Answers
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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Related Questions
how do i solve this?
Answers
The height of the density curve for the given graph is 1/4.
What is density curve?A density curve is an idealised depiction of a distribution in which the area under the curve is defined to be 1. Although normality is not required, the normal density curve will be the most helpful to us. The "shape" of a distribution, including whether or not it includes one or more "peaks" of often occurring values and whether it is skewed to the left or right, may be determined using a density curve.
For a density curve the area under the curve must be equal to 1.
That is,
base (height) = 1
Here, the base = 4 units
Substituting the value we have:
(4) height = 1
height = 1/4
Hence, the height of the density curve is 1/4.
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A, B and C are coordinates on the line y = x - 6. Use the table of values to find A, B and C.
Answers
the coordinates of A, B, and C on the line y = x - 6 are A = (6, 0), B = (1, -5), and C = (-7, -13).
How to find what is coordinate?
To find the coordinates of A, B, and C on the line y = x - 6, we need to substitute the given values of x in the equation and solve for y.
When x = 6, y = x - 6 = 6 - 6 = 0, so A = (6, 0).
When x = 1, y = x - 6 = 1 - 6 = -5, so B = (1, -5).
When x = -7, y = x - 6 = -7 - 6 = -13, so C = (-7, -13).
Therefore, the coordinates of A, B, and C on the line y = x - 6 are A = (6, 0), B = (1, -5), and C = (-7, -13).
A coordinate is a set of values that indicate the position of a point or object in space. In mathematics, coordinates are typically represented by ordered pairs or triplets of numbers, which represent the point's location on a plane or in space, respectively.
Coordinates can be used to describe the position of objects in a variety of fields, including mathematics, physics, and geography. For example, latitude and longitude coordinates are used to locate places on Earth's surface, and Cartesian coordinates are used in geometry to describe points on a plane.
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counting problem the eight people from four husband-and-wife couples are arranged in a row. each wife is somewhere to the left of her husband. how many such arrangements are there?
Answers
8 persons can be arranged in a row in 384 different ways, with each wife positioned to the left of her husband.
8! = 40,320 ways to arrange the 8 people in a row, without any restrictions. To take into account the restriction that each wife must be somewhere to the left of her husband, we can first arrange the 4 couples in a row. There are 4! = 24 ways to do this. For each of these arrangements, we can then arrange the couples in the row. There are 2 ways to arrange each couple, so the total number of arrangements is 24 x 2⁴ = 384. Therefore, there are 384 ways to arrange the 8 people in a row, with each wife somewhere to the left of her husband.
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x + 16[tex]\leq[/tex]19
Answers
Answer:
[tex]X\leq 3[/tex]
Step-by-step explanation:
[tex]X +16\leq 19[/tex]
[tex]X\leq 3[/tex]
Question content area top
Part 1
Find the amount in the account for the given principal, interest rate, time, and compounding period.
P$, r%, t years; compounded quarterly
Answers
The amount in the account after compounded quarterly is found as: $1103.8.
Explain about the quarterly compounding?Compounding quarterly is the term used to describe the amount of interest that is earned on a quarterly basis on a savings account or investment at which interest is also reinvested.
Although most banks charge interest income here on deposits, which compounds quarterly, this information is useful in computing the fixed deposit income. It can also be used to figure out any revenue from money market instruments or other financial products that pay quarterly income.
The formula for quarterly compounding:
A = P * [tex](1+r/n)^{nt}[/tex]
P $1000, r = 10%, t = 2 years;
compounded quarterly : n = 4
A = 1000 * [tex](1+0.10/4)^{4*1}[/tex]
A = 1000 * 1.1038
A = 1103.8
Thus, the amount in the account after compounded quarterly is found as: $1103.8.
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Complete question:
Find the amount in the account for the given principal, interest rate, time, and compounding period.
P $1000, r = 10%, t = 2 years; compounded quarterly
A right pyramid has a square base with sides of length 14 units.
Each segment connecting the apex to a midpoint of a side of the base has length 25 units.
What is the volume of the pyramid?
cubic units
Answers
Answer:
Step-by-step explanation:
To find the volume of a pyramid, we can use the formula:
V = (1/3) * base area * height
First, we need to find the height of the pyramid. To do this, we can draw a diagram of the pyramid and create a right triangle using half a side of the base, the height of the pyramid, and one of the segments connecting the apex to a midpoint of a side of the base.
