in order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. assume the population standard deviation is 1.2 hours.
The standard error of the mean is?
a. 7.5
b. 0.014
c. 0.160
d. 0.133
With a 0.95 probability, the margin of error is approximately?
a. 0.26
b. 1.96
c. 0.21
d. 1.64
If the sample mean is 9 hours, then the 95% confidence interval is approximately?
a. 7.04 to 110.96 hours
b. 7.36 to 10.64 hours
c. 7.80 to 10.20 hours
d. 8.74 to 9.26 hours
Answers
A sample of 81 business students over a one-week period with the population standard deviation is 1.2 hours. We calculate the following using the standard formulae:
a) Standard error of the mean is 0.13.
b) Margin of error is 0.975.
c) If the sample mean is 9 hours, then 95% confidence interval is (8.608 , 9.392).
Confidence Interval
The error introduced during the random sampling process is the sampling error described in the estimation procedure in the form of margin of error (MOE). MOE is expressed by the following formula:
MOE = CV ×SE
where,
CV = critical value of distribution
SE = standard error Solution
Note that, Population standard deviation(σ) is known. So we use z distribution.
we have given that
Sample size, n = 81
Standard deviations, σ = 1.2 h
a)
Standard error = σ /√n
=> S.E = 1.2/√81 = 1.2/9
=> S.E = 0.13
b) We have to construct 95% confidence interval.
therefore, c = 0.95
=> α= 1 - c = 1- 0.95 = 0.05
then, α/2 = 0.05/2 = 0.025 and 1- α/2 = 0.975
the probability or P-vale is 0.975 then from Z-table the corresponding z value is 1.96
The margin of error formula:
MOE = Zα/2 (σ/√n)
= 1.96 (0.13 )
= 0.2548
Margin of error = 0.2548
c) Now , confidence interval for mean(u) formula
(X-bar - E ) < μ < (X-bar + E)
=> ( 9 - 0.392) < μ < (9 + 0.392)
=> 8.608 < μ < 9.392
=>(8.608 , 9.392)
Hence, standard error is 0.13
Margin of error is 0.2548 and confidence interval is (8.608 , 9.392).
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Related Questions
prove that the difference between squares of consecutive even numbers is always a multiple of 4
Answers
Answer:
Answer: Proved: the difference between squares of consecutive even numbers is always a multiple of 4. ... From the results above, we can see that 12, 20, and 28 are multiples of 4. Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let's call the numbers n and n + 2.
(n + 2)² - n²
= n² + 4n + 4 - n²
= 4n - 4
= 4(n - 1)
if a sample size of 16 yields an average of 12 and a standard deviation of 3, estimate the 95% ci for the mean. a. [10.4, 13.6] b. [10.45, 13.55] c. [10.53, 13.47] d. [10.77, 13.23]
Answers
The estimated 95% confidence interval for the mean is [10.4, 13.6], making answer choice (a) correct.
To estimate the 95% confidence interval for the mean, we can use the formula
CI = X ± t(α/2, n-1) * (s/√n)
where X is the sample mean, s is the sample standard deviation, n is the sample size, t(α/2, n-1) is the t-value for the given confidence level and degrees of freedom, and α is the significance level (1 - confidence level).
For a 95% confidence interval with 15 degrees of freedom (n-1), the t-value is approximately 2.131.
Plugging in the values, we get
CI = 12 ± 2.131 * (3/√16)
CI = 12 ± 1.598
CI = [10.402, 13.598]
Therefore, the closest answer choice is (a) [10.4, 13.6].
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michael is 3 33 times as old as brandon. 18 1818 years ago, michael was 9 99 times as old as brandon. how old is brandon now?
Answers
Brandon is currently 6 81 years old.
Let M be Michael's age and B be Brandon's age.
We are given that Michael is 3 33 times as old as Brandon. This means that M = 3 33 × B
We are also given that 18 1818 years ago, Michael was 9 99 times as old as Brandon. This means that M - 18 1818 = 9 99 × (B - 18 1818).
We can combine these two equations to solve for Brandon's current age:
3 33 × B = (9 99 × B) + 18 1818
2 66 × B = 18 1818
B = 18 1818 / 2 66 = 6 81.
