This statement best illustrates money used as a medium of exchange. In this scenario, the individual goes to the store and exchanges $68 for a pair of jeans. Money serves as a medium of exchange when it is used to facilitate transactions between buyers and sellers. In this case, the buyer wants a pair of jeans, and the seller wants to sell them for $68. Without money, they would have to engage in bartering, which can be cumbersome and inefficient. Money makes the transaction smoother and allows both parties to get what they want. Overall, this example demonstrates how money is an essential tool for facilitating transactions in our modern economy.
Hi! Your question is about the function of money as illustrated by the example of paying $68 for a pair of jeans. This statement best illustrates money used as a medium of exchange.
In this scenario, money is being used as a medium of exchange because it is facilitating the transaction between you and the store. Instead of using barter or trading goods and services directly, you use money to acquire the pair of jeans. This makes transactions more efficient and convenient since it eliminates the need for a double coincidence of wants, which is when two parties each have something the other wants. As a medium of exchange, money serves as a universally accepted means to buy and sell goods and services, like your jeans purchase at the store.
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In interval estimation, the t distribution is applicable only when a. the variance of the population is known b. the sample standard deviation is used to estimate the population standard deviation c. the standard deviation of the population is known d. the population has a mean of less than 30
In interval estimation, the t distribution is applicable when the sample size is small and the population variance is unknown. Therefore, options a, c, and d can be eliminated.
The t distribution is used when the sample standard deviation is used to estimate the population standard deviation, which is usually the case in practice. When the sample size is small, using the t distribution instead of the standard normal distribution results in wider confidence intervals, which takes into account the uncertainty associated with estimating the population standard deviation from the sample.
The t distribution also approaches the standard normal distribution as the sample size increases. Therefore, the correct answer is b.
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Segment Base Length 0 400 500 1 2300 700 2 0 300 3 1000 580 4 2000 200 What are the physical addresses for the following logical addresses? 0, 330 1, 610 2, 255 3, 700 4, 312
Therefore, The physical addresses for the given logical addresses are 330, 2910, 255, 1700, and 2312.
To find the physical addresses for the given logical addresses, we need to use the segment base and segment limit values.
For logical address 0, we have segment base 0 and segment limit 400. So, the physical address would be 0 + 330 = 330.
For logical address 1, we have a segment base of 2300 and a segment limit of 700. So, the physical address would be 2300 + 610 = 2910.
For logical address 2, we have segment base 0 and segment limit 300. So, the physical address would be 0 + 255 = 255.
For logical address 3, we have a segment base of 1000 and a segment limit of 580. So, the physical address would be 1000 + 700 = 1700.
For logical address 4, we have a segment base of 2000 and a segment limit of 200. So, the physical address would be 2000 + 312 = 2312.
Therefore, The physical addresses for the given logical addresses are 330, 2910, 255, 1700, and 2312.
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The volume of a right cone is 512π units³. If its height is 24 units, find its
circumference
in terms of π
Using the given information, the circumference of the right cone is 16π units
Calculating the circumference of a coneFrom the question, we are to determine the circumference of the cone in terms of π
To determine the circumference, we will determine the radius of the cone
From the given information,
The volume of the cone is 512π units³
The height is 24 units
From the formula for calculating the volume of a cone
V = 1/3 πr²h
Where V is the volume
r is the radius
and h is the height
Thus,
We can write that
512π = 1/3πr² × 24
512π = πr² × 8
512 = r² × 8
r² = 512/8
r² = 64
r = √64
r = 8 units
Now, we can calculate the circumference by using the formula
C = 2πr
Where C is the circumference
C = 2 × π × 8
C = 16π units
Hence, the circumference is 16π units
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Solve right triangle
EF =
FG=
Measure E =
The value of the sides are;
FG = 4. 06
EF = 6. 59
<E = 38 degrees
How to determine the valueFrom the information given, we have;
Using the tangent identity;
tan 52 = 5.2/FG
cross multiply the values, we have;
FG = 4. 06
Then,
using the sine identity, we have;
sin 52 = 5.2/EF
cross multiply the values, we get;
EF = 6. 59
To determine the angle E, we have;
sin E = 4.06/6. 59
Divide the values
sin E = 0. 6160
E = 38 degrees
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A certain brand of satellite dish antenna is a paraboloid with a diameter of 6 feet and a depth of 2 feet. How far from the vertex of the dish should the receiver of the antenna be placed
The receiver should be placed 3/4 feet away from the vertex of the dish.
