Answers
Answer:
1200 in²------------------------
Find the perimeter of the triangular base and multiply it by the height.
S = PhS = (17 + 17 + 30)*15S = 64*15S = 960 in²Find the area of triangular bases:
B = (1/2)*8*30 = 120 in²Add up the two bases to the lateral area to get the total surface area:
A = 960 + 2*120A = 1200 in²Total surface area is 1200 in².
Related Questions
Solve: 3x - 3 = x + 1
Answers
Hello !
Answer:
[tex]\Large\boxed{ \sf x = 2}[/tex]
Step-by-step explanation:
Let's solve the following equation by isolating x.
[tex] \sf3x - 3 = x + 1[/tex]
First, add 3 to both sides :
[tex] \sf3x - 3 + 3 = x + 1 + 3[/tex]
[tex] \sf3x = x + 4[/tex]
Now let's substract x from both sides :
[tex] \sf3x - x = 4[/tex]
[tex] \sf2x = 4[/tex]
Finally, let's divide both sides by 2 :
[tex] \sf \frac{2x}{2} = \frac{4}{2} [/tex]
[tex] \boxed{ \sf x = 2}[/tex]
Have a nice day ;)
Let A = LU be an LU factorization. Explain why A can be row reduced to U using only replacement operations. (This fact is the converse of what was proved in the text.)
Answers
Any elementary row operation on A can be expressed as a product of replacement operations on A. This means that A can be row reduced to U using only replacement operations, which is the converse of what was proved in the text.
The LU factorization of a matrix A involves decomposing it into a lower triangular matrix L and an upper triangular matrix U, such that A = LU. This means that A can be written as the product of two triangular matrices, one of which is lower triangular and the other is upper triangular.
To show that A can be row reduced to U using only replacement operations, we need to prove that any elementary row operation performed on A can be expressed as a product of replacement operations on A.
First, consider the operation of multiplying a row of A by a scalar. This is a replacement operation, since it replaces one row of A with a multiple of itself.
Next, consider the operation of adding a multiple of one row of A to another row. This is also a replacement operation, since it replaces one row of A with a linear combination of itself and another row.
Finally, consider the operation of interchanging two rows of A. This can be expressed as a sequence of replacement operations: first, add one row to the other, then subtract the original row from the first row, and finally add the second row back to the first row.
To know more about LU factorization, refer to the link below:
https://brainly.com/question/30466122#
#SPJ11
use an addition or subtraction formula to simplify the equation. cos(θ) cos(2θ) + sin(θ) sin(2θ) = √2/ 2
Answers
The simplified form of the equation cos(θ) cos(2θ) + sin(θ) sin(2θ) = √2/ 2 is 4 cos³θ − 3 cos θ − √2/2 = 0.
The equation to use an addition or subtraction formula to simplify is given as:
cos(θ) cos(2θ) + sin(θ) sin(2θ) = √2/ 2
We know that cos 2θ = 2cos²θ − 1 and sin 2θ = 2sinθ cosθ.
Replacing these values in the above equation, we get:
cos θ (2 cos²θ − 1) + sin θ (2 sin θ cos θ) = √2/2
Simplifying the above equation, we get:
2 cos²θ cos θ − cos θ + 2 sin²θ cos θ = √2/2
Using the identity cos²θ + sin²θ = 1, we can substitute cos²θ = 1 − sin²θ in the above equation to get:
2 cos θ (1 − sin²θ) − cos θ + 2 sin²θ cos θ = √2/2
Simplifying further, we get:
2 cos θ − 2 cos³θ − cos θ + 2 sin²θ cos θ = √2/2
Rearranging and simplifying, we get:
(2 cos θ − cos θ − √2/2) + (2 cos³θ − 2 sin²θ cos θ) = 0
Using the identity sin²θ + cos²θ = 1, we can substitute sin²θ = 1 − cos²θ in the second term of the above equation to get:
(2 cos θ − cos θ − √2/2) + (2 cos³θ − 2 cos θ + 2 cos³θ) = 0
Simplifying, we get:
4 cos³θ − 3 cos θ − √2/2 = 0
Now, we can solve this cubic equation using a numerical method like the Newton-Raphson method to get the value of θ that satisfies the given equation.
