The set of all points in quadrant I not including the axis's can be represented by the following system of inequalities:
x > 0
y > 0
Inequalities are useful in modeling situations where there are constraints or limitations. For illustration, in real- life scripts, there may be limited coffers or capacity, or certain variables must fall within a specific range. Systems of inequalities are frequently used to represent these constraints or limitations graphically. One common operation of systems of inequalities is in optimization problems, where the thing is to maximize or minimize a particular function subject to certain constraints.
In these situations, the doable region, or the set of all points that satisfy the constraints, is frequently represented as a shadowed region on a graph. The optimal result is also set up by relating the point( s) within this region that maximize or minimize the function.
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A magazine listed the number of calories and sodium content (in milligrams) for 13 brands of hot dogs. Examine the association, assuming that the data satisfy the conditions for inference. Complete parts a and b
Option B is correct. In this context, the meaning is: Among hot dogs with the same number of calories, the sodium content varies, with a standard deviation of about 75 milligrams
The calculated test statistic is 3.75
How to get the correct optionThe test statistics can be gotten from the data that we already have available in this question
The coefficient is given as 2.235
The Standard error of the coefficient is given as 0.596
The formula used is given as
Such that t = coefficient / Standard error
where the coefficient = 2.235
The standard error = 0.596
We have to apply the values to formula:
= 2.235 / 0.596
= 3.75
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The cone is formed from 3,200 ft3 of gravel. If the height of the cone is 24 feet, what is the radius, in feet, of the base of the cone? Use the π button on your calculator to determine the answer. Round your answer to the nearest tenth of afoot. The radius of the base of the cone is approximately ____ feet
The radius of the base of the cone is approximately 12.65 feet if The cone is formed from 3,200 ft of gravel.
Height of cone = 24 feet
The volume of the cone = [tex]3,200 ft^3[/tex]
To find the volume of the cone, the formula used here is:
V =π* [tex]r^2h[/tex]
Here, the values of V and H are known terms. we need to calculate the radius r of the cone.
π = 3.14 constant value
Substituting the values in the above equation, we get:
[tex]3,200 = (1/3)^2*(24)*[/tex] π
[tex]r^2[/tex]= 3,200 / (8π)
[tex]r^2[/tex] = 400 / π
r = 12.65
Therefore, we can conclude that the radius of the base of the cone is 12.65 feet.
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PLEASE HELP WILL GIVE BRAINLEST !!!!
A pyramid has a base that is a regular hexagon with each side measuring 10 units. The base of the pyramid is shown below.If the pyramid has a height of 12 units, what is the approximate volume of the pyramid?
Answer:
Step-by-step explanation:
The volume of a pyramid can be calculated using the formula:
V = (1/3) * Base Area * Height
To calculate the volume of this pyramid, we need to first find the area of its regular hexagonal base. The formula for the area of a regular hexagon is:
A = (3√3/2) * s^2
where s is the length of one side of the hexagon. Substituting s = 10, we get:
A = (3√3/2) * 10^2 = 259.80 square units (approx)
Now we can use the formula for the volume of a pyramid to find the volume of this pyramid:
V = (1/3) * 259.80 * 12 = 1039.20 cubic units (approx)
Therefore, the approximate volume of the pyramid is 1039.20 cubic units.
For y = 72√x, find dy, given x = 4 and Δx = dx = 0.21
dy = (Simplify your answer.)
To find dy for the function y = 72√x, given x = 4 and Δx = dx = 0.21, we will first find the derivative of y with respect to x and then plug in the given values.
1. Differentiate y with respect to x: y = 72√x can be rewritten as y = 72x^(1/2)
Apply the power rule: dy/dx = 72 * (1/2)x^(-1/2)
Simplify: dy/dx = 36x^(-1/2)
2. Plug in the given values: x = 4 and dx = 0.21
dy/dx = 36(4)^(-1/2)
dy/dx = 36(1/√4)
dy/dx = 36(1/2)
dy/dx = 18
3. Calculate dy: dy = (dy/dx) * dx
dy = 18 * 0.21
dy = 3.78
So, for y = 72√x, dy is 3.78 when x = 4 and Δx = dx = 0.21.
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Can someone help me please
Answer:
A
Step-by-step explanation:
Simple interest gains interest only on the principal sum and so each year has the same interest. So, this example is not simple interest. Compound interest is calculated on the principal and the accumulated interest of the previous years. So, this is compound interest.
