The students score for the competitive exam is 110
How to calculate the students scoreTo find the score of the student, we can use the given information.
For correct answers
Number of correct answers = 70
Marks for correct answers
= Number of correct answers * Marks per correct answer
= 70 * 2
= 140
For wrong answers:
Number of wrong answers = 30
Marks for wrong answers
= Number of wrong answers * Marks per wrong answer
= 30 * -1
= -30
The total score
= Marks for correct answers + Marks for wrong answers
= 140 + (-30)
= 110
Hence the student's score is 110.
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Which is the value of this expression when j=-2 and k=-1 (jk^-2/j^-1k^-3)^3
The value of the expression when j=-2 and k=-1 is 8.
What is expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.
Let's substitute j=-2 and k=-1 in the given expression and simplify it:
(jk⁻²/j⁻¹k⁻³)³
= ((-2)(-1)⁻²)/((-2)⁻¹(-1)⁻³))³ // Substitute j=-2 and k=-1
= ((-2)/(1/(-1)²))/((-1/(-1)³)))³
= ((-2)/1)/(-1/1))³
= (-2)/(-1))³
= 8
Therefore, the value of the expression when j=-2 and k=-1 is 8.
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In your class, 10 out of 19 students have a job.
Task 1: Obtain a point estimate for the proportion of GSU students who have a job.
Task 2: What conditions must be met to create a confidence interval for the proportion of GSU students
who have a job? Are they met? (There are 5776 students enrolled at GSU).
Task 3: Regardless of your previous answer, create a 95% confidence interval for the proportion of GSU
students who have a job.
Task 4: Regardless of your previous answer, create a 99% confidence interval for the proportion of GSU
2
students who have a job.
Task 5: What sample size should be obtained if you want to be within 3 percentage points using your
estimate from the class data?
Task 6: What sample size should be obtained if you want to be within 3 percentage points using no prior
estimate
a) Point estimate = 10/19 = 0.526
b) The sample should be randomly selected from the population.
The sample size should be large enough such that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the proportion of students who have a job in the population.
The sampling distribution of the sample proportion should be approximately normal.
c) confidence interval = (0.259, 0.793)
d) confidence interval = (0.176, 0.876)
e) n = 365 students
Given data ,
a)
The point estimate for the proportion of GSU students who have a job is simply the proportion of students in the class who have a job, which is:
point estimate = 10/19 = 0.526 (rounded to three decimal places)
b)
To create a confidence interval for the proportion of GSU students who have a job, the following conditions must be met:
The sample should be randomly selected from the population.
The sample size should be large enough such that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the proportion of students who have a job in the population.
The sampling distribution of the sample proportion should be approximately normal.
c)
Assuming the conditions for a confidence interval are met, a 95% confidence interval for the proportion of GSU students who have a job can be calculated as follows:
margin of error = z√(p(1-p)/n)
where z is the z-score corresponding to a 95% confidence level (z = 1.96), p is the point estimate of the population proportion (0.526), and n is the sample size (19).
margin of error = 1.96 √(0.5260.474/19) = 0.267 (rounded to three decimal places)
confidence interval = point estimate ± margin of error = 0.526 ± 0.267
confidence interval = (0.259, 0.793)
Therefore, we can say with 95% confidence that the true proportion of GSU students who have a job is between 0.259 and 0.793.
d)
A 99% confidence interval for the proportion of GSU students who have a job can be calculated using the same formula as above, but with a z-score of 2.576 (corresponding to a 99% confidence level):
margin of error = 2.576sqrt(0.5260.474/19) = 0.350 (rounded to three decimal places)
confidence interval = 0.526 ± 0.350
confidence interval = (0.176, 0.876)
Therefore, we can say with 99% confidence that the true proportion of GSU students who have a job is between 0.176 and 0.876.
e)
To determine the sample size needed to be within 3 percentage points of the true proportion with the point estimate of 0.526, we can use the formula:
n = (z² * p * (1-p)) / E²
where z is the z-score corresponding to the desired confidence level (z = 1.96 for a 95% confidence level), p is the point estimate of the population proportion (0.526), and E is the desired margin of error (0.03).
n = (1.96^2 * 0.526 * 0.474) / 0.03^2
n = 364.16
Hence , we would need a sample size of at least 365 students to be within 3 percentage points of the true proportion using the point estimate from the class data.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.
We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding
m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.
m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.
m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).
m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.
m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.
