The probability density function is of E(Y1) and E(Y2) is 1/6 and variance is 1/18.
To find the expected value E(Y1+Y2), we can use the linearity of expectation and the fact that the expected value of a constant is that constant:
E(Y1+Y2) = E(Y1) + E(Y2)
To find E(Y1) and E(Y2), we need to integrate y1 and y2 respectively over their joint probability density function:
E(Y1) = ∫∫ y1 f(y1,y2) dy1 dy2
= ∫0^1 ∫0^(1-y1) 2y1 dy2 dy1
= ∫0^1 2y1(1-y1)/2 dy1
= ∫0^1 y1-y1^2 dy1
= [y1^2/2 - y1^3/3] from 0 to 1
= 1/6
Similarly,
E(Y2) = ∫∫ y2 f(y1,y2) dy1 dy2
= ∫0^1 ∫0^(1-y2) 2y2 dy1 dy2
= ∫0^1 2y2(1-y2)/2 dy2
= ∫0^1 y2-y2^2 dy2
= [y2^2/2 - y2^3/3] from 0 to 1
= 1/6
Therefore, E(Y1+Y2) = E(Y1) + E(Y2) = 1/6 + 1/6 = 1/3.
To find the variance V(Y1+Y2), we can use the formula:
V(Y1+Y2) = E((Y1+Y2)^2) - [E(Y1+Y2)]^2
To find E((Y1+Y2)^2), we need to integrate (y1+y2)^2 over their joint probability density function:
E((Y1+Y2)^2) = ∫∫ (y1+y2)^2 f(y1,y2) dy1 dy2
= ∫0^1 ∫0^(1-y1) (y1+y2)^2 2 dy2 dy1
= ∫0^1 [(2/3)y1^3 + y1^2 + (1/3)y1] dy1
= 5/18
Therefore, V(Y1+Y2) = E((Y1+Y2)^2) - [E(Y1+Y2)]^2 = 5/18 - (1/3)^2 = 5/18 - 1/9 = 1/18
The variance is 1/18.
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Evaluate using order of operations
3/4+5/6÷2/3
Answer:
2.375
Step-by-step explanation:
Solve the following inequality for z.
7 z + 7 > − 2 z − 4
Answer: z > -11/9
Step-by-step explanation:
7z + 7 > -2z - 4
+2z +2z
9z + 7 > -4
-7 -7
9z > -11
/9 /9
z > -11/9
Check all the correct statements.
Note: Push yourself to understand why these statements are true or false. If false think about an example that contradicts the statement, or think about how you would formulate the statement so it is correct. You will not see these exact questions in an exam, so it is important that you understand the concepts so you can answer a similar question that is formulated differently.
Check all the correct statements.
The internal energy of an ideal gas (those that obey PV = nRT) depends only the temperature of the system.
The internal energy of any gas depends only the temperature of the system.
The heat capacity of an ideal gas does not depend on what molecules the gas is made of.
At constant temperature, the internal energy of a real gas increases with increasing pressure because molecules are closer together. We assume that the conditions are such that attractions dominate over repulsions (i.e. the pressure values are not too high)
At constant temperature, the internal energy of a real gas decreases with increasing pressure because molecules are closer together. We assume that the conditions are such that attractions dominate over repulsions (i.e. the pressure values are not too high)
A cyclic path (initial state = final state) always results in ∆U = 0
∆U = 0 for any process that does not result in a change in temperature.
ΔU= qv only for a monoatomic ideal gas
The correct statements are regarding Ideal gas are: The heat capacity of an ideal gas does not depend on what molecules the gas is made of. A cyclic path (initial state = final state) always results in ΔU = 0.
"The internal energy of an ideal gas depends only on the temperature of the system." False, it depends on both temperature and the number of particles in the system.
"The internal energy of any gas depends only on the temperature of the system. "False, it also depends on the volume and pressure of the system, which can vary based on the type of gas and the conditions.
"At constant temperature, the internal energy of a real gas increases with increasing pressure because molecules are closer together. We assume that the conditions are such that attractions dominate over repulsions (i.e. the pressure values are not too high)." False, the statement should say that the internal energy decreases with increasing pressure, not increases.