Interest is 4%.
[tex]A = P*(1 + R \%)^n[/tex]
Here A is the amount we receive after n years, P is the principal and R is the rate of interest.
A = $1300 , R = 4%
[tex]1300 = P * (1+0.04})\\\\1300 = P * 1.04\\\\\dfrac{1300}{1.04}=P\\\\\\\dfrac{130000}{104}=P[/tex]
P = $ 1250
On Friday, Jacob planted a pinto bean in science class. When he returned to school on Monday, the bean had sprouted a stem that was 3 millimeters long. At the end of the week, Jacob's bean sprout had a stem that was 42 millimeters long. How many centimeters did Jacob's bean sprout grow during the week?
Jacob's bean sprout grew 3.9 centimeters during the week.
What is measurements?
Measurements in math involve the assignment of numerical values to physical quantities, such as length, area, volume, mass, time, temperature, and so on. Measuring objects or events allows us to compare and quantify them, and is an essential part of mathematical problem-solving, as well as many other fields of study
Jacob's bean sprout grew 42 millimeters - 3 millimeters = 39 millimeters during the week.
To convert millimeters to centimeters, we need to divide by 10 since there are 10 millimeters in 1 centimeter.
So, the growth in centimeters is 39 millimeters ÷ 10 = 3.9 centimeters.
Therefore, Jacob's bean sprout grew 3.9 centimeters during the week.
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I NEED HELP PLEASE!
1. 3 statements about limiting frictional force between two surfaces are given below.
A - Nature of surfaces in contact affects to limiting frictional force.
B - Normal reaction between them affects to limiting frictional force.
C - Area of surfaces in contact affects to limiting frictional force.
Correct statement / statements from above A, B, C is/ are,
(1) A
(2) B
(3) A and C
(4) A, B and C
The limiting frictional force depends only on:
A. The nature of surfaces in contact: Rough and irregular surfaces have higher friction than smooth surfaces. C. The area of surfaces in contact: Larger the contact area, higher is the friction between the surfaces.(3) A and C is the right optionWhich of the following is an even function? g(x) = (x – 1)2 1 g(x) = 2x2 1 g(x) = 4x 2 g(x) = 2x
The only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.
A function is even if it satisfies the property g(-x) = g(x) for all x.
Checking each of the given functions:
g(x) = (x - 1)^2 is not even, because g(-x) = (-x - 1)^2 = x^2 + 2x + 1, which is not equal to g(x) = (x - 1)^2.
g(x) = 2x^2 is even, because g(-x) = 2(-x)^2 = 2x^2 = g(x) for all x.
g(x) = 4x^2 is even, because g(-x) = 4(-x)^2 = 4x^2 = g(x) for all x.
g(x) = 2x is odd, because g(-x) = 2(-x) = -2x = -g(x) for all x.
Therefore, the only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.
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How to find the area of this whole figure? Please help me
The area of the whole figure is 31.5 sq. units.
What is the area of a figure?The area of a given figure connotes its expanse in a 2 dimensional plane. The shape and size of a given figure determines how to calculate its area.
From the given question, the figure given can be likened to a rhombus. So that;
area of a rhombus = (diagonal 1 * diagonal 2)/ 2
Then,
area of the figure = (diagonal 1 * diagonal 2)/ 2
where: diagonal 1 = 7.5, and diagonal 2 = 8.4
So that;
area of the figure = (7.5*8.4)/ 2
= 63/ 2
= 31.5
The area of the whole figure is 31.5 sq. units.
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Every time you practice, you gain more skills.
Conditional:
Hypothesis:
Conclusion:
Converse:
Inverse:
Contrapositive:
Hypothesis: Every time you practice, you gain more skills.
What happens when you practice?Conclusion: Gain of skills is a result of practice.
Converse: If you gain more skills, then you practice every time.
Inverse: If you don't practice, then you don't gain more skills.
Contrapositive: If you don't gain more skills, then you don't practice every time.
The hypothesis states that practicing leads to an increase in skills. This can be interpreted as a cause and effect relationship between the two variables.
The conclusion reiterates that gaining skills is a result of practice.
The converse of the statement flips the order of the hypothesis and the conclusion. It states that if you gain more skills, then you must have practiced every time.
This may not be entirely true because there can be other factors that contribute to the gain of skills besides practice.
The inverse of the statement negates both the hypothesis and the conclusion. It states that if you don't practice, then you don't gain more skills.