Learn more about numerical methods:
https://brainly.com/question/25427192
#SPJ11
Astronomers often measure large distances using astronomical units (AU)
where 1 AU is the average distance from
Earth to the Sun. In the image, d represents the distance from a start to the Sun. Using a technique called "stellar parallax," astronomers determined O is 0.00001389 degrees.
b) Write an equation to calculate d for any star.
(Your response must include an equal sign, and the variables d and O.)
Answers
The equation to calculate the distance d for any star using the angle O and the astronomical unit (AU) is: d = AU / tan(O), where tan(O) represents the tangent of the angle O in degrees.
In order to write an equation to calculate the distance d for any star using the given information, we can make use of the concept of stellar parallax.
Stellar parallax is a technique used by astronomers to measure the distance to stars by observing their apparent shift in position as seen from different points in Earth's orbit around the Sun.
The angle O in the diagram represents this shift in position.
Now, let's consider the basic principle of stellar parallax.
The distance d from the star to the Sun is inversely proportional to the angle O.
This means that as the angle O increases, the distance d decreases, and vice versa.
We can express this relationship mathematically using the equation:
d = k/O
In this equation, k represents a constant of proportionality.
The value of k depends on the units of measurement used for d and O. Since astronomical units (AU) are used to measure distance in this context, we can rewrite the equation as:
d = k/AU
By rearranging the equation, we can solve for k:
k = d [tex]\times[/tex] AU
Therefore, the equation to calculate the distance d for any star using the given angle O and astronomical units (AU) is:
d = k/O = (d [tex]\times[/tex] AU)/O
This equation allows astronomers to determine the distance to a star based on its observed stellar parallax angle O and the average distance from Earth to the Sun, represented by one astronomical unit (AU).
For similar question on distance.
https://brainly.com/question/29409777
#SPJ8
he method of data analysis depends on: a. analytical techniques. b. the population. c. research objectives. d. the length of field notes
Answers
The method of data analysis depends on the research objectives.
The chosen analytical techniques and approaches for data analysis should align with the specific goals and objectives of the research study.
Different research objectives may require different data analysis methods. For example, if the objective is to identify patterns or themes in qualitative data, methods such as thematic analysis or content analysis may be appropriate. On the other hand, if the objective is to determine the relationship between variables, quantitative analysis techniques like regression analysis or hypothesis testing may be used.
Therefore, the most crucial factor in determining the method of data analysis is the research objectives.
To know more about data analysis click here :
https://brainly.com/question/30094947
#SPJ4
a school guidance counselor is concerned that a greater proportion of high school students are working part-time jobs during the school year than a decade ago. a decade ago, 28% of high school students worked a part-time job during the school year. to investigate whether the proportion is greater today, a random sample of 80 high school students is selected. it is discovered that 37.5% of them work part-time jobs during the school year. the guidance counselor would like to know if the data provide convincing evidence that the true proportion of all high school students who work a part-time job during the school year is greater than 0.28. are the conditions for inference met for conducting a z-test for one proportion?yes, the random, 10%, and large counts conditions are all met.no, the random condition is not met.no, the 10% condition is not met.no, the large counts condition is not met.
Answers
The required, there is convincing evidence that the proportion of all high school students who work a part-time job during the school year is greater than 0.28.
The conditions for inference for conducting a z-test for one proportion are:
Random: The sample is selected using a random method, so this condition is met.
10%: The sample size (80) is less than 10% of the total population of high school students, so this condition is met.Large Counts: Both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the hypothesized proportion. In this case, np = 80 × 0.28 = 22.4 and n(1-p) = 80 × (1 - 0.28) = 57.6. Since both values are greater than 10, this condition is also met.Therefore, all the conditions for inference are met, and we can conduct a z-test for one proportion to test whether the proportion of all high school students who work a part-time job during the school year is greater than 0.28.
The null hypothesis is that the true proportion is 0.28, and the alternative hypothesis is that the true proportion is greater than 0.28. We can calculate the test statistic using the formula:
z = (p - P) / √[P(1-P) / n]
where p is the sample proportion (0.375), P is the hypothesized proportion (0.28), and n is the sample size (80).