"ΔU = 0 for any process that does not result in a change in temperature."False, ΔU can be non-zero even if there is no change in temperature, as long as there is a change in volume or pressure.
"ΔU = qv only for a monoatomic ideal gas." False, ΔU = q + w, where q is the heat added to the system and w is the work done on the system. The equation ΔU = qv only holds for a monoatomic ideal gas undergoing an isothermal expansion or compression.
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find the gradients of esm n with respect to w(1) and w(2). (note that you should always consider two possible values of yn).
The variables s, m, n, and y in this question are challenging to interpret without additional context. On the other hand, if y is a constant and s, m, and n are functions of w(1) and w(2)
With regard to w(1), esm's partial derivative is as follows:
Each of these partial derivatives can be calculated using the differentiation chain rule and the variables s, m, n, and y in this question are challenging to interpret without additional context. On the other hand, if y is a constant and s, m, and n are functions of w(1) and w(2):
∂(esm)/∂(w(1)) = yn * exp(-yn * n) * (-m) * 1/(1 + exp(-s)) * exp(s) / (1 + exp(s))^2 * x1
∂(esm)/∂(w(2)) = ∂(esm)/∂(n) * ∂(n)/∂(m) * ∂(m)/∂(s) * ∂(s)/∂(w(2))
∂(esm)/∂(w(2)) = yn * exp(-yn * n) * (-m) * 1/(1 + exp(-s)) * exp(s) / (1 + exp(s))^2 * x2.
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Consider the following 1st order differential equation. dx/dt = 4e^0.8 t - 0.5x In MATLAB, solve the system store values of x in a vector from t = 0 to t = 3 if x(0) = 2 using the following methods. You can put everything in one MATLAB script or write one script for each method. (a) Euler's method with a step size of 0.5 (b) Heun's method with a step size of 0.5 (c) Midpoint method with a step size of 0.5 (d) The analytical solution to this equation is given as: x = 4/1.3 (e^0.8 t - e^-0.5t) + 2e^-0.5t Plot the previous 3 numerical solutions and the analytical solution in one graph, and make sure you label the axes and legends
The Midpoint method is similar to Heun's method, but the equation becomes[tex]x_n+1 = x_n + hf(x_n + 0.5h, t_[/tex]
Euler's method is used to approximate the solution of a differential equation using a step size, h. The numerical solution is calculated using [tex]x_n+1 = x_n + hf(x_n, t_n)[/tex], where f is the derivative of x with respect to t. In this case, the equation becomes [tex]x_n+1 = x_n + 0.5(4e^(0.8t_n) - 0.5x_n)[/tex], where [tex]x_n[/tex] is the value of x at [tex]t_n[/tex] and [tex]x_n+1[/tex] is the value of x at[tex]t_n+0.5.[/tex]
Heun's method is also used to approximate the solution of a differential equation. Here, the equation becomes [tex]x_n+1 = x_n + 0.5(f(x_n, t_n) + f(x_n+1, t_n+0.5)),[/tex] where [tex]x_n+1[/tex] is estimated using the Euler's method.
The Midpoint method is similar to Heun's method, but the equation becomes[tex]x_n+1 = x_n + hf(x_n + 0.5h, t_[/tex]
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Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and (b) find the area of triangle PQR. 29. P(3, 1, 1), Q(5, 2, 4), R(8, 5, 3) 30. P(-2, 0, 4), Q(1,3, -2), R(0, 3, 5)
The area of triangle PQR in this case is 14.924
In geometry, the concept of vectors is very useful when dealing with points, lines, and planes in three-dimensional space. Vectors have both magnitude and direction, and they can be added, subtracted, and multiplied by scalars.
To find a nonzero vector orthogonal to the plane through the points P, Q, and R, we can use the cross product of two vectors in the plane. A cross product of two vectors gives us a vector that is perpendicular to both of them, so it will be orthogonal to the plane as well.
Let's take the vectors from P to Q and from P to R as our two vectors:
u = Q - P = <5-3, 2-1, 4-1> = <2, 1, 3>
v = R - P = <8-3, 5-1, 3-1> = <5, 4, 2>
To calculate the cross product u x v, we can use the following formula:
u x v = <(1)(2) - (3)(4), (3)(5) - (1)(2), (1)(4) - (2)(5)> = <-10, 13, -2>
So the vector <-10, 13, -2> is orthogonal to the plane through P, Q, and R. Note that this vector is nonzero because at least one of its components is not zero.