Based on the above analysis, the statements that are always true regarding the diagram are
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 = 180°
m∠2 + m∠3 + m∠5 = 180°
Therefore, the correct options are B, C, and E.
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Which proves that (x – 7) is a factor of the given polynomial function?
f(x) = x2 – 5x – 14
A. f(-7) = 0
B. f(0) = -7
C. f(1) = 7
D. f(7) = 0
What is the area of the composite figure?
54 units2
152 units2
136 units2
160 units2
The area of the composite figure is 136 sq. units.
Given that a composite figure we need to find it area,
The figure is composed of a triangle and a rectangle,
So to find its area we will simply calculate the areas of both the polygons and add them,
So, the area of a triangle = 1/2 x base x height
The area of a rectangle = length x width
So,
The required area = 1/2 x (16-8)(13-7) + 7 x 16
= 1/2 x 8 x 6 + 112
= 24 + 112
= 136
Hence, the area of the composite figure is 136 sq. units.
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The table below shows the spot rates for the given lengths of time. Numbers 4 5 6 of years Effective 2.5% 3.1% 3.4% 3.6% 4% 4.2% annual spot ratee Calculate the swap rate for a two- year deferred, three- year interest rate swap with settlement at the end of the year. [10]
The swap rate for a two-year deferred, three-yearinterest rate swap with settlement at the end of the year is 3.7%
How to calculate the rateImplied forward rate = (1+Present year rate)^Present year /(1+Previous year rate)^Previous year -1
The swap rate for a two-year deferred, three-yearinterest rate swap with settlement at the end of the year=
= [(1 +0.034)2 / (1+0.031)1 ] -1
= [1.069156 / 1.031] -1
= 1.037 - 1
= 0.037
= 3.7%
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Write An Equation For The Quadratic Graph
The quadratic equation shown in the graph is:
y = (x + 2)*(x - 1)
How to find the quadratic equation?Remember that if h and k are the zeros of a quadratic equation of leading coefficient a, we can write it as:
y = a*(x - h)*(x - k)
Here we can see that the zeros are:
x = -2
x = 1
Then we can write it as:
y = a*(x + 2)*(x - 1)
And the y-intercept is -2, then we can write:
-2 = a*(0 + 2)*(0 - 1)
-2 = a*-2
-2/-2 = a
1 = a
The quadratic equation is:
y = (x + 2)*(x - 1)
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A factory worker can make 15 products in 45 minutes. What is the workers unit rate of completion?
Answer:
[tex]\frac{1}{3}[/tex] product per minute
Step-by-step explanation:
We Know
A factory worker can make 15 products in 45 minutes.
What is the worker's unit rate of completion?
We Take
15 / 45 = [tex]\frac{1}{3}[/tex] product per minute
So, the workers unit rate of completion is [tex]\frac{1}{3}[/tex] product per minute
Write an exponential function in the form � = � � � y=ab x that goes through points ( 0 , 19 ) (0,19) and ( 2 , 1539 ) (2,1539).
The exponential function that passes through the points (0,19) and (2,1539) is y = 19(9)ˣ.
We can use the two given points to form a system of two equations in two unknowns (a and b) to find the exponential function in the form y = abˣ that passes through those points.
Using the point (0,19), we get
19 = ab⁰
19 = a
Using the point (2,1539), we get
1539 = ab²
Substituting a = 19 from the first equation, we get
1539 = 19b²
Solving for b, we get
b² = 81
b = 9 or b = -9
Since we are dealing with an exponential function that models a growth, we will choose the positive value for b. Thus, b = 9.
Now that we know a and b, we can write the exponential function in the form y = abˣ
y = 19(9)ˣ
Therefore, the exponential function is y = 19(9)ˣ
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--The given question is incomplete, the complete question is given
" Write an exponential function in the form y=ab^x that goes through points ( 0 , 19 ) (0,19) and ( 2 , 1539 ) (2,1539)."--
Kellen runs for at least 1 hour but for no more than 2 hours. He runs at at an average rate of 6.6 kilometers per hour. The equation that models the distance he runs for t hours is d=6.6t. Find the theoretical and practical domains of this equation.
Kellen runs for at least 1 hour but for no more than 2 hours. He runs at at an average rate of 6.6 kilometers per hour. The equation that models the distance he runs for t hours is d = 6. 6t
Find the theoretical and practical ranges of this equation.