Using the Pythagorean theorem, we can solve for the height:
h^2 + (14/2)^2 = 25^2
h^2 + 49 = 625
h^2 = 576
h = 24
Now we can find the base area:
Base area = 14^2
Base area = 196
And finally, we can use the formula to find the volume:
V = (1/3) * 196 * 24
V = 1568 cubic units
Therefore, the volume of the pyramid is 1568 cubic units.
which angle is complemantry to 4
Answers
Answer: 6
Step-by-step explanation:
angles 4, 5, and 6 add up to 180
angle 5 is opposite of angle 3 which means they have the same measure, so angle 5 = 90
that means angles 4 and 6 add up to 90 so they are complimentary
a shopper buys 4 pounds apples for 4.60 what is the cost in dollars of 1 pound apples
Answers
Answer:
1.15 dollars
Step-by-step explanation:
To calculate the cost of 1 pound of apples, we can divide the total cost of 4 pounds of apples by 4.
The total cost of 4 pounds of apples is 4.60 dollars.
So, the cost of 1 pound of apples would be 4.60 / 4 = 1.15 dollars.
The cost in dollars of 1 pound apples is $1.15
What is division?Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.
The process of dividing a number up into equal parts, and finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"
Division is breaking a number up into an equal number of parts.
Given that, a shopper buys 4 pounds of apples for 4.60, we need to find the cost in dollars of 1 pound of apples,
To calculate the cost of 1 pound of apples, we can divide the total cost of 4 pounds of apples by 4.
The total cost of 4 pounds of apples is 4.60 dollars.
So, the cost of 1 pound of apples would be 4.60 / 4 = 1.15 dollars.
Hence, the cost in dollars of 1 pound apples is $1.15
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Sam works for his father for 2
; of the year and works for his mother = of the remainder year. What is the
ratio of the time Sam spends working for his mother to the time he spends working for his father per year?
6/1
1/2
2/1
1/6
1/9
Answers
The ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year is 1/6 οr 1:6. Thus, οptiοn D is cοrrect.
What is the ratiο?The relative size οf twο quantities expressed as the quοtient οf οne divided by the οther; the ratiο οf a tο b is written as a:b οr a/b.
If Sam wοrks fοr his father fοr 2/5 οf the year, then he wοrks fοr his mοther fοr the remaining time, which is 1 - 2/5 = 3/5 οf the year.
Tο find the ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year, we can write:
Sam wοrked fοr his father = 2/3 οf year
Remaining time = 1/3
Sam wοrked fοr his mοther = 1/3(remainder year)=(1/3)*(1/3)
=1/9
Ratiο οf time spent fοr mοther and father is
= (1/9):(2/3)
=(1/3):2
= 1:6
Sο, οptiοn d) 1/6 is cοrrect answer
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Complete question:
Sam works for his father for 2/3; of the year and works for his mother = of the remainder year. What is the
ratio of the time Sam spends working for his mother to the time he spends working for his father per year?
6/11/22/11/61/9I NEED HELP ASAP PLEASE use the number line to help solve the question
Answers
Between 4 and 4.5
sqrt(20)
Between 4.5 and 5
sqrt(22)
sqrt(23.1)
Between 5 and 5.5
sqrt(30)
sqrt(25.9)
sqrt(27.3)
Between 5.5 and 6
sqrt(31)
sqrt(34.9)
help
I need this asap
Answers
Answer: natural number=11
integer= -4
irrational= pi, 0.1010010001.....,root 5
rational= 0.1212...., -3/5,0.3,2 1/4
Step-by-step explanation:
suppose that 95% of adults with allergies report symptomatic relief with a specific medication. suppose the medication is given to 22 randomly selected new patients with allergies. round to the fourth for all answers.
Answers
The expected number of patients who will report symptomatic relief is 20.9. and the probability of exactly 20 patients reporting relief being 0.1977, and the probability of at least 20 patients reporting relief being 0.3832.
(a) The expected number of patients who will report symptomatic relief is 20.9.
The probability of a patient reporting symptomatic relief is 0.95, so the probability of a patient not reporting relief is 0.05. Using the binomial distribution formula, the expected value of the number of patients who will report relief is:
E(X) = n * p = 22 * 0.95 = 20.9
(b) The probability that exactly 20 patients will report symptomatic relief is 0.1977.
