The composite functions fog and g • f are not equal to x. The function fog simplifies to 4x² - 20x + 25, while g • f simplifies to 45. Therefore, neither composite function equals x.
To determine whether the composite functions fog and g • f are equal to x, we need to evaluate each expression separately and compare the results.
1. fog (or f(g(x))):
f(g(x)) = f(2x - 5)
To compute f(2x - 5), we substitute (2x - 5) into the function f(x) = x²:
f(2x - 5) = (2x - 5)²
Expanding this expression, we get:
f(2x - 5) = 4x² - 20x + 25
Therefore, fog is not equal to x since f(2x - 5) simplifies to 4x² - 20x + 25, not x.
2. g • f (or g(f(x))):
g(f(x)) = g(25)
To compute g(25), we substitute 25 into the function g(x) = 2x - 5:
g(25) = 2(25) - 5
g(25) = 50 - 5
g(25) = 45
Therefore, g • f is not equal to x since g(25) evaluates to 45, not x.
In conclusion, neither fog nor g • f is equal to x. The composite functions do not simplify to x; fog simplifies to 4x²- 20x + 25, and g • f simplifies to 45.
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14.
Mogaka and Ondiso working together can do a piece of job in 6 days. Mogaka
working alone takes 5 days longer than Ondiso. How many days does it take
Onduso to do the work alone?
(3mks)
Answer:
10 days
Step-by-step explanation:
Mogaka and Ondiso working together can do a piece of job in 6 days. Mogaka working alone takes 5 days longer than Ondiso. How many days does it take Ondiso to do the work alone?
Let us represent :
The number of days
Mogaka worked alone = x
Ondiso worked alone = y
Total days worked together = T
Mogaka and Ondiso working together can do a piece of job in 6 days.
Hence,
1/x + 1/y = 1/T
Mogaka working alone takes 5 days longer than Ondiso.
x = y + 5
Therefore:
1/y + 5 + 1/y = 1/6
Multiply all through by (y+5)(y)
= y + y + 5 = (y+5)(y)/6
= 2y + 5/1 = (y+5)(y)/6
Cross Multiply
6( 2y + 5) = (y+5)(y)
12y + 30 = y² + 5y
= y² + 5y - 12y - 30 = 0
= y² - 7y - 30 = 0
Factorise
= y² +3y - 10y - 30 = 0
y(y + 3) - 10(y + 3) = 0
(y + 3)(y -10)= 0
y + 3 = 0, y = -3
y - 10 = 0
y = 10 days
Note that
The number of days Ondiso worked alone = y
Hence, it takes 10 days for Ondiso to work alone
What is the value of x?
5(x+2)=11
Answer:
X=1.8
Step-by-step explanation:
Step one: 5 times 1.8 equals 9.
Step two: 9+2=11
Please help me solve this.
Answer: 59
Step-by-step explanation:
Given
2b³+5 and b=3 ⇒ 2b³+5=2(3)³+5
Simplify exponents
2(3)³+5
=2(3×3×3)+5
=2×27+5
Multiplication
=54+5
Addition
=59
Hope this helps!! :)
Please let me know if you have any questions
Select the correct answer.
If you divide-16 into 5 equal parts, how much is each part equal to?
A.
-4
B.
-3.2.
C.
+2.4
D.
+5
Reset
Next
Answer:
-3.2
Step-by-step explanation:
Suppose that V₁, V2, , Um are linear dependent in a vector space V. For every & EV, show that 7₁, V2, , Um, 7 are also linearly dependent. 9
By supposing that V₁, V2, and Um are linearly dependent in a vector space V. For every & EV. V₁, V₂, ..., Uₘ are linearly dependent in a vector space V. As 7₁V₁ = 7(c₂V₂ + c₃V₃ + ... + cₘUₘ)
To show that 7₁V₁, 7₂V₂, ..., 7ₘUₘ, 7 is also linearly dependent for every 'c' in V, we can use the following approach: If V₁, V₂, ..., Uₘ are linearly dependent, then we can write at least one vector as a linear combination of the other vectors.
