The relationship between the two confidence intervals will be that the width of i81 will be 3 times the width of i9. So, the correct answer is option D.
What are confidence intervals?In statistics, a confidence interval is a range of values that is used to estimate the unknown population parameter. They are used to express the degree of uncertainty associated with a sample estimate of a population parameter.
Two 99 percent confidence intervals are going to be constructed to estimate the difference in means of two populations, r and w. One confidence interval, i9, is going to be constructed using samples of size 9 from each of r and w.
The other confidence interval, i81, is going to be constructed using samples of size 81 from each of r and w. When all other things remain the same, the width of 181 will be 3 times the width of Ig.
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Aaliyah puts 42 gal of water into her fish tank . This is 60% of the total number of gallons the fish tank can hold how many total gallons of water can the fish tank hold
Answer:
58.8 gallons
Step-by-step explanation:
for an astm grain size of 8, approximately how many grains would there be per square inch at a magnification of 100? without any magnification?
An ASTM grain size of 8 means that there are 8 grains per square inch at a magnification of 100. Without any magnification, it is not possible to determine the number of grains per square inch.
ASTM grain size is a measure of the size of the grains in a metal sample. The ASTM E112 defines the grain size number as the number of grains per square inch of metal surface area at a magnification of 100 times. So, an ASTM grain size of 8 means that there are 8 grains per square inch at a magnification of 100.
Without any magnification, it is not possible to determine the number of grains per square inch as the grains are too small to be visible to the eye. However, the ASTM grain size number can still provide information about the grain size distribution in the metal sample.
A metal sample with a smaller grain size number (i.e., larger grain size) will have fewer grains per square inch at a magnification of 100 than a metal sample with a larger grain size number (i.e., smaller grain size). This is because larger grains take up more surface area than smaller grains, resulting in fewer grains per unit area.
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A certain amount of money is shared between rui feng and vishalin the ratio of 5:9 if rui feng gets 44 dollar less than vishal find total amount of money shared between the two boys
The total amount of money shared between Rui Feng and Vishal is 154 dollars.
Let's assume that the amount of money shared between Rui Feng and Vishal is x dollars.
According to the given ratio, the amount of money received by Rui Feng is 5/14 of the total amount, and the amount received by Vishal is 9/14 of the total amount.
We are also given that Rui Feng receives 44 dollars less than Vishal. We can express this as:
9/14 x - 5/14 x = 44
Simplifying the equation, we get:
4/14 x = 44
Multiplying both sides by 14/4, we get:
x = 154
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can anyone help? Im not so good at math
Answer:
To solve for m, we need to isolate the variable by performing the same operation to both sides of the equation.
Dividing both sides of the equation by 6 will give us:
6m/6 = 33/6
Simplifying:
m = 5.5
Therefore, the solution to the equation 6m = 33 is m = 5.5.
To solve for p, we need to isolate the variable by performing the same operation to both sides of the equation.
Subtracting 7.04 from both sides of the equation will give us:
p + 7.04 - 7.04 = 11.8 - 7.04
Simplifying:
p = 4.76
Therefore, the solution to the equation p + 7.04 = 11.8 is p = 4.76.
To solve for n, we need to isolate the variable by performing the same operation to both sides of the equation.
First, we need to simplify both sides of the equation by finding a common denominator for the fractions:
n + (3/5) = 8/10 can be written as:
n + (3/5) = (4/5)
Next, we can subtract (3/5) from both sides of the equation:
n + (3/5) - (3/5) = (4/5) - (3/5)
Simplifying:
n = 1/5
Therefore, the solution to the equation n + (3/5) = (8/10) is n = 1/5.
These are your answers for questions 1-3.
past data suggest that the score increase has astandard deviation of about 50 points. how large a sample of high school students would be needed to estimate the mean change in sat score to within 2 points with 95% confidence
382 students
To estimate the mean change in SAT scores to within 2 points with 95% confidence, you would need a sample of at least 382 high school students. This is because the margin of error (2 points) must be smaller than the standard deviation (50 points). Thus, we use the formula margin of error = (z-score) x (standard deviation/√n), where n is the sample size, to calculate the required sample size. Solving for n yields 382 students.
