The 95% confidence interval for the population mean adjusted distribution volume, using the t-distribution, is given as follows:
(43.479, 61.281).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the rule presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The sample is given as follows:
22, 40, 41, 42, 43, 48, 51, 58, 62, 66, 67, 70, 71.
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 13 - 1 = 12 df, is t = 2.1788.
Using a calculator with the sample, the parameters for the interval are:
[tex]\overline{x} = 52.38, s = 14.73, n = 13[/tex]
Hence the lower bound of the interval is calculated as follows:
52.38 - 2.1788 x 14.73/sqrt(13) = 43.479.
The upper bound of the interval is calculated as follows:
52.38 + 2.1788 x 14.73/sqrt(13) = 61.281.
More can be learned about the t-distribution at https://brainly.com/question/17073112
#SPJ1
A stadium has 51,000 seats. Seats sell for $28 in Section A, $16 in Section B, and $12 in Section C. The number of seats in Section A equals the total number of seats in sections B and C. Suppose the stadium takes in $1,078,400 from each sold-out event. How many seats does each section hold?
Answer:
A: 25,500
B: 14,600
C: 10,900
Step-by-step explanation:
This is what we know:
a = b + c
a + b + c = 51,000 Substitute in a for b + c
a + a = 51000 Combine like terms.
2a = 51000 Divide both sides by 2
a = 25,500
28a + 16b + 12c = 1078400 Substitute in 25.600 for a
28(25500) + 16b + 12c = 1078400
714000 + 16b + 12c = 1078400 Subtract 714000 from both sides
16b + 12 c = 364400
25500 +b + c = 51000 Subtract 25500 from both sides
b + c + = 25500 Multiply this equation all the way through by -12 and add it to the bold equation above it.
-12b -12c = -306000
16b + 12c = 364400
4b = 58400 divide both sides by 4
b = 14600
a + b + c = 51000 Plug in what we know
25500 + 14600 + c = 51000
40100 + c = 51000 Subtract 40100 from both sides
c = 10900
Solve the following inequality. Write the inequality in interval notation, and graph it.
7 x plus 5 less than or equals minus 30
The inequality expression has a solution of (-oo, -5]
How to solve the inequality?From the question, the inequality is given as
7 x plus 5 less than or equals minus 30
The above inequality can be re-written as follows
7x + 5 ≤ -30
There are constants to add or subtract in the expression
So, we start by subtracting both sides of the expression by the constant -5
This gives
7x ≤ -35
Divide both sides by 7
So, we have the following representation
x ≤ -5
Express as interval notation
(-oo, -5]
Hence, the solution to the expression is (-oo, -5]
Read more about inequality at
brainly.com/question/25275758
#SPJ1
2sin3x - sqrt3 = 0
express as: x = _____ + _____ pi n
The trigonometric equation 2sin3x - √3 = 0 is expressed as x = π/9 + 2πn/3, 2π/9 + 2πn/3
How to solve trigonometric equations?
A trigonometric equation is defined as an equation involving one or more trigonometric ratios of unknown angles
Given: 2sin3x - √3 = 0
2sin3x - √3 = 0
2sin3x = √3
sin3x = √3/2
3x = sin⁻¹√3/2 (Note: sin⁻¹√3/2 = 60° = π/3 in radian)
3x = π/3, π -3 (Note: sine is positive in 1st and 2nd quadrant)
3x = π/3, 2π/3
x = π/9, 2π/9
x = π/9 + 2πn/3, 2π/9 + 2πn/3
Therefore, 2sin3x - √3 = 0 can be expressed as x = π/9 + 2πn/3, 2π/9 + 2πn/3
Learn more about trigonometric equations on:
https://brainly.com/question/28025415
#SPJ1
The cost in dollars y of producing x computer desks is given by y = 60x + 3000
The cost of producing 24 computer desks is $4440 .
In the question ,
it is given that ,
the equation representing the cost of producing "x" computer desks is
y = 60x + 3000 ,
we need to find the cost of producing 24 computer desks ,
substituting x = 24 in the cost equation for producing computer desks ,
we get ,
y = 60(24) + 3000
On further simplification ,
we get ,
= 1440 + 3000
Adding the numbers ,
we get ,
= 4440
the cost is $4440 .
