A random sample of 30 college students at University XYZ spent an average of $40.00 on a date with a standard deviation of $5.00. The boxplot for this data indicated the distribution was normal with one minor outlier. Compute a 95% confidence interval for the average amount spent by all students at University XYZ that are on a date.
Answers
We can be 95% confident that the true average amount spent by all students at University XYZ on a date falls within this interval.
To compute a 95% confidence interval for the average amount spent by all students at University XYZ on a date, we can use the formula:
Confidence Interval \(= \bar{X} \pm (t \times (s / \sqrt{n} ))\)
Where:
\(\bar{X}\) is the sample mean
t is the critical value for the desired confidence level (with n-1 degrees of freedom)
s is the sample standard deviation
n is the sample size
In this case, the sample mean (\(\bar{X}\)) is $40.00, the sample standard deviation (s) is $5.00, and the sample size (n) is 30.
Since the sample size is larger than 30 and the distribution is assumed to be normal, we can use a t-distribution to find the critical value.
With 30 degrees of freedom and a 95% confidence level, the critical value (t) can be obtained from a t-distribution table or a statistical software.
Let's assume the critical value is 2.042 (hypothetical value).
Substituting the values into the formula:
Confidence Interval = $40.00 ± (2.042 \(\times\) ($5.00 / √30))
Calculating the standard error (s / √n):
Standard Error = $5.00 / √30
Substituting the standard error value:
Confidence Interval = $40.00 ± (2.042 \(\times\) [Standard Error])
By evaluating the equation, the confidence interval for the average amount spent by all students at University XYZ on a date is approximately $38.43 to $41.57 (rounded to two decimal places).
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Related Questions
Please help I will give brainliest.
Answers
Answer:
3 Rd one
Step-by-step explanation:
donee....!!✓give me the branliest
Kala made 234 for hours of 18 work.
At the same rate, how many hours would she have to work to make 117?
Answers
Answer:
Step-by-step explanation:it would take 9 hours
Answer: 9
Step-by-step explanation: 234 divided by 18=13 117 divided by 13= 9
2. a farmer has 2,000 feet of fencing to enclose a pasture area. the field will be in the shape of a rectangle and will be placed against a river where there is no fencing needed. what is the largest area field that can be created and what are its dimensions?
Answers
The correct answer is 500 yards. The largest area for the field will be when the cube is a forecourt. With 2000 yds. of fencing, each side would be 2000/4 = 500 yds.
Long, or 500 yds. If there were no swash also, the largest area would be given by a square configuration since adding the length and dwindling the range of a square by the same value, t will drop the area by a square with sides of length. Now add the swash on one side. The swash acts like a glass.
As we guard in a cube on one side of the swash, imagine an identical cube on the other side. The maximum area is given when the two blocks form a square, that's when we have a cube doubly as long as wide.
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The value of the largest area of the field will be 5000 sq. ft.
From the given data,
Total pasture area of fencing =2,000 feet
The shape of the field =rectangular
As the area of the rectangle = l*b
So, we can write it as;
2000=x+2y, (As the area of surrounded by a river from one side, so we need to only fence twice of width and only one length (Side) of the rectangle.
Now applying the formula of the area of the rectangle
we will get it as:
\($$\begin{aligned}& A(x)=x\left(\frac{2000-x}{2}\right)=\frac{1}{2}\left[2000 x-x^2\right] \\& A^{\prime}(x)=\frac{1}{2}[2000-2 x]=0 \\\end{aligned}$$\)
Solving the value,
We will get: x=100 ft y=50 ft
So, determining the value of the largest area,
We will get it as:
A_{max}=(100)(50)=5000 Sq. ft.
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Evaluate each function. Drag the correct solution to each problem. Not all responses will be used.
Answers
Answer:
a) 1
b) 2
c) -1
Step-by-step explanation:
please help, passed due.
Answers
What is a place value chart in maths?
Answers
In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.
The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.
A place value chart can be used to understand the value of a digit in a number.
Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.
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33333333333333333333333333333
Answers
Answer: All three methods would be easy and effective
Step-by-step explanation:
Suppose a company wants to introduce a new machine that will produce a marginal annual savings in dollars given by S '(x)= 175 - x^2, where x is the number of years of operation of the machine, while producing marginal annual costs in dollars of C'(x) = x^2 +11x. a. To maximize its net savings, for how many years should the company use this new machine? b. What are the net savings during the first year of use of the machine? c. What are the net savings over the period determined in part a?
Answers
a) To maximize its net savings, the company should use the new machine for 7 years. b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar). c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).
Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.
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Which is the mode of this data set?
