As variability shows the degree to which a particular score (or set of scores) accurately captures the distribution as a whole, it plays a significant role in sampling.
The sampling variability is the degree to which estimates vary among samples. The range is another word for "variability," and it describes how different samples have different ranges of results.
A sampling error is a phrase that's similar to, almost a synonym for, an error. An error in sampling is a measurement of how far a value deviates from its "true" value rather than an error itself. The various inaccuracies are a reflection of the sampling variability or variation between your samples.
The variability of samples fluctuates as sample sizes are raised or lowered. The sample size that will provide you with reliable estimates of the sample mean, variance, and other statistics is not the "ideal" sample size. Instead, you use your best estimation, which is based on accepted statistical practices.
Estimates will typically vary from sample to sample and are unlikely to ever completely match the population parameter.
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An experiment is conducted where weights are added to a spring which is then measured. • When 4 grams are added to the spring, the spring stretches 12 centimeters. • When 6 grams are added to the spring, the spring stretches 18 centimeters. • Let w represent the amount of weight added to the spring. • Let s represent the distance the spring is stretched. Which of the following is true about the relationship between w and s?
The relationship between w and s can be represented as s = 3w.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
When 4 grams are added to the spring, the spring stretches 4 × 3 = 12 centimeters.
When 6 grams are added to the spring, the spring stretches 6 × 3 = 18 centimeters.
In this way, if w grams are added to the spring, the spring stretches w × 3 centimeters.
Let s represent the distance the spring is stretched.
s = 3w
Hence the required relationship is s = 3w.
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the geometric series $a ar ar^2 \cdots$ has a sum of $12$, and the terms involving odd powers of $r$ have a sum of $5.$ what is $r$?
The sum of an infinite geometric series is given by a+ar+ar^2 where a is the first term and r is the common ratio.
The sum of the series can be represented by :
a / ( 1 - r) = 12
a = 12 ( 1- r ) (1)
So....note that the sum of the terms with odd powers of r can be represented by :
ar + ar^3 + ar^5 + ar^7 + ..... + ar^(2n - 1) = 5 (2)
And note that the sum of the terms with even powers of r can be represented by :
a + ar^2 + ar^4 + ar^6 + ar^8 + ..... + ar^(2n) = 7 (3)
Multiply (2) by r on both sides
ar^2 + ar^4 + ar^6 + ar^8 + ..... + ar^(2n ) = 5r (4)
Subtract (4) from (3)
a = 7 - 5r (5)
Sub (5) into (1)
7 - 5r = 12(1 - r)
7 - 5r = 12 - 12r
7r = 5 → r = 5/7
Check
a = 7 - 5(5/7) = 24/7
a / ( 1 - r) =
(24/7) / ( 1- 5/7) =
(24/7) / ( 2/7) =
24 / 2 =
12
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After you multiply everything out in the box, then write your final answer below after you combine your like terms! (x+1)(x+5)
Answer:
x^2 + 6x + 5
see attached image for sol
Answer:
[x^2 + 6x + 5]
Step-by-step explanation:
(x + 1)(x + 5)
Utilize FOIL
First
Outer
Inner
Last
x * x = x^2
x * 5 = 5x
1 * x = x
1 * 5 = 5
x^2 + 5x + x + 5
Combine like terms:
[x^2 + 6x + 5]
problems 10,11,12,13 on homework 3 right triangles and trigonometry
The missing sides are of the given triangle are of 26.69 units and 11.33 units.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Given that:
One angle of a right angled triangle measures 67 degrees.
Hypotenuse of that right angled triangle measures 29 units.
To find:
Missing sides of the triangle.
Calculations:
The sine trigonometric ratio gives us ratio of perpendicular to hypotenuse from perspective of the considered angle.
Referring to the figure attached below,
sin∠ACB = AB/AC
sin 67° = AB/29
0.9025 = AB/29
i.e. AB = 26.69
Similarly,
cos∠ACB = AB/AC
cos 67° = AB/29
0.3907= AB/29
i.e. AB = 11.33
Thus, the missing sides are of the given triangle are of 26.69 units and 11.33 units.
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Which value is the solution to the equation 2b +5b - 7 = 14 when the replacement set is {2, 3, 4, 5}?
