Assuming the distribution is bell-shaped, the estimated standard deviation is 10.
Since the range is 60 and the distribution is bell shaped the N or Number will be 6
Thus, to calculate the standard deviation:
60/6 = 10
The standard deviation is a statistic that expresses the degree of variation or dispersion among a set of values. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.
None of the standard deviations are "good" or "bad.". They serve as gauges of your data's dispersion. Sometimes, when using ratings scales, we want a wide spread because it shows that the range of the group we are rating is covered by our questions and ratings.
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Forty percent of what number is 18?
Answer:
45
Step-by-step explanation:
Y = forty percent of blank to make 18
18 = 40/100 x Y
Y = 18 x 100/40
Y = 18 x 100 divided by 40
Y = 45
A television and DVD player cost total of $1192. The cost of the television is three times the cost of the DVD player. Find the cost of each, item.
Cost of television:
Cost of DVD player:
The cost of the DVD player and the cost of the television will be $298 and $894, respectively.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
A television and DVD player cost a total of $1192. The cost of the television is three times the cost of the DVD player.
Let 'x' be the cost of the DVD player and 'y' be the cost of the television. Then the equations are given as,
x + y = 1,192 ...1
y = 3x ...2
From equations 1 and 2, then we have
x + 3x = 1192
4x = 1192
x = $298
Then the value of 'y' is given as,
y = 3 (298)
y = $894
The cost of the DVD player and the cost of the television will be $298 and $894, respectively.
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Find each angle measure to the nearest degree.
3) sin U = 0.9945
4) tan C = 3.7321
The measure of angle U = 84° and the measure of angle C = 75°
The inverse of a trigonometric function.The sine, cosine, tangent, cotangent, secant, and cosecant functions are the fundamental trigonometric functions. Inverse trigonometric functions are just the inverse functions of these functions. They can also be referred to as antitrigonometric functions or arcus functions. To find the angle for any trigonometric ratio, these inverse trigonometric functions are applied.
Given that:
sin U = 0.9945
U = sin⁻¹ (0.9945)
U = 83.988°
U ≅ 84° ( to the nearest degree)
tan C = 3.7321
C = tan⁻¹ (3.7321)
C = 75°
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at 12/31 accounting records of Gordon Inc contain
AP $2500, Building $31250, Land $30,000, Notes Payable $ ?, Retained earnings
$125,000, AR $18750, Cash ?, Equipment $40,000, Captial Stock $12500
If the cash balance at 12/31 is $67,500 The notes payable balance is
To find the Notes Payable balance, we need to use the accounting equation:
Assets = Liabilities + Equity
We are given the following information:
AP = $2,500
Building = $31,250
Land = $30,000
Notes Payable = ?
Retained Earnings = $125,000
AR = $18,750
Cash = $67,500
Equipment = $40,000
Capital Stock = $12,500
We can add up the assets to get:
Assets = AP + Building + Land + AR + Cash + Equipment
= $2,500 + $31,250 + $30,000 + $18,750 + $67,500 + $40,000
= $190,000
We can rearrange the accounting equation to solve for liabilities:
Liabilities = Assets - Equity
Plugging in the values we have:
Liabilities = $190,000 - ($125,000 + $12,500)
= $190,000 - $137,500
= $52,500
Therefore, the Notes Payable balance is:
Notes Payable = Liabilities - AP
= $52,500 - $2,500
= $50,000
what is the equation of the secant line connecting the point (1,f(1)) to the point (0.9,f(0.9))? the equation of this secant line is y
(a) The equation of the secant line connecting (1, f(1)) and (0.9, f(0.9)) is y = -x + 2.1.
(b) The slope of the tangent line to f at x is f'(x) = -cos(x), and the equation of the tangent line at (x, f(x)) is y = -cos(x)*x + sin(x) + cos(x)*x.
In contrast to the tangent line, which meets a curve just once and has the same slope as the curve at that point, the secant line is a straight line that connects two locations on a curve. In this task, we are required to determine the equations of the secant and tangent lines at various places given a function f(x).
Using the two provided locations, we determine the slope of the secant line in section (a), which is equal to the difference between the y- and x-coordinates. The equation of the line is therefore written using the point-slope form, and it is y = -x + 2.1.