Therefore , The cost of producing 24 computer desks is $4440 .
The given question is incomplete , the complete question is
The cost in dollars y of producing x computer desks is given by y = 60x + 3000 , Find the cost of producing 24 computer desks .
Learn more about Equations here
https://brainly.com/question/13987961
#SPJ1
Complete the equation of the line through (-6, 5) and (-3, -3).
Use exact numbers.
y =
5
Answer:
(-6,5)(-3,-3)y
here is an equation I hope this helps :) <3
If the premier is 97 what is the square value of x
Answer: 21
Step-by-step explanation
if the premier is 97 the square value of x is 21
A net researched and found that 60% of students in his school ride the bus to school. Abner took a random sample of 50 students and found that 38 ride the bus to school. Which statement correctly describes the sample ratio?
Answer: 224 student ride the bus to school each day.
Step-by-step explanation:
In megan random sample of 60 students number of students preferred riding bus is found out to be 42 student.
Student riding the bus if the total number of students in the bus is 320
ratio of the student surveyed to the student ride bus =
=
Assuming the total number of student riding bus = x
now,
x = 224
hence, 224 student ride the bus to school each day.
Step-by-step explanation:
Which expression is equivalent to 8 ^ -3
The expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
First, let us understand the exponents or power:
A power, or index, is a little floating number that appears next to a number or letter.
It is denoted as a^m.
where a = base number
and m = power or index number.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe are given:
8^-3
We can solve as;
8^-3 = 8^(3 * -1) = (8^3) ^ -1 = 1 / 8^3 [since a⁻¹ = 1 / a]
So, 8^-3 = 1 / 8^3.
Thus, the expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
To learn more about laws of exponent visit:
brainly.com/question/28966438
#SPJ1
Hey can someone please find the area of this shape? Thank you so much I’ll give brainly. Please explain
Answer:
44.63
Step-by-step explanation:
( The heart shape makes two half circles and a square )
1 ) The two half circles together make a whole, so we can first find the area of that circle!
2 ) We can see that the dynamiter is 5in. We can cut this in half to find the radius...
5 ÷ 2 = 2.5
3 ) The area of a circle is found with the equation ( A = πr2 ). We can plug in the radius ( 2.5 ) to find the area...
A = π( 2.5 )2 = 19.635in
4 ) Now that we know the area of the circle we can find the area of the square. To find this we can use the equation ( A = a2 ) where a represents the edge length in this case 5in.
A = ( 5 ) 2 = 25in
5 ) We can now add the area of the circle and the area of the square to get the area of the heart!
19.635 + 25 = 44.63
Hope this helps! :)
integration of ∫x³+1/x³-x dx
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits \frac{x^3+1}{x^3-x} dx }} \end{gathered}$}[/tex]
We rewrite the integrand.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{x^3+1}{x^3+x}=1+\frac{1}{x-1}-\frac{1}{x} }} \end{gathered}$}[/tex]
We integrate terms by terms:
The integral of the constants have this constant multiplied by the variable of integration.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits 1 \ dx=x } } \end{gathered}$}[/tex]
That u = x -1. Then that du = dx and we put du.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\frac{1}{u} \ du }} \end{gathered}$}[/tex]
Integral 1/u is log(u). If you now substitute u further into:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{log(x-1) }} \end{gathered}$}[/tex]
The integral of the product of a function by a constant is the constant times the integral of this function:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\left(-\frac{1}{x}\right)dx=-\int\limits\frac{1}{x}dx }} \end{gathered}$}[/tex]
Integral 1/u is log(x). Therefore, the result is: -log(x).
The result is: x - log(x) + log(x - 1)
How do you find Circumcenter of a triangle?
Answer:
The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of the triangle intersect.
Step-by-step explanation:
The process of calculation of circumcenter has been given below.