Answer:
b = 3
Step-by-step explanation:
2b + 5b - 7 = 14
7b - 7 = 14 ( add 7 to both sides )
7b = 21 ( divide both sides by 7 )
b = 3
the value from the replacement set is 3
Does the value of the standard deviation depend on the value of the mean?A)No, because the center of a distribution and the spread are not related.B)Yes, because the mean must be known in order to calculate the standard deviation.C)Yes, because if the mean gets larger, the standard deviation will also get larger.
The correct option is A) No, because the center of a distribution and the spread are not related
How standard deviation depend on the value of the mean?The standard deviation is a measure of the spread or dispersion of a set of data. It is not directly related to the mean or average of the data.
The standard deviation is calculated based on the deviations of each data point from the mean, taking into account how many data points there are.
The mean does not affect the calculation of the standard deviation, as the formula for standard deviation is based solely on the data itself and not on any summary statistics like the mean.
The value of the standard deviation can remain the same even if the mean changes, and conversely, the mean can change without affecting the standard deviation.
Thus, option A) No, because the center of a distribution and the spread are not related is correct.
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are the following examples; the return on a mutual fund, time to completion of a task, or the volume of beer sold as 16 ounces, examples of continuous or discrete random variables?
The return on a mutual fund, time to completion of a task and the volume of beer sold as 16 ounces are the examples of continuous variables.
Discrete and continuous variables are the two categories into which they fall in mathematics.
A continuous variable is a variable that can take either an infinite or an uncountable number of values. For example, if a variable is continuous throughout a non-empty range of real numbers, it can take on any value within that range. As a result, it is argued that the set of real numbers between x and y, where x, y R, and x y, is uncountable and infinite.
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when each data value in one sample can be linked to a data value in another sample, the samples are said to be
When each value of the data in one of the sample linked to the data value in another given sample , then samples are known as paired samples.
Let us consider data value of sample one is A = { 1, 2, 3, 4, 5 }Now consider another sample as B = { a, b, c, d, e }1→a , 2→c , 3 →b , 4→e , 5→d.Each data value of one sample is linked with the data value of another sample.This relation of linking data values of two different samples is known as paired samples.All data values are uniquely associated with the other sample data values.Therefore, paired samples is representing the linking of data values of one sample to the data values of other sample.
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please solve for x.....
The values of x in the circles and secant lines are 2.3, 4 and 1
How to determine the values of xTo calculate x, we make use of the tangent-secant line theorem which stated that
c² = b * d
Using the above as a guide, we have the following:
Shape (10)
(14 + x + 2) * 14 = 16^2
This gives
16 + x = 18.3
Collect and evaluate the like terms
x = 2.3
Shape (11)
(4x + 9) * 9 = 15^2
This gives
4x + 9 = 25
Collect and evaluate the like terms
x = 4
Shape (12)
x * (x + 8) = 3^2
This gives
x^2 + 8x - 9 = 0
Factorize
(x + 9)(x - 1) = 0
So, we have
x = -9 and x = 1
x = -9 is invalid
Hence, the value is 1
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Joel wants to buy a new tablet from a store having a 20% off sale. The tablet he wants has an original cost of $190.
Which expressions would represent the sale price?
A. 0.80p
B. p + 0.20p
C. 1.20p
D. p - 0.20p
Answer:
D. p - 0.20p
Step-by-step explanation:
how many \textbf{nm} are there in 4.6 x 10^{-4} \textbf{m}? enter the appropriate exponent as a number and not a word.
There are 4.6×10⁵ nanometer present in "4.6×10⁻⁴ meter " .
The Unit nanometer (nm) is a very small unit of length measurement, used to measure the size of particles, proteins, and other small objects.
One meter is equivalent to 10⁹ nanometers, so converting from meters to nanometers is done by multiplying by 10⁹ .
To convert 4.6 × 10⁻⁴ meters to nanometers, we simply need to multiply the value by 10⁹ :
⇒ (4.6 × 10⁻⁴ meters)×(10⁹ nanometers/meter)
⇒ 46,000 nanometers = 4.6×10⁵ nanometers .
Therefore, 4.6×10⁻⁴ meter is equivalent to 4.6×10⁵ nanometers .