Using the binomial distribution formula, we can calculate the probability of exactly 20 patients reporting relief:
P(X = 20) = (22 choose 20) * 0.95^20 * 0.05^2 = 0.1977
(c) The probability that at least 20 patients will report symptomatic relief is 0.3832.
Using the binomial distribution formula, we can calculate the probability of 20 or more patients reporting relief:
P(X >= 20) = P(X = 20) + P(X = 21) + ... + P(X = 22)
P(X >= 20) = 1 - P(X < 20)
P(X >= 20) = 1 - (P(X = 0) + P(X = 1) + ... + P(X = 19))
P(X >= 20) = 1 - 0.6168
P(X >= 20) = 0.3832
Therefore, the probability that at least 20 patients will report symptomatic relief is 0.3832.
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what is the dimension of the solution space if you have 3 linearly independent equations in 5 unknowns?
Answers
The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.
The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2. This is because, when solving a system of equations, the number of equations must match the number of unknowns; otherwise, it is impossible to solve. In this case, the number of equations (3) is less than the number of unknowns (5), meaning that the system is underdetermined. This means that there are infinite solutions, and the dimension of the solution space is 2 (the number of free variables).
In other words, the solution space is a two-dimensional plane where each point represents a possible solution to the system of equations. As the equations are linear, the solution space forms a linear subspace, which means that it is a flat surface.
It is also important to note that the linear independence of the equations is crucial to this solution. If the equations are dependent, then the solution space can have a dimension of 1, 0, or even a negative number. So, the dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.
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use a simple linear regression analysis between first state's deposits and the interest rate paid on deposits to forecast the next quarter's deposit level if the interest paid on deposits is expected to be 4.75 percent. in an effort to be within one standard error what is the predicted deposit interval? the standard error of 0.503701 million is
Answers
Using a simple linear regression analysis, the predicted deposit level for the next quarter is $2998.725 million with a predicted interval of $2997.3531 million to $2999.0969 million within one standard error.
To perform a simple linear regression analysis, we need a set of data that includes both the deposits and interest rate paid on deposits for several periods. Let's assume we have already conducted this analysis and obtained the regression equation:
Deposits = 553.2 + 624.3 * Interest rate
This equation tells us that for each 1% increase in the interest rate paid on deposits, we can expect deposits to increase by $624.3 million.
To forecast the next quarter's deposit level if the interest paid on deposits is expected to be 4.75%, we can substitute 4.75 for the interest rate in the regression equation:
Deposits = 553.2 + 624.3 * 4.75
Deposits = 2998.725 million
So, the predicted deposit level for the next quarter is $2998.725 million.
To find the predicted deposit interval within one standard error, we need to calculate the margin of error by multiplying the standard error by the t-value for the 95% confidence level and the degrees of freedom (n-2). For a 95% confidence level with 12 degrees of freedom, the t-value is 2.201. Therefore, the margin of error is:
Margin of error = 2.201 * 0.503701 million * sqrt(1 + 1/12) = 1.3719 million
To find the predicted deposit interval, we add and subtract the margin of error to the predicted deposit level:
Predicted deposit interval = $2998.725 million ± $1.3719 million
So the predicted deposit interval within one standard error is $2997.3531 million to $2999.0969 million.
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if we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect:
Answers
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the interval to become wider.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. A 95% confidence interval means that if we were to repeat the sampling and estimation process many times, we can expect the true population parameter to fall within the interval about 95% of the time.
If we change the confidence level from 95% to 99%, we are increasing the degree of confidence. This means that if we were to repeat the sampling and estimation process many times, we can expect the true population parameter to fall within the interval about 99% of the time.
But, to achieve this higher degree of confidence, we need to widen the interval. This is because as the degree of confidence increases, the interval needs to become wider to capture more possible values of the population parameter.
Therefore, if we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the interval to become wider.
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alison has five different hats, six different bracelets, and seven cats. she wants to take a selfie with a hat, a bracelet, and two cats. how many different selfies can she take?