Let's assume V₁ can be written as a linear combination of the other vectors as follows:
V₁ = a₂V₂ + a₃V₃ + ... + aₘUₘ
where a₂, a₃, ..., aₘ are constants. Now, we can express the vector 7₁V₁ as:
7₁V₁ = 7₁a₂V₂ + 7₁a₃V₃ + ... + 7₁aₘUₘ
Since 7 is a constant, we can take it outside the bracket as:
7₁V₁ = 7(a₂7₁V₂ + a₃7₁V₃ + ... + aₘ7₁Uₘ)
Let's assume the sum inside the bracket is equal to 'b'. Then,
7₁V₁ = 7b
Since we know that V₁, V₂, ..., Uₘ are linearly dependent, we can write b as a linear combination of the other vectors as follows:
b = c₂V₂ + c₃V₃ + ... + cₘUₘ
where c₂, c₃, ..., cₘ are constants. Now, substituting the value of b in the equation for 7₁V₁, we get:
7₁V₁ = 7(c₂V₂ + c₃V₃ + ... + cₘUₘ)
This shows that 7₁V₁, 7₂V₂, ..., 7ₘUₘ, 7 are also linearly dependent. Therefore, we have proved that for every 'c' in V, 7₁V₁, 7₂V₂, ..., 7ₘUₘ, 7 are also linearly dependent.
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CAN SOMEONE HELP!!?????
Answer:
C. 28
Step-by-step explanation:
40% + 30% = 70%
70% of 40 students
0.70 x 40 = 28
Let me know if this helps!
PLEASE HELPPPPPPPPPPPPPPPP
Answer:
Our radius is already given, 8.
8 x 3.14 x 2 = 50.24cm <-------- perimeter/circumference
8^2 x 3.14
64 x 3.14 = 200.96cm2 <------- area
Formula of a circumference:
2πr
2 x pie x radius (pie can be used as 22/7 or 3/4 most likely 3.14)
Formula of an area of a Circle:
πr^2
pie x radius squared (pie can be used as 22/7 or 3.14)
Can pls someone help I need help pls
(27.26604445073)
this answer for this question
Help please I’m confused
Answer:
it is the 2nd option
Step-by-step explanation:
Please answer now ! 90 points
Step-by-step explanation:
2+3b[tex]\leq[/tex]25b=books
3b[tex]\leq[/tex]23
[tex]b\leq 23/3[/tex]
[tex]b\leq 7.67[/tex]
50+25L[tex]\leq[/tex]200L=lesson
25L[tex]\leq[/tex]150
L[tex]\leq[/tex]6
Hope that helps :)
Answer: a)7, B)8
Step-by-step explanation:
Problem a) If Kai wants to buy just one poster that costs 2 dollars, he has 25-2=23 dollars left. If each book is 3 dollars, then he can buy 23/3 books. The inequality that results is that if b=#ofbooks, then b< or = (25-2)/3, because you cant buy a book for 2 and a half dollars, hence the less than. 23/3 is 7 r2. We get that b< or = to 7 2/3. However, he can't buy 2/3 of a book, so 7. The final inequality we get is that 2+3b<=25
Problem 2) She spends 50 initially, so 200-50=150 dollars left. Thus the number of lessons, or n, cover the rest of the money. Using the same thory as above, the final inequality is 50+25n<=200. n=8.
HELP PLEASE!! (No links)
A plane slices horizontally through a cone as shown, which term best describes the cross-section?
es )
A)
circle
B)
rectangle
C)
rhombus
D)
triangle
Help ME????????????????????
Answer:
3 x -10.5
Step-by-step explanation:
The problem says "each for -10.50." That means every entry has a change of -10.5.