Assuming that the satellite dish antenna is a perfect paraboloid, the receiver should be placed at the focal point of the paraboloid, which is located at a distance of one-fourth of the diameter from the vertex of the dish.
The diameter of the dish is given as 6 feet, so the radius (half of the diameter) is 3 feet. The depth of the dish is given as 2 feet.
The equation of the paraboloid in standard form is:
[tex]z = (x^2 + y^2) / (4f)[/tex]
where z is the depth of the dish (2 feet), x and y are the coordinates of any point on the paraboloid, and f is the focal length.
At the vertex of the paraboloid (where x = y = 0), the depth of the dish is 0. So, we can use this information to find the focal length f:
[tex]2 = (0^2 + 0^2) / (4f)[/tex]
f = 1/4
The focal length is 1/4 feet, or 3 inches.
The distance from the vertex of the dish to the receiver is equal to the distance from the focal point to the vertex, which is:
d = 1/4 × 3 = 3/4 feet
So the receiver should be placed 3/4 feet away from the vertex of the dish.
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A university survey 350 undergraduate students to determine their plans after graduation. Among the surveyed students, 211 said that they planned to attend graduate school, while 139 said that they planned to get a job., what is the probability that a randomly selected surveyed student plans to go to graduate school
The probability that a randomly selected surveyed student plans to go to graduate school is 211/350 or approximately 0.603, which can also be expressed as a percentage of 60.3%.
A university surveyed 350 undergraduate students to determine their plans after graduation. Among the surveyed students, 211 planned to attend graduate school, while 139 planned to get a job. To find the probability that a randomly selected surveyed student plans to go to graduate school, divide the number of students planning to attend graduate school (211) by the total number of surveyed students (350). Probability = (Number of students planning to attend graduate school) / (Total number of surveyed students) = 211 / 350 ≈ 0.6029
Therefore, the probability that a randomly selected surveyed student plans to go to graduate school is approximately 0.6029 or 60.29%.
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Evaluate the indefinite integral: + C. 6 – 7x4 22 dx =
Given the function: ∫(6 - 7x^4 + 22) dx
To find the indefinite integral, we apply the power rule for integration, which states that ∫x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1. We integrate each term separately and then add the constants of integration.
For the first term, 6, we have:
∫6 dx = 6x + C₁
For the second term, -7x^4, we have:
∫(-7x^4) dx = (-7/5)x^5 + C₂
For the third term, 22, we have:
∫22 dx = 22x + C₃
Now, we combine these three integrals:
∫(6 - 7x^4 + 22) dx = (6x + C₁) + ((-7/5)x^5 + C₂) + (22x + C₃)
Simplifying the expression, we get:
∫(6 - 7x^4 + 22) dx = (-7/5)x^5 + 28x + C
Here, C is the combined constant of integration (C = C₁ + C₂ + C₃). This is the indefinite integral of the given function, and it represents a family of antiderivative functions that differ by a constant value.
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Please Help!!!
Mrs. Nogaki is 5.75 feet tall and her shadow is 8 feet long. She finds that the skyscrapers shadow is about 1183 feet long. How tall is the skyscraper?
The height of the skyscraper is 853.03 feet.
We can use proportions to solve the problem. Let x be the height of the skyscraper in feet. Then we can set up the proportion:
height of Mrs. Nogaki / length of her shadow = height of skyscraper / length of its shadow
or
5.75 / 8 = x / 1183
To solve for x, we can cross-multiply:
5.75 × 1183 = 8 × x
6824.25 = 8x
Dividing both sides by 8, we get:
x = 853.03125
Therefore, the height of the skyscraper is approximately 853.03 feet after rounding it to nearest hundredth.