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which is bigger 4.03 or 4.01
Answer:
4.03
Step-by-step explanation:
Answer options
2 units
4 units
6 units
10 units
As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.
what is triangle ?Three straight lines that cross at three different locations create the two-dimensional geometric outline of a triangle. A triangle's vertices, which are the three places at which those three lines intersect, are referred to as the triangle's sides. The dimensions of a triangle's edges and angles can be used to classify it. For instance, an isosceles triangle has two equal sides and two equal angles while an equilateral triangle has three equal sides and three equal angles of 60 degrees. An angle or side of a scalene triangle cannot be equivalent.
given
The right-angled triangle XYZ in the provided illustration has a side length of 6 units and an angle opposite to it that is labelled as 30°. The extent of the side YZ, denoted as x, must be determined.
To find x, we can use the trigonometric sine relation. The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. The hypotenuse in this instance is designated as 2x.
As a result, we have:
sin 30° = (6/2x)
Adding two times to both sides:
2x * sin 30° = 6
Using sin 30°, which has a value of 0.5:
x = (6/(2 * 0.5)) = 6/1 = 6
Consequently, the side YZ is 6 units long.
As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.
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in square units, what is the largest possible area a rectangle inscribed in the triangle shown here can have?
For the triangle shown, the area is (1/2) * 5 * 4 = 10 square units. The largest possible area of a rectangle inscribed in a triangle is equal to the area of the triangle.
The area of the triangle can be calculated using the formula: Area = (1/2) * Base * Height.
Note that the rectangle must be completely within the triangle and all of its sides must be parallel to the sides of the triangle. To calculate the area, the base and height of the triangle must be known. The base is the length of any one side, while the height is the perpendicular distance from the base to the opposite vertex.
In this case, the triangle is 5 units along the base and 4 units in height. The area can then be calculated as (1/2) * 5 * 4 = 10 square units.
It is also important to note that the rectangle can have sides of different lengths and will still have an area of 10 square units.
To summarize, the largest possible area a rectangle inscribed in the triangle shown can have is 10 square units. This can be calculated using the formula (1/2) * Base * Height. The rectangle can have sides of different lengths, but the area will remain the same.
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please help mee I need it
7 is the value of mixed fraction.
What exactly is a mixed fraction?
A mixed fraction is one that is represented by both its remainder and quotient. Two is the quotient and one is the remainder in the mixed fraction 2/3, for instance. Hence, a mixed fraction is created by combining a whole number and a proper fraction. A mixed number is one that includes both a whole number and a legal fraction.
= 6 30/44
= 294/44
= 6.6818
= 7 ( round off )
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a farmer wants to build a rectangular enclosure, using the side wall of his barn and the other 3 sides created by fencing. he has 70 meters of fencing. what is the largest area he can fence in?
The largest area a farmer can fence in is 612.5 m².
The given question is based on finding the largest area a farmer can fence in for building a rectangular enclosure.
The farmer is given with 70 meters of fencing for fencing 3 sides of a rectangular enclosure.
The enclosure's fourth side is the wall of the farmer's barn.
To find the largest area fenced in, the farmer must try to use all 70 meters of fencing to enclose as large an area as possible.
First, let's assume that the rectangular enclosure's width is x.
So, we can find the length by dividing the remaining length of fencing after subtracting the width of the fence from the total length of fencing.
The remaining length of fencing is 70 - 2x.
After calculating the length, the area of the rectangular enclosure can be calculated by multiplying length and width.
The formula for calculating the area of the rectangle is A = l x w.
A = (70 - 2x)x
= 70x - 2x²
To find the maximum area fenced in, differentiate A with respect to x and equate it to zero.
dA/dx = 70 - 4x
=0x = 17.5 meters.
After finding x, the length of the enclosure can be calculated by subtracting the width from the total length of fencing.
l = 70 - 2x = 70 - 2(17.5) = 35 meters.
Therefore, the largest area fenced in will be A = l x
w = 35 x 17.5 = 612.5 m².
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why does the gcf of the variables of a polynomial have the least exponent of any variable term in the polynomial brainly
The GCF (Greatest Common Factor) of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that is common to all the terms in the polynomial.
To understand this better, consider a polynomial like 6x²y³ + 9x³y². The GCF of this polynomial would be 3x²y², which is the largest factor that can divide both terms evenly.
Notice that the exponent of each variable in the GCF is the smallest exponent among the corresponding variable terms in the polynomial.
This is because any factor that is common to all terms in the polynomial must be able to divide each term without leaving a remainder. Therefore, the exponent of each variable in the GCF must be less than or equal to the exponent of that variable in every term of the polynomial.