Plugging in the values, we get:
z = (0.375 - 0.28) / √[0.28 × (1 - 0.28) / 80] = 2.22
Using a standard normal distribution table or calculator, we find that the p-value for a z-score of 2.22 is approximately 0.014. Since this is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is convincing evidence that the proportion of all high school students who work a part-time job during the school year is greater than 0.28.
Learn more about hypothesis tests here:
https://brainly.com/question/30588452
#SPJ1
4.
The net of a square pyramid and its
dimensions in units are shown in the
diagram.
What is the total surface area of the
pyramid in square units?
Big points
Answers
The total surface area of the given pyramid is 336ft²
We have.
The surface area of a solid object is a measure of the total area that the surface of the object occupies.
The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact.
Given is a net of a square pyramid and having dimensions,10 ft 8 ft 12 ft
The total surface area of the pyramid :-
= area of base square +(side)²
= 4 (1/2 x 12 x 8) + 144
= 144+192
= 336ft²
Hence, the total surface area of the given pyramid is 336ft²
Learn more about surface area, click;
brainly.com/question/29298005
#SPJ1
The complete question is :-
The net of a square pyramid and its dimensions are shown in the diagram. 10 ft 8 ft 12 ft What is the lateral surface area of the pyramid in square feet? A 384 ft? B 192 ft? C 160 ft? D 336 ft?
Referring to the "Market Returns" file, complete a regression equation using IBM as the Dependent Variable, and the S&P 500 as the Independent Variable. Approximately what percentage of the return for IBM is explained by the returns of the S&P? Approximately 25% Approximately 30% Approximately 22% Approximately 86%
Answers
The regression equation using IBM as the dependent variable and the S&P 500 as the independent variable can be used
to determine the percentage of the return for IBM that is explained by the returns of the S&P 500.
However, without access to the "Market Returns" file or the specific regression analysis results, it is not possible to determine the exact percentage.
The percentage of return for IBM explained by the returns of the S&P 500, also known as the coefficient of determination (R-squared), can range from 0% to 100%.
R-squared represents the proportion of the variance in the dependent variable (IBM) that is predictable from the independent variable (S&P 500).
A higher R-squared value indicates a stronger relationship between the variables and a higher percentage of the return for IBM being explained by the returns of the S&P 500. Without the regression analysis results, we cannot provide an accurate estimate of the percentage in this case.
Learn more about Market Returns here:
brainly.com/question/30048477
#SPJ11
a population of cattle is increasing at a rate of 400 80t per year, where t is measured in years. by how much does the population increase between the 5th and the 9th years? total increase =
Answers
Therefore, the population increases by 3516 cattle between the 5th and 9th years.
To find the population increase between the 5th and 9th years, we need to calculate the integral of the given rate function (400 + 80t) with respect to t from 5 to 9.
Step 1: Find the integral of the rate function.
∫(400 + 80t) dt = 400t + 40t^2 + C
Step 2: Calculate the population increase at t = 5 and t = 9.
For t = 5: 400(5) + 40(5^2) = 2000 + 1000 = 3000
For t = 9: 400(9) + 40(9^2) = 3600 + 2916 = 6516
Step 3: Find the difference between these two values.
Total increase = 6516 - 3000 = 3516
Therefore, the population increases by 3516 cattle between the 5th and 9th years.
To know more about function visit :
https://brainly.com/question/11624077
#SPJ11
located in the middle of the field has a circumference of 16π yards. A diagram of the soccer field is shown below. What is the area, in square yards, of the portion of the field that is outside of the circular area?
Answers
The portion of the field that is outside of the circular area is 9,398.4 yd².
What is the area of the circular portion?The radius of the circle is calculated as follows;
circumference of the circle = 16π yards
circumference = 2πr
where;
r is the radius of the circle2πr = 16π
r = 8 yards
The area of the circular portion is calculated as follows;
A = πr²
A = π x (8 yd)²
A = 201.6 yd²
The total area of the field is calculated as follows;
A = 120 yds x 80 yds
A = 9,600 yd²
The portion of the field that is outside of the circular area is calculated as follows;
= 9,600 yd² - 201.6 yd²
= 9,398.4 yd²
Learn more about area of field here: https://brainly.com/question/16655158
#SPJ1
Verify that (0, 0) and (10/3,0) are critical points of the following function: f(x, y) = 3x ^ 2 * y + 2x * y ^ 2 - 10xy - 8y ^ 2
Classify these given critical points into relative maximum, relative minimum or saddle
points.
