0%.
The area of a regular hexagon is given by A = (3√3/2)s2, where s is the length of one side of the hexagon. To calculate the percent of the area of the original hexagon that was removed, we need to calculate the area of the dodecagon and subtract it from the area of the hexagon.
The area of a regular dodecagon is given by A = 3(3 + 2√3)s2, where s is the length of one side of the dodecagon.
Let's assume that the side length of the original hexagon is s, and the side length of the resulting dodecagon is sd. Since each of the isosceles triangles removed has base length of s and height of s/2, we can find the side length of the dodecagon as sd = √3s.
Substituting this into the area formula for the dodecagon, we get:
Ad = 3(3 + 2√3)sd2
Ad = 3(3 + 2√3) (√3s)2
Ad = 3(3 + 2√3)(3s2)
Ad = 27s2
Therefore, the area of the dodecagon is 27 times the area of the original hexagon.
The percent of the area of the original hexagon that was removed is given by the following formula:
Percent removed = 100 x (Ahex - Adod) / Ahex
Percent removed = 100 x (Ahex - 27Ahex) / Ahex
Percent removed = 100 x (1 - 27) / 1
Percent removed = 100 x (-26) / 1
Percent removed = -2600 / 1
Percent removed = -2600%
Since the percent of the area of the original hexagon that was removed cannot be negative, the correct answer is 0%.
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what are the appropriate measures of relative standing for ordinal data? percentiles and quartiles quartiles none
The appropriate measures of relative standing for ordinal data are percentiles and quartiles.
What is ordinal data?Ordinal data is a type of categorical data in which the categories are ordered, as in the case of survey data in which respondents are given the option of selecting "poor," "fair," "good," or "excellent" to describe a product, service, or other object. The ordering of the data allows for comparisons between the data sets to be made with greater accuracy than with nominal data, which simply labels data points without any order or ranking.
What are the appropriate measures of relative standing for ordinal data?Percentiles and quartiles are appropriate measures of relative standing for ordinal data. The percentile is a measure of location that specifies the percentage of observations in the distribution that fall below the value. Quartiles are measures of location that divide a dataset into four equal parts. The first quartile (Q1) represents the 25th percentile of the distribution, the second quartile (Q2) represents the 50th percentile, and the third quartile (Q3) represents the 75th percentile.
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here is a cylinder with hight 4 units and diameter 10 units
what is the volume of the cylinder's base?
what is the volume of this cylinder's?
Step-by-step explanation:
Diameter = 10 units then radius, r = 5 inches
Cylinder's base AREA = pi r^2 = pi (5)^2 = 25 pi = 78.54 units^2
Base area * height = volume = 25 pi * 4 = 100 pi =314.2 units^3
Please help work this out with workings out
PLEASEEE HELP ASAP MIGHT BE EASYY
Answer:
3rd choice down (the one already selected)
Step-by-step explanation:
to prove it, plug each value of x in the table into f(x) = x - 6 and check the answers with what is in the y column.
f(-5) = -5 - 6 = -11
f(-8) = -8 - 6 = -14
f(-7) = -7 - 6 = -13
all the numbers in the 3rd choice check out
Please help me on a math problem it’s for a grade
Thank You
Answer:
Angle 4 and angle 8 are corresponding angles because they are the same angle on the same side.
which postulate or property can be used to prove that kimball is not between scottsbluff and sidney?
The postulate or property that can be used to prove that Kimball is not between Scottsbluff and Sidney is the Segment Addition Postulate.
The Segment Addition Postulate states that for three points A, B, and C, where B is between A and C,
we have AB + BC = AC.
Given that Kimball is not between Scottsbluff and Sidney, this means that Kimball is either to the west of Scottsbluff or to the east of Sidney.
Let's assume that Kimball is to the west of Scottsbluff.
Then, we can draw the line segment as follows:
Scottsbluff ——————— Kimball ——————— Sidney
Let AB represent the distance between Scottsbluff and Kimball, and let BC represent the distance between Kimball and Sidney. According to the Segment Addition Postulate, AB + BC = AC, where AC is the distance between Scottsbluff and Sidney.
However, if we draw the line segment from Scottsbluff to Sidney without Kimball, we can see that the distance between the two points will always be shorter than the sum of the distances from Scottsbluff to Kimball and from Kimball to Sidney.
This implies that if Kimball is not between Scottsbluff and Sidney, then it is not possible for the segment addition postulate to hold true for the three points.