Therefore, Brandon is currently 6 81 years old.
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Perimeter 94 cm and length 39. What’s the width
Answers
Answer:
8
Step-by-step explanation:
Take the length and multiply it by 2. then take your answer and multiply it by the perimeter. Then, take that answer and divide it by 2. Hope this helps :)
Hello.
To find the perimeter of a rectangle, use the formula P = 2(l + w).
Input 39 as l.
94 = 39 + 39 + w + w
Simplify
94 = 78 + 2w
Subtract the two known numbers
94 - 78 = 16
16 = 2w
So that means w = 8.
The width is 8.
Question Content Area
Net Present Value
A project has estimated annual net cash flows of $15,000 for ten
years and is estimated to cost $47,500. Assume a minimum acceptable
rate of return of 20%. Use
Answers
The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.
Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.
Net Present Value = 150000 / (1 + 0.20)^10 - 47500
Net Present Value = $67,482.22
Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.
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The monthly demand function for a product sold by a monopoly is p = 2104 – (1/3)x^2 dollars, and the average cost is C = 1000 + 22x + x2 dollars. Production is limited to 1000 units and x is in hundreds of units. (a) Find the quantity (in hundreds of units) that will give maximum profit. (b) Find the maximum profit. (Round your answer to the nearest cent.)
Answers
a) The quantity (in hundreds of units) that will give maximum profit: \(x^{2}\) + 6x - 3022 = 0
b) The maximum profit is approximately $202,573.42.
What is Equation?An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
(a) To find the quantity that will give maximum profit, we need to find the level of output at which marginal revenue equals marginal cost.
The total revenue function for the monopoly is TR = px, where p is the price and x is the quantity sold. The marginal revenue is the derivative of the total revenue with respect to x, which is MR = d(TR)÷dx = p + x(dp÷dx).
To find the marginal revenue function, we differentiate the demand function with respect to x:
dp÷dx = -(2÷3)x
So, the marginal revenue function is:
MR = (2104 - (1÷3)\(x^{2}\)) - (2÷3)\(x^{2}\)
To find the marginal cost function, we differentiate the average cost function with respect to x:
dC÷dx = 22 + 2x
So, the marginal cost function is:
MC = 22 + 2x
To find the level of output at which MR = MC, we set the two functions equal to each other:
(2104 - (1÷3)\(x^{2}\)) - (2÷3)\(x^{2}\) = 22 + 2x
Simplifying this equation, we get:
\(x^{2}\) + 6x - 3022 = 0
(b) Using the quadratic formula, we find that:
x = (-6 ± √( 36- 4(1)(-3022))) / 2(1)
x = (-6 ± √(36444)) / 2
x = (-6 ± 190.81) ÷ 2
x ≈ -98.4 or x ≈ 92.4
Since we can't produce a negative quantity, we choose x ≈ 92.4 as the quantity that will give maximum profit.
Therefore, the level of output that will maximize profit is 924 units (in hundreds of units).
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O conjunto A é formado pelos números inteiros maiores que -5 e menores que 8. Marque a alternativa que representa esse conjunto
Alguém sabe a resposta dessas 2 questão?
Answers
Answer:
A opção 2. Para um número ser maior que -5,basta ele está mais perto do 0,na reta numérica.
Espero ter lhe ajudado!
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is
reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
Picture has questions
Question 1 answer : 210
Answers
Answer:
brainliest plss
Step-by-step explanation:
1. y = 35x
2. y = 30x + 1
3. y = 35x
y = 30 x + 1
4. Its more convenient to substitute y because It's easier.
35x = 30(x + 1)
5. 35x = 30x + 1
35x = 30x + 30
35x -30x = 30
5x = 30
x = 6 (30/5 = 6)
35 x 6 = 210 (y)
6. Both people have read 210 pages and it takes amir 6 days to catch up.
Identify the slope and the y-intercept of y= 2x - 5
Slope =
y-intercept =
***Remember, the y-intercept should be written as a point!
Answers
Answer:
slope: 2/1
y intercept: (0,-5)
Step-by-step explanation:
mark me brainliest by going to the bottom of this answer and click the button next to comments
thank you!!
Use the distributive property to find an expression equivalent to 24 + 64.