This statement is true because practice is a necessary condition for gaining skills. However, it doesn't mean that practicing alone guarantees the gain of skills.
The contrapositive of the statement flips the order of the negated hypothesis and the negated conclusion. It states that if you don't gain more skills, then you didn't practice every time.
This statement is also true because if one doesn't practice, they cannot expect to gain more skills.
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Let f:R → R be a function that satisfies ∫f(t)dt then the value of f(log e 5) is
Unfortunately, I cannot provide an answer to this question as it is incomplete. The given information ∫f(t)dt is not enough to determine the value of f(log e 5). More information about the function f would be needed, such as its explicit form or additional properties. Please provide more context or information to help me answer your question accurately.
Given that f is a function f:R → R that satisfies ∫f(t)dt, we need to find the value of f(log e 5).
By definition, log e 5 is the natural logarithm of 5, which can be written as ln(5). Therefore, we want to find the value of f(ln(5)).
However, without further information on the function f or the integral bounds, it's not possible to determine the exact value of f(ln(5)). Please provide more details about the function or the integral to get a specific answer.
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Solve the equation and check your solution: x + 4 = -2 + x
The equation x + 4 = -2 + x has no solution for x
Solving the equation and checking the solutionFrom the question, we have the following parameters that can be used in our computation:
x + 4 = -2 + x
Subtract x from both sides of the equation
so, we have the following representation
x - x + 4 = -2 + x - x
When the like terms of the equation are evaluated, we have
4 = -2
The above equation is false
This is because 4 and -2 do not have the same value
Hence, the equation has no solution
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The probability that Sam parks in a no-parking zone and gets a parking ticket is 0. 07,and the probability that Sam Connor finr a legal parking space and has to park in the no-parking zone is 0. 50. On Monday,Sam arrives at school and has to park in a no-parking zone. Find the probability that he will get a parking ticket.
The probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.
We can use Bayes' theorem to solve this problem. Let A be the event that Sam gets a parking ticket and B be the event that Sam parks in a no-parking zone. Then, we want to find P(A|B), which is the conditional probability of A given B.
Bayes' theorem states that P(A|B) = P(B|A)*P(A)/P(B), where P(B|A) is the probability of B given A, P(A) is the prior probability of A, and P(B) is the prior probability of B.
From the problem, we know that P(A) = 0.07, P(B|A) = 1 (since if Sam parks in a no-parking zone, he will definitely get a parking ticket), and P(B|not A) = 0.50 (since if Sam finds a legal parking space, he has a 0.50 probability of parking in a no-parking zone).
To find P(B), we can use the law of total probability, which states that P(B) = P(B|A)*P(A) + P(B|not A)*P(not A), where P(not A) = 1 - P(A).
Therefore, P(B) = 10.07 + 0.50(1-0.07) = 0.5351.
Finally, we can use Bayes' theorem to find P(A|B):
P(A|B) = P(B|A)P(A)/P(B) = 10.07/0.5351 ≈ 0.1308.
Therefore, the probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.
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Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.
The values of the inverse trigonometric functions are 72°, 76° and 85°.
How to explain the stepsThe range of the inverse trigonometric function is limited to a certain interval based on the domain of the original trigonometric function.
Its also important to identify the trigonometric ratio that corresponds to the given value.
The value on degree for inverse of sin (2/3) will be 41.81° which is 42°. Also, inverse of tan(4) is 76° using the calculator.
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Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.
inverse of sin (2/3)
inverse of tan(4)
inverse of tan (0.1)
In the formula
A(t) = Pert for continuously compound interest, the letters P, r, and t stand for ---Select--- percent interest prime rate amount after t years principal number of years , ---Select--- interest rate per year rate of return investment amount investment per year interest rate per day , and ---Select--- number of months number of days number of time periods number of years number of times interest is compounded per year , respectively, and A(t) stands for ---Select--- amount of principal amount after t days amount of interest earned after t years amount of interest earned in year t amount after t years. So if $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $. (Round your answer to the nearest cent. )
In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for Principal, rate of interest, and time respectively, and A(t) stands for Amount after t amount of time. If $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $225.5.
The formula for Compound Interest at a continuous period of time is denoted by [tex]A(t) = Pe^{rt}[/tex]
where the Principal amount is multiplied by the exponential value of the interest rate and time passed.