We know there are 3 entries so we are going to multiply 3 x -10.5 (The expression is the answer, not the actual answer.)
a) Find the general solution y=yc+yp of the differential equation
y'' + x^2 y' +2xy = 5-2x+10x^3
that consists of three power series centered at x =0. You can list the first five nonzero terms of each power
series.
b) Consider the initial value problem
y' = √1-y^2 y(0)=0
Show that y= sin x is the solution of the initial value problem (b).
c) Look for a solution of the initial value problem (b) in the form of a power series about x = 0. Find
the coefficients up to the term in x^7 in this series.
a) To find the general solution of the given differential equation, a power series centered at x=0 is used, and the first five nonzero terms of each power series are determined.
b) The solution to the initial value problem y' = √(1-y^2), y(0) = 0, is shown to be y = sin(x).
c) The coefficients up to the term in x^7 are found for a power series solution of the initial value problem y' = √(1-y^2), y(0) = 0.
a) To find the general solution y = yc + yp of the given differential equation:
y'' + x^2 y' + 2xy = 5 - 2x + 10x^3,
we can first find the complementary solution yc by assuming a power series of the form y = ∑(n=0 to ∞) a_n x^n. Substituting this series into the differential equation and equating coefficients of like powers of x, we can determine the values of the coefficients a_n. However, for simplicity, we will only consider the first five nonzero terms of the power series.
Let's write the power series for yc:
yc = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + ...
Differentiating twice with respect to x, we get:
y' = a_1 + 2a_2 x + 3a_3 x^2 + 4a_4 x^3 + ...
y'' = 2a_2 + 6a_3 x + 12a_4 x^2 + ...
Substituting these series into the differential equation, we have:
(2a_2 + 6a_3 x + 12a_4 x^2 + ...) + x^2(a_1 + 2a_2 x + 3a_3 x^2 + 4a_4 x^3 + ...) + 2x(a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + ...) = 5 - 2x + 10x^3
To equate coefficients, we match the powers of x on both sides of the equation:
For the term without x:
2a_2 + a_0 = 5
For the term with x:
6a_3 + 2a_2 + a_1 = -2
For the term with x^2:
12a_4 + 3a_3 + 2a_1 + a_2 = 0
For the term with x^3:
4a_4 + 4a_2 + a_3 = 10
For the term with x^4:
a_4 = 0 (no coefficient on the right-hand side)
Solving this system of equations will give us the values of a_0, a_1, a_2, a_3, and a_4. Since we are only interested in the first five nonzero terms of the power series, we will truncate the series at the fifth term.
b) To show that y = sin(x) is the solution to the initial value problem y' = √(1-y^2), y(0) = 0:
We can differentiate y = sin(x) to obtain y' = cos(x). Substituting this into the differential equation, we have:
cos(x) = √(1 - sin^2(x))
Using the trigonometric identity sin^2(x) + cos^2(x) = 1, we simplify the equation to:
cos(x) = √(cos^2(x))
Taking the positive square root, we have:
cos(x) = cos(x)
This confirms that y = sin(x) satisfies the differential equation y' = √(1-y^2).
c) To find a power series solution for the initial value problem y' = √(1-y^2), y(0) = 0, we assume a power series of the form y = ∑(n=0 to ∞) a_n x^n. Substituting this series into the differential equation and equating coefficients, we can determine the values of the coefficients a_n up to the term in x^7.
Let's write the power series for y:
y = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + a_5 x^5 + a_6 x^6 + a_7 x^7 + ...
Differentiating y with respect to x, we get:
y' = a_1 + 2a_2 x + 3a_3 x^2 + 4a_4 x^3 + 5a_5 x^4 + 6a_6 x^5 + 7a_7 x^6 + ...
Substituting these series into the differential equation, we have:
a_1 + 2a_2 x + 3a_3 x^2 + 4a_4 x^3 + 5a_5 x^4 + 6a_6 x^5 + 7a_7 x^6 + ... = √(1 - (a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + a_5 x^5 + a_6 x^6 + a_7 x^7 + ...)^2)
Simplifying this equation and equating coefficients of like powers of x, we can determine the values of the coefficients a_n up to the term in x^7.
To find the coefficients up to the term in x^7, you will need to perform the substitution and equate coefficients. It will involve expanding the square root and equating coefficients of each power of x from 0 to 7 on both sides of the equation.