In summary, the GCF of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that can divide all terms in the polynomial evenly, and therefore, it must have the smallest exponent of each variable among all terms in the polynomial.
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pls help Mariah sells her paintings which she frames using pieces of wood that are 1 inch wide . Her paintings come in difference sizes , but the width is always 1.5 times the height Write an equation to represent the total area of her paintings and their frames .
if u can pls draw the height and width :)
Step-by-step explanation:
Lets use A for area, W for width, and H for height (sorry in advance for bad handwriting, I am writing using a mouse)
Since area is equal to width times height, lets make an equation given what we already know.
A = W * H
Now lets use the given parameters to create a proper area equation, partially answering the question.
A = (H*1.5) * H, H*1.5 being the width
Now we have the frames to add to this equation
Since these frames are 1 inch thick, this adds one inch to the width and the height.
You use order of operations to assume that we are calculating this by multiplying the height by 1.5 first, then adding the one inch to the width and height.
So our final equation is:
A = ((h*1.5)+1) * (h+1)
Lets give some example values
Height is 6, width is 6*1.5, meaning width is 9
After, we add one to the height and the width, meaning the height is 7 and the width is 10.
Lets multiply these together, and the total square area is 70 inches squared.
how many acres are in a government rectangular survey that consists of the sw 1/4, ne 1/4, and nw 1/4 of section 13, blendon township?
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
We have,
In the Government Rectangular Survey System, a section is a square tract of land measuring 1 mile by 1 mile, covering an area of 640 acres.
Each section is divided into quarters.
If we consider the SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township, the total acreage can be calculated as follows:
SW 1/4:
This represents one-fourth of the section.
The SW 1/4 of Section 13 is 640 acres / 4 = 160 acres.
NE 1/4:
The NE 1/4 of Section 13 is also 160 acres.
NW 1/4:
The NW 1/4 of Section 13 is 160 acres.
To find the total acreage, add up the individual acreages:
160 acres (SW 1/4) + 160 acres (NE 1/4) + 160 acres (NW 1/4)
= 480 acres
Therefore,
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
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how many ways can patricia choose 4 pizza toppings from a menu of 19 toppings if each topping can only be chosen once?
There are 3876 ways in which Patricia can choose 4 pizza toppings from a menu of 19 toppings if each topping can only be chosen once. In permutation, the order is very important, and it is denoted by "P." which means that each item can only appear once in the lineup, and there are no duplicates. The formula for permutation is given as: P(n, r) = n!/(n-r)!
What is combination?In a combination, the order is not essential, and it is denoted by "C." It means that things can be jumbled up, and there are no duplicates. The formula for a combination is given as: C(n, r) = n! / (r! * (n-r)!)How to calculate the number of ways to choose 4 pizza toppings from a menu of 19 toppings?
To calculate the number of ways to choose 4 pizza toppings from a menu of 19 toppings, we need to use the combination formula, which is: C(n, r) = n! / (r! * (n-r)!)Here, n = 19 and r = 4, so the formula becomes: C(19,4) = 19!/(4!(19-4)!) = 19!/(4!15!) = (19*18*17*16)/(4*3*2*1) = 38,76. Therefore, there are 3876 ways in which Patricia can choose 4 pizza toppings from a menu of 19 toppings if each topping can only be chosen once.
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a manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409.0 409.0 gram setting. it is believed that the machine is underfilling the bags. a 38 38 bag sample had a mean of 406.0 406.0 grams. a level of significance of 0.05 0.05 will be used. state the hypotheses. assume the variance is known to be 400.00 400.00 . enter the hypotheses:
The null and alternative hypotheses for the manufacturer of banana chips can be defined as:
H0: µ = 409 (Null Hypothesis)
Ha: µ < 409 (Alternative Hypothesis)
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409.0 409.0 gram setting. It is believed that the machine is underfilling the bags. A 38 bag sample had a mean of 406.0 grams. A level of significance of 0.05 will be used. State the hypotheses. Assume the variance is known to be 400.00. Enter the hypotheses.
