The dimensions of the strongest beam are 27 inches x 13.5 inches.
What is a dimension?In general, dimension refers to a measurable extent of a physical quantity, such as length, width, height, depth, or time. These dimensions provide a framework for describing and measuring objects and events in the physical world. In geometry, dimension are refers to the number of coordinates needed to specify a point in a space. In physics, the concept of dimension is used to describe the properties of space and time.
We know that the strength of the beam is directly proportional to its width multiplied with the square of its height. Let's call the width of the beam "w" and the height "h". Then we can write the strength of the beam as:
S = kwh², where "k" is the constant of proportionality.
We want to find the dimensions of the strongest beam, which means we want to find the values of "w" and "h" that will maximize the strength "S". To do this, we need to find the maximum value of the function S = kwh² subject to the constraint that the diameter of the log is 18 inches.
The diameter of the log is equal to the width of the beam plus twice the height of the beam:
d = w + 2h
Since the diameter of the log is 18 inches, we can write:
w + 2h = 18
or
w = 18 - 2h
Substituting this expression for "w" into the equation for the strength of the beam, we get:
S = k × w(18-2h) × h²
Expanding and simplifying this expression, we get:
S = 36kh³ - 2kh⁴
To find the maximum value of S, we take the derivative of S with respect to h and set it equal to zero:
dS/dh = 108kh² - 8kh³ = 0
Simplifying this expression, we get:
h²(108 - 8h) = 0
This equation has two solutions: h = 0 and h = 13.5.
Since a beam with height equal to zero would have zero strength, we reject the solution h = 0. Therefore, the maximum strength is achieved when h = 13.5 inches.
To find the corresponding width, we can use the equation we derived earlier:
w = 18 - 2h = 18 - 27 = -9
Since the width of the beam cannot be negative, we reject this solution as well.
Therefore, the required dimensions of the strongest beam are:
Width = 2h = 2(13.5) = 27 inches
Height = h = 13.5 inches
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The piecewise function g(x) is shown in the graph.
Graph with three pieces. The first piece is a horizontal line from the left with an open right endpoint at negative 2 comma negative 1. The second piece is curved with a solid point at negative 1 comma 0, which ends at 1 comma 1. The last piece starts with a solid circle at 0 comma 1 and increases to the right as it passes through 4 comma 5.
Which of the following represents g(x)?
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than or equal to x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than or equal to x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
The description that correctly represents g(x) is g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0 (third option).
What represents g (x)?Looking at the graph, we can see that:
g(x) is equal to -2 for x ≤ -1.g(x) is a quadratic function that passes through the point (-1,0) and (1,1), with a vertex at (0,1), for -1 < x ≤ 0.g(x) is a linear function that passes through the point (0,1) and (4,5), for x > 0.Thus, the correct piecewise function that represents g(x) is:
g(x) = {-2 if x ≤ -1
{ (x-1)^2 if -1 < x ≤ 0
{ -x+1 if x > 0
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You are trying to determine if a router you’re thinking of purchasing will give off a strong enough wifi signal to cover the area in your house. The router you have selected will cover an area of 850 ft^2.
The wi-fi router shall not be strong enough to cover the area of the house.
How to determine whether a wi-fi router can cover a given area
According to the statement, we must determine if a wi-fi router can cover all the area of a house, described by a rectangle. The area formula of rectangle is introduced below:
A = b · h
Where:
A - Area, in square feet.b - Base, in feet.h - Height, in feet.Now we proceed to determine the area of the house:
A = (50 ft) · (50 ft)
A = 2500 ft²
The wi-fi router shall not cover the entire area of the house.
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At the school's holiday craft fair, Colette and her classmates get to make gingerbread houses. Their teacher divides a bag of licorice ropes evenly among the 9 students at the table. Each student gets 3 licorice ropes to decorate the roof of his or her gingerbread house.
Answer: So, what are you asking?
Step-by-step explanation:
Find the perimeter and area of each
How to solve this problem?
Answer:
Step-by-step explanation:
Perimeter: 34 yd
Area: 37 yd²
What is the probability of pulling a colored pair of socks from the drawer, if you have 3 pairs of white socks and 5 pairs of colored socks?