In part (b), we use the definition of the derivative to find the slope of the tangent line at a given point x. We then use the point-slope form of a line to write the equation of the tangent line, which has the same slope as the derivative and passes through the point (x, f(x)). In this case, the slope of the tangent line is -cos(x), and the equation of the tangent line is
y = -cos(x)*x + sin(x) + cos(x)*x.
The complete question is provided in the image below.
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Decide how many solutions this equation has:
x2 - 2x + 1 = 0
Richard used a radius measure of a circle to be 3.6 inches when he calculated the area of a circle. The correct radius measure was actually 3.5 inches. What is the difference between Richard’s measured area of the circle and the actual area of the circle?
a. 0.1π square inches
b. 0.71π square inches
c. π square inches
d. 0 square inches
e. 2.4 square inches
As a result, the answer is (e) 2.4 square inches, which is the difference between Richard's measured and real circle area.
What is area?In mathematics, area is a measure of the amount of space occupied by a two-dimensional object, such as a rectangle, triangle, circle, or any other shape. It's a scalar quantity that describes the size of a region in two-dimensional space. The units of area are typically square units, such as square inches, square centimeters, square meters, etc. In general, the area of a shape is a measure of how much space it occupies, and it is an important concept in geometry, engineering, and many other fields.
Here,
The formula for the area of a circle is given by:
A = πr²
Where r is the radius of the circle.
Using the incorrect radius of 3.6 inches, the calculated area would be:
A = π * (3.6 inches)² = 40.44 square inches
Using the correct radius of 3.5 inches, the actual area would be:
A = π * (3.5 inches)² = 38.5 square inches
So, the difference between Richard's measured area of the circle and the actual area of the circle would be:
40.44 square inches - 38.5 square inches = 1.94 square inches
Therefore, the answer is (e) 2.4 square inches that is the difference between Richard’s measured area of the circle and the actual area of the circle.
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Kendallyn wants to know the height of a sailboat mast. if the sailboat mast casts a shadow 45 meters long and a nearby marble column that is 8 meters tall casts a shadow 15 meters long, then the sailboat mast is___ meters long. Write your answer as a whole number or a decimal.
The sailboat mast casts a shadow 45 meters long and a nearby marble column that is 8 meters tall casts a shadow 15 meters long, then the height of the sailboat mast is 24 meters.
We can use proportions to solve this problem. Let's let h be the height of the sailboat mast, then we have:
h/45 = 8/15
Cross-multiplying, we get:
15h = 8 * 45
Simplifying, we get:
15h = 360
Dividing by 15, we get:
h = 24
Therefore, the height of the sailboat mast is 24 meters. This means that the sailboat mast is 3 times as tall as the marble column, since its shadow is 3 times as long.
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Suppose the data have a bell-shaped distribution with a mean 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data between 15 and 45.
Select one:
a. 95.00%
b. 97.35%
c. 99.70%
d. 81.50%
According to the empirical rule, for a bell-shaped distribution with a mean of 30 and a standard deviation of 5 is approximately 99.7%,
Using the empirical rule, we know that for a normal distribution with a mean of 30 and a standard deviation of 5, approximately:
68% of the data falls within 1 standard deviation of the mean, which in this case is between 25 and 35.95% of the data falls within 2 standard deviations of the mean, which in this case is between 20 and 40.99.7% of the data falls within 3 standard deviations of the mean, which in this case is between 15 and 45.Therefore, the percentage of data between 15 and 45 is approximately 99.7%, which corresponds to option c.
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X
5
Z
10
5√3
Y
Find sin cos tan
The trigonometry ratios have their values to be
sin(x) = √3/2cos(x) = 0.5tan(x) = √3How to determine the trigonometry ratiosThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Hypotenuse = 10
Adjacent = 5
Opposite = 5√3
Using the above as a guide, we have the following:
sin(x) = Opposite/Hypotenuse
cos(x) = Adjacent/Hypotenuse
tan(x) = Opposite/Adjacent
Using the above as a guide, we have the following:
sin(x) = 5√3/10 = √3/2
cos(x) = 5/10 = 0.5
tan(x) = 5√3/5 = √3
The above are the values of the trigonometry ratios based on the attached figure
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Part 2
Bc my autocorrect messed up my other question.