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Suppose that you roll a dice. For each roll, you are paid the face value. If a roll gives 4, 5 or 6, you can roll the dice again. Once you get I, 2 or 3, the game stops. What is the expected payoff of this game
The expected payoff of this game is $1.97
To find the expected payoff of this game, we need to calculate the probability of each outcome and multiply it by the corresponding payoff.
There are six possible outcomes for the first roll, each with a probability of 1/6. If we roll a 1, 2 or 3 on the first roll, the game stops and the payoff is the face value of the roll. So the expected payoff for these outcomes is:
(1/6) x 1 + (1/6) x 2 + (1/6) x 3 = 1
If we roll a 4, 5 or 6 on the first roll, we get to roll again. There are also six possible outcomes for the second roll, each with a probability of 1/6. If we roll a 1, 2 or 3 on the second roll, the game stops and the payoff is the sum of the face values of both rolls. So the expected payoff for these outcomes is:
(1/6) x (1+4) + (1/6) x (2+5) + (1/6) x (3+6) = 5
If we roll another 4, 5 or 6 on the second roll, we get to roll again. But the probability of this happening is (3/6) x (1/6) = 1/12. So we can ignore this possibility for now.
Now we can calculate the overall expected payoff by multiplying the probability of each outcome by the corresponding payoff and adding them up:
(1/6) x 1 + (1/6) x 2 + (1/6) x 3 + (1/6) x 5 + (1/12) x (5+1+4) = 1.97
So the expected payoff of this game is $1.97. However, it's important to note that this is just an average value and doesn't guarantee that you will actually win this amount in any given game. It's also important to consider the risk involved in playing this game, as the possibility of rolling multiple times and losing could result in a significant loss.
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4 sevenths of people in a room are seating in seven tenths of the chairs the rest of the people are standing. if there are 8 empty chairs, how many people are in the room
We know that the total number of people in the room is a whole number, so we can round up to 33 people.
Let's start by using variables to represent the unknowns in the problem.
Let's say the total number of people in the room is "x" and the total number of chairs in the room is "y".
According to the problem, 4/7 of the people in the room are seated, which means that 3/7 of the people are standing. We also know that 7/10 of the chairs are occupied, which means that 3/10 of the chairs are empty.
We can set up two equations based on the information given:
(4/7)x = 7/10y (equation 1)
3/10y = 8 (equation 2)
We can solve for "y" in equation 2:
3/10y = 8
y = (8 x 10) / 3
y = 26.67
We know that the total number of chairs in the room is a whole number, so we can round up to 27 chairs.
Now we can use equation 1 to solve for "x":
(4/7)x = 7/10(27)
(4/7)x = 18.9
x = (18.9 x 7) / 4
x = 32.925
We know that the total number of people in the room is a whole number, so we can round up to 33 people.
Therefore, there are 33 people in the room.
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What is the surface area of the pyramid
Answer:
147.2
Step-by-step explanation:
square area = 6*7=42
2 triangles w height of 8 = 2* 1/2 *8*7 =56
2 triangles w height of 8.2 = 2* 1/2 *8.2*6 =49.2
sum of all 3 = 147.2
it is given that M[4 2]= [1 0]
5 3 0 1
where M is a 2×2 matrik. Find M
The matrix M is:
M = [ 1/2 -1/2 ]
[ 0 0 ]
How to solveLet M = [a b]
[c d]
The matrix equation becomes:
[ a b ] [4 2] = [1 0]
[ c d ] [5 3] [0 1]
Which yields the linear system:
4a + 2b = 1
5c + 3d = 0
4c + 2d = 0
5a + 3b = 1
Now the matrix M is:
M = [a b]
[0 0]
Using the first and fourth equations:
4a + 2b = 1
5a + 3b = 1
Solving this system, we find a = 1/2 and b = -1/2.