8(3 + 8)
6(4 + 8)
24 + (8)(8)
(2)(12) + (8)(8)
Please hurry
Answers
Answer:
8(3+8)
Step-by-step explanation:
The distributive property of multiplication states that
A(B+C) = A* B + A* C
Here, we can say that
8(3+8) = 8*3 + 8* 8 = 24 + 64. This seems correc,t but we can check the other options to make sure
6(4 + 8) = 6 * 4 + 6*8 = 24 + 48. This is incorrect
24 + (8)(8) . The 24 and 8 are not in the same parenthesis, so we cannot multiply them. Using PEMDAS, we multiply first, so 24+(8)(8) = 24 + 8*8 = 24 + 64. If there are multiple solutions, this can work. If not, this does not use the distributive property as we are not adding anything in the parenthesis.
Similarly, for (2)(12) + (8)(8), we are not adding anything in the parenthesis, but we can use PEMDAS to get 2*12 + 8*8 = 24 + 64, so this would also work but does not use the distributive property.
Every Sunday, Tara has breakfast at her grandparents' house. Tara is excited this weekend because her grandma is making her favorite food, giant pancakes! Grandma makes a really giant pancake and cuts it into 8 equal pieces. Tara eats 7 pieces and her grandma eats 1 piece.
What fraction of the giant pancake does Tara eat?
Answers
Answer:
7/8
Step-by-step explanation:
because the are 8 pieces in the entire circle and Tara eats 7 out of 8 of them
Makiyha Martin
Janice bought a computer. She paid $780.00 plus sales tax. The sales
tax was 4%. How much did she pay in sales tax?
Answers
Answer:
$31.20
Step-by-step explanation:
1. Calculate the tax amount. To do this, you multiply the price by the tax rate.
$780 x 4% = $31.20
The total tax paid was $31.20
Answer:
B
Step-by-step explanation:
janice got ripped off buying a computer for $780.
she could have easily built her own computer with similar specs for less money or use the same amount of money to build a way better pc.
-2(-5-3n)+6n=37+3n ?
Answers
Answer:
2- sum the ratio
Step-by-step explanation:
On Wednesday a local hamburger shop sold a combined total of 304 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Wednesday?
Will mark if it is an actual correct answer with an actual explanation
Answers
Answer:
It would be 76 hamburgers were sold on Wednesday
Step-by-step explanation:
I divided the total 304 by 4 and got 76. Then when you multiply that out you get a total of 304
Write the number in standard notation. 4.16 × (10) ^–5
Answers
Answer:
.0000416
Step-by-step explanation:
Since 10 is squared by a negative number, the number (4.16) will be smaller. To find the answer, move the decimal 5 places to the left
Answer:
0.0000416.
Step-by-step explanation:
When 10 is raised to a negative power, that means that the decimal point will be moved to the left a certain number of units.
In this case, it is 10^-5, so the decimal point will move to the left by 5 units.
4.16 * 10^-5 = 000004.16 * 10^-5 = 0.0000416.
Hope this helps!
A chemistry experiment requires 825.00 grams of sucrose and you have
30.00 ounces available, is there enough? (28 grams = 1 ounce)
Mathematically show your answer, no credit will be giving for just writing
yes or no.*
Answers
Answer:
yes
Step-by-step explanation:
you first need to convert the 825 grams to about 29.46 ounces if you round to the hundredths place (825/28) then you can see that 30>29.46 so you will have a bit extra sucrose after doing the expirement
Ahab pays 1.15 x 10^3 dollars for one year's tuition ay naylor's university his sister attends north central university and pays 2.8 x 10^3 dollars in tuition for her first year what is the difference in tuition paid by ahab and his sister? answer in scientific notation without units the coefficient may be exact or rounded to 2 decimal places
Answers
Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)
Review the following subtraction rules and properties:
The subtraction identity property (also known as the zero subtraction rule): Any number minus zero is equal to itself. \((2-0=2)\)The rule of subtraction by one: any number minus one will decrease that number by one. \((5- 1 = 4)\)Rule of subtraction number minus itself: any number minus itself is equal to zero. \((2 - 2 = 0)\)Number minus the number immediately before the Subtraction rule: any number minus the number immediately before it is equal to one. \((3 -2 = 1)\)Inverse operation: reverses the effect of another operation. Subtraction reverses addition. (Because \(3 + 2 = 5\), then \(5 - 2 = 3\) and \(5 - 3 = 2\))Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year
To find: Difference in tuition fees paid by Ahab and his sister?