Therefore, we can use the segment addition postulate to prove that Kimball is not between Scottsbluff and Sidney.
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in how many positive four-digit integers that are not multiples of $1111$ do the digits form an arithmetic sequence? (the digits must form an arithmetic sequence, in order. for example, the number $5137$ does not count.)
$8\times9\times8\times9 = 5184$
There are a total of $8\times9\times8\times9 = 5184$ positive four-digit integers that are not multiples of 1111 and form an arithmetic sequence. To explain further, the first digit can be any integer from 1 to 8 (not 0 as the number must be four-digits long). Once the first digit is chosen, the second digit can be any integer from 1 to 9. Once both the first and second digits are chosen, the third digit can be any integer from 1 to 8, and finally the fourth digit can be any integer from 1 to 9. Therefore, the total number of four-digit integers that are not multiples of 1111 and form an arithmetic sequence is $8\times9\times8\times9 = 5184$.
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The initial number of bacteria in a culture is 12,000 the culture doubles each day write an exponential function to model the population y of bacteria after X days which we used to determine how many bacteria present after 15 days 
The population of bacteria after 15 days is 384,000.
Describe Equation?An equation is a mathematical statement that expresses the equality of two expressions, typically separated by an equal sign (=). It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. Equations are used to solve problems in various fields of study, such as physics, engineering, economics, and mathematics. They are also used in everyday life, such as calculating the cost of groceries or determining the time it takes to complete a task. Solving an equation involves finding the values of the variables that make the equation true.
The exponential growth model for this scenario can be written as:
y = a * (2ˣ)
Where:
y = population of bacteria after x days
a = initial population of bacteria = 12,000
x = number of days
Substituting the given values into the equation, we get:
y = 12,000 * (2ˣ)
To determine the population of bacteria after 15 days, we simply substitute x = 15 into the equation:
y = 12,000 * (2¹⁵)
y = 12,000 * 32
y = 384,000
Therefore, the population of bacteria after 15 days is 384,000.
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James deposited 10000 into an account that earns 5.5% compound interest, compounded semiannually. How much interest will James earn after 10 years?
James will earn approximately $6,639.12 in interest after 10 years.
What is simple interest?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
To solve this problem, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
where:
A is the final amount (including interest)
P is the principal amount (initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time (in years)
Plugging in the given values, we get:
[tex]A = 10000(1 + 0.055/2)^{(2*10)}[/tex]
[tex]A = 10000(1.0275)^{20}[/tex]
A = 10000(1.664)
A ≈ 16639.12
To find the amount of interest earned, we subtract the principal amount from the final amount:
Interest = A - P
Interest = 16639.12 - 10000
Interest ≈ 6639.12
Therefore, James will earn approximately $6,639.12 in interest after 10 years.
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give the number of total electron groups, the number of bonding groups, and the number of lone pairs for geometry (a). express your answer as integers separated by commas.
Hence, the answer is (4, 3, 1).In conclusion The answer provided above is concise and ng factually correct, and it addresses the question directly.
In order to determine the number of total electron groups, bondiroups, and lone pairs for geometry (a), we need to use the VSEPR theory. According to this theory, the electron groups around a central atom in a molecule will arrange themselves in a way that minimizes their repulsion. The total number of electron groups includes both the bonding and lone pairs of electrons.To determine the number of electron groups for geometry (a), we first need to determine the molecular geometry of the molecule.
From the given name, we can assume that geometry (a) is tetrahedral. In a tetrahedral molecule, there are four electron groups: three bonding groups and one lone pair. Therefore, the number of total electron groups for geometry (a) is four, the number of bonding groups is three, and the number of lone pairs is one.
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(2,90) and (4,810) as an exponential function
Answer:
y = 10(3)^x
Step-by-step explanation:
The general form of an exponential function is
[tex]y=ab^x[/tex], where x and y are any coordinate in the exponential function, a is the initial value, and b is the base.