Answers
The points (0, 0) and (10/3, 0) are critical points of the function f(x, y) = 3x^2 * y + 2x * y^2 - 10xy - 8y^2. The point (0, 0) is a saddle point, while the point (10/3, 0) is a relative minimum.
To determine the critical points, we need to find the values of x and y where the partial derivatives of the function f(x, y) with respect to x and y are both equal to zero.
Taking the partial derivative with respect to x, we have:
∂f/∂x = 6xy + 2y^2 - 10y
Taking the partial derivative with respect to y, we have:
∂f/∂y = 3x^2 + 4xy - 10x - 16y
Setting both partial derivatives equal to zero and solving, we find two critical points: (0, 0) and (10/3, 0).
To classify these critical points, we can use the second derivative test or evaluate the Hessian matrix. However, in this case, evaluating the Hessian matrix is not necessary. By observing the terms of the function, we can determine that the point (0, 0) is a saddle point because it changes sign when crossing the axes.
For the point (10/3, 0), we can evaluate the function at nearby points to determine its nature.
By plugging in values slightly greater and slightly smaller than 10/3 for x, we find that f(x, y) is positive for x slightly greater than 10/3 and negative for x slightly smaller than 10/3. Therefore, (10/3, 0) is a relative minimum.
Learn more about saddle point here: brainly.com/question/31405597
#SPJ11
The graph fix) = (x + 2)²-7 is translated 5 units right, resulting in the graph of g(x). Which equation represents the new function, g(x)?
A:g(x)= (x+7)^2-7
B:g(x) = (x-3)^2-7
C:g(x) = (x-2)^2-12
D:g(x) = (x+2)^2-2
Answers
Answer:
Step-by-step explanation:
D
Answer:
D. g(x) = (x+2)² - 2
Step-by-step explanation:
f(x) = (x + 2)² - 7
translated 5 units right (positive) → f(x) + 5
= (x + 2)² - 7 + 5
= (x + 2)² - 2
Subject : Mathematics
Level : JHS
Chapter : Transformation (Function)
as part of a promotion, people who participate in a survey are sent a free coupon for one of three winter activities: skiing, snow tubing, or sleigh rides. participants have an equal chance of receiving each type of coupon. if 900 people participate, how many would be expected to receive a coupon for sleigh rides
Answers
It is expected that 300 participants out of the 900 who participate in the survey would receive a coupon for sleigh rides.
To determine the number of participants expected to receive a coupon for sleigh rides, we need to divide the total number of participants (900) by the number of coupon options (3) since each option has an equal chance of being received.
The expected number of participants receiving a coupon for sleigh rides can be calculated as follows:
Total participants / Number of coupon options = Expected number of participants receiving a sleigh ride coupon
900 participants / 3 coupon options = 300 participants.
Therefore, it is expected that 300 participants out of the 900 who participate in the survey would receive a coupon for sleigh rides.
It's important to note that this calculation assumes an equal chance of receiving each type of coupon and does not consider any specific preferences or biases that participants may have.
The calculation is based on the assumption of a random distribution of coupons among the participants.
For similar question on survey.
https://brainly.com/question/14610641
#SPJ11
pls help ty sm ok down below
Answers
Answer:
A. 424.12 [tex]in^{2}[/tex]
Step-by-step explanation:
The volume for a cylinder is (pi)(r^2)(h)
[tex]\pi r^{2} h[/tex]
radius = 3
height = 15
(pi) (9) (15)
135pi = 424.1150082 = 424.12
hope this helps :)
What is the perimeter of a rectangle that measures 7 3/4 inches by 10 1/8 inches?
Answers
Answer:
35.75 (inches)
Step-by-step explanation:
7 3/4 is the width and 10 1/8 is the length.
perimeter = 2L + 2W
= 2 (10 1/8) + 2(7 3/4)
= 20 2/8 + 14 6/4
= 20.25 + (14 + 1 + 2/4)
= 20.25 + (15 + 1/2)
= 20.25 + 15 + 0.5
= 35.75 (inches)
Pearson's r is the technical term for the correlation coefficient most often used in psychological research.
true/false
Answers
True. Pearson's r is indeed the technical term for the correlation coefficient that is most often used in psychological research. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It quantifies the extent to which changes in one variable are associated with changes in the other variable.