The null and alternative hypotheses for the manufacturer of banana chips can be defined as:
H0: µ = 409 (Null Hypothesis)
Ha: µ < 409 (Alternative Hypothesis)
Where µ is the population mean of the weight of banana chips in a bag. The level of significance is 0.05. As the population variance is known, the z-test can be performed. To test the above hypotheses, we can calculate the test statistics as shown below :
z = (X - µ) / [σ / √(n)]
Where, X = Sample mean = 406, Population mean = 409, Population standard deviation = 20 (Square root of variance = √400) , Sample size = 38 substituting the given values, we get
= (406 - 409) / [20 / √(38)]z = -1.581
According to the z-distribution table, the probability of getting a value less than or equal to -1.581 is 0.0562. It means the p-value is 0.0562. Since the p-value (0.0562) > α (0.05), we fail to reject the null hypothesis H0.
Therefore, there is not enough statistical evidence to conclude that the bag filling machine is underfilling the bags at the 409-gram setting. Thus, the given statement is false.
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A math teacher gives her class the following problem.
Barry is selling magazine subscriptions for a school fundraiser. He has already sold 15 subscriptions. He plans to sell 3 subscriptions per week until he reaches a total of 30 subscriptions sold. How many weeks will it take Barry to achieve his goal.
One student in the class solves the problem arithmetically as shown below.
The linear expression that could be used to find the number of weeks until he reaches 30 subscriptions is given as follows:
A. 15 + 3x = 30.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The parameters for this problem are given as follows:
m = 3, as each week, 3 subscriptions are sold.b = 15, which is the initial number of subscriptions.Hence the number of subscriptions after x weeks is given as follows:
y = 3x + 15.
The number of weeks to reach 30 subscriptions (y = 30) is given as follows:
3x + 15 = 30.
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What is the area of this figure?
Answer: 75 [tex]m^{2}[/tex]
Step-by-step explanation:
5*5 + 5*10 = 25 + 50 = 75
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20. while standard deviation and beta are both measures of risk, there are differences between the two. which of the following is correct? a. beta measures all risk b. beta measures only systematic risk c. beta measures only unsystematic risk d. standard deviation and beta are different, but both measure total risk
Standard deviation and beta are both measures of risk, however Beta is used to measure systematic risk. The correct answer is option (B), beta measures only systematic risk.
Standard deviation and beta are both measures of risk, however, there are differences between them. Standard deviation is a measure of the variation or dispersion of a set of data values. It shows the average deviation of each value from the mean. It is expressed in the same units as the original data.
Beta, on the other hand, is a measure of the systematic risk of an investment relative to the market as a whole. It reflects the extent to which the return on a particular security or portfolio moves with the overall market, and is often used in the Capital Asset Pricing Model (CAPM) to estimate the required rate of return for an investment. It measures the sensitivity of the security's returns to the market.
The systematic risk of an investment is the risk that is associated with the market as a whole, rather than with a particular security. It is often referred to as market risk because it is based on factors that affect the entire market, such as changes in interest rates, inflation, or economic conditions.
Unsystematic risk, on the other hand, is the risk that is specific to a particular security or industry, and is caused by factors that affect that particular security or industry, such as management changes, lawsuits, or other events that affect the company's operations.
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the mean of eight numbers is 25. when two extra numbers are included the mean of the ten numbers is 24. find the mean of the two extra numbers.
The mean of eight numbers is 25, and when two extra numbers are included the mean of the ten numbers is 24. This means that the two extra numbers must be lower than 25 in order to bring down the mean of the ten numbers to 24.
To find the mean of the two extra numbers, we need to subtract the sum of the first eight numbers from the sum of all ten numbers.
The sum of the first eight numbers is 8 x 25 = 200, and the sum of all ten numbers is 10 x 24 = 240.
Subtracting 200 from 240 gives us 40.
Since there are two extra numbers, we need to divide 40 by 2 to find the mean.
the mean of the two extra numbers is 40 / 2 = 20.
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what is 7x=14 show your work
Answer:
x=2
Step-by-step explanation:
7x=14
divide by 7 on each side to get x by itself
x=14/7
x=2
I just need help with this, please! 10 points!
The given data comprises of a right triangle in which the base is denoted by x whose value is found to be 10.01.
Define trigonometric identity of sine?It states that the ratio of the length of the side opposite to the angle to the length of the hypotenuse is equal to the sine of the angle.
The given data comprises of a right triangle in which the base is denoted by x and the perpendicular is 8. The angle formed between the base and hypotenuse is 53 degree.
To solve this problem, we can use the trigonometric identity of sine.
Mathematically, it can be expressed as:
sin 53° = Perpendicular/Hypotenuse
8/x = sin 53°
x = 8/sin 53°
x = 8/ 0.7986
x ≈ 10.01
Hence, the value of x is 10.01.
