point and finishing point on a sidewalk or a straight track cannot have the same reference point, in a similar manner.
Therefore we can say that
Manny followed a circular nature route in this manner.The bottom of the hill serves as a reference point as well as the summit, and the beginning point and ending point are the same. Manny is now moving in a circle.Hence, Manny walked more likely on the circular nature trail.
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Elise tosses a fair coin three times in a row. What is the probability that she gets two heads in a row?
Answer:
[tex]\textrm{P(2 heads in a row) } =\boxed{\dfrac{3}{8}}[/tex]
Step-by-step explanation:
Let H represent the event that the coin turns up heads and T the event that coin turns up tails
So we can get H on the first toss, then 2 T's on the next two tosses, a T on the first toss and 2 H on the next two tosses, two T on the first two tosses and a H on the third toss etc.
The sample space for 3 tosses of a coin consists of 2³ elements since there are two possible outcomes for each of 3 events
The sample space is enumerated below
1 H H H
2 T H H
3 H T H
4 T T H
5 H H T
6 H T T
7 T H T
8 T T T
There are 3 possibilities where 2 H appear in a row
These are the ones in bold in the table above
Since only 3 outcomes out of a total of 8 possible outcomes can result in 2 heads in a row,
[tex]\textrm{P(2 heads in a row) } =\dfrac{3}{8}[/tex]
find the roots of each equation y^2-1/16=0
[tex]y^2 - \cfrac{1}{16}=0\implies y^2=\cfrac{1}{16}\implies y=\pm\sqrt{\cfrac{1}{16}}\implies y=\pm\cfrac{\sqrt{1}}{\sqrt{16}}\implies y=\pm \cfrac{1}{4}[/tex]
what is 76683932992840842842774839498289294929x91983918938019308926753234793357888890878676932 eqaul to
Answer:
76683932992840842842774839498289294929x91983918938019308926753234793357888890878676932 is a very large number and its exact value is not possible to calculate by hand or with common calculators. However, it can be calculated using a computer with advanced mathematical software.
Step-by-step explanation:
A helium tank shaped like a cylinder has 1,296π in3 of space inside the tank. If the diameter of the helium tank is 12 inches, what is its height?
6 inches
9 inches
24 inches
36 inches
The height of the helium tank is; Option D: 36 inches
How to find the volume of a cylinder?The formula for the volume of a cylinder is;
V = πr²h
Where;
V is volume
r is radius
h is height
We are given;
Radius(r) = diameter/2 = 12/2
r = 6 inches
Volume; V = 1296π in³
1296π = π * 6² * h
h = 1296/36
h = 36 inches
We conclude that is the height if the helium tank
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Answer:
its height is 36 inches
Step-by-step explanation:
There's a 20% increase on a $2.80 candy bar find the new price
Answer:
1300.00%
Step-by-step explanation:
14. A father is twice as old as his son now. Ten years ago, the ratio of their ages was 5:2. Find their present ages.
Answer:
We can set up two equations to represent the information given in the problem:
F = 2S (where F is the father's present age and S is the son's present age)
(F - 10) / (S - 10) = 5/2
We can substitute equation 1 into equation 2:
(2S - 10) / (S - 10) = 5/2
We can cross-multiply and simplify to solve for S:
2S - 10 = 5S - 25
3S = 35
S = 35/3
S = 11.67
So the son is currently 11.67 years old. To find the father's age, we can use equation 1:
F = 2S
F = 2 * 11.67
F = 23.33
So the father is currently 23.33 years old.
a popular restaurant chain will open a new franchise if a study shows that more than 60% of residents in an area would purchase food from the restaurant. an analyst of a particular area randomly selects 500 residents and surveys them about their interest in the restaurant. of the 500 residents, 320 stated they would purchase food from the restaurant. which hypotheses test the proportion of residents who would purchase food from the restaurant in this area?
The proportion of people in the area who would purchase food from the restaurant is greater than 60%.
Hypothesis testing is used to determine if the proportion of people in a particular area that would purchase food from a particular restaurant is greater than 60%. The null hypothesis, denoted by H0, is that the proportion of people who would purchase food from the restaurant is 60%, or p=0.6. The alternative hypothesis, denoted by H1, is that the proportion of people who would purchase food from the restaurant is greater than 60%, or p>0.6.
To conduct the test, we can use a one-sample proportion test, which is a type of statistical test that compares an observed proportion to a hypothesized proportion. To calculate the test statistic, we can use the formula:
Test statistic = (observed proportion - hypothesized proportion) / (standard error of the proportion)
In this case, the observed proportion is 320/500 = 0.64 and the hypothesized proportion is 0.6. Therefore, the test statistic is:
Test statistic = (0.64 - 0.6) / (square root of (0.6 * (1 - 0.6) / 500))
Test statistic = 0.04 / (square root of (0.6 * 0.4 / 500))
Test statistic = 0.04 / 0.0341
Test statistic = 1.17
The test statistic is 1.17, which is greater than the critical value of 1.645. Therefore, we can reject the null hypothesis and conclude that the proportion of people in the area who would purchase food from the restaurant is greater than 60%.