Pearson's correlation coefficient, denoted by the symbol r, is specifically used to assess the linear relationship between two continuous variables. It ranges from -1 to 1, where a value of -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
Psychological research often involves examining the relationships between various psychological constructs, such as intelligence and academic performance, self-esteem and mental health, or stress and job satisfaction. Correlation analysis using Pearson's r allows researchers to determine the strength and direction of these relationships.
By calculating Pearson's correlation coefficient, researchers can assess the degree of association between variables and make informed interpretations about the nature and strength of the relationship. This information is valuable in understanding patterns, making predictions, and informing interventions or treatments in psychological research and practice.
Learn more about Correlation here: brainly.com/question/32386183
#SPJ11
Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury?
0.05 – 0.1y = 0.12 – 0.06y
0.05y + 0.1 = 0.12y + 0.06
0.05 + 0.1y = 0.12 + 0.06y
0.05y – 0.1 = 0.12y – 0.06
Answers
An equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is: C. 0.05 + 0.1y = 0.12 + 0.06y.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided, a linear equation that models the first water body with respect to its rising rate and number of hours (y) is given by;
R = 0.05 + 0.1y ....equation 1.
Similarly, a linear equation that models the first water body with respect to its rising rate and number of hours (y) is given by;
R = 0.12 + 0.06y ....equation 2.
By equating the two equations, we have:
0.05 + 0.1y = 0.12 + 0.06y
Read more on equation here: https://brainly.com/question/28098605
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Consider the heat equation of the temperature of a solid material. The Dirichlet boundary conditions means to fix the at both boundaries of the solid material. The Neumann boundary conditions means to fix the at both boundaries of the solid material.
Answers
Thank you for your question. In the context of the heat equation, we are concerned with the temperature distribution of a solid material over time. The equation governing this distribution is known as the heat equation.
The boundaries of the solid material refer to the edges or surfaces of the material. In the case of the Dirichlet boundary condition, the temperature at these boundaries is fixed or specified. This means that we know exactly what the temperature is at these points, and this information can be used to solve the heat equation.
On the other hand, the Neumann boundary condition specifies the rate of heat transfer at the boundaries. This means that we know how much heat is flowing in or out of the solid material at these points. The Neumann boundary condition is particularly useful when we have external sources of heat or when we are interested in how heat is being exchanged with the surrounding environment.
In summary, the Dirichlet and Neumann boundary conditions provide essential information for solving the heat equation and determining the temperature distribution of a solid material.
Hi! I'd be happy to help you with your question about the heat equation and boundary conditions. Consider the heat equation for the temperature of a solid material. The Dirichlet boundary conditions mean to fix the temperature at both boundaries of the solid material, while the Neumann boundary conditions mean to fix the temperature gradient (or the rate of change of temperature) at both boundaries of the solid material.
To know more about equation visit:
https://brainly.com/question/29174899
#SPJ11
Find the length of the path over the given interval. (9 sin 5t, 9 cos 5t), 0 ≤ t ≤ π
Answers
The length of the path traced by the curve (9 sin 5t, 9 cos 5t) over the interval 0 ≤ t ≤ π is 45π units.
To find the length of the path traced by the curve (9 sin 5t, 9 cos 5t) over the interval 0 ≤ t ≤ π, we can use the arc length formula for parametric curves.
The arc length formula for a parametric curve (x(t), y(t)) over an interval [a, b] is given by:
L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt
In this case, we have x(t) = 9 sin 5t and y(t) = 9 cos 5t.