The given question is incomplete , the complete question is
How many "nm" are there in 4.6×10⁻⁴ m ?
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What is the lateral surface area of the rectangular prism below? QUICK
The lateral surface area of the rectangular prism is 36 squared centimeters.
What is lateral surface area of a shape?Lateral surface of any given shape is all its surface excluding its base and top. Such that the lateral surface area of a given shape is the area of all its surface apart from that of its base and top.
In the given rectangular prism, its lateral surface area can be determined as:
i. area of a rectangle 1 = length x width
= 6 * 2
= 12
area of its rectangular sides = 2 * 12
= 24 squared centimeters
ii. area of a rectangular surface 2 = 3 * 2
= 6
area of its rectangular sides 2 = 2 * 6
= 12 squared centimeters
Therefore,
its lateral surface area = 24 + 12
= 36 squared centimeters
The lateral surface area of the prism is 36 squared centimeters.
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He gives away $800 each month. If he gives away 60% of his budget, then how much is it over budget? 
He is over budget by $1,333.33 - $800 = $533.33 per month.
What is budget?
Budget can be defined as a financial plan that outlines expected income and expenditures for a specific period of time, usually a month or a year. It is a tool used to manage personal to ensure that there is enough money coming in to cover all of the necessary expenses and to prioritize spending in a way that aligns with one's financial goals.
Budget helps to track and control spending, identify areas where expenses can be reduced and make adjustments as needed to stay on track.
If he gives away 60% of his budget, then his monthly budget is $800 / 0.6 = $1,333.33.
So, he is over budget by $1,333.33 - $800 = $533.33 per month.
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The perimeter of a square is represented by the expression 4(4x−6). Which statement is true?
Responses
A. The perimeter can also be represented by the expression 8x−2 because 4(4x−6) can be simplified to 8x−2.The perimeter can also be represented by the expression 8 x minus 2 because 4 times open paren 4 x minus 6 close paren can be simplified to 8 x minus 2 point
B. The perimeter can also be represented by the expression 8x−6 because 4(4x−6) can be simplified to 8x−6.The perimeter can also be represented by the expression 8 x minus 6 because 4 times open paren 4 x minus 6 close paren can be simplified to 8 x minus 6 point
C. The perimeter can also be represented by the expression 16x−6 because 4(4x−6) can be simplified to 16x−6.The perimeter can also be represented by the expression 16 x minus 6 because 4 times open paren 4 x minus 6 close paren can be simplified to 16 x minus 6 point
D. The perimeter can also be represented by the expression 16x−24 because 4(4x−6) can be simplified to 16x−24.
Answer:
A. The perimeter can also be represented by the expression 8x−2 because 4(4x−6) can be simplified to 8x−2.
Please help simplify the algebraic fraction
[tex] \frac{x {}^{2} - 4xy + 4y {}^{2} }{2x - 4} \div \frac{x - 2y}{x - 2} \times \frac{x { }^{2}- 4 }{4} [/tex]
After simplification, value of expression is (x - 2y) (x² - 4) / 8.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The algebraic fraction is,
⇒ (x² - 4xy + 4y²) / (2x - 4) ÷ (x - 2y) / (x - 2) × (x² - 4) / 4
Now, Simplify the expression as;
⇒ (x² - 4xy + 4y²) / (2x - 4) ÷ (x - 2y) / (x - 2) × (x² - 4) / 4
⇒ (x² - 4xy + 4y²) / (2x - 4) × (x - 2) / (x - 2y) × (x² - 4) / 4
⇒ (x² - 4xy + 4y²) / (2x - 4) × (x - 2) / (x - 2y) × (x - 2) (x + 2)/ 4
⇒ (x - 2y)² / 2(x - 2) × (x - 2) / (x - 2y) × (x - 2)(x + 2) / 4
⇒ (x - 2y) / 2 × (x² - 4) / 4
⇒ (x - 2y) (x² - 4) / 8
Thus, After simplification, value of expression is (x - 2y) (x² - 4) / 8.