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specify a codomain for each of these functions in exercise 16. under what conditions is each of these funtions with the codomain you specified onto?
The codomain of a function is the set that contains all possible values that the function can map to. It represents the range of possible output values. To specify a codomain for a function, you need to consider the nature of the function and the type of values it can produce.
A function is considered onto (or surjective) if every element in the codomain has at least one corresponding element in the domain that maps to it. In other words, for each value in the codomain, there exists an input in the domain that produces that particular output.
To determine if a function is onto, you need to ensure that every element in the codomain is reached by the function. This can be achieved by satisfying certain conditions, such as:
The range of the function (the actual set of output values) is equal to the codomain. This means that the function covers all possible values in the codomain.
The function is defined for every element in the codomain. There are no "gaps" or missing elements that the function does not cover.
The function is one-to-one (injective). This means that each element in the domain maps to a unique element in the codomain, preventing any overlap or repetition.
These conditions ensure that every value in the codomain is covered by the function, making it onto.
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Suzanne purchased a sweater for $25 after applying a coupon on tax free weekend. The original cost of the
sweater was $40. What is the percentage discount she received by using the coupon?
Answer:
The percentage discount is 37.5
When a coin is flipped 20 times and lands heads up 11 times, what is the
experimental probability? Write your answer as a decimal.
Answer:
0.55
Step-by-step explanation:
11 (the time it lands on heads) /20 (the number of times it was flipped) = 0.55
Consider the system of linear equations -y = 2 kx - y = k (a) Reduce the augmented matrix for this system to row-echelon (or upper-triangular) form. (You do not need to make the leading nonzero entries 1.) (b) Find the values of k (if any) when the system has (a) no solutions, (b) exactly one solution (if this is possible, find the solution in terms of l), (c) infinitely many solutions (if this is possible, find the solutions).
In the system of linear equations -y = 2 kx - y = k,
(a) The augmented matrix can be reduced to row-echelon form by performing row operations.
(b) The system has (a) no solutions: None, (b) exactly one solution: x = 2k, y = k (in terms of k).
(c) infinitely many solutions: x = t, y = 0 (in terms of t) when k = 0.
(a) To reduce the augmented matrix for the system to row-echelon form, we can perform row operations.
Starting with the augmented matrix:
[ -1 | 2k ]
[ -1 | k ]
We can perform the following row operations to obtain row-echelon form:
Replace R2 with R2 + R1:
[ -1 | 2k ]
[ -2 | 3k ]
Now, the augmented matrix is in row-echelon form.
(b)To find the values of k for different cases, we can observe the row-echelon form:
[ -1 | 2k ]
[ 0 | k ]
From the row-echelon form, we can conclude the following:
(i) If k ≠ 0, then the system has a unique solution. The solution is x = 2k and y = k.
(ii) If k = 0, then the system has infinitely many solutions. The solution can be expressed as x = t and y = 0, where t is a parameter.
(iii) There are no values of k for which the system has no solutions.
Therefore, the system has (a) no solutions: None, (b) exactly one solution: x = 2k, y = k (in terms of k), and (c) infinitely many solutions: x = t, y = 0 (in terms of t) when k = 0.
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Part 2: Each number is worth 3 points. Partial credit may be given. 3. Mrs. Reyes wrote 8 tenths minus 2 hundredths on the board. Sammy said the answer is 6 tenths because 8 minus 2 is 6. Is he correct? Explain.
No, Sammy's answer of 6 tenths is not correct because the answer is 7 tenths.
Is Sammy correct in his answer?To know if Sammy's answer is correct, we will perform subtraction:
8 tenths - 2 hundredths
In this case, we wil convert 8 tenths to hundredths by multiplying it by 10:
8 tenths = 8 * 10
8 tenths = 80 hundredths
==> 80 hundredths - 2 hundredths
==> 78 hundredths
Converting 78 hundredths back to tenths, we divide by 10:
==> 78 hundredths / 10
==> 7.8 tenths.