Brenda earns $5 each week for chores. x represents the number of weeks brenda did her chores. t represents the total dollars she earned. create an equation representing this situation
The situation is modeled by the linear equation:
t = $5*x
How to write the equation?We know that Brenda earns $5 each week for chores. The variable x represents the number of weeks brenda did her chores, and t represents the total dollars she earned.
Then if she works for x weeks, the amount that she earns is x times $5, then the equation will be a linear one:
t = $5*x
That is the equation.
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what is the value of sec^-1(1.4)
The calculated value of sec^-1(1.4) is 44.41 degrees
What is the value of sec^-1(1.4)The inverse secant function, denoted as sec^-1(x), returns the angle whose secant is x.
In other words, if secθ = x, then sec^-1(x) = θ.
To find the value of sec^-1(1.4), we need to find the angle whose secant is 1.4.
However, we know that the range of the secant function is [-∞, -1] ∪ [1, ∞], which means that sec^-1(x) is only defined for values of x that fall within this range.
Uisng a graphint tool, we have
sec^-1(1.4) = 44.41
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how do you do this equation?
hi
First, dont keep the equation this way.
f(x) = 2 (x+2) +4x
f(x) = 2x+4+4x
f (x) = 6x+4
after :
x= 0 f(x) = 4
x= 2 f(x)= 16
x= 10 f(x) = 64
x = 30 f(x) = 94
100 points and I will give brainlist but before I get released, I have to verify answers
A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.
The step in which Johnetta made her error include the following: A. step 1.
What is a fraction?In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
Based on the information provided above, the division can be calculated as follows;
Fraction = (-5/8) ÷ (-3/4)
Fraction = -5/8 × (-4/3)
Fraction = -20/24
For Johnetta, we have:
Fraction = 7/9 ÷ 3/8
Fraction = 7/9 × 8/3
Fraction = 56/27
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The equity sections for Atticus Group at the beginning of the year (January 1) and end of the year (December 31) follow.
2. The total dollar amount for each cash dividend is $23,700.
Outstanding common shares, dividend and capitalization1. Calculation of outstanding common shares on each cash dividend date:
January 5: No change in outstanding shares since the date of record is January 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400 (47,400 issued - 3,000 treasury shares = 44,400 outstanding).April 5: No change in outstanding shares since the date of record is April 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400.July 5: No change in outstanding shares since the date of record is July 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400.October 5: No change in outstanding shares since the date of record is October 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400.2.
Calculation of total dollar amount for each cash dividend:
January 5: $0.50 per share x 47,400 outstanding shares = $23,700April 5: $0.50 per share x 47,400 outstanding shares = $23,700July 5: $0.50 per share x 47,400 outstanding shares = $23,700October 5: $0.50 per share x 47,400 outstanding shares = $23,700Therefore, the total dollar amount for each cash dividend is $23,700.
3.
Calculation of the capitalization of retained earnings for the stock dividend:
Market value per share on July 31: $12Number of outstanding shares before stock dividend: 47,400Number of shares to be issued for the stock dividend: 20% x 47,400 = 9,480Total value of shares to be issued for the stock dividend: 9,480 shares x $12 per share = $113,760The capitalization of retained earnings for the stock dividend is equal to the total value of shares issued, which is $113,760.Learn more on dividends here https://brainly.com/question/2960815
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The equity sections from Atticus Group’s 2016 and 2017 year-end balance sheets follow Stockholders’ Equity (December 31, 2016)
Common stock—$4 par value, 100,000 shares
authorized, 40,000 shares issued and outstanding . .. . . . . . . . . . $160,000
Paid-in capital in excess of par value, common stock .. . . . . . . . . . . . . . . . 120,000
Retained earnings .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320,000
Total stockholders’ equity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $600,000
Stockholders’ Equity (December 31, 2017)
Common stock—$4 par value, 100,000 shares
authorized, 47,400 shares issued, 3,000 shares in treasury . .. . . . . . . $189,600
Paid-in capital in excess of par value, common stock . . . . . .. . . . . . . . . . . . 179,200
Retained earnings ($30,000 restricted by treasury stock) .. . . . . . . . . . . . . 400,000
768,800
Less cost of treasury stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (30,000)
Total stockholders’ equity . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . $738,800
The following transactions and events affected its equity during year 2017.