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Solve the following system by substitution
6. -2x + 2y = 4
x = y + 2
Answer:
Step-by-step explanation:
Answer: No Solution
1. Substitute the given value of x into the equation:
-2(y+2)+2y=4
2. Solve the equation for y
No Solution :-)
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Infinitely many solutions
∞
x - y = 2
2x - 2y = 4
x = y + 2
2•(y +2) - 2y = 4
0 = 0 => Infinitely many solutions
a vending machine contains $3.00 in nickels and dimes. if the number of dimes is 5 more than twice the number of nickels, how many coins of each type
Answer:
tmr afternoon on a thursday bc im getting a hamburger with no honey mustard.
Step-by-step explanation:
im doing it rn.
To solve this problem, we can set up an equation by considering the value of nickels and dimes. By solving the equation, we can find the number of nickels and the number of dimes.
Explanation:Let's assume the number of nickels as x.
The value of nickels is 0.05x dollars.
The number of dimes is stated as '5 more than twice the number of nickels,' which can be expressed as (2x + 5) dimes.
The value of dimes is 0.10(2x + 5) dollars.
Since the total value of the coins is $3.00, we can set up the equation:
0.05x + 0.10(2x + 5) = 3.00
Solving the equation will give us the number of nickels and dimes.
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Finding the Area of a Circle continued Find the missing measurements. Use 3.14 for T. Show your work.
Radius: 6 mm
Diameter: 12 mm
Area:.
Radius:
Diameter: 24 cm
Area:
Radius:
Diameter: 16 ft
Area:
Radius:
Diameter: 2 km
Area:
Answer:
Step-by-step explanation:
1. Area=113.1 mm^2
2. Radius=12mm
Area=452.4 mm^2
3. Radius=8 mm
Area=201.06 mm^2
4. Radius=1 km
Area=3.1416 km^2
A builder is using the drawing below to build a house. If the owner decides to increase the living room dimensions by 20%, what is the new length and width of the living room floor?
A.14.4 feet x 9.6 feet
B.144 feet x 96 feet
C.13.2 feet x 8.2 feet
D.10 feet x 8 feet
Percentage increment means the part of original value is added to the value. The new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long. The option A is the correct option.
What is the percentage of a number?
Percentage of a number or ratio is fraction of hundred. It is expressed with the sign "%".
Given information-
The length of the living room is 12 feet.
The width of the living room is 8 feet.
The owner increases the 20 percent of length and 20% width.
Suppose new length is feet long. As the owner increases the 20 percent of length. Thus the new length will be sum of original length and the 20 percent of it. Hence,
Thus the new length of the living room is 14.4 feet long.
Suppose new width is feet long. As the owner increases the 20 percent of width. Thus the new width will be sum of original width and the 20 percent of it. Hence,
Thus the new width of the living room is 1.6 feet long.
Hence the new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long. The option A is the correct option.
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can someone help me do this graph for math
The one of many solutions of the system is x = 0 and y = 0.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
A system of equations,
x + 6y = 0
30y = -5x
Simplifying,
x + 6y = 0
Both are the same equation,
so there are infinitely many solution possibles.
Therefore, solution is x = 0 and y = 0.
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assume z is a standard normal random variable. then p(1.41 < z < 2.85) equals . a. .4772 b. .3413 c. .8285 d. .0771
The value of P(1.41 < Z < 2.85) is 0.0771.
Hence, the correct answer is d.
A normally distributed random variable with mean μ= 0 and standard deviation σ= 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.
Because the Standard Normal Distribution is a probability distribution, the area under the curve between two points indicates the likelihood that variables will take on a range of values.
The whole area under the curve is one, or one hundred percent.
The mean and variance of a normal distribution are governed by two factors.
A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
The probability that a standard normal random variable Z is between 1.41 and 2.85 can be found using a standard normal table with a standard normal cumulative distribution function.
The answer is approximate:
P(1.41 < Z < 2.85)
= P(Z < 2.85) - P(Z < 1.41)
= 0.9927 - 0.9185
= 0.0742
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Describe the likelihood of the event given its probability. The probability that the sun rises tomorrow is 1.
Answer
Because 1 = 100%, it is certain that the sun will rise tomorrow
Step-by-step explanation:
A and B and C are three villages on a highway. The distance between A and B is 18km. A motorbiker moved from A at speed of 10km/hr. At the same time , another man at village B started moving at 4km/hr. How long does it take the motorbiker to catch up to the man ? If they both reach C at the same time then what is the distance between C and B.