The equation's usable range is 6.6 km d 13.2 km.
What is an expression?Expression is the relation of the numbers and the variables written by the use of mathematical signs.
Kellen exercises for a minimum of an hour and a maximum of two hours. As a result, the equation's useful domain is 1 t 2. Since that time can take on any positive or negative value, the theoretical scope of the equation d = 6.6t is all real numbers.
Substitute the values of the practical domain into the equation.
t = 1, d = 6.6(1) = 6.6 km.
t = 2, d = 6.6(2) = 13.2 km.
Therefore, the equation's usable range is 6.6 km d 13.2 km.
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You can rent a car from company a for $40 plus $50 per Day write an expression to find the cost of a car per day, D
find the distance between 5,1 and 5,4
Answer:
3
Step-by-step explanation:
By using distance formula
√(x2-x1)^2+(y2-y1)^2
√(5-5)^2+(4-1^2
√0+(3)^2
√9
=3
is x+10 a factor of f(x)=5x^3+60x^2+109x+90
Answer: x + 10` is **not** a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`.
Step-by-step explanation: To determine if `x + 10` is a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`, we can use the Factor Theorem. The Factor Theorem states that if `f(a) = 0`, then `x - a` is a factor of `f(x)`.
In this case, we want to determine if `x + 10` is a factor of `f(x)`, so we can let `a = -10` and evaluate `f(-10)`:
`f(-10) = 5(-10)^3 + 60(-10)^2 + 109(-10) + 90`
`= -5000 + 6000 - 1090 + 90`
`= -1000`
Since `f(-10) ≠ 0`, we can conclude that `x + 10` is **not** a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`.
Rocco wants to use the rest of the money in his savings account to buy a set of golf irons that has
an original price of $350 including tax. Does Rocco have enough money to buy the golf irons?
Explain your answer.
We get a negative number, which means that Rocco does not have enough money to make the purchase. In fact, he is short by $158.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. Equations are used to represent relationships between variables and to solve problems in various fields such as mathematics, physics, engineering, and economics. In an equation, there are typically two sides separated by an equals sign (=). The expressions on each side of the equals sign may include variables, constants, mathematical operations, and functions. The goal of solving an equation is to find the value(s) of the variable(s) that make both sides of the equation equal.
Here,
If Rocco has only $192 in his savings account and the set of golf irons costs $350, then he does not have enough money to buy the golf irons.
To see why, we can subtract the price of the golf irons from Rocco's savings:
$192 (Rocco's savings) - $350 (price of golf irons) = -$158
Therefore, Rocco does not have enough money to buy the set of golf irons with the remaining amount in his savings account.
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Given Z find |Z| please help
Answer:
|Z| = √((-6)^2 + 12^2) = √(36 + 144) = √180
= (√36)(√5) = 6√5
I need help with this problem if do thank you a lot
Answer:
The equation of the circle is (x + 7)^2 + (y - 13)^2 = 25.
Step-by-step explanation:
The equation of a circle with a center (a,b) and radius r is given by:
(x - a)^2 + (y - b)^2 = r^2
So, for the center (-7, 13) and a radius of 5 units, the equation of the circle is: (x - (-7))^2 + (y - 13)^2 = 5^2
Simplifying this equation, we get:
(x + 7)^2 + (y - 13)^2 = 25
Therefore, the equation of the circle with center (-7,13) and radius 5 units is (x + 7)^2 + (y - 13)^2 = 25.
Simplify the following expression:
√ 16+√ 25 + 5
OA. 14 + 0i
OB. 9-5i
OC. 5+√41i
OD. 5+9i
Answer:
D. 5 +9i
Step-by-step explanation:
You want to simplify the expression ...
√(-16) +√(-25) +5
Imaginary numbersWe know that the value of √(-1) is represented by the constant i. This means we can simplify the expression like this:
[tex]\sqrt{-16}+\sqrt{-25}+5\\\\=\sqrt{-1(4^2)}+\sqrt{-1(5^2)}+5\\\\=4i+5i+5\\\\=\boxed{5+9i}\qquad\text{matches choice D}[/tex]
<95141404393>
The price of a desk was originally $80. The desk is now on sale for 16% off. What is the sale price of the desk? Use y to represent the sale price of the desk and write an equation to represent the problem.