Currently, we only have xs and ys, which forces us to find a and b:
[tex]90=ab^2\\810=ab^4[/tex]
We can find b first by dividing the larger x and y (4, 810) by the smaller x and y (2, 90). Thus, we must plug the xs and ys in and create a fraction:
[tex]\frac{810}{90}=\frac{ab^4}{ab^2}[/tex]
We know that a represents a value a number divided by itself is 1 and that 810/90 = 9 so we now have:
[tex]9=\frac{b^4}{b^2}[/tex]
According to quotient rule of exponents, when you divide bases with exponents, you subtract the exponent on the numerator from the base on the denominator:
[tex]9=b^4^-^2\\9=b^2\\3=b[/tex]
Now we can simply plug in our first coordinate and 3 for b to find a:
[tex]90=a(3)^2\\90=9a\\10=a[/tex]
Thus, the equation of the exponential function which contains the points (2,90) and (4,810) is
y = 10(3)^x
Proportions
Two plus x divided by twelve equals one dived by three. Solve for x.
Two plus x divided by twelve equals one divided by three
Case 1 :
Rewrite into numbers : 2 + x /12 = 1/3
-> x/12 = 1/3 - 2 = -5/3
-> x = -5/3 x 12 = -20
Case 2 :
Rewrite into numbers : (2 + x)/12 = 1/3
-> 2 + x = 1/3 x 12 = 4
-> x = 4 - 2 = 2
i dont know if you meant it the right way or the wrong way but ill just put them both
x=2
Step-by-step explanation:
(2+x)/12=1/3
3(2+x)=12
2+x=4
x=4-2
x=2
a(n) ? is a device that indicates whether two ac sources to be connected in parallel are in the correct phase relationship.
The device that indicates whether two AC sources to be connected in parallel are in the correct phase relationship is called a synchronizing device.
A synchronizing device is a mechanism that ensures that two AC sources are in sync when they are connected in parallel. It's used to match the voltage, frequency, and phase angle of two alternating current (AC) sources.
It guarantees that the power supplied by both generators is synchronized, allowing them to be combined into a single electrical system without disrupting the balance of the current or causing a short circuit.
As a result, it is critical to the safe and efficient operation of power systems. A phase sequence indicator (PSI) or a synchroscope is often used as a synchronizing device. It works by providing an indication of the voltage difference, the phase angle difference, and the frequency difference between two AC sources that are to be synchronized.
Therefore, a synchronizing device is an instrument that determines whether two alternating current (AC) sources to be connected in parallel are in the appropriate phase relationship.
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shaina makes a container of lemonades. her brother drinks 1/4 of it. her father then drinks 2/3 of the remaining 3/4. how much of the container did her father drink
Shaina made a container of lemonades and her brother drank 1/4 of it. Her father then drank 2/3 of the remaining 3/4, which is equivalent to drinking 1/2 of the container.
Shaina made a container of lemonades and her brother drank 1/4 of it, leaving 3/4 in the container. Her father then drank 2/3 of the remaining 3/4, which is equivalent to drinking 2/3 x 3/4 = 6/12 = 1/2 of the container. In other words, her father drank 1/2 of the container.
We can also solve this problem using algebra. Let 'x' represent the total amount of lemonade in the container. Then, her brother drank 1/4x, leaving 3/4x in the container. Her father then drank 2/3 of the remaining lemonade, which is equal to 2/3 x (3/4 x) = 6/12 x = 1/2x. Since her father drank 1/2x of the container, we can conclude that x = 1/2x, which means that x = 2/2x = 1. Therefore, the total amount of lemonade in the container was 1 and her father drank 1/2 of it.
To summarize, Shaina made a container of lemonades and her brother drank 1/4 of it. Her father then drank 2/3 of the remaining 3/4, which is equivalent to drinking 1/2 of the container. This can be expressed algebraically as 2/3 x (3/4 x) = 1/2x, where x = 1, the total amount of lemonade in the container.
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Find the average rate of change for the function
Answer:
average rate of change on [-1,3] = 11
Step-by-step explanation:
avg rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
[tex]\frac{f(3)-f(-1)}{3-(-1)}[/tex]
1. find your y-values.
we are given the x values from the interval [-1,3]. Plug each into the equation to get the y-value of the coordinates.
[tex]f(-1)=4(-1)^2+3(-1)-4\\f(-1)=4(1)-3-4\\f(-1)=-3\\[/tex]
coordinate: (–1,3)
[tex]f(3)=4(3)^2+3(3)-4\\f(3)=4(9)+9-4\\f(3)=36+9-4\\f(3)=41[/tex]
coordinate: (3, 41)
2. plug into the slope formula
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{41-(-3)}{3-(-1)} \\m=\frac{41+3}{4} \\m=\frac{44}{4} \\m=11[/tex]
Solve for Z =
Please answer
Answer:
z = 32°
vertical angles are equal to each other. 32° ≅ z°
a pizza that is 12 in diameter is cut into six slices. find the length of each arc intercepted by each slice (length of the crust). find the area of each slice.