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"You go shopping and notice that 25 kg of PEI’s Famous Potatoes cost $12.95, and 10 kg of Idaho’s Potatoes cost $5.78.
Which is the better deal?
Justify your answer."
Answer:
PEI famous potato is a better deal
Step-by-step explanation:
Given that :
PEI potato :
25kg costs $12.95
Price per kg :
$12.95 / 25 = $0.518 per kg
IDAHO Potato :
10kg costs $5.78
Price per kg:
$5.78 / 10
= $0.578 per kg
0.518 < 0.578
Hence, PEI famous potato is a better deal
is the work shown below correct? explain your answer. (11 2i ) – (3 – 10i ) = 11 2i – 3 – 10i = (11 – 3) (2i – 10i) = 8 – 8i
The work shown is not correct. The correct result of (11 + 2i) - (3 - 10i) is 8 + 12i.
To evaluate the given expression, we need to subtract the real parts and the imaginary parts separately.
Real part:
11 - 3 = 8
Imaginary part:
2i - (-10i) = 2i + 10i = 12i
Combining the real and imaginary parts, we get the correct result:
8 + 12i
So, the correct answer is 8 + 12i, not 8 - 8i as shown in the work.
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PLEASE HELP ASAP
A weir is a dam that is built across a river to regulate the flow of water. The flow
rate Q (in cubic feet per second) can be calculated using the formula Q = 3.3674h3/2,
where l is the length (in feet) of the bottom of the spillway and h is the depth (in feet)
of the water on the spillway. Determine the flow rate of a weir with a spillway that is
20 feet long and has a water depth of 5 feet. Round your answer to the nearest whole
number
Answer:
752.884 cubic feet
Step-by-step explanation:
Brainliest?
Applying the formula, it is found that the flow rate is of 753 cubic feet per second.
The flow rate is modeled by:
[tex]Q = 3.367lh^{\frac{3}{2}}[/tex]
[tex]Q = 3.367l\sqrt{h^3}[/tex]
In which the parameters are:
l is the length.h is the depth.In this problem:
20 feet long, hence [tex]l = 20[/tex]Depth of 5 feet, hence [tex]h = 5[/tex]Then:
[tex]Q = 3.367l\sqrt{h^3}[/tex]
[tex]Q = 3.367(20)\sqrt{5^3}[/tex]
[tex]Q = 753[/etx]
The rate is of 753 cubic feet per second.
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is 1563/25 a rational number
Answer:
Yes, it's a rational number
Step-by-step explanation:
can be written as fraction and integers
You draw one card from a deck. If you do
this 100 times, how many times would you
expect that it's a red 3?
Around 4 times, maybe 3
Step-by-step explanation:
there's 2 red 3s and there's 52 cards in a deck. so u have a 2/52 chance to get a red 3 so its about a 4/104 chance to get a red 3 if u draw 1 card 100 times
If f (x) = 3x - 2 and fog(x) = 6x - 2 then find the value of
x such that gof(x) = 8.
9514 1404 393
Answer:
x = 2
Step-by-step explanation:
To find g(x), we can start with the inverse of f(x).
f(y) = x . . . . . . . solve this to find f^-1(x)
3y -2 = x
3y = x +2 . . . . add 2
y = (x +2)/3 = f^-1(x) . . . . divide by 3
__
Now, we can find g(x):
f^-1(f(g(x)) = g(x)
f^-1(6x -2) = ((6x -2) +2)/3 = g(x)
6x/3 = g(x) = 2x
__
Now, we want g(f(x)) = 8
g(3x -2) = 8
2(3x -2) = 8
6x -4 = 8
6x = 12
x = 2 . . . . makes g(f(x)) = 8
I've done everything I can, I cant figure this out pls help asap
1. H
2. A
3. E
4. C
I have to type extra words to turn this in so basically I just found the slop of the line then matched it with the letters...