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)
We need to find the length of AB, BC and AC
The length will be obtained in terms of x and y
On solving the equations, we will obtain the value of x and y
The value of x and y is the required coordinate of the circumcenter.
To learn more about circumcenter of a triangle, refer to the link-
brainly.com/question/2294833
#SPJ4
PLEASE I REALLY NEED THIS ANSWER!! Find the volume of a cube with the given side length.
1/5b^3
A cube is a three-dimensional solid object which has six square faces, facets or sides, and each meeting at a vertex.
How to find the Volume of a cube?
Volume is defined as the measurement of space occupied by the three-dimensional object.
Volume (V) = s³ where
V=volume
S=sides
V= (1/3b³)³
applying the power law of indices
V = (1/3b)∧9 cubic units
Learn more about the volume of cube on brainly.com/question/28134860
#SPJ1
(-3y)^4 write the power as a product of powers
Answer: 81y^4
Step-by-step explanation:
expand then calculate, -3 to the power of 4+81 then 81 added to y ^4 81y^4 is your finally power.
What is the curved surface area of a cylinder with the circumference of 4 and height of 6
The curved surface area of a cylinder is 24cm²
Given the following data;
Base circumference = 4 cm
Height = 6 cm
How to find the curved surface area of a cylinder?Suppose that:
Radius of the considered cylinder = 'r' units
Height of the considered cylinder = 'h' units
Then, the curved surface area of that cylinder is 2πr h
To find the curved surface area (CSA) of the cylinder we have;
CSA of a cylinder = 2πrh
But 2πr = 4 cm
Now Substituting the values into the equation, we have,
CSA of a cylinder = 6 x 4
CSA of a cylinder = 24 cm²
Hence, The curved surface area of a cylinder is 24cm²
Learn more about surface area of a cylinder here:
https://brainly.com/question/11385509
#SPJ1
Write an equation for the line in the following problems.
I NEED THIS ASAP
Answer:
Graph 1: y = (-3x/5) + 1
Graph 2: y = 4
Step-by-step explanation:
Both functions are linear, so we can use a linear equation to model these functions. Using slope-intercept form, "y=mx+b" will be easiest, since the graph is shown.
Graph 1:
(1 - (-2))/(0 - 5) = (1 + 2)/-5 = -3/5 = slope
y-intercept (0, 1)
y = (-3x/5) + 1
Graph 2:
(4 - 4)/(1 - 0) = 0 = slope
y-intercept (0, 4)
y = 0x + 4
y = 4
Answer:
First equation : [tex]y=-\frac{3}{5}x +1[/tex]
Second equation : y = 4
Step-by-step explanation:
We want to write equations for the two given lines in slope intercept form
y = mx + b
Where m = slope and b = y intercept
Identifying the y intercept
First lets find the y intercept.
The y intercepts is where the line passes the y axis.
By looking at the first line it appears that the line passes the y axis at (0,1) meaning the y intercept is 1 so b = 1
Identifying the slope
We can find the slope using the slope formula
slope = (y1-y2)/(x1-x2)
Where the values of x and y derive from any two points on the line. (x1,y1) and (x2,y2)
The points used may vary as there are many options however I have chosen (0,1) and (-5,4)
So (x1,y1) = (0,1) and (x2,y2) = (-5,4)
Meaning x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4
( we now plug these into the slope formula )
Again recall slope = (y1-y2)/(x1-x2)
==> plug in x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4
slope = (1-4)/(0-(-5))
==> reduce subtraction
slope = -3/5
so our slope(m) is -3/5
Plugging in slope and y intercept into slope intercept form
Finally we plug in the values of m and b into slope intercept form to get the equation
Again we have y = mx + b
m = -3/5 and b = 1
So our equation is y = -3/5x + 1
Identifying equation for second line
When we have a horizontal line our equation is going to be put in y = b form where b = the y value that the line crosses. (or y intercept)
Here the line goes through the y value of 4 so b = 4
Hence, the equation of the second line would be y = 4
Complete the equation for this model .
Answer:
Step-by-step explanation:
the anser is 3 + 5 =8
Dave rented a limousine for his wife's birthday. The hourly rate is $70. They used the limousine for 3 hours, plus Dave gave the driver a 10% tip. How much did he spend in total for the hourly charges plus tip?