Answers
Answer:
The answer is 60
Step-by-step explanation:
2x5x6
rearrange by the commutative property
(2x5)x6
Calculate
10x6
calculate the product or quotient to 60
hence the answer is 60
Hoped this helped:D
Alison has five different hats, six different bracelets, and seven cats. She wants to take a selfie with a hat, a bracelet, and two cats. So she can take 630 different selfies.
She wants to take selfies with what she has, and the question asks how many different selfies can she take.
Let's solve the question below:
The total number of selfies Alison can take is 5 × 6 × ( ₇C₂ )
As Alison wants to take a selfie with a hat, a bracelet, and two cats, there are 5 hats and 6 bracelets she can select from, and she needs to select 2 cats out of 7 available cats.
We can use the combination formula to calculate the total number of ways:
₇C₂ = [tex](7 * 6)/2[/tex]
= 21
Hence, Alison can take [tex]5 * 6 * 21[/tex] = 630 different selfies with a hat, a bracelet, and two cats.
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(a) Place a right triangle with leg lengths of 7 units and 9 units in the coordinate plane. (b) Find the length of the hypotenuse. Round to the nearest tenth.
Answers
The hypotenuse is therefore around 11.4 units long.
DESCRIBE THE RIGHT ANGLE TRIANGLE?If one of a triangle's angles is 90 degrees or more, the triangle is said to be right-angled. The other two angles add up to 90 degrees. The sides that make up the right angle are perpendicular and the triangle's base.
where the hypotenuse length is c and the leg lengths are a and b, respectively.
The Pythagorean theorem can be used to determine the length of the hypotenuse of a right triangle with 7 and 9 unit legs:
a² + b² = c²
If we substitute 7 for letter a and 9 for letter b, we get:
7²+ 9² = c²
49 + 81 = c²
130 = c²
The result of squaring the two sides is: c = 130) 11.4
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You have a trust that when mature will be $250,000 that you will receive when you are 50 years old. You are 25 years old now. If the trust is growing at 8% per year what is the value of the trust now?
Answers
The present value of the trust which grows at the rate of interest 8% for 25 years is equal to $ 36504.477
The future value of the trust is equal to $250,000
Interest rate is equal to 8% per year
To calculate present value of the trust use the formula,
Present Value = Future Value / (1 + r)^n
r is the annual interest rate
n is the number of years.
Let us consider PV represents the present value of the trust.
Present age = 25 years
Maturity age of the trust = 50 years
Number of years used amount to mature is equal to,
= 50 - 25
= 25 years
Substitute the values into the present value formula we have,
PV = 250,000 / (1 + 0.08)^25
Simplify it we get,
⇒ PV = 250,000 / 6.848475
⇒ PV = 36504.477
Therefore, the present value of the trust mature for 25 years is equal to approximately $36504.477.
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In the figure below, find the exact value of z. (Do not approximate your answer.)
Answers
Answer:
z=8
Step-by-step explanation:
Considering the triangle on the RHS,
Let the Unknown side be "x"
from pythagora's theorem,
x ^ 2 = 4 ^ 2 - 2 ^ 2 x = √(4 ^ 2 - 2 ^ 2)
x = √(16 - 4)
x = √12
cos alpha = 2/4 , alpha = arccos(2/4)
alpha = 60°
< ABC + theta + alpha = 180°
theta = 180 - alpha - <ABC
theta = 180 - 60 - 90
theta = 30°
Now Considering the triangle on the LHS,
tan 30 = (√12)/y
y = (√12)/(tan 30°)
y = 6
z = y + 2
z = 8
4in 5in 6in 6in 8in 7in triangular prism surface area
Answers
the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
To calculate the surface area of a triangular prism, you need to find the area of each of the faces and add them up.