55, 78, 43, 39, 78, 61, 75, 50, 43, 78
Answers
Answer:
78
Step-by-step explanation:
Mode = number that appears most in a set of numbers
The number that appears the most in this set is 78. So, the mode is 78. Hope it helps!
Answer:
Step-by-step explanation:
arrange in ascending order
39,43,43,50,55,61,75,78,78,78
mode=78
or a new cookbook is becoming popular. the local bookstore ordered 86 copies in may, 172 copies in june, 344 copies in july, and 688 copies in august. what kind of sequence is this?
Answers
This is a geometric sequence with a common ratio of 2. So the predicted order quantity for September is 1376 copies.
In a geometric sequence, each term is found by multiplying the previous term by a fixed number called the common ratio. In this case, we can see that each month's order quantity is double the previous month's order quantity. This makes it a geometric sequence with a common ratio of 2.
To verify, we can divide any term by its preceding term and see that we always get the same ratio of 2. For example:
June order / May order = 172 / 86 = 2
July order / June order = 344 / 172 = 2
August order / July order = 688 / 344 = 2
Knowing that this is a geometric sequence with a common ratio of 2, we can use the formula for the nth term of a geometric sequence to find the order quantity for any given month:
an = a1 * r^(n-1)
where:
an = the nth term
a1 = the first term
r = the common ratio
n = the number of terms
For example, to find the order quantity for September (the 5th month), we can plug in the values:
a5 = 86 * 2^(5-1) = 86 * 16 = 1376
So the predicted order quantity for September is 1376 copies.
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Is the relation a function?
{(-6, 3), (-1,0), (2, 4), (-1, -7), (5, 2)}
Answers
Answer:
It is not a function
Step-by-step explanation:
It is not a function because the domain -1 repeats itself.
Domain: x axis number
Find the length of QR
Answers
Answer:
QR = 15
Step-by-step explanation:
The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.
(QR+5) *5 = 10^2
(QR+5) *5 = 100
Divide each side by 5.
(QR+5) *5/5 = 100/5
(QR+5) = 20
Subtract 5 from each side.
QR = 20-5
QR = 15
An independent set in a graph is a set of vertices S⊆V that contains no edge (so no pair of neighboring vertices is included). The max independent set problem is to find an independent set of maximum size in a graph G. (a) Write the max independent set problem as an integer linear program. (b) Write an LP relaxation for the max independent set problem. (c) Construct an example (a family of graphs) to show that the ratio LP-OPT / OPT can be at least cn where c>0 is some absolute constant and n is the number of vertices of the graph. (d) What is the (exact) relation between the size of a max independent set and the size of min vertex cover of a graph? (e) Using this relation, what does the 2-approximation algorithm for vertex cover imply for an approximation algorithm for max independent set?
Answers
The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.
The solution for this question is discussed below:
a) The integer linear program for the max independent set problem is as follows:
maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.
b) The LP relaxation for the max independent set problem is as follows:
Maximize ∑x_iSubject to:
xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.
c) The family of graphs is as follows:
Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.
d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.
e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.
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dave drives to work. while driving the car over nine days, he observes his daily average speed and lists it in the table below. day average speed (mph) 1 45 2 62 3 44 4 70 5 59 6 66 7 54 8 63 9 67 the median speed at which dave drove to work was .
Answers
The median speed at which Dave drove to work is 62 mph.
To find the median speed at which Dave drove to work, we need to arrange the average speeds in ascending order and determine the middle value.
Arranging the average speeds in ascending order:
44, 45, 54, 59, 62, 63, 66, 67, 70
Since we have nine values, the middle value is the 5th value, which is 62.
Therefore, Dave's average speed on the way to work was 62 mph.
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3. Given a nonempty polyhedron P={(x,y)∈Rn×Rk:Ax+By≥b}, let Q denote its projection onto x-space, i.e., Q={x∈Rn:∃y∈Rk,Ax+By≥b}. Prove or disprove the following statements by counterexamples: 1) Suppose that (x^,y^) is an extreme point of P. Is x^ an extreme point of Q ? 2) Suppose that x^ is an extreme point of Q. Does there exist a y^ such that (x^,y^) is an extreme point of P ? 3) Suppose that x^ is an extreme point of Q and P does not contain a line. Does there exist a y^ such that (x^,y^) is an extreme point of P ?
Answers
P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.
1) The statement is true. Suppose (x^,y^) is an extreme point of P. To show that x^ is an extreme point of Q, we need to prove that for any two distinct points x_1, x_2 in Q, the line segment connecting x_1 and x_2 lies entirely in Q. Since Q is the projection of P onto x-space, it means that for any x in Q, there exists y in R^k such that Ax + By ≥ b.