Make a word using all of these letters
RrCsVb
This doesn't have to be an actual word but one that is memorable. Please use all of the words
Answer:
CrabSVR
BRscrV
ScarbRV
VRbScCr
Step-by-step explanation:
I can suggest that some of these words might be memorable because they are short and have a combination of consonants and vowels that make them sound unique and catchy. For example, "ScrubVR" has a rhythmic and playful sound to it, while "BRscrV" has a more abbreviated and tech-like feel to it. Ultimately, what makes a word memorable is highly subjective and varies from person to person.
Answer: he right
Step-by-step explanation:
Jennifer was given $600. She decided to save 15% of the money.
How much did she save? $____.00
Do not type in the dollar sign. Just type in the missing amount.
Answer: She saved 90 dollars.
To solve this we must find amount of 600 that makes 15 percent.
15 % of 600 is 90. This means that Jennifer saved up 90 dollars
I hope that this helps & Good Luck <3 !!!
A game manufacturer is designing a pocket travel-edition of one of its top-selling games. The tull-size triangular game board and the proposed travel board are represented below
where ABC-A XYZ and the given side lengths are measured in centimeters
32
52
Which of these are true? Choose all that are comect
The perimeter of the full-size game board is six times the perimeter of the travel-edition game board
The travel-edition side comesponding to the 48-cm side on the tull-size board will measure 13 centimeters.
The travel-edition side comesponding to the 48-cm side on the full-size board will measure 12 centimeters
The three angles represented on the travel-edition board are congruent to their comesponding angles on the full-size board
Based on the given information and measurements, the following statements are true:
What are the true statements?The perimeter of the full-size game board is six times the perimeter of the travel-edition game board: This statement is false. The perimeter of the full-size game board can be calculated as the sum of the lengths of its three sides: AB + BC + AC = 32 + 52 + 52 = 136 cm. The perimeter of the travel-edition game board can be calculated as the sum of the lengths of its three sides: AX + XY + YZ = 13 + 21 + 18 = 52 cm. Therefore, the perimeter of the full-size game board is 2.62 times the perimeter of the travel-edition game board, not 6 times.
The travel-edition side corresponding to the 48-cm side on the full-size board will measure 12 centimeters: This statement is false. The travel-edition side corresponding to the 48-cm side on the full-size board is side XY. The length of XY can be calculated using proportions: XY/48 = YZ/52, which gives XY = 48*18/52 = 16.62 cm (rounded to two decimal places).
The travel-edition side corresponding to the 48-cm side on the travel-edition board will measure 13 centimeters: This statement is true. The travel-edition side corresponding to the 48-cm side on the travel-edition board is side AX, which has a length of 13 cm.
The three angles represented on the travel-edition board are congruent to their corresponding angles on the full-size board: This statement is true. The three angles of a triangle are determined by the lengths of its sides, so if two triangles have the same side lengths, their angles must be congruent as well.
Therefore, the three angles represented on the travel-edition board (at vertices A, X, and Y) are congruent to their corresponding angles on the full-size board (at vertices A, B, and C).
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Predict the missing component in the nuclear equation.
The missing component in the nuclear equation.137Cs55 → X + -e will be 137Ba56. option B is correct.
What is nuclear reaction?The particles in the nucleus are changed, and one element is transformed into another element when particles in the nucleus are gained or lost.
Nuclear reactions are processes in which one or more nuclides are produced from the collisions between two atomic nuclei or one atomic nucleus and a subatomic particle.
This was the first observation of an induced nuclear reaction, that is, a reaction in which particles from one decay are used to transform another atomic nucleus.
The most notable man-controlled nuclear reaction is the fission reaction which occurs in nuclear reactors. A target nucleus is within the range of nuclear forces for the time allowing for numerous interactions between nucleons.
therefore, option B is correct.
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Choose the number of possible combinations shown by this tree diagram.
2 combinations
4 combinations
5 combinations
6 combinations
Bacteria colonies can increase by 45% every 7 days. If you start with 200 bacteria microorganisms, how large would the colony be after 35 days? First, identify I, the starting amount. Future Amount = [?](1+ Remember: Future Amount = (1 + r)t
After 35 days, the colony will be 1281.95.
What are Exponential Functions?Exponential functions are functions where the independent variable, x is in the exponent.
Given that,
Bacteria colonies can increase by 45% every 7 days.
We know that,
Future amount = l (1 + r)^t
where l is the starting amount, r is the growth rate and t is the time.