Differentiating x(t) and y(t) with respect to t, we get:
dx/dt = 45 cos 5t
dy/dt = -45 sin 5t
Substituting these derivatives into the arc length formula, we have:
[tex]L =\int\limits^\pi_0 \sqrt{ (45 cos 5t)^2 + (-45 sin 5t)^2) } dt[/tex]
[tex]L =\int\limits^\pi_0 \sqrt{ 2025 cos^2 5t + 2025 sin^2 5t) } dt[/tex]
[tex]L =\int\limits^\pi_0 \sqrt{ 2025 } dt[/tex]
L = 45 [tex]\int\limits^\pi_0 dt[/tex]
L = 45 [t] evaluated from 0 to π
L = 45 (π - 0)
L = 45π
Learn more about path at https://brainly.com/question/32356448
#SPJ11
Triangle XYZ ~ triangle JKL. Use the image to answer the question.
a triangle XYZ with side XY labeled 8.7, side XZ labeled 8.2, and side YZ labeled 7.8 and a second triangle JKL with side JK labeled 12.18
Determine the measurement of KL.
KL = 9.29
KL = 10.92
KL = 10.78
KL = 11.48
Answers
The measurement of KL if triangles XYZ and JKL are similar is:
B. KL = 10.92
How to Find the Side Lengths of Similar Triangles?Where stated that two triangles are similar, it means they have the same shape but different sizes, and therefore, their pairs of corresponding sides will have proportional lengths.
Since Triangle XYZ and JKL are similar, therefore we will have:
XY/JK = YZ/KL
Substitute the given values:
8.7/12.18 = 7.8/KL
Cross multiply:
8.7 * KL = 7.8 * 12.18
Divide both sides by 8.7:
8.7 * KL / 8.7 = 7.8 * 12.18 / 8.7 [division property of equality]
KL = 10.92
Learn more about similar triangles on:
https://brainly.com/question/27996834
#SPJ1
Find the area of the figure.
A composite figure made of a triangle, a square, and a semicircle. The diameter and base measure of the circle and triangle respectively is 6 feet. The triangle has a height of 3 feet. The square has sides measuring 2 feet.
Answers
The total area of the composite figure in this problem is given as follows:
41.3 ft².
How to obtain the area of the composite figure?The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.
The figure in this problem is composed as follows:
Triangle of base 6 feet and height 3 feet.Semicircle of radius 3 feet. -> as the radius is half the diameter.Square of side length 2 feet.Then the total area of the figure is given as follows:
A = triangle + semicircle + square
A = 0.5 x 6 x 3 + π x 3² + 2²
9 + 28.3 + 4 = 41.3 ft².
More can be learned about area of composite figures at brainly.com/question/10254615
#SPJ1
Home Insurance costs an average of 0.4% of the purchase price of your home and must be purchased every year. If you home costs $290,000.00, how much is the annual Home Insurance bill?
Answers
Answer:
Cost of the house = $290,000.00
Insurance cost = 0.4%
Annual Home Insurance Bill = (290,000 X 0.4)/100
= 116,000 ÷ 100
= 1,160
Consider two independent random variables X and Y. X has a Uniform distribution on the interval (0, 3). The probability density function of Y is given by fY (y) = y^2/9 if 0 < y < 3; 0 otherwise (a) Calculate P(X / Y > 1). (b) Calculate P(X + Y > 2). (c) Calculate P(X * Y > 3)
Answers
Answer : ∫∫[Y > 3/X] (1/3) * (y^2/9) dx/dy.
(a) To calculate P(X/Y > 1), we need to find the probability that the ratio of X to Y is greater than 1.
The joint probability density function of X and Y, since they are independent, is given by f(X,Y) = fX(x) * fY(y).
Given that X has a Uniform distribution on (0, 3), the probability density function of X, fX(x), is:
fX(x) = 1/(3-0) = 1/3 for 0 < x < 3, and 0 otherwise.
The probability density function of Y, fY(y), is given as:
fY(y) = y^2/9 for 0 < y < 3, and 0 otherwise.
Now, we can calculate P(X/Y > 1) as follows:
P(X/Y > 1) = ∫∫[X/Y > 1] f(X,Y) dxdy
= ∫∫[X > Y] fX(x) * fY(y) dxdy
= ∫∫[X > Y] (1/3) * (y^2/9) dxdy
= ∫[0,3] ∫[0,x] (1/3) * (y^2/9) dydx
= (1/3) ∫[0,3] [(1/9) * (y^3/3)] evaluated from 0 to x dx
= (1/3) ∫[0,3] (x^3/27) dx
= (1/3) * [(1/108) * (x^4)] evaluated from 0 to 3
= (1/3) * [(1/108) * (3^4 - 0^4)]
= (1/3) * [(1/108) * 81]
= 1/4.