To find the area of triangle PQR, we can use the fact that the area of a triangle is half the magnitude of the cross product of two of its sides. Let's take the sides from P to Q and from P to R again, and calculate their cross product:
u x v = <(3)(1) - (-6)(3), (-6)(2) - (3)(3), (3)(3) - (3)(2)> = <21, -21, 3>
So the vector <21, -21, 3> is orthogonal to the plane through P, Q, and R. Again, we can use the cross product of u and v to find the area of triangle PQR, which is:
|u x v| = sqrt(21^2 + (-21)^2 + 3^2) = √(891)
|u x v| = 1/2 * √(891) =14.924
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Given: hypotenuse = 5
adjacent = 3
Find Find opposite =
Answer:
Opposite is = 4
Step-by-step explanation:
Fromthe question Hypotenuse = 5
Adjacent = 3
opposite = ?
Let opposite = x
Hypotenuse² = adjacent² + opposite²
5² = 3² + x²
25 = 9 + x²
25 - 9 = x²
16 = x²
[tex] \sqrt{16} = \sqrt{ {x}^{2} } \\ = \sqrt{16} = x \\ = 4 = x [/tex]
Therefore opposite is = 4.
the graph doesn't have 4 quadrants
Answer:
a graph does have 4 quadrants
Step-by-step explanation:
the area (P,P) (P,N) (N,P) (N,N)
Key: P=postive
N=negitive
1 in a school test consisting of 10 questions, 5 points are awarded for a correct answer but 3 points are deducted for an incorrect answer. a blank answer scores 0. mike scored a total of 0 and he did not leave all of the answers blank
a) Either 3 or 4 questions did Mike answer correctly.
b) Either 7 or 8 questions did Sheila answer correctly.
What is a equation in math?In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
a) Let mike did x correct
then, incorrect will be (10- x)
The equation is:
Now, 5x + (10 - x) (-3) = 0
=> 5x - 30 + 3x = 0
=> 8x = 30
=> x = 30/8
=> x > 3 and x < 4
b) Let Sheila did y correct
then, incorrect = (10 - y)
Now, 5y + (10 - y) (-3) = 32
=> 5y - 30 + 3y = 32
=> 8y = 62
=> y > 7 and y< 8
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The given question is incomplete, complete question is:
In a school test consisting of 10 questions, 5 points are awarded for a correct answer but 3 points are deducted for an incorrect answer.
A blank answer scores (). Mike scored a total of () and he did not leave all of the answers blank. (a) How many questions did Mike answer correctly? _ _ _ _ _ _ _ _ Sheila scored a total of 32. (b) How many questions did Sheila answer correctly?
A population of 40 foxes in a wildlife preserve doubles in size every 15 years. The function y=40•2*, where x is the number of 15 years periods, models the population growth. How many foxes will there be after 30 years?
Answer:
There will be 160 foxes after 30 years.
Step-by-step explanation:
If the population of 40 foxes doubles every 15 years, then after 15 years (one period) it will be 2 times the initial population (240 = 80), and after 30 years (two periods) it will be 2 times the population after 15 years, which is 280 = 160.
Using the given function, we can also plug in x = 2 (since 30 years is two 15-year periods) and solve for y:
y = 40 * 2^2
y = 40 * 4
y = 160
Therefore, there will be 160 foxes after 30 years.
On the first day it was posted online, a music video got 2000 views. The number of views that the video got on the second day was 2400. On the third day the video got 2880 views and so on.
Write the explicit formula for the number of views on the nth day
Answer: The number of views on the nth day can be represented by the explicit formula:
V(n) = 2000 * 2^(n-1)
where n is the number of the day and V(n) is the number of views on the nth day. The formula uses the formula for exponential growth, where the number of views on each day is double the number of views from the previous day.
Step-by-step explanation:
PLEASE HELP !! Tammy was comparing information for two cell phone plans.
Plan A: $480/year
Plan B: $250/6 months
One year = 12 months = 6 months x 2
So, if Plan B costs $250 every 6 months, you simply have to multiply 250 by 2 which equals:
250 x 2 = 500
In conclusion, Plan A is $480/year and Plan B is $500/year.