Hence we are given here
P = $200, r = 4% = 0.04, and the amount to be calculated for t = 3 years
Hence we will find the amount by replacing these values to get
A(3) = 200 × e⁰°⁰⁴ ˣ ³
= $200 × e⁰°¹²
= $225.499
rounding it off to the nearest cent gives us
$225.5
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Correct Question
In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for ______ , _______ , and __________ respectively, and A(t) stands for _______ .
So if $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $__________. (Round your answer to the nearest cent.)
A cylindrical jar of peanut butter has a height of 4 inches and a diameter of 3 inches. How many cubic inches of peanut butter can the jar hold? Use π = 3.14.
28.26 in3
37.68 in3
113.04 in3
150.72 in3
The jar can hold 28.26 cubic inches of peanut butter
How to calculate the amount of cubic inches of peanut butter?The first step is to write out the parameters
A cylindrical jar of peanut has a height of 4 inches
The diameter is 3 inches
The next step is to calculate the radius, this is done by dividing the diameter by 2
radius= 3/2
= 1.5
The formula used to calculate the cubic inches of peanut butter is
V= πr²h
= 3.14 × 1.5² × 4
= 3.14 × 2.25 × 4
= 28.26
Hence the jar can hold 28.26 cubic inches of peanut butter
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Here is a set of data showing the test scores for US History class:
56, 88, 70, 72, 90, 85, 99, 65, 66, 54, 74, 85, 91, 92, 72, 88, 97, 62, 88 Create a stem and leaf plot to show this data. Hint: Decide how many stems you will need.
can somebody help me ?
Hi! I'd be happy to help you create a stem and leaf plot using the provided set of data for US History class test scores.
Step 1: Arrange the data in ascending order.
54, 56, 62, 65, 66, 70, 72, 72, 74, 85, 85, 88, 88, 88, 90, 91, 92, 97, 99
Step 2: Determine the range of the data.
The data ranges from 50s to 90s, so we will need 5 stems: 5, 6, 7, 8, and 9.
Step 3: Create the stem and leaf plot using the stems and corresponding leaves (the units digits of the data).
5 | 4 6
6 | 2 5 6
7 | 0 2 2 4
8 | 5 5 8 8 8
9 | 0 1 2 7 9
Here is the completed stem and leaf plot for the US History class test scores. The stems represent the tens digits (50s, 60s, 70s, 80s, 90s), and the leaves represent the units digits of the scores in each range.
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The function f(x) = 2x + 7x{-1} has one local minimum and one local maximum. This function has a local maximum at x = with value and a local minimum at x = with value
The function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.
To find the local maximum and minimum of the function f(x) = 2x + 7x⁻¹, we need to find the critical points of the function and then use the second derivative test to determine if they are local maxima or minima.
First, we find the derivative of f(x):
f'(x) = 2 - 7x⁻²
Setting f'(x) = 0, we get:
2 - 7x⁻² = 0
Solving for x, we get:
x = ±√(2/7)
Next, we compute the second derivative of f(x):
f''(x) = 14x⁻³
At x = ±√(2/7), we have:
f''(±√(2/7)) = ±∞
Since f''(±√(2/7)) has opposite signs at the critical points, ±√(2/7), we conclude that f(x) has a local maximum at x = -√(2/7) and a local minimum at x = √(2/7).
To find the values of the local maximum and minimum, we plug them into the original function:
f(-√(2/7)) = 2(-√(2/7)) + 7/(-√(2/7)) = -3√14
f(√(2/7)) = 2(√(2/7)) + 7/(√(2/7)) = 3√14
Therefore, the function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.
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Let S be the part of the plane 3+ + 2) + z = 1 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F = 3i+3j + 4k across the surface S.
The surface integral of the dot product between the vector field F = 3i + 3j + 4k and the unit normal vector of the surface S is equal to zero.
To use Stokes' theorem to find the flux of the vector field F = 3i + 3j + 4k across the surface S, which is the part of the plane 3x + 2y + z = 1 in the first octant and oriented upward.
Stoke's theorem statement is “the surface integral of the curl of a function over the surface bounded by a closed surface will be equal to the line integral of the particular vector function around it.” Stokes theorem gives a relation between line integrals and surface integrals.
First, we need to parametirize the curve C that bounds the surface S. Since S is in the first octant, x, y, and z are all non-negative.