Just write me the equation
please help me find the area!! please
Blake & McKenzie Tax Services is a company serving 72 clients (as of the beginning of last month that is working on reorganizing its balanced scorecard. Currently, the company has the following performance metrics: online client satisfaction rating, client growth percentage (the number of total clients at the beginning of the current month compared to the number of total clients at the beginning of the prior month, market share, and profit margin. The company tracks these metrics from month to month. The company's target client growth percentage is 4% per month. Its target average online client satisfaction rating is 4.8 stars. Last month, the company noted the following data related to these metrics:
New clients 7
Lost clients 4
Market share 1.52%
Profit margin 65%
1. Working together in teams, create strategic objectives that each of the company's four performance metrics might represent.
2. Determine whether the company achieved its client growth percentage target last month.
3. Suppose that last month, the company received 55 five-star reviews, 10 four-star reviews, 3 three-star reviews, 1 two-star review, and 1 one-star review (some clients did not submit a review). Determine whether the company met its average online client satisfaction rating target.
4. Come up with at least one strategic initiative for the strategic objective of any performance metric target that you know the company did not meet last month.
Possible strategic initiatives for the strategic objective to satisfy clients:
• Implement additional training course on serving and interacting with clients
How to solvea. client review and client growth percentage metrics likely relate to a strategic objective to satisfy and increase clients. The market share and profit margin metrics likely relate to a strategic objective to increase profits.
b.
New clients during the month
7
Lost clients during the month
(4)
Increase in clients
3
Total clients at the beginning of last month
÷ 72
Client growth percentage last month
4.17%
target met
c.
Number of 5-star reviews
55 × 5 =
275
Number of 4-star reviews
10 × 4 =
40
Number of 3-star reviews
3 × 3 =
9
Number of 2-star reviews
1 × 2 =
2
Number of 1-star reviews
1 × 1 =
1
Sum total of stars
327
Total number of reviews
÷ 70
Average online client satisfaction rating
4.67
stars, target
not met
d.
Possible strategic initiatives for the strategic objective to satisfy clients:
• Implement additional training course on serving and interacting with clients
• Invite clients to provide additional feedback through a brief online survey
• Have the company owner send a personal apology to any clients providing a review of 2 stars or less, and offer them some kind of compensation; also ask for their feedback regarding what caused them dissatisfaction
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i need help on this equation
[tex]{\Large \begin{array}{llll} \cfrac{x^{-\frac{1}{2}}}{x^{\frac{2}{3}}x^{\frac{3}{2}}}\implies \cfrac{1}{x^{\frac{2}{3}}x^{\frac{3}{2}}x^{\frac{1}{2}}}\implies \cfrac{1}{x^{\frac{2}{3}+\frac{3}{2}+\frac{1}{2}}}\implies \cfrac{1}{x^{\frac{2}{3}+2}}\implies \cfrac{1}{x^{\frac{8}{3}}} \end{array}}[/tex]
A call center claims that the mean wait time for a customer to connect with a customer care executive is less than 2 minutes. A random sample of 50 calls at the call center yielded a test statistic of -1.07. What is the corresponding p-value? Round your answer to three decimal places.
The corresponding p-value is 0.147 rounded to three decimal places.
Now, For find the p-value, we need to use a t-distribution with (n - 1) degrees of freedom,
where n is the sample size.
Since n = 50,
Hence, we have;
n - 1 = 50 - 1 = 49 degrees of freedom.
Hence, Using a t-table or calculator with 49 degrees of freedom, we find that the p-value for a t-statistic of -1.07 is approximately 0.147.
Therefore, the corresponding p-value is 0.147 rounded to three decimal places.
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747.748 + 848.398 + 8,327.82 =
Answer:
Answer: 9,924.966.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Sorry it is hard to explain the process by typing!
tally's teacher divides her class of 16 students into 4 equally sized teams red team yellow team green team and blue team what is the probability that tally will be on the red team answerd in simplified form
Tally's probability of being on the red team is 1/4, or 0.25 when represented as a decimal.
How to determine the probability that tally will be on the red teamEach team has four students because there are four equal-sized teams.
So Tally's chances of being on the red team are 4 (the number of students on the red team) divided by 16 (the total number of students):
4/16 = 1/4
As a result, Tally's likelihood of being on the red team is 1/4, or 0.25 when represented as a decimal.
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plsssssssssssssssssssssssssssssssssssssssssssssssss
Answer: 22√3
Step-by-step explanation:
When finding perimeter you take l+l+w+w, or 2l + 2w.