Jan. 5 Declared a $0.50 per share cash dividend, date of record January 10.
Mar. 20 Purchased treasury stock for cash.
Apr. 5 Declared a $0.50 per share cash dividend, date of record April 10.
July 5 Declared a $0.50 per share cash dividend, date of record July 10.
July 31 Declared a 20% stock dividend when the stock’s market value was $12 per share.
Aug. 14 Issued the stock dividend that was declared on July 31.
Oct. 5 Declared a $0.50 per share cash dividend, date of record October 10.
Required
1. How many common shares are outstanding on each cash dividend date?
2. What is the total dollar amount for each of the four cash dividends?
3. What is the amount of the capitalization of retained earnings for the stock dividend?
Vanessa invests $20,000 in an account at 9.1% interest compounded continuously. Find the total value of the investment after 19 years.
Answer:
Step-by-step explanation:
17.5
Jilby Share if you could find it :) If 3+1=34 2+2=44 2+3=65 5+3=158 then 7+2=?
Find the surface area
Round to the nearest tenth
The surface area of the triangular prism is 672 square millimeters.
what is surface area ?
Surface area is a metric used to determine how much overall space an object occupies. the total volume of the area of surface of a three-dimensional shape. The term "surface area" refers to a three-dimensional shape's entire surface area.
The triangular base has a height of 7 mm and a base of 24 mm, so its area is:
[tex]1/2 * base * height = 1/2 * 24 \ mm * 7\ mm = 84 \ mm^2[/tex]
There are two identical triangular faces, so their combined area is:
[tex]2 * 84 \ mm^2 = 168\ mm^2[/tex]
The three rectangular faces are all the same size, with a length of 24 mm and a height of 7 mm, so the area of each is:
[tex]length * height = 24 \ mm * 7 \ mm = 168 \ mm^2[/tex]
There are three rectangular faces, so their combined area is:
[tex]3 * 168\ mm^2 = 504\ mm^2[/tex]
To find the total surface area, we add the area of the two triangular faces to the area of the three rectangular faces:
[tex]168 \ mm^2 + 504 \ mm^2 = 672 \ mm^2[/tex]
Therefore, the surface area of the triangular prism is 672 square millimeters.
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Jacob took out a loan from a bank today (now). The original agreement stated that to pay off the loan he had to make two equal payments: The first payment of $3000 was due 6 months from now, and the second payment of $3000 was due 12 months from now.
Suppose he renegotiated with the bank so that instead of the original agreement he will make a single payment 24 months from now to pay off the two original obligations.
What single payment 24 months from now will he have to make if the simple interest rate is 10%? The agreed focal date is 24 months from now.
The single payment Jacob would make in 24 months from now, to pay off the two obligations under the new agreement is $7,620.
We shall be solving this using the formula for Simple Interest,
What is the formula for Simple Interest?The interest accrued on each payment can be calculated using the formula for Simple Interest:
Interest = Principal × Rate × Time
where:
Principal = amount borrowed,
Rate = simple interest rate,
Time = time period in years.
Under the original agreement, Jacob shall make two payments of $3000 each, one 6 months from now and the other 12 months from now.
For payment1, the interest accrued would be:
Interest1 = $3000 × 0.10 × (6/12) = $150
For payment2, the interest accrued would be:
Interest2 = $3000 × 0.10 × (12/12) = $300
So the total amount Jacob was to pay under the original agreement is:
Total1 = $3000 + $150 + $3000 + $300 = $6,450
Now let's calculate the amount Jacob would have to pay under the new agreement.
Original principal for each payment is $3000.
The interest accrued on the sum of both payments can be calculated using the same formula for simple interest:
Interest3 = ($3000 + $150 + $3000 + $300) × 0.10 × (24/12) = $720
So the total amount Jacob would pay under the new agreement is:
Total2 = $3000 + $150 + $3000 + $300 + $720 = $7,620
So, Jacob would make a single payment of $7,620, 24 months from now,
to pay off both loans under the new agreement.
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Substitute the supplied value and simplify both sides of the equation, if necessary. Then decide if the supplied value is or is not a solution.