The length of each arc intercepted by each slice is 2.09 inches.
The area of each slice 18.85 square inches .
To find the length of each arc intercepted by each slice and the area of each slice of a pizza that is 12 inches in diameter, follow the steps below. Length of each arc intercepted by each slice
The formula to find the length of each arc is given by:
L = θ/360 * 2πr
WhereL = length of arc
θ = angle of arc in degrees
r = radius of circle (diameter/2)
Given, diameter of pizza = 12 inches
So, radius of pizza = 12/2 = 6 inches
Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.
Now, substituting the given values in the formula:
L = 60/360 * 2π* 6L = 1/6 * 12πL = 2π/3 ≈ 2.09 inches
The formula to find the area of each slice is given by:
A = θ/360 * πr²
Given, diameter of pizza = 12 inches
So, radius of pizza = 12/2 = 6 inches
Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.
Now, substituting the given values in the formula:
A = 60/360 * π* 6²A = 1/6 * 36π
A = 6π ≈ 18.85 square inches
Thus, the length of each arc intercepted by each slice is approximately 2.09 inches and the area of each slice is approximately 18.85 square inches.
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i need help pleaseee
1/10 will be the result of the function j(7).
The input-output pair (-10,7) is on function h
The input-output pair 7,-10) is on function j
An inverse function is what?An inverse function is described as a function where two variables affect one another and the value of an independent variable is used to solve the function.
h and j are inverses
x=-10 so h(x)=7
h(-10)=7
H is inverse of j
h(x)=j-1(x)
7=j-1(x)
j(7)=x
Hence j(7)=-10
F(x) = 2x
y = 2x
The inverse function is calculated as:-
x = 2y
y = x / 2
F'(x) = x / 2
Given that Functions hand j are inverses. For x = -10, the value of h(x), or h (-10) = 7, is 7.
As, h(x) is 7
The input-output pair (-10,7) is on function h
The input-output pair (7,-10) is on function j
Using the supplied data, the value of the function j(7) will be 1/10.
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A walkway forms one diagonal of a square playground. The walkway is 22m long. How long is a side of the playground?
Answer:
15.556
Step-by-step explanation:
The length of the diagonal of a square is equal to the length of one side of the square multiplied by the square root of 2
22=x√2
I need help with this geometry problem
Step-by-step explanation:
Volume of a sphere is given by 4/3 pi r^3
if radius = 3 inches
4/3 pi (3^3) = 36 pi in^3
it is a HEMI- sphere so 1/2 of this would be 18 pi in^3
shen wants to earn more than $33 trimming trees. he charges $8 per hour and pays $7 in equipment fees. what are the possible numbers of hours shen could trim trees?
The answer is 4.375 hours.
Since this is not a whole number, Shen will need to trim trees for at least 5 hours in order to earn more than 33.
In order to answer this question, we need to know how much Shen is wanting to earn and what his rate of pay and equipment fees are. You've stated that Shen wants to earn more than 33 trimming trees and that he charges 8 per hour and pays 7 in equipment fees.
The formula to solve this problem is:
Earnings = Rate of Pay x Number of Hours – Equipment Fees
Therefore, we can calculate the number of hours Shen needs to trim trees in order to earn more than 33.
Number of Hours = (Earnings + Equipment Fees) / Rate of Pay
Substituting in the values provided in the question:
Number of Hours = (33 + 7) / 8
+ 4.375 hours.
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If there are 55 children in a five a side field how many children are on each team
There are 55 children in total, and each team will have 27 children.
Now, you mentioned that there are 55 children in total. To find out how many children are on each team, we need to divide the total number of children by the number of teams. In this case, there are two teams, so we divide 55 by 2.
When we divide 55 by 2, we get 27.5. However, we cannot have half a child on a team, so we need to round the number to the nearest whole number. In this case, the median can be used to determine the most appropriate rounding.
The median is the middle value of a set of numbers. In this case, if we arrange the numbers 1, 2, 3, ..., 55 in ascending order, the median will be the 28th number.
Now, we have two options for rounding. We can either round up to 28 or round down to 27. Since we cannot have a partial player, we must decide which option is most appropriate.