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(Picture included). The equation y= - 1/3x + 4 represents EF. Which of the following equations and accompanying justifications correctly represents a line that is parallel to EF?
Answer choices:
A. Y= 3x - 5 the slopes are opposite reciprocals
B. Y = 1/3x - 8 the slopes are opposites
C. Y = -1/3x + 5 1/3 the slopes are equal
D. Y = -2/3x + 4 the y intercepts are equal
The equation and the accompanying justification that describes a line that is parallel to EF is: C. Y = -1/3x + 5 1/3 the slopes are equal.
What is the Equation of Parallel Lines?If two lines are said to be parallel to each other, their equations that is expressed as y = mx + b, will have the same slope value of m. Y = mx + b is the slope-intercept form of any equation that represents a line.
Given that the equation y = -1/3x + 4 represents the line EF, its slope is -1/3. This means the slope of any line that is parallel to y = -1/3x + 4 will be the same as -1/3.
Therefore, the correct justification is: C. Y = -1/3x + 5 1/3 the slopes are equal.
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The manager of a sport store wants a 25% markup on the selling price of nike baseball gloves in order to have a markup of $50. how much can the manager afford to pay for each baseball glove?
$116.67
$66.67
$150
$200
The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of amount $50 and a 25% markup on the selling price.
$50 / 0.25 = $200
To calculate the cost of the Nike baseball gloves with a markup of 25% and a margin of $50, use the following formula:
Cost = (Price + Markup) / (1 + Markup Percentage)
Cost = ($50 + $50) / (1 + 0.25)
Cost = $100 / 1.25
Cost = $80
Therefore, the manager can afford to pay amount $80 for each baseball glove.
The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of $50 and a 25% markup on the selling price.
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If p varies directly as r square p =3.2 when r=4 find the value of p when r=6.5
Answer:
I hope this is right :)..
How do we use the CONVERSE of the Pythagorean Thm. to determine if a triangle is acute, obtuse, or right
The angles in a triangle are less than 90 degrees, the triangle is acute, greater than 90 degrees, the triangle is obtuse, and exactly 90 degrees, the triangle is a right triangle.
What is the converse of the Pythagorean theorem?
The converse of the Pythagorean theorem states that if the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
To determine if a triangle is acute, obtuse, or right, we can use the following:
If all the angles in a triangle are less than 90 degrees, the triangle is acute.
If one angle in a triangle is greater than 90 degrees, the triangle is obtuse.
If one angle in a triangle is exactly 90 degrees, the triangle is a right triangle, using the converse of the Pythagorean theorem, c² = a² + b².
Hence, the angles in a triangle are less than 90 degrees, the triangle is acute, greater than 90 degrees, the triangle is obtuse, and exactly 90 degrees, the triangle is a right triangle.
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what is the least possible value of 8x-13 when 9 <= 3/4 +x
show ur work
Answer: 53
Step-by-step explanation:
If 9 ≤ 3/4 + x,
x ≥ 8 1/4 (Transpose the 3/4)
So, the least possible value of 8x - 13 will be when x is the least or, x is 8 1/4
or 33/4
8 x 33/4 - 13 = 66 - 13 = 53
Answer:
I hope my answer is correct!
The least possible value of 8x-13 when 9 <= 3/4 +x is -13. This is because when x = 9, 8x-13 = 8(9)-13 = 72-13 = 59, which is the least possible value of 8x-13 when 9 <= 3/4 +x.
Is Jennifer or Jacqueline correct?
Answer:
Jennifer
Step-by-step explanation:
The domain of a function is the set of x-values that result in defined and real values for that function.
In this case the requirement was to plot a graph so that the domain is between -4 and 5 inclusive
We can represent this mathematically as -4 ≤ x ≤ 5
If you look at both graphs, Ashton's graph on the left has a minimum
x-value of -4 and a maximum x-value of 5. So his graph is correct
Carlie's graph on the right does have a minimum x-value of -4 but its maximum x-value is between 2 and 3. So this graph is incorrect
Therefore Jennifer's statement is correct
Answer: Jennifer
liam sells sandwiches at an arena. he earns $10.50 per hour plus $0.40 for each sandwich he sells. how many sandwiches does he need to sell during a 6-hour shift to earn $125
Answer:
He needs to sell 157 sandwiches to earn $125
Step-by-step explanation:
●$10.50×6 hrs= $63
●$125 - $63= $62 {So he needs to sell $62 worth of sandwiches}
●$0.40 × 157= $62
pov:《$62 + $63 = $125》
Answer:
155 sandwiches
Step-by-step explanation:
First we see what the base rate is for his six-hour shift. We do this by multiplying 10.50 by 6 which is 63. Then we do 125-63 which is 62. As he gets 42 cents per sandwich so we do 62÷0.40, which equals 155 so he needs to sell 155 sandwiches.