–2p – 17 = 3(p – 5) {–2}
Starting with the original equation:
-2p - 17 = 3(p - 5)
Distributing the 3 on the right side:
-2p - 17 = 3p - 15
Subtracting 3p from both sides:
-5p - 17 = -15
Adding 17 to both sides:
-5p = 2
Dividing by -5:
p = -2/5
Now, we can substitute this value of p back into the original equation and check if it is a solution:
-2(-2/5) - 17 = 3((-2/5) - 5)
4/5 - 17 = 3(-27/5)
-136/5 = -81/5
The left side does not equal the right side, so the supplied value of p = -2/5 is NOT a solution to the equation.
Hope this helps :)
suppose that a and b are positive for which log9(a) = log15(b) = log25(a + 2b). What is the value of b over a
Thus, the value of b over a for the given logarithmic function is obtained as: b/a = 1 + √2.
Explain about the logarithmic function:The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent with which b must be raised in order to obtain a number x is the logarithm of x to the base b.
A base must still be raised to a certain exponent or power, or logarithm, in order to produce a specific number. If bˣ = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.
Given that:
log9(a) = log15(b) = log25(a + 2b)
Let , log9(a) = log15(b) = log25(a + 2b) = x
Then,
log9(a) = x (taking antilog)
log3²(a) = x
a = 3²ˣ
log15(b) = x (taking antilog)
log(3*5)(b) = x
b = 3ˣ.5ˣ
log25(a + 2b) = x (taking antilog)
log5²(a + 2b) = x
a + 2b = 5²ˣ
Now,
b²/a = a + 2b
(b/a)² = 1 + 2*(b/a)
If t = b/a, then t² - 2t -1 = 0
On factorization:
t = 1 ± √2 ( a and b are positive integer)
b/a = 1 + √2
Thus, the value of b over a for the given logarithmic function is obtained as: b/a = 1 + √2.
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What is the linear equation for your line of best fit? What does the slope of this line mean? What does the y-intercept of this line mean? (It's scattered plot points)
Answer:
need better photos
Step-by-step explanation:
Answer: Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
Step-by-step explanation:
Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
Find the size of angle p. Give your answer
in degrees (°).
137⁰
60°
60°
112°
р
134
Not drawn accurately
PLEASE HELPPP
Answer:
76°
Step-by-step explanation:
The sum of the interior angles of any quadrilateral is 360°.
p = 360 - 60 - 134 - 90 = 76
Whitney bought a fountain online. It cost $60 plus 10% shipping and handling. What was the total cost?
Answer:
66 because 10 percent of 60 is 6 so add 60 and 6
Uncle Fred gives his nephew, Jack, and niece, Jill, £60 between them every year
at Christmas. He splits it between them in the ratio of their ages.
(a) The first time he does this Jack is 1 and Jill is 3. How much does Jill
receive?
(b) How much does Jack receive the following Christmas?
(c) How old will Jack be when he receives £25 from Uncle Fred at Christmas?
a) Jill receives £45
b) Jack receives £20 the following Christmas
c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.
Explain the term years
Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.
According to the given information
(a) Let's first find the total ratio of their ages:
1 + 3 = 4
So Jack's share will be:
1/4 x £60 = £15
And Jill's share will be:
3/4 x £60 = £45
Therefore, Jill receives £45.
(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:
2/6 x £60 = £20
So Jack receives £20.
(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:
1/4 x £60 = £25
Multiplying both sides by 4/60, we get:
x = 5/4
So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.
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A sum of money has a value of$3000 eight-
een months from now. If money is worth 6%
compounded monthly, what is its equivalent value
(a) now?
(b) one year from now?
(c) three years from now?
Answer:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where A is the future value, P is the present value, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.
(a) To find the present value of the money, we need to solve for P in the formula above. We are given that A = $3000 and t = 18/12 = 1.5 years. The interest rate is 6% per year, compounded monthly, which means n = 12. Substituting these values into the formula, we get:
3000 = P(1 + 0.06/12)^(12*1.5)
Simplifying and solving for P, we get:
P = 3000 / (1 + 0.06/12)^(12*1.5)
P = $2,572.39
Therefore, the equivalent value of the money now is $2,572.39.