Therefore, P(X/Y > 1) = 1/4.
(b) To calculate P(X + Y > 2), we need to find the probability that the sum of X and Y is greater than 2.
We can calculate this as follows:
P(X + Y > 2) = ∫∫[X + Y > 2] f(X,Y) dxdy
= ∫∫[X > 2 - Y] fX(x) * fY(y) dxdy
= ∫∫[X > 2 - Y] (1/3) * (y^2/9) dxdy.
To solve this integral, we can break it into two parts based on the range of Y:
For 0 < y < 2:
∫∫[X > 2 - Y] (1/3) * (y^2/9) dxdy = ∫[0,2] ∫[2-y,3] (1/3) * (y^2/9) dxdy.
For 2 < y < 3:
∫∫[X > 2 - Y] (1/3) * (y^2/9) dxdy = ∫[2,3] ∫[0,3] (1/3) * (y^2/9) dxdy.
Calculating these integrals will give us the desired probability.
(c) To calculate P(X * Y > 3), we need to find the probability that the product of X and Y is greater than 3.
Similarly, we can set up the
integral:
P(X * Y > 3) = ∫∫[X * Y > 3] f(X,Y) dxdy
= ∫∫[Y > 3/X] fX(x) * fY(y) dxdy
= ∫∫[Y > 3/X] (1/3) * (y^2/9) dxdy.
We can then evaluate this integral over the appropriate ranges to find the desired probability.
Learn more about function : brainly.com/question/30721594
#SPJ11
A proportional relationship is graphed
and goes through the point (3, 12).
Determine the y-coordinate of another
point that lies on the graph of the line if
the x-coordinate is 2.
A 5
B 6
C 7
D 8
Answers
Find the surface area of the portion of the surface z = y^2 + ? 3x lying above the triangular region T in the xy-plane with vertices (0, 0),(0, 2) and (2, 2).
Answers
The surface area of the portion of the surface z = y^2 + 3x lying above the triangular region T is 30.67 square units.
To find the surface area of the portion of the surface z = y^2 + 3x lying above the triangular region T in the xy-plane, we can use the surface area formula for a surface given by z = f(x, y):
Surface Area = ∬T √(1 + (fx)^2 + (fy)^2) dA
where T is the region in the xy-plane, fx and fy are the partial derivatives of f(x, y) with respect to x and y, respectively, and dA is the differential area element in the xy-plane.
In this case, we have z = y^2 + 3x, so the partial derivatives are:
fx = 3
fy = 2y
Now, let's find the limits of integration for T. The vertices of the triangle T are (0, 0), (0, 2), and (2, 2). The base of the triangle is along the x-axis from x = 0 to x = 2, and the height varies from y = 0 to y = 2.
Thus, the limits of integration for T are:
0 ≤ x ≤ 2
0 ≤ y ≤ 2x
Now, we can calculate the surface area:
Surface Area = ∬T √(1 + (fx)^2 + (fy)^2) dA
= ∫[0, 2] ∫[0, 2x] √(1 + (3)^2 + (2y)^2) dy dx
Simplifying the integrand:
Surface Area = ∫[0, 2] ∫[0, 2x] √(1 + 9 + 4y^2) dy dx
= ∫[0, 2] ∫[0, 2x] √(10 + 4y^2) dy dx
Now, we can integrate with respect to y:
Surface Area = ∫[0, 2] [1/4 (10y + 2y^3/3)]|[0, 2x] dx
= ∫[0, 2] (5x + (8x^3)/3) dx
Integrating with respect to x:
Surface Area = [5x^2/2 + (8x^4)/12]| [0, 2]
= [5(2)^2/2 + (8(2)^4)/12] - [5(0)^2/2 + (8(0)^4)/12]
= 10 + (64/3)
= 30.67
Therefore, the surface area of the portion of the surface z = y^2 + 3x lying above the triangular region T is approximately 30.67 square units.