480 < 500 so Tammy is correct, Plan B costs more.
Find the volume of the right cone below. Round your answer to the nearest tenth if necessary.
Step-by-step explanation:
the volume of such a cone is
pi×r² × h / 3
r is the radius of the ground circle, h is the straight inner height.
the radius is as always half of the diameter, so in our case
6/2 = 3 units.
so, the volume is
pi×3² × 11 / 3 = pi×9×11/3 = pi×3×11 = 33pi =
= 103.6725576... units³ ≈
≈ 103.7 units³
. payroll mix-up five paychecks and envelopes are addressed to five different people. the paychecks are randomly inserted into the envelopes. what are the probabilities that (a) exactly one paycheck will be inserted in the correct envelope and (b) at least one paycheck will be inserted in the correct envelope? 43. game show on a game show, you are gi
The probability of exactly one paycheck being in the correct envelope is 1 in 5, while the probability of at least one paycheck being in the correct envelope is 4 in 5.
The probability of exactly one paycheck being in the correct envelope can be calculated by taking the number of possible outcomes where one paycheck is in the correct envelope (1) and dividing it by the total number of possible outcomes (5). This yields a probability of 1 in 5. The probability of at least one paycheck being in the correct envelope is calculated by taking the total number of possible outcomes where at least one paycheck is in the correct envelope (4) and dividing it by the total number of possible outcomes (5). This yields a probability of 4 in 5. Thus, the probability of exactly one paycheck being in the correct envelope is 1 in 5, while the probability of at least one paycheck being in the correct envelope is 4 in 5.
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Let C1be the circle radius 2 centered at the origin, oriented counterclockwise, let C2 be the
center radisus 1 and center at the origin, oriented clockwise and let C= C1 U C2. Use Green’s
theorem to evaluate the line integral H
C(4x2 y3)dx+ ( x3 + y2)dy
Using Green's theorem the line integral H C(4x2 y3)dx+ ( x3 + y2)dy is 70.6858.
Step: 1
Given
[tex]\int\limi {4x2 - y3} \, dx + (x3+y2) dy[/tex]
Formula for Greens theorem
δQ/δx = 3x2
Explanation:
partial derivative w.r.t x i . e y is constant
partial derivative w.r.t y i. e x is constant
power rule of derivative is
d/dx Xn = nXⁿ⁻¹
Step: 2
[tex]\int\limits\int\li {dQ/dy + dP/dx dA} \, dx = \int \int {3(x2+y2)} \, dx[/tex]
Explanation:
in polar coordinates x2 + y2 = r2 and dA = radθ
Step: 3
given
C1 = r1 = 2
C2 = r2 = 1
the limits for r is 1 ≤ r ≤ 2
since it is a circle the limits for θ
0 ≤ θ ≤ 2π
Explanation: Please refer to solution,
now integrate w.rt θ
= 45/4[θ] 2π
= 45/4[2π - 0]
= 45/4(2π)
= 45/2(π)
= 45π/2 ≈ 70.6858.
by greens theorem,
[tex]\int 4x2 y3)dx+ ( x3 + y2)dy \, dx[/tex] is 70.6858.
Green’s theorem is substantially used for the integration of the line combined with a twisted aeroplane . This theorem shows the relationship between a line integral and a face integral. It's related to numerous theorems similar as Gauss theorem, Stokes theorem.
Green’s theorem is used to integrate the derivations in a particular plane. However, it's converted into a face integral or the double integral or vice versa using this theorem, If a line integral is given.
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Katie made a bag of trail mix with1/2 cup of raisins, 3/5 cup of banana chips, and 3/8 cup of peanuts. How much trail mix did she make
So, Katie made 1 19/40 number cups of trail mix.
What is denominator?In mathematics, the denominator is the bottom number in a fraction, and it represents the total number of equal parts into which the whole has been divided. The denominator is written below the numerator, which is the top number in a fraction, and it indicates the number of those equal parts that are being considered or used in the fraction.
given by the question.