The boundary C consists of three line segments: (i) from (0, 0, 0) to (1/3, 0, 0), (ii) from (1/3, 0, 0) to (0, 1/2, 0), and (iii) from (0, 1/2, 0) to (0, 0, 0). Next, calculate the curl of F, which is the cross product of the del operator and F:
curl(F) = (∂Fz/∂y - ∂Fy/∂z)i - (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k = (0 - 0)i - (0 - 0)j + (0 - 0)k = 0.
Since curl(F) = 0, the line integral of F over C is also 0.
According to Stokes' theorem, the flux of F across S equals the line integral of F over C, which we found to be 0.
Therefore, the flux of the vector field F = 3i + 3j + 4k across the surface S is 0.
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Solve problems 1 and 4 ONLY with the rules given on the paper.
The solution to the equations obtained using inverse trigonometric function values are;
1. x ≈ 0.65
4. x ≈ 0.95
What are trigonometric functions?Trigonometric functions indicates the relationships between the angles in a right triangle and two of the sides of the triangle. Trigonometric functions are periodic functions.
The value of x is obtained from the inverse trigonometric function of the output value of the trigonometric function, as follows;
The inverse function for sine is arcsine
The inverse function for cosine is arccosine
The inverse function for the tangent of an angle is arctangent
1. sin(x) = 0.6051
Therefore; x = arcsine(0.6051) ≈ 0.65 radians
The value of x in the interval [0·π, 2·π] is x ≈ 0.65
4. tan(x) = 1.3972
Therefore, x = arctan(1.3972) ≈ 0.95
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PLease help 1 and 2 Pythagorean Theorem and if you can explain please
Answer:
Step-by-step explanation:
The Pythagorean theorem has the formula a squared(leg) + b squared(leg) = c squared(longest leg). This means [tex]12^{2} +16^{2} =20^{2} -- > 144+256=400[/tex] which is true meaning number 1 is a right triangle. [tex]10^{2} +49.5^{2} = 50.5^{2} -- > 100+2450.25=2550.25[/tex] is true meaning number 2 is also a right triangle because the sum of the shortest legs squared are equal to the longest leg (hypotenuse) squared.
AH = Actual Hours SH = Standard Hours AR = Actual Rate SR = Standard Rate Compute the direct labor rate and efficiency variances for the period and classify each as favorable, unfavorable or no variance
To compute the direct labor rate and efficiency variances, we will use the given terms: Actual Hours (AH), Standard Hours (SH), Actual Rate (AR), and Standard Rate (SR). Here's a step-by-step explanation:
Step 1: Calculate the Actual Labor Cost
Actual Labor Cost = AH * AR
Step 2: Calculate the Standard Labor Cost
Standard Labor Cost = SH * SR
Step 3: Calculate the Labor Rate Variance
Labor Rate Variance = (AR - SR) * AH
Step 4: Classify the Labor Rate Variance
If the Labor Rate Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.
Step 5: Calculate the Standard Labor Cost for Actual Hours
Standard Labor Cost for Actual Hours = AH * SR
Step 6: Calculate the Labor Efficiency Variance
Labor Efficiency Variance = (AH - SH) * SR
Step 7: Classify the Labor Efficiency Variance
If the Labor Efficiency Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.
By following these steps, you can compute the direct labor rate and efficiency variances for the period and classify each as favorable, unfavorable, or no variance.
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143°
(8x+55)° find the value of X
Answer:11
Step-by-step explanation:Vertically opposite angles are the same.
Alternate(Z)angles are the same.Therefore we have an angle of 143 vertically opposite to the equation.143-55=88
88/8=11
When solving two-step equations, you are using the reverse order of operations to solve the two-step equations.
Select one:
True
False
Therefore , the solution of the given problem of equation comes out to be False.
What is an equation?In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.
Here,
False.
The order of operations we use to solve two-step equations is the same order we use to solve every other mathematical statement,
which is commonly recalled by the acronym PEMDAS. (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).
The fundamental distinction is that we are carrying out the operations against the equation's representation. For instance, consider the following equation:
=> 2x + 5 = 11
To get the following result, we would first subtract 5 from both sides, then divide by 2.
=> x = 3
In order to "undo" the operations that were carried out on the variable in the original equation, we are utilising the same series of operations as usual, but in reverse order.
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4. Use the data below for the calculations.
Average hours sleeping per weeknight: 4, 5, 8, 12, 10, 6, 7, 9, 8, 8, 6, 6, 4, 3, 9
Mean:
Median:
Mean Absolute Deviation:
Absolute Deviation from Median:
The mean is 7
The median is the middle value, which is 7.