(b) To find the equivalent value of the money one year from now, we need to calculate the future value of $1 after one year, and then multiply it by the present value we found in part (a). The future value of $1 after one year, at 6% per year, compounded monthly, is:
FV = 1*(1 + 0.06/12)^(12*1)
FV = $1.06168
Multiplying this by the present value we found in part (a), we get:
$2,572.39 * $1.06168 = $2,735.92
Therefore, the equivalent value of the money one year from now is $2,735.92.
(c) To find the equivalent value of the money three years from now, we need to calculate the future value of $1 after three years, and then multiply it by the present value we found in part (a). The future value of $1 after three years, at 6% per year, compounded monthly, is:
FV = 1*(1 + 0.06/12)^(12*3)
FV = $1.19102
Multiplying this by the present value we found in part (a), we get:
$2,572.39 * $1.19102 = $3,066.63
Therefore, the equivalent value of the money three years from now is $3,066.63.
if a sample of 32 runners is taken from a population of 201 what is the mean
If a sample of 32 runners is taken from a population of 201, the mean is equal to 201.
What is a population?In Statistics and science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.
What is a sample?In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.
In this context, we can reasonably infer and logically deduce that the mean (μ) could be equal to 201 runners because it represent the average.
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Which of the following criteria is required to ensure
communication competence?
A. The message achieves the intended effect
B. The message is grammatically correct
C. the message is free from too much emotion
D. the message is well received
Subject: Professional Communication
the criteria is required to ensure communication competence is The message achieves the intended effect. Option A
What is communication competence?Communicative competence is simply described as the ability to achieve communicative goals in an appropriate and socially way.
It is well organized and goal-oriented, this means that it involves the ability to evenly select and apply skills that are appropriate and are also effective in a given context.
The different components of communication competence are;
Grammatical competencesociolinguistic competencediscourse competencestrategic competence.Hence, the message should always be effective for the context.
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17. A babysitter charges a fee for every hour they work. Which statement below could be a
description of the point (1, 8) from this situation?
The point (1, 8) would then represent that the babysitter charges $8 per hour
Which statement could be a description of the point (1, 8)The point (1, 8) in this situation could mean that the babysitter charges $8 for one hour of work.
In general, when working with a fee-per-hour situation, we can use the slope-intercept form of a linear equation, y = mx + b,
Where y represents the total fee, x represents the number of hours worked, m represents the rate (fee per hour), and b represents the initial fee (fee for zero hours worked).If we assume that the initial fee is $0, then the equation for the babysitter's fee would be y = mx, where m is the hourly rate.
The point (1, 8) would then represent that the babysitter charges $8 per hour, since when x = 1 (one hour of work), y = 8 (the fee for one hour).
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Susan Marciano invested part of her $10,000 bonus in a fund that paid a 9% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was $540.
Susan invested $7000 in the fund that paid a 9% profit, and the remaining (10,000 - 7000) = $3000 in the stock that suffered a 3% loss.
How can we find the amount of each investment?Let's assume that Susan invested x dollars in the fund that paid a 9% profit, and the remaining (10,000 - x) dollars in the stock that suffered a 3% loss.
The net profit from the investment in the fund would be 9% of x, or 0.09x dollars.
The net loss from the investment in the stock would be 3% of (10,000 - x), or 0.03(10,000 - x) dollars.
Given that her overall net profit was $540, we can write the equation:
0.09x - 0.03(10,000 - x) = 540
Now let's solve for x:
0.09x - 0.03(10,000 - x) = 540
0.09x - 300 + 0.03x = 540
0.12x = 540 + 300
0.12x = 840
x = 840 / 0.12
x = 7000
So, Susan invested $7000 in the fund that paid a 9% profit, and the remaining (10,000 - 7000) = $3000 in the stock that suffered a 3% loss.
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Draw a coordinate plane
K(10.....) L(......20), and M(30.....) are on that line too
write their missing coordinates
PLEASE HELP! An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1200, determine the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is what?
(Round to three decimal places as needed.) Thanks!
The likelihood that the average tariff rate of 400 shipments of ethanol picked at random will be inside $80 of the average tariff rate of all shipments is roughly 0.789, or 78.9%.