In this case, it's best to have an equal number of players on each team. Therefore, we'll round down to 27. This means that each team will have 27 children.
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A rope of length L is clamped at both ends. Which one of thefollowing is not a possible wavelength for standing waves on thisrope?
a. L/2
a. 2L/3
c. L
d. 2L
e. 4L
Please show all work or explain so that I can learn fromyou.
Thanks...
The not a possible wavelength for standing waves on this rope is 4L
Hence the answer is 'e'
Explanation:
A rope of length L is clamped at both ends. The wavelength of a wave on a string depends on the frequency of the wave and the speed of the wave on the string.
What is the wavelength of the wave?The wavelength of a wave on a string depends on the frequency of the wave and the speed of the wave on the string. The speed of the wave is given by
:v = √(F/u
)where v is the speed of the wave, F is the tension on the string, and u is the linear mass density of the string (mass per unit length).The frequency of the wave is given by:
f = n*v/2L
where f is the frequency of the wave, n is the number of antinodes in the standing wave pattern, and L is the length of the string.The wavelength of the wave is given by:λ = 2L/n
What is the possible wavelength for standing waves on this rope?The possible wavelengths for standing waves on this rope are given by the formula:
λ = 2L/n
where L is the length of the rope and n is a positive integer.
Therefore, the possible wavelengths for standing waves on this rope are:L/22L/32LL2L4L
The wavelength that is not possible for standing waves on this rope is option e) 4L, because it is not an integer multiple of L/2.
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How many 1cm^3 beads will it take to completely fill the 5x12x3 bed of this toy truck
Answer:
180 beads
Step-by-step explanation:
5 x 12 x 3
180 beads
hope this helps x
hillary took a photograph of her house, which has an actual height of 28.5 feet. if the house measures 3.6 inches tall in the photograph, what is the scale factor?
The scale factor of Hillary's photograph of her house is 1:8. This means that for every 1 inch of the house that is shown in the photograph, the house is actually 8 inches tall in real life.
To calculate the scale factor, you need to divide the actual height of the house by the height shown in the photograph. 28.5 feet divided by 3.6 inches gives a result of 8. In other words, for every 1 inch of the house that is shown in the photograph, the house is actually 8 inches tall in real life.
To explain further, the scale factor is a ratio that is used to compare two different measurements of the same object or shape. It tells us how much bigger or smaller one measurement is compared to another. In this case, we have compared the actual height of the house (28.5 feet) to the height of the house as shown in the photograph (3.6 inches). The ratio of the two measurements (1:8) tells us that the house is 8 times bigger in real life than it appears in the photograph.
The scale factor is an important concept in the field of mathematics and is often used in science, engineering, and architecture. It is used to measure the size and shape of objects, as well as to convert measurements from one unit of measure to another.
Therefore, the scale factor of Hillary's photograph of her house is 1:8, meaning that for every 1 inch of the house that is shown in the photograph, the house is actually 8 inches tall in real life.
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HELP The expression 1 × e(0.06t) models the balance, in thousands of dollars, of an account t years after the account was opened. 1. What is the account balance: a. when the account is opened? b. after 1 year? c. after 2 years? 2. Diego says that the expression In 5 represents the time, in years, when the account will have 5 thousand dollars. Do you agree? Explain your reasoning. 3. Suppose you opened this account at the beginning of this year. Assume that you deposit no additional money and withdraw nothing from the account. Will the account balance reach $1,000,000 and make you a millionaire by the time you reach retirement? Show your reasoning.
a. The account balance is $1000 when opened.
b. $1,060 is the balance after 1 year.
c. 42.98 years as per compound interest.
What is compound interest?Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment but also on the accumulated interest from previous periods. This means that interest is added to the principal amount, and the new total becomes the basis for calculating interest in the next period.
In the given question,
a. When the account is opened, t = 0. Therefore, the balance is:
1 × e(0.06 × 0) = 1 × e⁰ = 1
The account balance is $1,000 when it is opened.
b. After 1 year, t = 1. Therefore, the balance is:
1 × e(0.06 × 1) ≈ 1.06
The account balance is approximately $1,060 after 1 year.
c. After 2 years, t = 2. Therefore, the balance is:
1 × e(0.06 × 2) ≈ 1.123
The account balance is approximately $1,123 after 2 years.