So, the matrix M is:
M = [ 1/2 -1/2 ]
[ 0 0 ]
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The region in the first quadrant enclosed by the curves y = 0, x = 2, x = 5and is rotated about the x-axis.The volume of the solid generated is:
The volume of the solid generated is [tex]\frac{117}{3} π[/tex]
To find the volume of the solid generated by rotating the region in the first quadrant enclosed by the curves y = 0, x = 2, x = 5 about the x-axis, we need to use the disk method.
The radius of each disk is given by the distance from the x-axis to the curve y = f(x), which in this case is just the value of x itself since the curves y = 0 and x = 2 bound the region.
So, we can set up the integral as follows:
[tex]V = \int\limits {x} \, [a,b] πr^2 dx[/tex]
V = ∫[2,5] πx^2 dx
[tex]V = \int\limits {x} \, [2,4] πx^2 dx[/tex]
[tex]V= π(\frac{125}{3} ) - π (\frac{8}{3} )[/tex]
[tex]V=\frac{117}{3} π[/tex]
Therefore, the volume of the solid generated is [tex]\frac{117}{3} π[/tex] cubic units.
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A survey showed that 14 out of 20 employees at a company preferred to invest money into a retirement fund. If there are 950 employees at this company, how many could be expected to invest money into a retirement fund?
Expect 665 out of the 950 employees to invest money into a retirement fund.
If 14 out of 20 employees prefer to invest in a retirement fund, then the fraction of employees who prefer to invest in a retirement fund is:
14/20
To find the expected number of employees who prefer to invest in a retirement fund out of a total of 950 employees, we can set up a proportion:
14/20 = x/950
where x is the expected number of employees who prefer to invest in a retirement fund.
We can solve for x by cross-multiplying:
14 x 950 = 20( x)
13300 = 20x
x = 665
Therefore, we can expect 665 out of the 950 employees to invest money into a retirement fund.
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What is the surface area of the cylinder in square inches? Use the formula SA = 2B + Ph and 3.14 to approximate
π
. Round your answer to the nearest hundredth.
root a+b=7 and root b +a - 11 If a and b are real numbers that satisfy the equation above, what is the value of a and b respectively?
a = 4 and b = 5 are the answers to the system of equations.
Let's square both sides of the first equation to eliminate the square root:
√a + b = 7
(√a + b)² = 7²
a + 2√ab + b² = 49
a + b² = 49 - 2√ab ---(1)
Now, let's square both sides of the second equation:
√b + a = 11
(√b + a)² = 11²
b + 2√ab + a² = 121
a² + b + 2√ab = 121 ---(2)
We can use equation (1) to substitute for √ab in equation (2):
a + b² = 49 - 2√ab
√ab = (49 - a - b²)/2
Substituting for √ab in equation (2), we get:
a² + b + 2(49 - a - b²)/2 = 121
Simplifying and rearranging, we get:
a² - a + b² - b - 36 = 0
(a - 1/2)² + (b - 1/2)² = 37.25
This is the equation of a circle centered at (1/2, 1/2) with a radius √37.25. We need to find the points where this circle intersects the line defined by equation (1).
Substituting b = 49 - a - 2√(a(49 - a))/2 into equation (1), we get:
a + (49 - a - 2√(a(49 - a)))² = 49 - 2√a(49 - a)
Simplifying and rearranging, we get:
4a³ - 294a² + 2421a - 5929 = 0
Using a numerical solver or the rational root theorem, we can find that one solution of this cubic equation is a = 4.
Substituting this value back into equation (1), we can solve for b:
4 + b² = 49 - 2√(4b)
b² + 2√(4b) - 45 = 0
Using the quadratic formula, we get:
b = 5
Therefore, the solutions of the system of equations are a = 4 and b = 5.
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Complete question:
√a+b=7 and √b +a = 11 If a and b are real numbers that satisfy the equation above, what is the value of a and b respectively?