To find the total amount of trail mix Katie made, we need to add up the amounts of each ingredient:
1/2 cup of raisins +
3/5 cup of banana chips +
3/8 cup of peanuts
To add these fractions, we need to find a common denominator. The smallest number that all the denominators (2, 5, and 8) divide into evenly is 40. We can convert each fraction to have a denominator of 40:
1/2 cup of raisins = 20/40 cup
3/5 cup of banana chips = 24/40 cup
3/8 cup of peanuts = 15/40 cup
Now we can add them up:
20/40 cup + 24/40 cup + 15/40 cup = 59/40 cup
So, Katie made 59/40 cup of trail mix. However, we can simplify this fraction:
59/40 cup = 1 19/40 cup
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What is the value of x in the equation below? 150 = 35 x
Answer:
x = 30/7 = 4 2/7
Step-by-step explanation:
150 = 35x
35x = 150
x = 150/35
x = 30/7
x = 4 2/7
Answer:
x = 30/7 =4 2/7 or 4.2
Step-by-step explanation:
tell me love brainiest.
select all that apply which of the following name an angle in the drawing
∠ECB and ∠ACB are the angles.
What is an angle?
An angle is formed when two lines or rays meet at the common vertex. The angle is represented by ∠ and it is measure in °.
In the given figure,
The line FA and BD intersects at the point C.
When two lines intersect at the same vertex it makes an angle.
So there is an angle at the point C.
From the given options, the angles are ∠ECB and ∠ACB.
Option (i) and (iv) is the correct option.
Hence, ∠ECB and ∠ACB are the angles.
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Q1 PLEASE HELP ASAP !!!
Answer: 10
Step-by-step explanation:
Rework Cantor’s proof from the beginning. This time, however, if the digit under consideration is 4, then make the corresponding digit of M an 8; and if the digit is not 4, make the associated digit of M a 4.
M is not on the list, and thus the list cannot be a complete listing of all real numbers between 0 and 1.
What is inductive reasoning?Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.
Here,
Georg Cantor's diagonal argument is proof by contradiction that shows that there are more real numbers than natural numbers. Here's how the proof can be reworked with the given modification:
Suppose that we have a list of all real numbers between 0 and 1, written in decimal form. We will show that this list cannot be a complete listing of all real numbers between 0 and 1.
Let M be a new real number whose decimal expansion is obtained by following the following rule: if the nth digit of the nth number on the list is 4, then the nth digit of M is 8; if the nth digit of the nth number on the list is not 4, then the nth digit of M is 4.
Since each number on the list has a unique decimal expansion, M is a real number between 0 and 1, and its decimal expansion is different from the nth number on the list in the nth digit for all n.
Therefore, M is not on the list, and thus the list cannot be a complete listing of all real numbers between 0 and 1.
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Solve x2 + 4x + 12 = 0 by completing the square.
(options in attachment)
Answer:
second option
Step-by-step explanation:
x² + 4x + 12 = 0 ( subtract 12 from both sides )
x² + 4x = - 12
to complete the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(2)x + 4 = - 12 + 4
(x + 2)² = - 8 ( take square root of both sides )
x + 2 = ± [tex]\sqrt{-8}[/tex] = ± [tex]\sqrt{4(2)(-1)}[/tex] = ± ([tex]\sqrt{4}[/tex] × [tex]\sqrt{2}[/tex] × [tex]\sqrt{-1}[/tex] ) = ± 2[tex]\sqrt{2}[/tex] i
subtract 2 from both sides
x = - 2 ± 2[tex]\sqrt{2}[/tex] i
then
x = - 2 + 2[tex]\sqrt{2}[/tex] i , x = - 2 - 2[tex]\sqrt{2}[/tex] i
A grocer can buy raspberries from a local farmer for $1.04 per pound (lb). Her last raspberry order from the farmer cost $171.08 How many pounds of raspberries did
the grocer order? Round your answer to the nearest tenth if needed
Answer
Duration: 0010:10
f(x) pounds of raspberries from the local farmer
The grocer ordered approximately 164.3 pounds of raspberries from the local farmer. We can round this to the nearest tenth if needed, which would give us an answer of 164.3 pounds.