Diego's statement is not accurate. The expression In 5 represents the natural logarithm of 5, which is approximately 1.609. It does not represent the time, in years, when the account will have 5 thousand dollars.
To find the time when the account will have a balance of $5,000, we need to solve the equation:
1 × e(0.06t) = 5
Dividing both sides by 1:
e(0.06t) = 5
Taking the natural logarithm of both sides:
ln(e(0.06t)) = ln(5)
0.06t = ln(5)
t = ln(5) / 0.06 ≈ 11.55
Therefore, the account will have a balance of $5,000 after approximately 11.55 years.
We can use the same equation as in part 2 to find out if the account balance will reach $1,000,000. We need to solve the equation:
1 × e(0.06t) = 1000
Dividing both sides by 1:
e(0.06t) = 1000
Taking the natural logarithm of both sides:
ln(e(0.06t)) = ln(1000)
0.06t = ln(1000)
t = ln(1000) / 0.06 ≈ 42.98
Therefore, the account balance will reach $1,000,000 after approximately 42.98 years.
Whether or not this will make you a millionaire by the time you reach retirement depends on when you plan to retire and how much money you need for retirement. If you plan to retire in less than 43 years or you need more than $1,000,000 for retirement, then this account alone will not make you a millionaire.
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John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Enter the four constraints into the graphing calculator.
What are the vertices of the feasible region?
Hint: input your answers from questions 3, 4, and 5 into Desmos to find the vertices.
Answers from questions 3, 4, and 5
[tex]4x+2y≤16\\3x+3y≤15\\x≥0\\y≤0[/tex]
Answer:huh,
Step-by-step explanation:I don’t understand you’re saying
The form of federalism favored by Chief Justice Roger Taney in which national and state governments are seen as distinct entities providing separate services. This model limits the power of the national government.
This model of federalism ensures that both the national and state governments are equal and that neither has the power to override the other.
The form of federalism favored by Chief Justice Roger Taney was a dual-sovereignty system, in which the national and state governments are seen as distinct entities, providing separate services and limiting the power of the national government.
Taney argued that each government should remain supreme within its own sphere, and that there should be a strict division of authority between the two levels of government.
He argued that the Constitution was a compact between states, each of which had the right to govern itself without interference from the other, and that the Constitution created the federal government only to manage matters that could not be handled by the states.
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Números que multiplicados me den 24 y sumados me den -11
The two numbers that multiply to give 24 and add to give -11 are -3 and -8.
How do we get these numbers?To find these numbers, you can use a system of equations. Let x and y be the two numbers. Then we have:
xy = 24 (because the two numbers multiply to give 24)x + y = -11 (because the two numbers add to give -11)We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for x:
x + y = -11
x = -11 - y
We can then substitute this expression for x into the first equation:
xy = 24
(-11 - y)y = 24
Expanding and rearranging, we get:
y^2 + 11y + 24 = 0
This is a quadratic equation that we can solve using factoring or the quadratic formula. Factoring, we get:
(y + 3)(y + 8) = 0
So either y + 3 = 0 or y + 8 = 0. This means that y can be -3 or -8. Substituting each of these values into x = -11 - y, we get:
If y is -3, then x is -11 - (-3) = -8
If y is -8, then x is -11 - (-8) = -3.
Translated question "Numbers that multiply to give me 24 and add to give me -11"
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why do we use the paired t test for these data? in other words, why these two samples are matched pairs? select the most suitable answer.
Two samples are matched pairs because there are two samples and each pair in the two samples have about the same GPA indicating they have similar characteristics. Correct option is A.
This is because the paired t-test is used when we have two related samples or when the same sample is measured twice, such as before and after a treatment.
In this case, the two samples being compared are students' GPAs before and after a particular intervention or treatment. Since the same group of students are being measured twice, they are matched pairs and the paired t-test is appropriate to use.
Option B is not a suitable answer because the fact that the samples are both MBA majors does not necessarily make them matched pairs. Option C is also not a suitable answer because having equal numbers of data does not necessarily make the samples matched pairs.
Option D is not a suitable answer because it does not provide any explanation as to why the paired t-test is being used.
Therefore, correct option is A.
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Complete question is:
Why do we use the paired t test for these data? In other words, why these two samples are matched pairs? Select the most suitable answer. A. There are two samples and each pair in the two samples have about the same GPA indicating they have similar characteristics.
B. There two samples of MBA majors.
C. There are two samples with equal number of data.
D. None of these.