A.
$252
B.
$189
C.
$287
D.
$231
Answer:
$231
Step-by-step explanation:
3 hours for 70 dollars an hour we multiply 70 by 3
70x3
210
And then to get the 10 percent tip we multiply 210 by .10
210x.10
21
And now we add 210 and 21 to get 231
Hopes this helps please mark brainliest
Erica worked 14 hours last week and 20 hours this week. If she earns $9 per hour how much did she earn during these two weeks?
Answer: $306
Step-by-step explanation:
You can find the answer by multiplying 9 by each of the values.
14 * 9 = 126
20 * 9 = 180
Add these values together and you get 306 !
Can you solve these 2 problems please
Answer:
1) The top angle = 128°
Right angle = 52°
Bottom angle = 128°
Left angle = 52°
2) The top angle = 159°
Right angle = 21°
Left angle = 21°
Step-by-step explanation:
The left problem would involve verticle angles being congruent to each other.
[tex]5x + 2 = x + 42\\\\6y + 8 = 7y - 12[/tex]
Solve each equation:
[tex]5x + 2 = x + 42\\4x = 40\\x = 10[/tex]
[tex]6y + 8 = 7y - 12\\20 = y[/tex]
Substitute:
The top angle = 128°
Right angle = 52°
Bottom angle = 128°
Left angle = 52°
The right problem would involve supplementary angles.
[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\\27x + 24 + 4x + 1 = 180[/tex]
Solve for second equation (for simplicity) :
[tex]27x + 24 + 4x + 1 = 180\\31x + 25 = 180\\31 = 155\\x = 5[/tex]
Substitute x = 5 into other equation :
[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\frac{1}{4}y - 1 + 27(5) + 24 = 180\\\frac{1}{4}y = 22\\y = 88[/tex]
Substitute :
The top angle = 159°
Right angle = 21°
Left angle = 21°
The population of California was about 37 million in 2010 and increasing by 1.0% each year. Create a formula to estimate the population of California in 2020.
The population of California by the year 2020 is 41 million.
What is population growth?The term population has to do with the number of people that live in a place or a town. We have the following information from the question;
Initial population (Po) = 37 million
Population growth rate (r) = 1.0%
Time interval (t) = 10 years
P = The population of the city of California at the time t
Now using the formula;
P = Poe^rt
P = 37 * 10^6 e^0.01 * 10
P = 4.089 * 10^7 or 41 million
They would have a population of 41 million in ten years.
Learn more about population growth:https://brainly.com/question/18415071
#SPJ1
The revenue for a business, as a function of units produced, x, is shown below
by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to break even.
R(x) = 12x
C(x) = x + 264
Profit function = P(x) = 11x - 264 and 24 Units must be produced for the business to break even.
What is a Profit function?
A mathematical link between a company's overall profit and output is called a profit function. It is greatest when the firm's marginal revenue and cost are equal. It is equal to total revenue minus total costs.
How to calculate the profit function?
Profit function = Revenue function - Cost function
P(x) = R(x) - C(x)
Here, we have
R(x) = 12x
C(x) = x + 264
by applying the Profit function formula, we get
P(x) = 12x - x - 264
P(x) = 11x - 264
At this point, there is no profit or loss.
so, at break-even P(x) = 0
11x - 264 = 0
x = 24
Hence, Profit function = P(x) = 11x - 264, and 24 Units must be produced for the business to break even.
To learn more about the profit function from the given link
https://brainly.com/question/18617994
#SPJ1
three rectangular prims have the same based area but different heights as the height of these prisms increase the volume increases what is the independent variable in this situation
The independent variable while calculating the volume of a rectangular prisms with equal base area and different height is the height
What is an independent variable?The input values for a specific function are represented by the independent variable (x).
During an experiment, the independent variables are kept under control. The outputs of the function are represented by the dependent variable (y). The quantities being measured are the dependent variables in an experiment.