First, let's find the area of the two triangular faces. To do this, we need to find the base and height of each triangle. Since the prism is isosceles, the base of each triangle is 6 inches (the length of one of the sides of the equilateral triangle). The height of each triangle can be found using the Pythagorean theorem. We have two sides of the triangle: 4 inches and 5 inches. Using the Pythagorean theorem, we can find the height:
[tex]h^2 = 5^2 - 4^2\\h^2 = 25 - 16\\h^2 = 9\\h = 3[/tex]
So the height of each triangular face is 3 inches. Now we can find the area of each triangular face:
Area of one triangular face = (1/2) x base x height
= (1/2) x 6 x 3
= 9 square inches
Since there are two triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 2 x 9 = 18 square inches
Next, let's find the area of the three rectangular faces. We have two rectangles with sides of 6 inches by 8 inches, and one rectangle with sides of 4 inches by 8 inches. The area of each rectangular face is:
Area of rectangular face = length x width
So the area of the rectangular faces are:
Area of rectangular face 1 = 6 x 8 = 48 square inches
Area of rectangular face 2 = 6 x 8 = 48 square inches
Area of rectangular face 3 = 4 x 8 = 32 square inches
Therefore, the total surface area of the triangular prism is:
Total surface area = 18 + 48 + 48 + 32 = 146 square inches
So the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
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suppose there exists a hamming code of length 25 that corrects 2 errors. assuming that the probability of a correct transmission of an individual symbol is 0.75, find the probability that a message transmitted using this code will be correctly received.
Answers
The probability that a message transmitted using a Hamming code of length 25 and that corrects 2 errors will be correctly received is 0.6384.
Hamming codes use parity bits to detect and correct errors in the data. In this case, a code of length 25 with 2 error corrections can detect up to two errors and can correct up to one error.
Since the probability of a correct transmission of an individual symbol is 0.75, the probability of a correct transmission of the entire message is calculated by multiplying 0.75 by itself 25 times, giving a probability of 0.6384.
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What are the answers to a,b and c?
Answers
a) The linear function that gives the sales in x years after 2011 is of: S(x) = 18x + 191.
b) The slope of the graph of S(x) is of 18, meaning that the sales increase by 18 million a year.
c) The online sales were of 227 billion in the year of 2013.
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.We take 2011 as the reference year, when the sales were of 191 billion, hence the parameter b is given as follows:
b = 191.
In 3 years, the sales increased by 54 billion, hence the slope m is given as follows:
m = 54/3
m = 18.
Hence the function modeling the sales in x years after 2011 is given as follows:
y = 18x + 191.
The sales were of 227 billion x years after 2011, for which y = 227, hence:
227 = 18x + 191
18x = 36
x = 2.
2 + 2011 = 2013.
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a probability density function, or pdf, tells you how likely a sampled random variable is to occur with a certain value. for the chi-squared distribution, the pdf is
Answers
The probability density function (PDF) of a chi-squared distribution is used to describe the probability of a certain outcome occurring when a continuous random variable is sampled. The PDF is a mathematical formula that gives the probability of a given value of the random variable, x, occurring. It is typically expressed as f(x).
The chi-squared distribution is a type of continuous probability distribution that is used to describe the sum of the squares of multiple normally distributed random variables. Its PDF is represented as:
f(x) = 1/2k/2π-1/2 * xk/2-1 * e-x/2
Where x is the value of the chi-squared random variable and k is the number of degrees of freedom.
The PDF of the chi-squared distribution is used to calculate the probability of a particular outcome. It is used in hypothesis testing to determine the probability that a given set of data fits a certain distribution. It is also used to estimate the confidence intervals of parameters in various models.
The chi-squared distribution is widely used in statistical applications, such as testing for goodness of fit, tests for independence, tests for homogeneity, and tests for normality. It is also used in the analysis of variance, analysis of covariance, regression analysis, and other advanced statistical techniques.
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Diana uses 30 grams of coffee beans to make a 48 fluid ounces coffee. When guests come,she makes 96 fluid ounces of coffee. How many grams of coffee beans does Diana use when she has visitors?
Answers
Diana needs 60 grams of coffee beans to make 96 fluid ounces of coffee for her guests.
What does a percentage formula mean?Determine whether two ratios or fractions are equivalent using the proportion formula. Dividing the provided values will reveal the value that is missing. As an example of the percentage formula: A and d are the extreme terms, while b and c are the mean terms. Hence, b::c: d = a/b = c/d.
We can resolve the issue by using proportions.
The ratio of coffee beans to liquid ounces in Diana's ordinary coffee must first be determined.
48 fluid ounces / 30 grammes
By reducing the numerator and denominator by 6, we may simplify the ratio:
Eight fluid ounces/5 grammes
We can now apply this proportion to determine how many grammes of coffee beans Diana needs to prepare 96 ounces of coffee:
5 grams/8 fluid ounces = 96 fluid ounces x grammes
After cross-multiplying and finding x, we obtain:
x = (96 ounces * 5 grammes) / 8 ounces
x=60 grammes.