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
Given,
o determine how many pounds of raspberries the grocer ordered, we can use the formula:
Total cost = Price per pound x Number of pounds
We know that the price per pound is $1.04, and the total cost of the last order was $171.08. Let's use "x" to represent the number of pounds of raspberries the grocer ordered:
$171.08 = $1.04 x
To solve for x, we can divide both sides by $1.04:
x = $171.08 / $1.04
x ≈ 164.3
Therefore, The grocer ordered approximately 164.3 pounds of raspberries from the local farmer. We can round this to the nearest tenth if needed, which would give us an answer of 164.3 pounds.
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what is square root?
Answer:
a number which produces a specified quantity when multiplied by itself
Step-by-step explanation:
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9. The symbol for the square root is "√". So, √9 = 3.
There are two types of square roots: the principal square root and the negative square root. The principal square root is the positive value that, when multiplied by itself, gives the original number. The negative square root is the negative value that, when multiplied by itself, gives the original number. For example, the square roots of 9 are 3 and -3, because both 3 x 3 = 9 and -3 x -3 = 9.
The square root of a number can be approximated using a calculator or can be found using mathematical techniques such as the Newton-Raphson method. The square root of a number can also be expressed as an irrational number, meaning that it cannot be expressed as a fraction of two integers. For example, the square root of 2 is an irrational number that cannot be expressed exactly as a fraction.
Sample Means will vary from sample to sample even if all the samples are the same sizeand all thes samples are selected from the same population. (hint: think about the mean murder rates from 50 samles taken from 90 cities we looked at in class.)
True or False
Sample Means will vary from sample to sample even if all the samples are identical in size and all these samples are favored from the same population. Thus the statement in the question is true.
The sample means would differ from sample to sample, and a histogram might be used to depict their dispersion. We call this distribution the sample distribution. We refer to it as "sampling" since it is the distribution that results from "sampling" frequently. The size of the samples will determine how variable the sample means are, as bigger samples are more likely to produce estimated means that are more closely aligned with the population's actual mean.
For any given sample, the mean, median, minimum, maximum, or any other statistic may deviate from the population. Here, tools like the t-test may be used to assess if the difference between the sample and the population is statistically significant.
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You are visiting your friend Fabio's house. You find that, as a joke, he filled his swimming pool with Kool-Aid, which dissolved perfectly into the water. However, now that you want to swim, you must remove all of the Kool-Aid contaminated water. The swimming pool is round, with a 19 foot radius. It is 10.5 feet tall and has 7 feet of water in it.
How much work is required to remove all of the water by pumping it over the side? Use the physical definition of work, and the fact that the weight of the Kool-Aid contaminated water is ?=65.7lbs/ft3
The work is required to remove all the water by pumping it over the side will be: 54,221,971.6 ft-lbs
To calculate the work required to remove all of the water, we need to consider the gravitational potential energy of the water. The work done to remove the water is equal to the change in potential energy of the water.
First, we need to calculate the volume of the water in the pool. The pool is a cylinder with a height of 10.5 feet and a radius of 19 feet. The volume of the water is:
[tex]V = \pi r^2h = π(19ft)^2(7ft) = 2,586.6 ft^3[/tex]
Next, we need to calculate the weight of the water in the pool. The weight of the water is equal to its volume times its density. The density of Kool-Aid contaminated water is given as 65.7 lbs/ft^3. The weight of the water in the pool is:
[tex]W = Vpg = 2,586.6ft^3 * 65.7lbs/ft^3 * 32.2ft/s^2 \\\\[/tex]
= 5,169,044.8 ft-lbs
Finally, we can calculate the work required to remove the water by pumping it over the side. Since the water is being lifted to a height of 10.5 feet, the work required is equal to the weight of the water times the height:
W = Fd = Wwater × h
= 5,169,044.8 ft-lbs × 10.5 ft
= 54,221,971.6 ft-lbs
Therefore, approximately 54,221,971.6 ft-lbs of work is required to remove all of the water from the pool.
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Julia has 9 one pound bags of sand each a different color. For a art project she will use 1/8 lb of each bag of sand to create sand art jar. How much sand will be in the jar?
a. 8/9, b. 1/72, c. 1 1/9, d. 1 1/8
The perimeter of a rectangular field that measures 2 feet by 18 inches is _________ ft. (Watch your units)
7
84
40
6
Answer:
40 ft
Step-by-step explanation:
We know the measurements of the field so just add all the numbers up.