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PLS HELP ME ASAP I WILL MARK THE BRAINLIEST!!!!
The fourth term of the arithmetic progression is found to be 29.
Explain about the arithmetic progression?A sequence is a collection of numbers that move from expression to term according to a specific pattern or rule.
You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequence data, quadratic sequences, and special sequences.
An ordered collection of integers with a shared distinction between each word is known as an arithmetic sequence.It constitutes an arithmetic sequence if we add as well as subtract by the same amount each time to create the sequence.The given equations are:
a1 = 5
an = 2[tex]a_{n - 1}[/tex] + 3
put n = 1, 2 , 3...
Second term will be:
a2 = 2[tex]a_{2 - 1}[/tex] + 3
a2 = 2[tex]a_{1}[/tex] + 3
Put the value of a1 = 5
a2 = 2*5 + 3
a2 = 13
Now, the common difference d = 13 - 5 = 8
a4 = a1 + (n - 1)d
a4 = 5 + (4 - 1)*8
a4 = 5 + 3*8
a4 = 29
Thus, the fourth term of the arithmetic progression is found to be 29.
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Which of the following limits are indeterminate forms?Given that lim x->a f(x)=0lim x->a g(x)=0lim x->a h(x)=1lim x->a p(x)=infinitylim x->a q(x)= infinity. THEN(a) lim x->a f(x)/g(x)= (b) lim x->a f(x)/p(x)=(c) lim x->a h(x)/p(x)=(d) lim x->a p(x)/f(x)=(e) lim x->a p(x)/q(x)=
In conclusion, the indeterminate forms among the given limits are
(a) lim x->a f(x)/g(x)
and
(e) lim x->a p(x)/q(x).
The indeterminate forms are expressions that cannot be directly determined or evaluated when approaching a specific limit. In calculus, there are several common indeterminate forms such as 0/0, ∞/∞, 0⋅∞, ∞−∞, 0^0, 1^∞, and ∞^0.
Let's analyze each given limit:
(a) [tex] lim x->a f(x)/g(x) = 0/0[/tex]: This is an indeterminate form because it is of the form 0/0.
(b) lim x->a f(x)/p(x) = 0/∞: This limit is not indeterminate; it equals 0 since the numerator is 0 while the denominator approaches infinity.
(c) lim [tex]x->a h(x)/p(x) = 1/∞[/tex]: This limit is not indeterminate; it equals 0 because the numerator is a constant value (1) and the denominator approaches infinity.
(d) [tex]lim x->a p(x)/f(x) = ∞/0[/tex]: This limit is not an indeterminate form, but rather an undefined form because division by zero is undefined.
(e) [tex] lim x->a p(x)/q(x) = ∞/∞[/tex]: This is an indeterminate form because it is of the form ∞/∞.
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Really appreciated :) 25 points
Answer:
a. 9
b. 4
c. 4/9
Step-by-step explanation:
a. If we are picking 1 card out of 9, then there are 9 possible outcomes:
1, 2, 3, 4, 5, 6, 7, 8, or 9
This can also be represented as 9 choose 1 ([tex]_9C_1[/tex]).
b. We have to identify the number of prime numbers in the set:
2, 3, 5, 7
↑ 4 numbers
Note: Prime numbers can only be divided by themselves and 1 to result in a whole number.
c. We can represent the probability of selecting a prime number by dividing the number of prime numbers by the total number of numbers.
# of primes / # of numbers = 4 / 9
please help me solve this geometry proof i’ll mark brainliest
BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)
What is triangle congruency?Triangle congruence: Two triangles are said to be congruent if their three corresponding sides and their three corresponding angles are of identical size.
You can move, flip, twist, and turn these triangles to produce the same effect. When relocated, they are parallel to one another.
Two triangles are congruent if they satisfy all five conditions for congruence.
They include the right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and angle-side-angle (SSS) (RHS).
So, in the given △DAB and △DCB:
AC = AC = Common
∠DAC = ∠BAC = AC is the angle bisector
∠DCA = ∠BCA = AC is the angle bisector
Then, △DAB ≅ △DCB under the ASA congruency rule,
Then, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)
Therefore, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)
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how would you interpret the findings of a correlation study that reported a linear correlation coefficient of 0.3?