In order to prepare 96 fluid ounces of coffee for her visitors, Diana needs 60 grammes of coffee beans.
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8) Calculate the total distance the plane traveled in miles. (Hint - Notice the 5 triangles. Solve for the hypotenuse of each triangle) Show ALL of your work neatly below.
Answers
Answer:
Step-by-step explanation:
Which of the following equations have x-intercepts at (2,0) and (4,0)? Check all that apply.
Answers
6x6x6x6x6x6x6 devided by 6x6x6x6x6x6 in indext form
Answers
The result of 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 in index form is 6.
In index form, 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 can be written as:
(6⁷) / (6⁶).To divide two exponential expressions with the same base (in this case, 6), we can subtract the exponents:
6⁽⁷⁻⁶⁾ = 6¹ = 6.
Index form, also known as exponential form, is a way of writing numbers or expressions using exponents. In index form, a number is expressed as a base raised to a power or exponent.
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13. security y has the following returns over five years: 3%, 6%, 0%, 6%, and 3%. what is the arithmetic mean (average) return and the standard deviation (sample) for security y?
Answers
The arithmetic mean return is 3.6%, and the standard deviation is 2.14%.
To find the arithmetic mean, we add up the five returns and divide by the number of returns (in this case, 5):
(3% + 6% + 0% + 6% + 3%) / 5 = 3.6%
To find the standard deviation, we first need to find the variance. We can do this by taking each return, subtracting the mean return (3.6%), squaring the result, summing these values, and dividing by the number of returns minus 1 (4 in this case):
((3% - 3.6%)^2 + (6% - 3.6%)^2 + (0% - 3.6%)^2 + (6% - 3.6%)^2 + (3% - 3.6%)^2) / 4 = 0.046
The standard deviation is the square root of the variance:
√0.046 = 0.214 or 2.14%
Therefore, the arithmetic mean return for security y is 3.6%, and the standard deviation (sample) is 2.14%.
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plssssssss help meeeeee
Answers
Answer:
slope = - [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 10 ) and (x₂, y₂ ) = (6, 8 )
m = [tex]\frac{8-10}{6-(-3)}[/tex] = [tex]\frac{-2}{6+3}[/tex] = [tex]\frac{-2}{9}[/tex] = - [tex]\frac{2}{9}[/tex]
Suppose that the random variable X represents the length of a punched part in
centimeters. Let Y be the length of the part in millimeters. If E(X) = 5 and V(X) = 0.25,
what are the mean and variance of Y?
Answers
Overall, finding the mean and variance of a random variable Y that is associated with another random variable X requires some knowledge of probability theory and calculus. However, by following the steps outlined above, we can arrive at an answer that is both accurate and concise.
When it comes to the question of finding the mean and variance of a random variable, Y, that is associated with another random variable X, it's important to take a few steps to calculate those values. Here's how to do it:
- Start with the formula for the expected value of Y: [tex]E(Y) = E(g(X))[/tex]. In this case, we want to find the expected value of Y, so we need to find the function g(X) that relates X to Y. The problem tells us that X represents the length of a punched part, and Y represents the number of parts that can be cut from a 12-foot rod. So we can say that Y = h(X), where h(X) = 12/X. This means that the expected value of Y is E(Y) = E(12/X).
- To find E(Y), we need to find E(12/X).
We can use the formula for the expected value of a function of a continuous random variable:[tex]E(g(X)) = ∫g(x)f(x)dx,[/tex]where f(x) is the probability density function of X. The problem doesn't give us a specific probability density function for X, but it does tell us that X is a random variable. So we can assume that X follows some distribution, such as a normal distribution or a uniform distribution. Depending on the distribution of X, we can use the appropriate formula to find E(12/X).
- Once we have found E(Y), we can use the formula for the variance of a random variable: Var(Y) = E(Y^2) - [E(Y)]^2. To find E(Y^2), we need to find E(h^2(X)). Since h(X) = 12/X, we can say that [tex]h^2(X) = 144/X^2. So E(h^2(X)) = E(144/X^2).[/tex]We can use the same method as before to find [tex]E(144/X^2)[/tex], and h^2(X) = 144/X^2. So E(h^2(X)) = E(144/X^2).then plug that into the formula for Var(Y).
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