Learn more about surface area at https://brainly.com/question/13262852
#SPJ11
cassie can run 100 meters in 24.73 seconds. how many ninutes would it take cassie to run 1 kilometer?
Answers
Answer:
22,281.73
Step-by-step explanation:
1 kilometer = 1000 Meters
Subtract the 100 meters you already have from 1000.
Multiply 900 times 24.73
Add 22,257 to 24.73
= 22,281.73
identify the number of real roots for given function
Answers
The number of real roots for the functions are
Graph 1 = 4Graph 2 = 1Graph 3 = 2Graph 4 = 0Graph 5 = 1Graph 6 = 1How to identify the number of real roots for the functionsFrom the question, we have the following parameters that can be used in our computation:
The graphs
The number of real roots of a function is the number of times the function intersects with the x-axis
This in other words means the zeros of the function
Using the above as a guide, we have the roots of the graphs to be
Graph 1 = 4
Graph 2 = 1
Graph 3 = 2
Graph 4 = 0
Graph 5 = 1
Graph 6 = 1
Read more about function at
https://brainly.com/question/16550963
#SPJ1
63.64, 65, 66, 67 and 68 Find the slope of the tangent line to the given polar curve at the point specified by the value of e. 63. T = 2 cos 8, 8= */3 64 Answer 64. r = 2+ sin 30, 0 = 7/4
Answers
The slope of the tangent line to the polar curve at the specified points is -8√3 for the polar curve T = 2cos(8) at θ = π/3, and the slope is zero for the polar curve r = 2 + sin(30) at θ = 7π/4.
The slope of the tangent line to the polar curve at the specified points is as follows:
63. For the polar curve T = 2cos(8), where θ = π/3, the slope of the tangent line can be found by taking the derivative of r with respect to θ and evaluating it at the given value of θ. The derivative of r = 2cos(8) with respect to θ is dr/dθ = -16sin(8), and when θ = π/3, the slope of the tangent line is -16sin(π/3) = -16(√3/2) = -8√3.
64. For the polar curve r = 2 + sin(30), where θ = 7π/4, the slope of the tangent line can be found by taking the derivative of r with respect to θ and evaluating it at the given value of θ. The derivative of r = 2 + sin(30) with respect to θ is dr/dθ = 0, as the derivative of a constant is zero. Therefore, the slope of the tangent line is zero.
In summary, the slope of the tangent line to the polar curve at the specified points is -8√3 for the polar curve T = 2cos(8) at θ = π/3, and the slope is zero for the polar curve r = 2 + sin(30) at θ = 7π/4.
Learn more about slope here:
https://brainly.com/question/2491620
#SPJ11
Which expression is equivalent to √17?
Answers
The expression that is equivalent to √17 is √(68)/2
How to determine the expression that is equivalent to √17?From the question, we have the following parameters that can be used in our computation:
Expression = √17
Multiply the expression by 1
so, we have the following representation
Expression = √17 * 1
Express 1 as 2/2
so, we have the following representation
Expression = √17 * 2/2
The square root of 4 is 2
So, we have
Expression = √(17 * 4)/2
Evaluate the products
Expression = √(68)/2
Hence, the expression that is equivalent to √17 is √(68)/2
Read more about expression at
https://brainly.com/question/15775046
#SPJ1
The length of a rectangle is 2 units more than 6 times its width, w. Which expression represents the perimeter of the rectangle?
Answer options:
- 12w+4
-14w+4
-6w^2 +2 (plus two is separate from the exponent)
-14w^2+4w (plus 4w is separate from the exponent as well)
im actually begging bro this is due tmrw
Answers
The expression representing the perimeter of the rectangle is:
B. 14w + 4
What is the Perimeter of a Rectangle?To find the expression representing the perimeter of the rectangle, we need to understand the relationship between the length and width of the rectangle.
Let's start by assigning variables:
Length of the rectangle = L
Width of the rectangle = w
According to the given information, the length is 2 units more than 6 times the width:
L = 6w + 2
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (Length + Width)
Substituting the values, we have:
Perimeter = 2 * (L + w)
= 2 * ((6w + 2) + w)
= 2 * (7w + 2)
= 14w + 4
Learn more about Perimeter of a Rectangle on:
https://brainly.com/question/24571594
#SPJ1