Now, let's assume x_1 and x_2 are two distinct points in Q. Since they belong to Q, there exist corresponding y_1 and y_2 in R^k such that Ax_1 + By_1 ≥ b and Ax_2 + By_2 ≥ b. Since P is a polyhedron, the set of points that satisfy Ax + By ≥ b is a convex set. Therefore, the line segment connecting x_1 and x_2, denoted by [x_1, x_2], lies entirely in P. Since the projection of a convex set onto a subspace is also a convex set, [x_1, x_2] lies entirely in Q. Thus, x^ is an extreme point of Q.
2) The statement is false. Suppose x^ is an extreme point of Q. It does not necessarily imply the existence of a corresponding y^ such that (x^, y^) is an extreme point of P. This is because the projection Q onto x-space may not capture all the extreme points of P. It is possible for multiple points in P to project to the same point in Q, making it impossible to uniquely determine y^.
3) The statement is true. If x^ is an extreme point of Q and P does not contain a line, then there exists a corresponding y^ such that (x^, y^) is an extreme point of P. Since P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.
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In which number is the digit 6 one hundred times larger than it is in the number 647?
A. 5,638
B. 6,523,532
D. 38,641
C. 65,398
Answers
Answer:
65,398
Step-by-step explanation:
In the numbers 5,638 and 38,641, the digit 6 is the SAME value as in 647. In the number 6,523,532, the digit 6 is 10,000 times larger than in 647. In the number 65,398 the digit 6 is 100 times larger than in 647.
Hello! I’m really struggling with this, any help is appreciated (:
Answers
Hi, It's the 3rd option
Thanks, It was little hard to find the answer. I am not totally sure about it but as far as I understand this question. the third option is correct.
:)
Elva monitors her savings account online. On Monday she withdraws money, and the change to her balance is -$51.25. On Tuesday she deposited money and the change to her balance is +$39.50. She wants to know the total change in her account after the two transactions
Answers
Answer:
So You have to minus $39.50-$61.25 to getnegative 11.75
Write an inequality with the solution x > or equal to 4. The inequality should have the variable on both sides, a fractional coefficient of the variable on the left side, and a fraction anywhere on the right side.
Answers
The inequality equation ( x ≥ 4 ) is given as ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
x ≥ 4 be equation (1)
On simplifying the equation , we get
Divide by 4 on both sides of the equation , we get
( x / 4 ) ≥ 1
Adding x on both sides of the equation , we get
x + ( x/4 ) ≥ 1 + x
Now , adding ( 1/4 ) on both sides of the equation , we get
x + ( 1/4 ) + ( x/4 ) ≥ 1 + x + ( 1/4 )
On simplifying the equation , we get
( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
Therefore , the value of A is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
Hence , the inequality equation is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
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Answer number 6 please. Bots don’t answer I’m just trying to get help
Answers
Answer:
B
Step-by-step explanation:
20 × 2/5 = 8
15 × 2/5 = 6
5 × 2/5 = 2
p/s : the pic is for question no 7. i thought that you want the number 7 so i solved it first. then i reread your question. then i realized u actually want number six. so...
yeah, your welcome :)
what is the quotient
will mark as brainliest
Answers
The quotient is \(x-1+\frac{9}{x+6}\)
What is the formula of division?The formula to calculate the division of two numbers is: Dividend ÷ Divisor = Quotient + Remainder. Here, The dividend is the number, which is being divided. The divisor is the number, which divides the number (dividend) into equal parts.
Division in maths is the process of breaking a number up into equal parts, and finding out how many equal parts can be made. For example, dividing 15 by 3 means splitting 15 into 3 equal groups of 5.
In the above question we simply have to divide the dividend that is \(x^2+5x+3\) with x + 6
and then we will get the quotient as x - 1 and remainder 9 .
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Rachel is painting the walls of her bedroom. She makes a pink color of paint
by mixing some cups of red paint into some white paint. She added three
cups of red paint to four gallons of white paint to get the perfect pink color,
Question: Rachel wants to make more of the pink paint that matches the color
she made before. She starts with 10 gallons of white paint. How many cups of
red paint should Rachel add so that the pink color matches?
Answers
Answer:
8 cups
Step-by-step explanation:
first it was 4 gallons and 3 cups x2=8 gallons 6 cups then just go to 10 gallons 8 cups
The product of a number and twenty-seven.
Answers
Answer:
27+a
Step-by-step explanation:
a spinner has six equal parts labeled from 1 to 6. the spinner is spun twice. what is the probability of getting a 3 twice in a row?