An investigator examined the effects of practice on problem-solving performance. Study participants were randomly assigned to two conditions. Seventy-five participants tried to solve 30 problems after having a 10 minute practice session on a similar set of problems. A different seventy-five tried to solved the same 30 problems, but with no practice sessions. The average number of correct solutions was compared for people in the practice condition and those in the no-practice condition. What is the most appropriate statistical test to apply in this situation
The most appropriate statistical test to apply in this situation is an independent samples t-test. This test is used to compare the means of two independent groups on a continuous dependent variable, which in this case is the average number of correct solutions.
The study participants were randomly assigned to two different conditions, and the goal is to compare the means of the two groups (those who had a practice session and those who did not) on the dependent variable of problem-solving performance (measured by the average number of correct solutions).
The t-test would allow the researcher to determine if there is a significant difference between the means of the two groups, taking into account the variability within each group. Specifically, the researcher would calculate a t-value based on the difference between the means of the two groups and the standard error of the difference. This t-value would be compared to a critical value based on the degrees of freedom (which in this case would be 148, calculated as 75 + 75 - 2). If the calculated t-value exceeds the critical value, the researcher can conclude that there is a significant difference between the means of the two groups. A p-value can also be calculated to determine the probability of obtaining such a result by chance.Know more about the statistical test
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Let $f$ be a linear function with the properties that $f(1) \le f(2)$, $f(3) \ge f(4)$, and $f(5) = 5$. Which of the following statements is true? A) $f(0) < 0$ B) $f(0) = 0$ C) $f(1) < f(0) < f(-1)$ D) $f(0) = 5$ E) $f(0) > 5$
f(0) = 5, and the correct answer is [tex]\boxed{\text{(D)}}.[/tex]
Since f is a linear function, we can express it in the form f(x) = ax + b for some constants a and b .
We want to use the given information to determine a and b, and then answer the question about f(0).
The condition f(1) ≤ f(2) tells us that a + b ≤ 2a + b, or equivalently, a ≥0.
The condition f(3) ≥ f(4) tells us that 3a + b ≥ 4a + b, or equivalently, a ≤ 0.
Thus, we must have a=0, which means that f(x) = b is a constant function.
Since f(5) = 5, we have b=5, so f(x) = 5 for all x.
Therefore, f(0) = 5, and the correct answer is [tex]\boxed{\text{(D)}}.[/tex]
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PLS HELP!!!
What is the radical form of each of the given expressions?
Drag the answer into the box to match each expression.
Answer:
[tex] {5}^{ \frac{2}{3} } = \sqrt[3]{ {5}^{2} } [/tex]
[tex] {5}^{ \frac{1}{2} } = \sqrt{5} [/tex]
[tex] {3}^{ \frac{2}{5} } = \sqrt[5]{ {3}^{2} } [/tex]
[tex] {3}^{ \frac{5}{2} } = \sqrt{ {3}^{5} } [/tex]
rue or false: When using a least squares regression line, we should not predict a value of y unless the given value of x is in the experimental region
It is false that when using a least squares regression line, we should not predict a value of y unless the given value of x is in the experimental region
Determining the true statementA least square regression line equation is represented as
y = mx + c
From the question, we have the statement:
When using a least squares regression line, we should not predict a value of y unless the given value of x is in the experimental region
The above statement is false
This is because whether the x values is in the experimental region or not, the y value can be predicted
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Find the volume of a cone with a base diameter of 6 in and a height of 11 in
The volume of the cone is V = 103.62 inches³
Given data ,
Let the volume of the cone be V
Let the height of the cone be h = 11 inches
Let the base of the cone be = 6 inches
So , radius r = 3 inches
Now , Volume of Cone = ( 1/3 )πr²h
V = ( 1/3 ) x 3.14 x ( 3 )² x ( 11 )
V = 103.62 inches³
Hence , the volume is 103.62 inches³
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What type of ANOVA is used when there are two independent variables each with more than two levels, and with different participants taking part in each condition
The type of ANOVA used when there are two independent variables each with more than two levels, and with different participants taking part in each condition is called a Two-Way Between-Subjects ANOVA.