You must guess a number between 0 and 100, inclusive. Everyone in our class is also guessing a number between 0 and 100, inclusive. Whoever guesses the number closest to two-thirds of the average guess by our class wins $5.
If everyone picks zero, they all win. Only Nash equilibrium is when everyone guesses zero or an extremely low number.
There is no purely dominant tactic in this game. There is a special pure strategy Nash equilibrium, though. Through the iterative elimination of weakly dominated techniques, this equilibrium can be discovered.
Since it cannot potentially be 2/3rds of the average of any guess, guessing any number that lies above 66.67 is dominated for every player. These might be taken away.
Any estimate above 44.45 is weakly dominated for every player once these techniques are removed for each player since no player would guess above 66.67 and 2/3 of 66.67 is roughly 44.45. This procedure will keep going until all numbers higher than 0 are gone.
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Find the length of the curve. r(t) = < 6t, t^2, 1/9(t^3) > , 0 ≤ t ≤ 1
Please show step by step the simplifications and calculations for this problem, thanks!
The curvature of the curve is 55/9 in accordance with the provided declaration.
What in mathematics is a curve?Curve, An abstract phrase used to express the trajectory of a steadily moving particle in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a linear model or a collection of connected line segments. The IS curve displays variants of interest rates plus production levels where anticipated expenditure and income are equal. The many interest and income configurations along whom the merchandise is in homeostasis are represented by the IS Curve.
[tex]\mathbf{r}(t)=\left\langle 6 t, t^2, \frac{1}{9}\left(t^3\right)\right\rangle[/tex]
So,
[tex]x(t)=6 t, y(t)=t^2, z(t)=\frac{1}{9}\left(t^3\right)[/tex]
Then,
[tex]\begin{aligned}& x^{\prime}(t)=\frac{d}{d t}(6 t) \\& =6 \cdot \frac{d}{d t}(t)\end{aligned}[/tex]
= 6(1)
= 6
[tex]\begin{aligned}& y^{\prime}(t)=\frac{d}{d t}\left(t^2\right) \\& =2 t^{2-1}\end{aligned}[/tex]
= 2t
And,
[tex]\begin{aligned}& z^{\prime}(t)=\frac{d}{d t}\left(\frac{1}{9}\left(t^3\right)\right) \\& =\frac{1}{9}\left(3 t^{3-1}\right) \\& =\frac{1}{9}\left(3 t^2\right) \\& =\frac{1}{3}\left(t^2\right)\end{aligned}[/tex]
Now calculating length of the given curve from 0 to 1,
[tex]\begin{aligned}& L=\int_0^1 \sqrt{(6)^2+(2 t)^2+\left(\frac{1}{3}\left(t^2\right)\right)^2} d t \\& =\int_0^1 \sqrt{(6)^2+2 \cdot 6 \cdot \frac{1}{3}\left(t^2\right)+\left(\frac{1}{3}\left(t^2\right)\right)^2} d t \\& =\int_0^1 \sqrt{\left(6+\frac{1}{3}\left(t^2\right)\right)^2} d t\end{aligned}[/tex]
[tex]\begin{aligned}& =\int_0^1\left(6+\frac{1}{3}\left(t^2\right)\right) d t \\& =\int_0^1 6 d t+\int_0^1 \frac{1}{3}\left(t^2\right) d t \\& =6 \int_0^1 d t+\frac{1}{3} \int_0^1 t^2 d t \\& =6[t]_0^1+\frac{1}{3}\left[\frac{t^{2+1}}{2+1}\right]_0^1 \\& =6[1-0]+\frac{1}{3}\left[\frac{t^3}{3}\right]_0^1\end{aligned}[/tex]
[tex]\begin{aligned}& =6(1)+\frac{1}{3}\left[\frac{1^3}{3}-\frac{0^3}{3}\right] \\& =6+\frac{1}{3}\left[\frac{1}{3}-0\right] \\& =6+\frac{1}{9} \\& =\frac{54+1}{9}\end{aligned}[/tex]
= 55/9
Therefore, required arc length is 55/9
NOTE:
For a vector valued function,
[tex]\mathbf{r}(t)=\langle x(t), y(t), z(t)\rangle[/tex] arc length fro a to b
[tex]L=\int_a^b \sqrt{\left(x^{\prime}(t)\right)^2+\left(y^{\prime}(t)\right)^2+\left(z^{\prime}(t)\right)^2} d t[/tex]
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