Answer:
[tex]22\sqrt{3}[/tex]
Step-by-step explanation:
To find the perimeter, we have to add up all four sides.
[tex]5\sqrt{3} +3\sqrt{12} +5\sqrt{3} +3\sqrt{12}[/tex]
write this on your calculator then you'll get [tex]22\sqrt{3}[/tex]
Hope this helps
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Which of the following equations describes the nth term for the sequence
The nth term of the sequence 4/5, 1/5, 1/20. 1/80..... is an = 4/5(1/4)^(n - 1)
How to determine the value of tthe nth term of the sequence?The definition of the function is given as
4/5, 1/5, 1/20. 1/80.....
The above definitions imply that we simply multiply 1/4 to the previous term to get the current term
Using the above as a guide, we have
First term, a = 4/5
Ratio, r = 1/4
So, we have the following equation
an = 4/5(1/4)^(n - 1)
Hence, the value of the nth term is an = 4/5(1/4)^(n - 1)
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Can someone help with these two questions on my Calc 3 hw? It is due tonight. Thank you!
Question #14:
Find the work done by the force field, [tex]\vec F(x,y,z)= < x-y^2, \ y-z^2, \ z-x^2 >[/tex],
on a particle that moves along the line segment from (0,0,1) to (3,1,0).
The parametrized form of a line is given as,
[tex]x=x_0+v_xt[/tex]
[tex]y=y_0+v_yt[/tex]
[tex]z=z_0+v_zt[/tex]
Where [tex](x_0,y_0,z_0)[/tex] is a point the line passes through and [tex]\vec v= < v_x,v_y,v_z >[/tex] is the direction of the line.
[tex]\Longrightarrow \vec v= < 3-0,1-0,0-1 > \Longrightarrow \boxed{ \vec v= < 3,1,-1 > }[/tex]
[tex]\Longrightarrow \boxed{(x_0,y_0,z_0)=(0,0,1)}[/tex]
[tex]z=-t+1, 0\leq t\leq 1[/tex]
This would imply that, [tex]dx=3dt,dy=dt,dz=-dt[/tex]
[tex]Work, W=\int\limits^a_b {\vec F(x,y,z) \cdot} < dx,dy,dz > \,dt[/tex]
[tex]\Longrightarrow \vec F(x,y,z)= < 3t-t^2, \ t-(-t+1)^2, \ -t+1-(3t)^2 >[/tex]
[tex]\Longrightarrow \boxed{\vec F(x,y,z)= < 3t-t^2, \ -t^2+3t-1, \ -9t^2-t+1 > }[/tex]
[tex]\Longrightarrow W=\int\limits^1_0 { [ < 3t-t^2, \ -t^2+3t-1, \ -9t^2-t+1 > \cdot} < 3,1,-1 > ] \,dt[/tex]
[tex]\Longrightarrow W=\int\limits^1_0 { [( 3t-t^2)(3)+(-t^2+3t-1)(1)+(-9t^2-t+1)(-1) ] \,dt[/tex]
[tex]\Longrightarrow W=\int\limits^1_0 { [ 9t-3t^2-t^2+3t-1+9t^2+t-1 ] \,dt[/tex]
[tex]\Longrightarrow W=\int\limits^1_0 { [5t^2+13t-2 ] \,dt[/tex]
Using the power rule to integrate: [tex]\frac{d}{dx}[x^n]=nx^{n-1}[/tex]
[tex]\Longrightarrow W=\frac{5}{3}t^3+\frac{13}{2}t^2-2t \left. \right|_{0}^1[/tex]
[tex]\Longrightarrow W=[\frac{5}{3}(1)^3+\frac{13}{2}(1)^2-2(1)]-[0][/tex]
[tex]\Longrightarrow W=\frac{5}{3}+\frac{13}{2}-2[/tex]
[tex]\Longrightarrow \boxed{ W=\frac{37}{6}} \therefore Sol.[/tex]
Question #15:
Given:
[tex]w_m=170 \ lb[/tex]
[tex]w_c=25 \ lb[/tex]
[tex]w_m+w_c=195 \ lbs[/tex]
[tex]r_s=25 \ ft[/tex]
[tex]h_s=90 \ ft[/tex]
[tex]1 \ rev. =2\pi \Rightarrow 3 \ rev. =\bold{6\pi}[/tex]
Find:
[tex]W= \ ?? \ ft-lbs[/tex]
Equation:
[tex]W=\int\ {\vec F \cdot } \, d\vec r \Longrightarrow W=\int\ {[\vec F(\vec r(t)) \cdot r'(t)}]dt[/tex]
[tex]\vec F(x,y,z)= < 0,0,195 > \ and \ r(t)= < 25cos(t),25sin(t),\frac{90}{6\pi}t >[/tex]
[tex]r'(t)= < -25sin(t),25cos(t),\frac{15}{\pi} >[/tex]
[tex]\Longrightarrow W=\int\ {[\vec F(\vec r(t)) \cdot r'(t)}]dt[/tex]
[tex]\Longrightarrow W=\int\ {[ < 0,0,195 > \cdot < -25sin(t),25cos(t),\frac{15}{\pi} > ]dt[/tex]
[tex]\Longrightarrow W=\int\ {[ (195)(\frac{15}{\pi}) ]dt[/tex]
[tex]\Longrightarrow W=\int\ {\frac{2925}{\pi} dt[/tex]
Limits: [tex]0\leq t\leq 6\pi[/tex]
[tex]\Longrightarrow W=\int\limits^{6\pi}_0 {\frac{2925}{\pi} } \, dt[/tex]
[tex]\Longrightarrow W= {\frac{2925}{\pi}t \left. \right|_{0}^{6\pi}[/tex]
[tex]\Longrightarrow W= [{\frac{2925}{\pi}(6\pi)]-[0][/tex]
[tex]\Longrightarrow \boxed{W= 17,550 \ ft-lbs} \therefore Sol.[/tex]
Let me know if these were correct! As I strive to give the most accurate answers! Thank you.