This type of ANOVA examines the effects of two independent variables on a dependent variable. The two independent variables are referred to as factors, and each factor has multiple levels or conditions. The between-subjects design means that each participant only takes part in one condition of each factor.
This type of ANOVA allows researchers to determine if there are significant main effects and interactions between the two independent variables on the dependent variable.
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The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 66%. What is the probability that it will rain on exactly one of the five days they are there
Thus, the probability that it will rain on exactly one of the five days during the Hiking Club's camping trip in the State park is approximately 4.38%.
We can use the binomial probability formula to calculate the probability of rain on exactly one of the five days during the Hiking Club's camping trip in the State park. The formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where:
- P(X = k) is the probability of k successes (rain) in n trials (days)
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success (rain) on any given day (66% or 0.66)
- n is the number of trials (5 days)
- k is the number of successes (1 day with rain)
Plugging the values into the formula, we get:
P(X = 1) = C(5, 1) * 0.66^1 * (1 - 0.66)^(5 - 1)
First, we find the number of combinations C(5, 1) which is 5.
Next, we calculate the probabilities:
0.66^1 = 0.66
(1 - 0.66)^4 = 0.34^4 = 0.0133
Now, we multiply everything together:
P(X = 1) = 5 * 0.66 * 0.0133 ≈ 0.0438
So, the probability that it will rain on exactly one of the five days during the Hiking Club's camping trip in the State park is approximately 4.38%.
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The legal description of a parcel in a subdivision that has been recorded with lot and block numbers on a plat of survey is
The legal description of a parcel in a subdivision that has been recorded with lot and block numbers on a plat of survey is the written description of the boundaries and location of the property, including the lot and block numbers as identified on the plat of survey. This legal description is used to define and identify the property for legal purposes such as real estate transactions, property taxes, and land use regulations.
The legal description of a parcel in a subdivision that has been recorded with lot and block numbers on a plat of survey is known as a "Lot and Block" description. This description typically includes the subdivision name, the specific lot number, and the block number within that subdivision. This information is used to accurately identify and locate the property within the larger plat of survey, ensuring proper documentation and reference for legal and real estate purposes.
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You have reached the right row of shelves to find a book with the call number GT2853 A515 A48 2012. Which specific shelf would contain your book
Based on the call number GT2853 A515 A48 2012, your book would be located on the shelf that is labeled with the letters "GT" which typically corresponds to the subject area of anthropology.
Within the GT section, you would then look for the number range of 2853, followed by the letters A515, which further narrow down the subject matter of your book. Finally, the letters A48 indicate the author's last name, and the publication year of 2012 helps to differentiate any other books with similar call numbers. So, the specific shelf that would contain your book would be the one labeled with "GT 2853 A515."
To locate the book with the call number GT2853 A515 A48 2012, follow these steps:
1. Look for the shelves labeled with "GT" (the alphabetical portion of the call number).
2. Within the "GT" section, search for the numeric range that includes "2853" (the first number in the call number).
3. Once you've found the 2853 section, look for the "A515" subsection (the second part of the call number, usually in alphabetical and numerical order).
4. Lastly, locate the specific shelf containing "A48 2012" (the third part of the call number). This will lead you to the book you are looking for.
By following these steps, you will find the specific shelf that contains your book with the call number GT2853 A515 A48 2012.
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Given a sample mean is 82, the sample size is 100, 90% confidence level and the population standard deviation is 20. Calculate the margin of error to 2 decimals.
Given a sample mean is 82, the sample size is 100, 90% confidence level and the population standard deviation is 20, the margin of error is 3.29.
To calculate the margin of error, we need to use the formula:
Margin of error = Z-score * (population standard deviation / square root of sample size)
Where the Z-score corresponds to the confidence level. Since we have a 90% confidence level, the Z-score is 1.645.
Plugging in the given values, we get:
Margin of error = 1.645 * (20 / sqrt(100))
Margin of error = 1.645 * 2
Margin of error = 3.29 (rounded to 2 decimals)
Therefore, the margin of error is 3.29.