As regard the problem, the base area is a constant, the volume calculated is the dependent variable while the height iis the independent variable.
Learn more about variables here;
https://brainly.com/question/29348198
#SPJ1
The black graph is the graph of y = f(x).
Choose the equation for the red graph.
A. y - 1 = f(x)
B. = f(x)
C. y = f(x - 1)
D. y = f()
1
Answer:
It's A.
Step-by-step explanation:
If you subtract from y, the graph moves to the right. If you add, it moves to the left.
A rental car company charges $53 per day to rent a car and $0.08 for every mile driven. Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend. Use the drop-down menu below to write an inequality representing dd, the total number of days Rashaad can rent the car while staying within his budget.
The inequality that can be used to represent the total number of days Rashaad can rent the car while staying within his budget is d ≤ 4 .
How to represent inequality?The rental car company charges $53 per day to rent a car and $0.08 for every mile driven.
Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend.
Therefore, the inequality to represent the total number of days Rashaad can rent the car can be represented as follows:
Therefore,
53d + 0.08(475) ≤ 250
53d + 38 ≤ 250
53d ≤ 250 - 38
53d ≤ 212
divide both sides of the inequality by 53
53d / 53 ≤ 212 / 53
d ≤ 4
learn more on inequality here: https://brainly.com/question/28954536
#SPJ1
what is the factored form of the expression 2m^3 -26m^2+80m?
Who can team up with me ?
ANSWER 2m(m-8)(m-5)
EXPLANATION
Factor the expression: 2m(m²-13m+40)
Rewrite the term: 2m(m²-8m-5m+40)
Regroup terms into two proportional parts : 2m((m²-8m)+(-5m+40))
Factor the expression: 2m(m(m-8)-5(m-8))
Factor the expression: 2m(m-8)(m-5)
Answer: 2m(m-8)(m-5)
An arithmetic sequence is shown below:
150, 100, 50, 0, -50, ....
Construct the explicit formula to represent the sequence above. (Rubric 1B)
ARITHMETIC SEQUENCE
an= a1 + (n−1)d
Answer:
an= -50n +200
Step-by-step explanation:
an = a1+(n-1)d=150-50n+50=-50n+200
(7 x 4) x 3 = 3 x (4 x 7)
which property is used
a) commutative
b) assositative
c) identity
d) distributive
Answer:
b) associative
Step-by-step explanation:
The associative property of multiplication was used to change the position of the parentheses
The lines in the graph of part A don’t intersect at two whole numbers on the coordinate grid. Estimate the values of the solution to the nearest one-fourth of a unit. Then substitute the x- and y-values of the approximate solution into the two equations. How close do you get to the constant numbers in each equation?
(4.25,6.5) is the solution of the equation.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The estimate is pretty close for both equations. For the first equation, the estimate results in a value that is only 0.2125 units away from the constant.
For the second equation, the estimate results in a value that is only 0.25 units away from the constant.
The solution lies at approximately (4.25,6.5).
Hence (4.25,6.5) is the solution of the equation.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
3. You are working as a computer programmer in a company that makes computer games. You are getting paid $50 per hour for your work. At the end of the day you earned $400. How many hours did you have to
work to earn that amount of money? Let h represent the number of hours you worked. Choose the equation below that does not represent this situation.
400-(h+h) x 50
400-hx 50
50h = 400
400 h+h+h+h+h+h+h+h
Answer: I think A? not fully sure
Step-by-step explanation:
Find tα/2 for n = 18 and a 99% confidence interval.
The value of tα/2 of the t-test is 2.898
How to determine tα/2?A t-test is a statistical test that is used to compare the means of two groups. tα/2 refers to the t critical value from the t-distribution table that corresponds to α/2
Given: n = 18 and a 99% confidence interval
We have to find the critical t value for 99% confidence level and sample size of 18
Degrees of freedom = n - 1 = 17
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
In the t table (check the attached image), we have to check the value against the column 0.005 and for 17 degrees of freedom.
The value obtained from the table is 2.898
Therefore, tα/2 = 2.898
Learn more about t-test on:
https://brainly.com/question/6501190
#SPJ1