Answers
The probability of getting 3 twice in a row is 1/36
A spinner has 6 equal parts labeled from 1 to 6.
The spinner is spun twice.
First time what is the conditions {1,2,3,4,5,6}
Second time choices are
{1,1} {1,2} {1,3} {1,4} {1,5} {1,6}
{2,1} {2,2} {2,3} {2,4} {2,5} {2,6}
{3,1} {3,2} {3,3} {3,4} {3,5} {3,6}
{4,1} {4,2} {4,3} {4,4} {4,5} {4,6}
{5,1} {5,2} {5,3} {5,4} {5,5} {5,6}
{6,1} {6,2} {6,3} {6,4} {6,5} {6,6}
So we have total 6*6 = 36 choices
{3,3} comes only 1 times.
We know the formula for probability:
Probability(Event) = Favorable Outcomes/Total Outcomes.
Favorable Outcomes = 1.
Total Outcomes=36.
So the probability of getting a 3 twice in a row is 1/36.
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The graph of y = f(x) is shown below. Find all values of x where f(x) = 0
Answers
The values of x when f(x) = 0 are 2 and 8
Graphs are used mostly to show the relationship between two variables (usually x and y).
The graph of y = f(x) is attached
To get the values of x when f(x) = 0 , we consider where the line of the graph crosses the x-axis.
The graph crosses the x-axis at:
x = 2
x = 8
This means that the values of x when f(x) = 0 are 2 and 8
Therefore, in the graph of y = f(x), the values of x where f(x) = 0 are 2 and 8
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Disclaimer : The question mentined is not provided with a graph, the above solution is done as per the graph attached.
The velocity of a ball thrown upward into the air is given by v(t)= -32t+96 where t is measured in seconds and velocity v in feet per second calculate the displacement of the ball between t=1 and t=4
Answers
Answer:
The displac ment between t = 1 and t = 4 is 272 feet
Step-by-step explanation:
To get the displacement of the ball, we first need to get the equation for the position of the ball with respect to time.
We can do this by differentiating the velocity equation given:
v(t) = -32t +96
integrating between the limits of t = 1 and t = 4, we have
\(s = \int\limits^4_1 {-32t +96} \, dt\)
\(s(t) = -32t^2/2 +96t\)
\(s =[ -16t^2 +96t] t = 4, t =1\)
where t = 4.
s = 256 + (96) =352 feet
Where t = 1
s = 80
Displacement of the ball = 352 -80 = 272ft
The displac ment between t = 1 and t = 4 is 272 feet
Help Please... 15 points :)
Answers
Answer:
√100 = 10, √36 = 6, √225 = 15
Step-by-step explanation:
100 can be made by 10^2 (10 x 10), 36 has factors of 6 and can be made by 6^2, and 225 can be made by 15^2.
\( \sqrt{100} = \sqrt{10 \times 10} \) = \(\boxed{10}\)
\( \sqrt{36} = \sqrt{6 \times 6} \) = \(\boxed{6}\)
\( \sqrt{225} = \sqrt{15 \times 15} \) = \(\boxed{15}\)
\(\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}\)
Please help answer this question.
Answers
The correct expression which can be used to find AC is,
⇒ 7.8 (cos 23°)
We have to given that;
A triangle ABC shown in figure.
Now, We can formulate;
cos 23° = AC / AB
cos 23° = AC / 7.8
AC = 7.8 (cos 23°)
Thus, The correct expression which can be used to find AC is,
⇒ 7.8 (cos 23°)
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ethans cooking recipe uses 3 cups of sugar to make 21 cookies mias recipe uses 4 cups to make 28 cookies which has a greater sugar/cookie ratio
Answers
find the standard form of the equation for the cirle with the following properties (-2,(1)/(7)) and tangent to the y-axis
Answers
The standard form of the equation of the circle is(x + 2)² + (y - 1/7)² = 4.
The standard form of the equation for the circle with center (h, k) and radius r is given by ( x - h)² + (y - k)² = r².
To find the standard form of the equation for the circle with the given properties,we need to determine the values of h, k, and r.
Let's begin by determining the center of the circle.
(h, k) = (-2, 1/7)
Therefore, the equation of the circle can be written as follows:
(x + 2)² + (y - 1/7)² = r²
To find the value of r, we will use the fact that the circle is tangent to the y-axis.
The distance from the center of the circle to the y-axis is given by the absolute value of the x-coordinate of the center, which is 2.
Therefore, the radius of the circle is r = 2.
Thus, the equation of the circle can be written in standard form as follows:(x + 2)² + (y - 1/7)² = 4.
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