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if the student decides to attend a college that is not expensive and within 200 miles from home during his first two years of college, and then will transfer to a college that is not expensive but is far from home, how many selections of two colleges are possible?
The number of possible selections depends on the student's preferences and budget, so it is not possible to give an exact answer.
There are an infinite number of possible combinations of two colleges that the student could attend for his first two years of college.
The student could attend any college that is not expensive and within 200 miles from home for his first two years, and then transfer to any college that is not expensive but is far from home for his third and fourth years.
Since there is no limit on the number of colleges that could be chosen for the first two years, and no limit on the number of colleges that could be chosen for the third and fourth years, the number of possible combinations of two colleges is infinite.
Therefore, the number of possible selections depends on the student's preferences and budget, so it is not possible to give an exact answer.
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Click on the region of the graph
that contains the solution set of
the system of linear inequalities.
y≤ - 1/3x
y ≥ 2x
The system of linear inequalities is y ≤ -1/3x and y ≥ 2x. To graph this system, we start by graphing the boundary lines, which are y = -1/3x and y = 2x.
The line y = -1/3x has a negative slope, and it passes through the origin (0,0). We can plot this point and another point on the line to draw the line. For example, if x = 3, then y = -1.
The line y = 2x has a positive slope, and it passes through the origin (0,0). We can plot this point and another point on the line to draw the line. For example, if x = 3, then y = 6.
Now, we need to shade the region that satisfies both inequalities. Since y ≤ -1/3x is a downward-sloping line and y ≥ 2x is an upward-sloping line, the region that satisfies both inequalities is the triangular region below the line y = -1/3x and above the line y = 2x.
We shade this region in the graph by clicking on the area bounded by these two lines and below the x-axis. This represents the solution set of the system of linear inequalities.
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H. Cochran, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2,350,000. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $2,590,000 in annual sales, with costs of $1,610,000. Assume the tax rate is 21 percent and the required return on the project is 11 percent. What is the project’s NPV?
The NPV of the project is $331,085.70. Since the NPV is positive, the project should be undertaken as it creates value for the company.
To calculate the NPV of the project, we need to estimate the cash flows generated by the project and discount them back to their present value using the required return of 11 percent.
The annual cash inflows generated by the project are the annual sales of $2,590,000 minus the annual costs of $1,610,000, which equals $980,000. We can calculate the annual depreciation expense as the initial fixed asset investment of $2,350,000 divided by the three-year tax life, which equals $783,333 per year.
Using the straight-line depreciation method, the fixed asset will have a book value of $1,566,667 (i.e., $2,350,000 - $783,333) at the end of year 3, which is equal to its estimated salvage value. Therefore, the after-tax salvage value is:
($1,566,667 - $0) x (1 - 0.21) = $1,235,000
Now we can calculate the annual after-tax cash flows:
Year 1: $980,000 - $301,667 = $678,333
Year 2: $980,000 - $301,667 = $678,333
Year 3: $980,000 - $301,667 + $1,235,000 = $1,913,333
where $301,667 is the annual depreciation expense.
To calculate the NPV, we need to discount these cash flows back to their present value at the required return of 11 percent. Using a financial calculator or spreadsheet software, we find that the NPV of the project is:
NPV = -$2,350,000 + $678,333/(1+0.11)^1 + $678,333/(1+0.11)^2 + $1,913,333/(1+0.11)^3 = $331,085.70
Therefore, the NPV of the project is $331,085.70. Since the NPV is positive, the project should be undertaken as it creates value for the company.
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Maria, Justin, and Chris have a total of $135 in their wallets. Maria has $10 more than Chris. Justin has 3 times what Chris has. How much does each have
Answer:
Chris = $25
Maria = $35
Justin = $75
Step-by-step explanation:
Chris's amount is x.
x + 3x + (x + 10) = 135
x = 25
Substitute 25 for x.
25 + 3(25) + (25 + 10) = 135
135 = 135
True