Here,
l = 200
r = 45% = 45 / 100 = 0.45
t = 35 / 7 = 5
Substituting,
Future amount = (200) (1 + 0.45)⁵
= 1281.95
Hence the required amount is 1281.95.
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Contessa is solving an absolute value inequality. She writes the compound inequality -7<=8-3q<=7 as her first step. Which inequality is Contessa solving?
The inequality that Contessa is solving is obtained as 5 ≥ q ≥ 1/3.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The given compound inequality is = -7 ≤ 8 - 3q ≤7
To solve this compound inequality, start by subtracting 8 from each part of the inequality -
-15 ≤ -3q ≤ -1
Next, divide each part by -3, remembering to flip the direction of the inequalities since it is getting divided by a negative number -
5 ≥ q ≥ 1/3
So the solution to the inequality -7 ≤ 8-3q ≤ 7 is the set of all q values that lie between 1/3 and 5, including the endpoints 1/3 and 5.
Note that this solution set is different from the solution set of the absolute value inequality |8-3q| < 7, which does not include the endpoints.
Therefore, the inequality is 5 ≥ q ≥ 1/3.
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The equation:
(x³+2x²) (3x²+2x+1)=x³ (3x² + 2x+1) + 2x² (3x² + 2x+1) is an example of which method/property?
A. Distributive Property
B. FOIL
C. Vertical multiplication
D. Collect like terms
d. In this situation, what does the solution to the equation C(t) = 2 tell us? Find
that solution.
e. Write an equation that would allow us to find the age of the car when we know
C(t).
ora 1 Unit 4
n 17
CC BY 2019 by Illustrative Mathematics®
The equation C(t) = 2 tells us that at a moment of t, the numeric value of the variable C is of 2 units.
How to define the ordered pair and how it relates to the numeric value?The general format of an ordered pair is given as follows:
(x,y).
The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.
The ordered pair for this problem is given as follows:
(t, C(t)) = (t,2).
Meaning that at a moment of t, the numeric value of the variable C is of 2 units.
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what is the kinetic energy of 1500 kg pick-up truck traveling at 31.0 m/sec.
The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec will be 720 kJ.
What is kinetic energy?If the body of the mass (m) is moving with a velocity (v), then the body possesses the energy which is known as kinetic energy. The SI unit of the kinetic energy is Joule. Then the formula is given as,
KE = 1/2 x mv²
The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec is given as,
KE = 1/2 x 1500 x 31²
KE = 720,750 Joule
KE = 720 kJ
The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec will be 720 kJ.
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The population of Lcavetown is 123,000 people, and is decreasing at a rate of 9,4% per year What will the population of Leavetown be 100 years from now? (round to the nearest person)
Answer:
6
Step-by-step explanation:
You want the population of Leavetown in 100 years if it is 123,000 now and decreasing at the rate of 9.4% per year.
Exponential equationThe exponential equation that models the population is ...
p = 1230000·(1 -0.094)^t
where t is the number of years later.
ApplicationFor t=100, the attached calculation shows the population in 100 years is about 6 persons.
I've been working on this problem for the last hour and can't quite seem to get it right.
A tank is full of water. Find the work required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3. (Assume a = 4 ft, b = 5 ft, and c = 6 ft.)
The work required to pump the water which weighs 62.5 lb/ft3 out of the spout is 15000 foot-pounds.
To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then multiply by the height of the spout to find the potential energy of the water.
First, we need to find the volume of the tank, which is given by:
V = a * b * c = 4 ft * 5 ft * 6 ft = 120 ft^3
Next, we can find the weight of the water in the tank, using the fact that water weighs 62.5 lb/ft^3:
W = V * ρ = 120 ft^3 * 62.5 lb/ft^3 = 7500 lb
So the weight of the water in the tank is 7500 pounds.
Now, we can find the potential energy of the water by multiplying the weight by the height of the spout. Let's assume the spout is 2 feet above the top of the tank:
PE = W * h = 7500 lb * 2 ft = 15000 ft-lb
So the work required to pump the water out of the spout is 15000 foot-pounds (ft-lb). This means that if we used a pump that was 100% efficient, it would require 15000 ft-lb of work to pump all the water out of the tank. However, in reality, pumps are not 100% efficient, so the actual work required would be greater than 15000 ft-lb.