What is probability?The probability that an event will occur or that a proposition is true is quantified by probability theory, a branch of mathematics. A number from zero to one, where 0 approximately indicates how likely the event will happen and 1 generally indicates certainty, is the probability given an occurrence. In mathematics, probability is a measure of how likely an event is to take place. Probability levels can also be expressed as percent between 0 and 100 percent in addition to the numerals 0 to 1. the percentage of all outcomes out of all equally likely alternatives that lead to a specific occurrence, represented as a ratio.
given,
To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means is approximately normal, with mean equal to the population mean and a standard deviation determined by dividing the population's standard deviation by the sample size square root.
We are given that the standard deviation of the population of tariff rates is $1200. Let mu be the population mean tariff rate, and x-bar be the sample mean tariff rate. We want to find the probability that the sample mean is within $80 of the population mean, i.e., |x-bar - mu| <= $80.
Using the formula for the standard error of the mean, we have:
SE = sigma/sqrt(n) = $1200/sqrt(400) = $60
Now, we can standardize the variable z = (x-bar - mu)/SE, and find the probability of |z| <= 80/60 = 4/3 using a standard normal distribution table or calculator.
P(|z| <= 4/3) = 0.7887
Therefore, the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.789 or 78.9% (rounded to three decimal places).
Interpretation: Sampling error refers to the natural variation in sample statistics (such as the sample mean) that occurs due to chance, even when the sample is randomly selected and representative of the population. In this case, the probability of the sample mean tariff rate being within $80 of the population mean is high (78.9%), which suggests that the amount of sampling error in estimating the population mean using a sample of 400 observations is relatively small.
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a table of values for Function A and the graph of B are shown
The equation of the third linear function is:
y = (-1/3)x + (8/3)
How do we calculate?To find a linear function with a rate of change between Function A and Function B, we need to calculate the rates of change for each function.
For Function A, the rate of change is:
(2 - (-4)) / (6 - (-1)) = 6/7
For Function B, we find the rate of change by selecting any two points on the graph, such as (2, 6) and (-4, 7):
(6 - 7) / (2 - (-4)) = -1/6
So the rate of change for Function A is 6/7, and the rate of change for Function B is -1/6.
To find a linear function with a rate of change between these two values, we can select any value between 6/7 and -1/6. Let's choose a rate of change of -1/3.
We can use the point-slope form of a linear equation to write the equation of the line with a rate of change of -1/3 and passing through the point (2, 6):
y - 6 = (-1/3) * (x - 2)
y = (-1/3)x + (8/3)
In conclusion, the equation of the third linear function is:
y = (-1/3)x + (8/3)
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the libarian tracked how many books she checked out on selected days in January and Feburary .She displayed her information in the two dot plots shown. Find the median, mode and range for both dot plots.
The median, mode and range for both dot plots are:
Median = 7.5 and 5Mode = 7 and 8 & 4 and 5Range = 3 and 7Finding the median, mode and range for both dot plots.The median
This is the middle value
From the dot plots, we have the middle values to be
Group A = (7 + 8)/2 = 7.5
Group B = 5
So, we have
Median Group A = 7.5
Median Group B = 5
The mode
This is the number of books with the highest dots
From the dot plots, we have the modal values to be
Mode Group A = 7 and 8
Mode Group B = 4 and 5
The range
This is the difference between the smallest and highest number of books with the highest dots
From the dot plots, we have the range to be
Group A = 9 - 6 = 3
Group B = 10 - 3 = 7
So, we have
Range Group A = 3
Range Group B = 7
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A bike shop has 11 red bikes, 3 blue bikes, 4 orange bikes, and 12 sliver bikes
Answer:
It Does. Cool
Answer:
c.) silver bikes
Step-by-step explanation:
Given the bike shop has 11 red bikes, 3 blue bikes, 12 silver bikes
here, the number orange bikes = 4
Given for every 1 orange bike there 3 __ bikes
Divide each number of bikes by the number of orange bikes
For 11 red bikes
= 11/4 = 2.75 [which means for 1 orange bike 2.75 red bikes ]
For 3 blue bikes
= 3/4 = 0.75 [ which means for 1 orange bike 0.75 blue bikes ]
For 12 silver bikes
= 12/4 = 3 [ which means for 1 orange bike 3 silver bikes ]
For every 1 orange bike, there are 3 silver bikes.