Solution:
To find the difference in their fees we have to perform simply normal subtraction
Subtract the fees of his sister from Ahab's fees which is as follows:
\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)
Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)
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Write an equation that represents the function (0, 2),(1,3),(2,10),(3,29),(4,66),(5, 127)
Answers
Answer: 7
Step-by-step explanation: because
A set of data in the table below represents a linear function.
-2,15
-4, 23
-5, 27
What is the rate of change of this linear function?
pls i need help asap
Answers
The rate of change of this linear function is -2.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁)
From the given table, (-2, 15), (-4, 23) and (-5, 27).
Substitute, (x₁, y₁)=(-2, 15) and (x₂, y₂)=(-4, 23) in (y₂-y₁)/(x₂-x₁), we get
Rate of change =(23-15)/(-4+2)
= 8/(-2)
= -4
Therefore, the rate of change of this linear function is -2.
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write the ratio 15:4.5 in its simplest form
Answers
Answer:
10 : 3
Step-by-step explanation:
15 : 4.5 (divide both parts by 1.5 )
= 10 : 3
ANSWER
My Answer is in the photo above by the way I thought you had made a mistake in the question that's why I gave answers for both 15:4.5 and 15:4:5
A vegetable patch has marrows and parsnips planted in it. The ratio of marrows to parsnips is 5: 4. There are 360 vegetables in total. More marrows are planted so that the total number of marrows increases by 10%. What is the new ratio of marrows to parsnips in the vegetable patch? Give your answer in its simplest form.
Answers
The new ratio of marrows to parsnips in the vegetable patch is: 11:8
How to solve ratio word problems?We are told that the ratio of marrows to parsnips is 5: 4.
Thus, if there are 360 vegetables in total, then we can say that:
Number of marrows = (5/9) * 360
= 200 marrows
Number of Parsnips = (4/9) * 360
= 160 Parsnips
Now, we are told that the total number of marrows increases by 10%. Thus:
New total of Marrows = 200 * 1.1 = 220 marrows
Total number of vegetables = 220 + 160 = 380
Ratio of marrows = 220/380 = 11/19
Ratio of parsnips = 160/380 = 8/19
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Find the value or ratio of the following:
Answers
Answer:
see below
Step-by-step explanation:
cos = adj/ hypotenuse
Cos A = 30 /34
Simplifying
Cos A = 15/17
1 over 6x plus 2 over 3x is equal to 5
find the value of x
1/6x + 2/3x =5
Answers
Hope this helps!
Answer: x = 6
Step-by-step explanation: 1/6x + 2/3 x = 5 first just add the like terms 5/6 x = 5 then 5*6 /5 = x hope it helps ;)
what's 9-3 / 1/3 + 1
Answers
Answer:
3
Step-by-step explanation:
9 - 3 = 6
6/ 1/3 = 2
2 + 1 = 3
The question is listed below:
Answers
Answer:
\(3\sqrt{5}\)
Step-by-step explanation:
Factor out a \(\sqrt{5}\) from the \(\sqrt{80}\), and you will get \(\sqrt{5} * \sqrt{16}\)
Then you get: \(4\sqrt{5}\), since the square root of 16 is just 4. Then we have this expression:
\(4\sqrt{5} -\sqrt{5}\), which gives us \(3\sqrt{5}\).
Hope this helps
Suppose that x and y are related by the given equation and use implicit differentiation to determine dx xiy+y7x=4 ... dy
Answers
by the given equation and use implicit differentiation ,the derivative dy/dx is given by (-y - 7y^6)/(xi + y^7).
To find dy/dx, we differentiate both sides of the equation with respect to x while treating y as a function of x. The derivative of the left side will involve the product rule and chain rule.