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(book exercise 1.2.37 determine in terms of h the first two terms and the error term in the taylor series for ln(3-2h)
Answer:
which book are u talking about.. post the question please..
consider a system using a multilevel feedback queue scheduler. its scheduler is configured to have four queues, which are, in order of highest priority to lowest priority: q1, q2, q3, and q4. the queues have quantums sized 5s, 10s, 20s, and 40s, respectively. for each of the following three processes, determine which queue it is in when it begins its final quantum
In this example, process A completed its final quantum in q4, process B completed its final quantum in q4, and process C completed its final quantum in q4.
To determine which queue each process is in when it begins its final quantum, we need to know the length of time each process has been running and how many times it has already used each queue's quantum. Without that information, we cannot determine which queue a process will be in at a specific point in time. However, we can provide an example of how a process might move between the queues over time.
Let's consider the following three processes:
Process A - CPU burst time = 100s
Process B - CPU burst time = 30s
Process C - CPU burst time = 50s
Assume that all three processes arrive at the scheduler at the same time and are added to q1, the highest priority queue.
When the scheduler begins, it will select the first process in q1, which is process A. Since q1 has a quantum of 5s, process A will run for 5s before it is preempted and placed at the back of q2.
The next process in q1 is B. B will also run for 5s before being preempted and placed at the back of q2.
Next, the scheduler will select process C from q1. C will run for 5s before being preempted and placed at the back of q2.
Now the scheduler has completed one round-robin cycle through q1, and all the processes in q1 have used up their q1 quantum. The scheduler will move on to q2 and select the first process in that queue, which is process A. Since q2 has a quantum of 10s, process A will run for an additional 5s before being preempted and placed at the back of q3.
The next process in q2 is B. B will run for 10s before being preempted and placed at the back of q3.
Next, the scheduler will select process C from q2. C will run for 10s before being preempted and placed at the back of q3.
Now the scheduler has completed one round-robin cycle through q2, and all the processes in q2 have used up their q2 quantum. The scheduler will move on to q3 and select the first process in that queue, which is process A. Since q3 has a quantum of 20s, process A will run for an additional 10s before being preempted and placed at the back of q4.
The next process in q3 is B. B will run for 20s before being preempted and placed at the back of q4.
Next, the scheduler will select process C from q3. C will run for 20s before being preempted and placed at the back of q4.
Now the scheduler has completed one round-robin cycle through q3, and all the processes in q3 have used up their q3 quantum. The scheduler will move on to q4 and select the first process in that queue, which is process A. Since q4 has a quantum of 40s, process A will run for an additional 20s before completing its CPU burst.
The next process in q4 is B. B will run for 30s before completing its CPU burst.
Finally, the scheduler will select process C from q4. C will run for 40s before completing its CPU burst.
However, it's important to note that the exact behavior of the scheduler will depend on the length of time each process has been running and how many times it has already used each queue's.
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Add. Write your answer in simplest form.
3/8 + 2/5 WILL GIVE BRAINLIST IF RIGHT!!!
An experiment observing the growth of two germ strand populations finds these patterns.
• The population of the first germ is represented by the function A(x) = (1.3)^x+9
• The population of the second germ is represented by the function B (x) = ^4x+1
Which function best represents function R, the ratio of the population of the second germ to the population of the first germ?
A. R(x) = (1.3)^3x-8
B
An experiment observing the growth of two germ strand populations finds these patterns.
• The population of the first germ is represented by the function A(x) = (1.3)^x+9
• The population of the second germ is represented by the function B (x) = ^4x+1
Which function best represents function R, the ratio of the population of the second germ to the population of the first germ?
A. R(x) = (1.3)^3x-8
B. R(x) = (1.3)^5x+10
C.R(x) = (2.6) ^3x-8
D. R(X) =(2.6) ^4x^2+9
The right answer, based on the provided assertion, is (C) R(x) = 2.6³ˣ⁻⁸.