Answer:
Let A B = x miles = 18
B C = y miles
t1 = (18 + y) / 10 time for biker 1 to reach C
t2 = y / 4 = y / 4
t1 = t2 both bikers reach C at same time
(18 + y) / 10 = y / 4
72 + 4 y = 10 y
y = 12 distance from B to C
Check:
A C = 12 + 18 = 30 km
t1 = (18 + 12) / 10 = 3 hr
t2 = 12 / 4 = 3 hrs
So both meet at C in 3 hrs
what are the common factors of 6 12 and 30
Answer:
HCF = 6.
Step-by-step explanation:
The Highest Common factor is 6.
Other common factors are 1, 2 and 3.
if a process is best situated close to the information corner of the om triangle, then this must mean:
Capacity is very expensive, so it is run at high utilization. There is a lot of variability in arrivals and processing times. Waiting or throughput times are long for this process.
Gaining understanding of the trade-offs operations managers must make is a major contribution of OR/MS models. One such trade-off concerns capacity, inventory, and variability: while the firm would want to function at 100% capacity utilization with very no inventory and tolerate high levels of unpredictability, this is not realistic.
The trade-off between these three competing goals is demonstrated and clarified using the conventional G/G/1 queueing paradigm. This insight can be described as a relationship between capacity, inventory, and the third parameter of information in situations where greater information can be used to lessen the variability in services or in arrivals (rather than variability).
Adopting the terminology of Lovejoy (1998), this inter- relationship is referred to as the OM triangle. Finding her company's ideal location in relation to the OM triangle is the manager's responsibility, as was mentioned in this article.
With variable arrival and processing times, there is a long wait period. It should have high utilization because of expensive capacity.
Therefore, the correct option is All the other answers are correct (A).
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complete question: If a process is best situated close to the inventory corner of the OM triangle, then this must mean:
a. All the other answers are correct.
b. Capacity is very expensive, so it is run at high utilization.
c. There is a lot of variability in arrivals and processing times.
d. Waiting or throughput times are long for this process.
what is 4-2y+(-8y)+7.5 in a simplified answer
Answer:
The expression 4 - 2y - 8y + 7.5 can be simplified as follows:
4 - 2y - 8y + 7.5
= 4 - (2y + 8y) + 7.5
= 4 - 10y + 7.5
= 4 + 7.5 - 10y
= 11.5 - 10y
So, the simplified answer is 11.5 - 10y.
Answer: -10y+11.5
Step-by-step explanation:
a scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. how many cells will the population contain when the bacteria is destroyed?
Since the cell population doubles at constant intervals, we can use the formula for exponential growth: N = N0 * 2^(t/k), where N0 is the initial population, t is the time elapsed, and k is the doubling time.
Since we are told that the population will double four hours from now, and since we are not given the initial population or the doubling time, we cannot determine the final population when the bacteria will be destroyed.
As the division two hours ago and the division just now, the population quadrupled that is two doubling periods, so each doubling period is about an hour.
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) Express 8x-x² in the form a- (x + b)²
Pls bro help
Answer: To express the expression 8x - x² in the form a - (x + b)², we can complete the square method.
First, we'll add (1/2)^2 = 1/4 to both sides of the expression:
8x - x² + 1/4 = 1/4
Next, we'll rearrange the left-hand side to the desired form:
(2x - 1/2)² - 1/4 = 1/4
Now, we can identify a = -1/4, b = 1/2, so the expression is:
a - (x + b)² = -1/4 - (x + 1/2)²
Step-by-step explanation:
Q1.
There are a total of 96 children in Years 4, 5 and 6
37 of these children cannot swim.
11 children in Year 4 cannot swim.
21 children in Year 5 can swim.
There are 30 children in Year 6
18 of these 30 children can swim.
(1) Work out the number of children in Year 4 who can swim.
(ii) Work out the total number of children in Year 5
Answer:
Question 1:
Of the 37 children that can't swim, 11 are in Year 4.
Therefore, 26 children in Year 4 can swim.
Question 2:
There are 21 children in Year 5 who can swim.
In Year 6, there are 30 children, 18 of which can swim.
Therefore, a total of 21 + 18 = 39 children who can swim.