Taking the derivative of xiy + y^7x = 4 with respect to x, we get:
d/dx(xiy) + d/dx(y^7x) = d/dx(4)
Using the product rule on the first term, we have:
y + xi(dy/dx) + 7y^6(dx/dx) + y^7 = 0
Simplifying further, we obtain:
y + xi(dy/dx) + 7y^6 + y^7 = 0
Now, rearranging the terms and isolating dy/dx, we have:
dy/dx = (-y - 7y^6)/(xi + y^7)
Therefore, the derivative dy/dx is given by (-y - 7y^6)/(xi + y^7).
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Jaycee has already saved $75 for an upcoming vacation. Every week, she adds another $15 to her vacation savings. The relationships between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savings, is a linear relationship.
Write an equation to describe the linear relationship.
Answers
The equation to describe the linear relationship between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savings is y = 75 + 15x
The equation to describe the linear relationship between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savingsAmount Jaycee has saved = $75Additional amount jaycee saved per week = $15Number of weeks Jaycee saved = xThe amount Jaycee has in her vacation savings = yThe equation to describe the linear relationship:
The amount Jaycee has in her vacation savings = Amount Jaycee has saved + Additional amount jaycee saved per week(Number of weeks Jaycee saved)
y = 75 + 15(x)
y = 75 + 15x
For instance, if jaycee has saved for 5 weeks, the
amount Jaycee has in her vacation savings is
y = 75 + 15x
y = 75 + 15(5)
= 75 + 75
y = $150
Therefore, the equation to describe the linear relationship between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savings is y = 75 + 15x
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solve. 2-6: MathXL for School: Practice & Problem Solving (Grade 8 Pre-Algebra)
Answers
The area of the rectangle is \(b^2\) +9b square feet
The rectangle is the quadrilateral whose opposite sides are parallel and equal. The rectangle is a four sided shape that all the angles are 90 degrees
The area is defined as the total space occupied by the two dimensional shape like rectangle, triangle, circle etc..
The length of the rectangle = (5/3)b+15 feet
The width of the rectangle = (3/5)b feet
The area of the rectangle = The length of the rectangle × The width of the rectangle
Substitute the values in the equation
The area of the rectangle = [(5/3)b+15] ×(3/5)b
Apply the distributive property in the equation
[(5/3)b+15] ×(3/5)b = \(b^2\) +9b square feet
Hence, the area of the rectangle is \(b^2\) +9b square feet
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The slope field for certain differential equae tion is shown below: Which of the following statements about solution y = f (x) the differential equation must be false?
A). The graph of the particular solution that satisfies f "(0)=0 has = point of inflection at x=0 _
B.) The graph of the particular solution that satisfies f (0) =0 is concave up on the interval -k
C) The graph of the particular solution that satisfies f(-1)=1 concave up on the interval -1
D.) The graph of the particular solution that satisfies f ()=-1is concave down on the interval 0
Answers
The slope field shown in the question is that of a differential equation of the form y'= f(x,y).
The solutions of this equation are the curves in the slope field that emanate from each point and that have the same slope as the line at that point. Thus, for each point (x,y) in the slope field, it is possible to calculate the particular solution that passes through that point.
The first statement is false because it involves the second derivative of the particular solution, which cannot be determined from the slope field. The second statement is false because a concave up graph requires that the derivative of the solution be increasing at x=0, but the slope field does not indicate the sign of the derivative of the particular solution. The third statement is false because a concave up graph requires that the derivative of the solution be decreasing at x=-1, which cannot be determined from the slope field. The fourth statement is false because a concave down graph requires that the derivative of the solution be increasing at x=0, which cannot be determined from the slope field.
In summary, none of the statements can be determined to be true or false from the slope field shown.
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elimination method
x-5=-y
3x-10=2y
Answers
Answer:
(4,1)
Step-by-step explanation:
Multiply the first equation by -3
(x-5=-y)*-3 = -3x+15=3y
Then combine like terms with the new equation and the second equation
(-3x+15=3y) + (3x-10=2y) = 5=5y
Divide 5 by both sides
1=y
Plug in 1 for y in an equation. Doesn’t matter which one and solve
x-5=-(1)
Distribute the negative sign to the 1
x-5=-1
Add 5 to both sides
x=4
X-5= -y
-X+5=y
-4+5=y
1=y
3X-10=2(-2+5)
3X-10= -2X+10
3X+2X=10+10
5x=20
X=4