Mean Absolute Deviation: 2
How to solve for the mean absolute deviationStep 3: Find the absolute deviation of each value from the mean:
|4-7.067|, |5-7.067|, |8-7.067|, |12-7.067|, |10-7.067|, |6-7.067|, |7-7.067|, |9-7.067|, |8-7.067|, |8-7.067|, |6-7.067|, |6-7.067|, |4-7.067|, |3-7.067|, |9-7.067|
These absolute deviations are: 3.067, 2.067, 0.933, 4.933, 2.933, 1.067, 0.067, 1.933, 0.933, 0.933, 1.067, 1.067, 3.067, 4.067, 1.933.
Step 4: Find the mean of these absolute deviations to find the mean absolute deviation:
Mean Absolute Deviation = (3.067+2.067+0.933+4.933+2.933+1.067+0.067+1.933+0.933+0.933+1.067+1.067+3.067+4.067+1.933) / 15 = 2
Step 5: Find the absolute deviation of each value from the median:
|4-8|, |5-8|, |6-8|, |6-8|, |6-8|, |7-8|, |8-8|, |8-8|, |8-8|, |9-8|, |9-8|, |10-8|, |12-8|, |8-8|, |3-8|
These absolute deviations are: 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 4, 0, 5.
Therefore, the absolute deviation from the median is 5.
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A three digit number is such that twice the hundreds digit is more than the tens digit by 2. The unit digit is thrice the hundred digit. When the digits are reversed the number is increased by 594. Find the number.(5 marks)
Answer:
Step-by-step explanation:
Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.
From the problem, we have two equations:
Equation 1: $2a=b+2$
Equation 2: $c=3a$
We can use these equations to solve for $a$, $b$, and $c$.
Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.
Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.
Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.
Thus, the original three-digit number is $abc=824$.
When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.
Therefore, the answer is $\boxed{824}$.
A health insurance company wants to know the proportion of admitted hospital patients who have a type 2 diabetes at orlando health hospitals. how large of a sample should be taken to estimate the proportion within 6% at 93% confidence?
To estimate the proportion of admitted hospital patients who have type 2 diabetes at Orlando Health Hospitals within a certain margin of error and confidence level,
we can use the following formula to determine the necessary sample size:
[tex]n = [(Z^2 * p * q) / E^2] / [1 + ((Z^2 * p * q) / E^2N)][/tex]
where:
n = sample size
Z = z-score for the desired confidence level (in this case, 1.81 for a 93% confidence level)
p = estimated proportion of patients with type 2 diabetes (unknown)
q = 1 - p
E = margin of error (0.06)
N = population size (unknown)
Since we do not know the estimated proportion of patients with type 2 diabetes or the population size,
we can assume a conservative estimate of p = q = 0.5, which maximizes the sample size required.
Plugging in the values, we get:
[tex]n = [(1.81^2 * 0.5 * 0.5) / 0.06^2] / [1 + ((1.81^2 * 0.5 * 0.5) / 0.06^2N)][/tex]
Simplifying, we get:
[tex]n = 1242.95 / [1 + (2.4 / N)][/tex]
To satisfy the requirements of the problem, we need to round up to the nearest whole number, so we need a sample size of at least 1243 patients.
Note that if we had a better estimate for p or N, we could use those values in the formula to get a more precise sample size.
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Is the triangle similar to PQR? State whether each triangle similar to PQR by answering yes or no
Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.
Describe Congruency of triangle?Congruency of triangles refers to the condition in which two or more triangles have the same size and shape. In other words, if two or more triangles have congruent sides and angles, then they are said to be congruent.
The criteria for determining the congruency of triangles are based on the properties of sides and angles. There are various ways to show that two triangles are congruent, including the following:
Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence: If two angles and a side not between them in one triangle are equal to two angles and the corresponding side not between them in another triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence: If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.
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A string has a length of 80 cm. It is cut into pieces in the ratio 1: 4: 5. Calculate the length of the longest piece.
First, we need to find the total number of parts in the ratio 1:4:5:
1 + 4 + 5 = 10
This means that the string is divided into 10 equal parts. To find the length of each part, we divide the total length of the string by the number of parts:
80 cm ÷ 10 = 8 cm
Now, we can find the length of the longest piece, which is 5 times the size of each part:
8 cm x 5 = 40 cm
Therefore, the length of the longest piece is 40 cm.