The linear correlation coefficient of 0.3 indicates a moderate positive correlation between the two variables.
This suggests that when one variable increases, the other variable tends to increase too. However, there is not a strong linear relationship between the two variables, meaning that the increase in one variable does not guarantee a predictable change in the other variable.
When interpreting the findings of a correlation study, it is important to note the strength of the relationship between the two variables. A linear correlation coefficient of 0.3 indicates a moderate positive correlation, meaning that the two variables increase together but there is not a strong linear relationship between the two variables.
This means that the increase in one variable does not guarantee a predictable change in the other variable. To put it another way, the strength of the correlation means that when one variable increases, it is likely that the other will increase as well, but it is not guaranteed.
Therefore, caution should be used when making predictions based on the results of a correlation study.
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an ai that plays the game of go has a 90\% chance of winning each game it plays against a human grandmaster. what is the binomial probability of the human beating the ai 1 out of 3 games?
The probability of the human Grandmaster winning one out of three games against the AI is approximately 0.243 or 24.3%.
Let's denote the probability of the human Grandmaster winning one game as p. Then the probability of the AI winning one game is 0.9, which means the probability of the human winning one game is 0.1. Since we want to calculate the probability of the human winning one game out of three, we can use the binomial distribution formula:
[tex]P(X=k) = (^n _k) \times p^k \times (1-p)^{(n-k)}[/tex]
Where:
P(X=k) is the probability of getting k successes in n trials
(n choose k) is the binomial coefficient, which is the number of ways to choose k successes from n trials
p is the probability of success in one trial
(1-p) is the probability of failure in one trial
k is the number of successes we are interested in (in this case, k=1)
n is the total number of trials (in this case, n=3)
Plugging in the values, we get:
P(X=1) = (3 choose 1) * 0.1^1 * 0.9^(3-1) = 3 * 0.1 * 0.81 = 0.243 or 24.3%
This means that there is a decent chance for the human to win at least one game, but it is still more likely for the AI to win all three games.
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deduce that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the slim. in particular, the sum cannot be uniformly distributed on the numbers from 2 to 12. g
We know that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the sum. In particular, the sum cannot be uniformly distributed on the numbers from 2 to 12.
Explanation:
When we roll a fair die (i.e. an unbiased die), the probabilities of getting any one of the six possible numbers {1, 2, 3, 4, 5, 6} are equal to 1/6 each. But, when we use a biased die, the probabilities of getting any of the six possible numbers will no longer be equal. Some numbers will be more likely to occur, while others will be less likely to occur
For example:
if one of the dice has a weight in such a way that it always rolls a 6, then the probability of getting a sum of 2 will be zero, the probability of getting a sum of 7 will be 1/6, and the probability of getting a sum of 12 will be zero.However, if the dice are biased in some other way, we can still get non-zero probabilities for the sums of 2, 7, and 12. But, the probability of getting those three sums will not be the same. For instance, if one die is biased to always roll a 1, and the other die is biased to always roll a 6, then the probabilities of getting each of the sums 2, 7, and 12 are as follows:
P(2) = P(1, 1) = (1/6)² = 1/36
P(7) = P(1, 6) + P(6, 1) + P(2, 5) + P(5, 2) + P(3, 4) + P(4, 3) = 6(1/6)(1/6) = 1/6P(1
2) = P(6, 6) = (1/6)² = 1/36
So, the probability of getting a sum of 7 is six times as likely as getting a sum of 2 or 12. Therefore, the sum cannot be uniformly distributed on the numbers from 2 to 12.
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Can someone help me with this aleks
I think the best way to do this is by splitting up the trapezoid into two shapes since it is not a regular trapezoid. We can make a split to form a small right triangle on the left and a regular trapezoid on the right.
Small right triangle on the left:
4 inch side length and 6 inch hypotenuse with the Pythagorean theorem will give us the missing side.
missing side = square root of 6^2-4^2 = [tex]2\sqrt{5}[/tex]
Then the area is [tex]\frac{1}{2}*4*2\sqrt{5}=4\sqrt{5}[/tex]
Regular trapezoid on the right:
Area will be [tex]\frac{6+(17-2\sqrt{5})}{2}*4=46-4\sqrt{5}[/tex]
Summing up the two areas to get the total we have [tex]4\sqrt{5}+46-4\sqrt{5}=46[/tex] in^2.
what are coordinate planes explain:
Answer:
a two-dimension surface formed by two number lines.