What does an arithmetic the expression mean?Mathematical expressions consist of at least two integers or factors, a minimum of one math procedure, and a sentence. It's possible to multiply, divide, add, or remove with this mathematical procedure. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
To find the ratio of the population of the second germ to the population of the first germ, we can divide the function for the population of the second germ by the function for the population of the first germ. That is:
R(x) = B(x) / A(x)
Plugging in the given functions, we get:
R(x) = (x+1) / (1.3)ˣ⁺⁹
To simplify this expression, we can use the properties of exponents and rewrite it as:
R(x) = 2.6ˣ⁻⁸
Therefore, the function that best represents the ratio of the population of the second germ to the population of the first germ is R(x) = 2.6ˣ⁻⁸
So, the correct option is (C) R(x) = (2.6)³ˣ⁻⁸.
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Evaluate h - 3 for h = 1
The result of the function is h = 1 is equal to -2
Evaluating linear equationsLinear equations are equations that has a leading degree of 1.
Given the linear equation f(h) = h - 3
We need to determine the resulting value when h is equal to 1
f(1) = 1 - 3
f(1) = -2
Hence the value of the function given if the value of h is 1 is -2
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Find the area of the isosceles triangle
The area of the isosceles triangle is 96 ft²
How to determine the areaThe formula for area of a triangle is expressed as
Area = 1/2bh
Where , b is the base and h is the height
We have that;
Base = 16ft
Using the Pythagorean theorem, we have;
20² - 16² =h²
Find the squares
h = √144
h= 12ft
Substitute the values
Area = 1/2 × 12 × 16
Multiply the values
Area = 96 ft²
Hence, the value is 96 ft²
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find the mean and median of each of the following sets of data. determine the deviation from the mean for each data point within the sets and find the mean deviation for each set. 24.49 24.68 24.77 24.83 24.73
The average distance from the mean is 0.09.
The mean is also known as the average and is calculated by adding up all the values in the set and then dividing the sum by the total number of values.
So, for the given set of data: 24.49, 24.68, 24.77, 24.83, 24.73, the mean would be calculated as follows:
Mean = (24.49 + 24.68 + 24.77 + 24.83 + 24.73) / 5
= 24.70
It tells us what the typical value is within the data set. In this case, the mean value of the data set is 24.70.
Next, let's find the median of the set of data. The median is the middle value of a data set when it is arranged in numerical order. In this case, the data set is already arranged in numerical order, so we can easily find the median.
The median value of the data set is the middle value, which is 24.77.
Now, we will calculate the deviation from the mean for each data point within the set. The deviation from the mean tells us how far each value is from the mean value. This is calculated by subtracting the mean from each value in the set.
Deviation from the mean for each data point:
-0.21, -0.02, 0.07, 0.13, 0.03
As you can see, some values are above the mean, and some are below the mean. The deviation from the mean can be used to determine how spread out the data is from the mean value.
Finally, we will calculate the mean deviation for the set. The mean deviation is the average of the absolute values of the deviation from the mean.
Mean deviation = (|(-0.21)| + |(-0.02)| + |0.07| + |0.13| + |0.03|) / 5
= 0.09
The mean deviation tells us the average distance from the mean value.
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a monkey presses the keys on a typewriter randomly. suppose the typewriter only contains the 26 letters of the alphabet (no space or other characters), and the monkey chooses the next key to press uniformly at random from the 26 options. suppose the monkey types n letters in total.
The probability of typing any particular sequence of n letters is (1/26)^n. The probability of word of length m (where m ≤ n) is (1/26)^m. The probability of at least one occurrence is 1 - (25/26)^(n-m+1). The number of times the monkey types a specific word of length m is (n-m+1)*(1/26)^m.
Assuming that the monkey's key presses are truly random and independent of each other, the probability of the monkey typing any particular sequence of n letters is (1/26)^n. This is because there are 26 choices for each letter, and the probability of the monkey choosing any particular letter is 1/26.
The probability of the monkey typing a specific word of length m (where m ≤ n) is (1/26)^m. This is because the monkey must type the specific sequence of m letters in order, and each letter has a probability of 1/26 of being typed.
The probability of the monkey typing at least one occurrence of a specific word of length m is 1 - (25/26)^(n-m+1). This is because the monkey has n-m+1 opportunities to type the word, and the probability of missing the word in any one opportunity is 25/26 (since there are 25 other letters that the monkey could type instead).
The expected number of times the monkey types a specific word of length m is (n-m+1)*(1/26)^m. This is the product of the probability of the monkey typing the word in any given opportunity (which is (1/26)^m), and the number of opportunities the monkey has to type the word (which is n-m+1).
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