Using the interactive tool, select the Market Research data and request a sample size of 41. Request a plot of the Age variable. a. With Overall Mean selected, what is the length of the first dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)
The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively.
What is length?Length is a concept used to describe the magnitude of a particular object or distance between two points. It is typically measured in units such as feet, inches, meters, miles, and kilometers. Length is often used to describe the size of an object and the distance between two points. Length can also be used to measure the time required to travel between two points. Length is a fundamental concept in mathematics, physics, and engineering.
The first dotted line shown at the top of the chart is 23.39.
b. With Overall Mean selected, what is the length of the second dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)
The second dotted line shown at the top of the chart is 23.28.
c. With Overall Mean selected, what is the length of the third dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)
The third dotted line shown at the top of the chart is 24.17.
Conclusion: The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively. This data can be used to analyze the age of respondents in Market Research.
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If 35% of students went to Disneyland and 1924 of students went to Knotts what is the total number of students
The total number of students is 2960.
How to find the total number of student?35% of students went to Disneyland and 1924 of students went to Knotts.
Therefore, the total number of student can be calculated as follows:
The total number of student is the total number of student that went to Disneyland and Knotts.
let
x = total number of student
Therefore,
35% of x = Student that went to Disneyland
Hence,
65% of x = 1924
65 / 100 x = 1924
cross multiply
65x = 192400
divide both sides of the equation
x = 192400 / 65
x = 2960
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A random sample of 21 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 910 and the sample standard deviation is s = 20 Use Appendix D to find the values of Student’s t.
1. Construct an interval estimate of mu with 99% confidence. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
2. Construct an interval estimate of mu with 99% confidence, assuming that s = 40. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
3. Construct an interval estimate of mu with 99% confidence, assuming that s = 80. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
1. The 99% confidence interval is from 877.094 to 942.906.
2. The 99% confidence interval is from 883.267 to 936.733.
3. The 99% confidence interval is from 838.437 to 981.563.
What is interval?
In statistics, an interval refers to a range of values in which a population parameter, such as the mean or proportion, is estimated to lie with a certain level of confidence.
Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.
The 99% confidence interval for the population mean is:
lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(20/√21) = 877.094
upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(20/√21) = 942.906
Therefore, the 99% confidence interval is from 877.094 to 942.906.
Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.
The 99% confidence interval for the population mean is:
lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(40/√21) = 883.267
upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(40/√21) = 936.733
Therefore, the 99% confidence interval is from 883.267 to 936.733.
Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.
The 99% confidence interval for the population mean is:
lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(80/√21) = 838.437
upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(80/√21) = 981.563
Therefore, the 99% confidence interval is from 838.437 to 981.563.
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