2 + 2 + 18 + 18 = 40 ft.
A couple has four children. One child has phenylketonuria (PKU). What is the probability of occurrence of PKU in the second generation?
The answer given question : Is 50%,probability of each child inheriting two copies of the mutated gene is 25%. And the Overall, without additional information about the genetic makeup of the second-generation partners, it is impossible to determine the exact probability of occurrence of PKU in their children.
phenylketonuria (PKU) is an inherited disorder caused by a mutation in a gene that produces an enzyme called phenylalanine hydroxylase. This enzyme is necessary for the breakdown of the amino acid phenylalanine, and without it, phenylalanine can build up to toxic levels in the body, leading to brain damage and other serious health problems.
PKU is an autosomal recessive disorder, which means that a person must inherit two copies of the mutated gene (one from each parent) in order to develop the condition. If only one copy of the mutated gene is inherited, the person is a carrier of the disorder but does not develop PKU.
Given that one of the four children in the first generation has PKU, we can assume that both parents are carriers of the disorder. The probability of each of their children inheriting a single copy of the mutated gene (i.e., becoming carriers like their parents) is 50%, and the probability of each child inheriting two copies of the mutated gene (i.e., developing PKU) is 25%.
The occurrence of PKU in the second generation will depend on the genetic makeup of the partners who have children. If both partners are carriers, there is a 25% chance that each of their children will develop PKU. If one partner is a carrier and the other is not, there is no chance that their children will develop PKU, but each child will have a 50% chance of being a carrier
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Consider measurements of the width w and length l of a piece of paper used to calculated the area of the paper using A = w × l.1. If the length of the paper is measured twice using a ruler marked with 1 mm increments, and the measurements give values of1=298 mm and l=294 mm, what value should be used for l? for δl? Express your answer in the form l±δl2. If the width of the paper is also measured twice using a ruler marked with 1 mmincrements to give a value ofw=210 mm both times, what value should be used for w? for δw? Express your answer in the form w±δw3. What is the area of the paper? What is the uncertainty in the area? Express your answer in the form A±δA
The length of the paper should be taken as the average of the two measurements, which is l = (298 + 294) / 2 = 296 mm.
The uncertainty in the length measurement can be estimated as half of the difference between the two measurements, which is δl = (298 - 294) / 2 = 2 mm. So, the value for l and δl can be expressed as l ± δl = 296 ± 2 mm.
Since the two measurements of the width both give the same value of 210 mm, we can assume that the width measurement has no uncertainty. The value for w and δw can be expressed as w ± δw = 210 ± 0 mm.
The area of the paper can be calculated as A = w × l = 210 × 296 = 62040 mm^2.
The uncertainty in the area can be estimated as the product of the uncertainties in the length and width measurements, which is δA = δw × l + w × δl = 0 × 296 + 210 × 2 = 420 mm^2. So, the area and its uncertainty can be expressed as A ± δA = 62040 ± 420 mm^2.
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Thomas is finding the coordinates of the image of a polygon with vertices W(2, 2), X(2, 4), Y(4, 4), and Z(4, 2) after a reflection across the y-axis. Describe his error.
The coordinates of W′X′Y′Z′ are W′(2, –2), X′(2, –4), Y′(4, –4), and Z′(4, –2).
After reflection, Coordinates of W'X'Y'Z' are
W'(-2, 2), X'(-2 , 4), Y' (-4, 4), and Z' (-4, 2)
What is reflection?
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure. The reflected image should have the same shape and size, but the image faces in the opposite direction.
Given,
Vertices of a polygon WXYZ
W(2, 2), X(2, 4), Y(4, 4), and Z(4, 2)
There is reflection over y-axis
For reflection over y - axis , y=f(-x)
Thomas reflected y coordinate y → -y
but x coordinate should be reflected, then x → -x
W(2, 2) → W'(-2, 2)
X(2, 4) → X'(-2 , 4)
Y(4, 4) → Y' (-4, 4)
Z(4, 2) → Z' (-4, 2)
Hence, W'(-2, 2), X'(-2 , 4), Y' (-4, 4), and Z' (-4, 2) are coordinates of W'X'Y'Z'
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