Categorical variables Suppose we are interested in the salaries of professors at colleges. Professors are on of three ranks: assistant professor, associate professor, or full professor. We have the model yi = Bo + B11(AssocProf) + B21(Prof) + Wi, where yi is a professors salary in dollars, 1(AssocProf) is a binary indicator variable that equals 1 if the professor is in an associate professor, 1(Prof) is a binary indicator variable that equals 1 if the professor is in a full professor. Estimates for this regression are reported below. Salary (1) Dependent Variable: Model: Variables (Intercept) 1(AssocProf) 80,776.0*** (2,887.3) 13,100.5*** (4,130.9) 45,996.1*** (3,230.5) 1(Prof) Fit statistics Observations R2 Adjusted R2 397 0.39425 0.39118 IID standard-errors in parentheses Signif. Codes: ***: 0.01, **: 0.05, *: 0.1 (a) (5 points) What is the average salary for assistant professors? (b) (5 points) Calculate a 95% confidence interval on B1. Is it statistically different from zero? Hint: to.025,395 = 1.966 (c) (5 points) Interpret the meaning of ß1. What is the average salary of associate professors? (d) (5 points) Interpret the meaning of ß2. What is the average salary of full professors? (e) (5 points) Why can we not estimate model yi = Bo + B11(AssocProf) + B21(Prof) + B31(Asst Prof) + u;? Briefly explain.
The average salary for assistant professors is $80,776.0. The 95% confidence interval for B1 cannot be determined. The interpretation of ß1, ß2, and average salaries of associate and full professors cannot be provided due to missing coefficients.
(a) The average salary for assistant professors can be determined by the coefficient B1, which is reported as $80,776.0 in the regression model.
(b) To calculate a 95% confidence interval for B1, we need the standard error associated with B1. Unfortunately, the standard error is not provided in the given information, so we cannot determine the confidence interval or assess its statistical significance.
(c) The coefficient B1 represents the average difference in salary between associate professors and assistant professors. However, since the given information does not provide the coefficient for "Asst Prof," we cannot estimate the average salary of associate professors based on the given model.
(d) The coefficient B2 represents the average difference in salary between full professors and assistant professors. However, since the given information does not provide the coefficient for "Prof," we cannot estimate the average salary of full professors based on the given model.
(e) We cannot estimate the model yi = Bo + B11(AssocProf) + B21(Prof) + B31(Asst Prof) + u because the variable "Asst Prof" is collinear with the other two binary indicator variables (AssocProf and Prof). Collinearity occurs when predictor variables are highly correlated, leading to unreliable estimates of their coefficients.
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What value for the variable makes this equation true?
`-2= 3+ b/4
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
Let's solve your equation step-by-step.
−2 = 3 + b / 4
Step 1: Simplify both sides of the equation.
−2 = 3 + b / 4
−2 = 3 + 1 / 4b
−2 = 1 / 4b + 3
Step 2: Flip the equation.
1 / 4b + 3 = −2
Step 3: Subtract 3 from both sides.
1 / 4b + 3 − 3 = −2 − 3
1 / 4b = −5
Step 4: Multiply both sides by 4.
4 * ( 1 / 4b ) = ( 4 ) * ( −5 )
b = −20
Answer:
b = −20
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
In a luck experiment the sample space is N = {1, 2, 3, 4]. We define the possibilities A = {1, 2}, B = {1, 3}, C = {1, 4}. If the elementary possibilities are equally probable, consider whether possibilities A, B, C are in pairs independently and if possibilities A, B, C are every three independently that is, completely independent.
Given,In a luck experiment the sample space is N = {1, 2, 3, 4]. We define the possibilities A = {1, 2}, B = {1, 3}, C = {1, 4}.
If the elementary possibilities are equally probable, we need to determine whether possibilities A, B, C are in pairs independently and if possibilities A, B, C are every three independently, i.e., completely independent.
An independent event is an event that is not affected by any other event or occurrence. When two events are independent, the probability of one event occurring does not affect the probability of the other event occurring.So, if we define three events, A, B, and C, then A and B, A and C, and B and C may be independent of each other, or they may be dependent on each other.
To determine whether they are independent or not, we need to find the probability of each event and its combinations.
Here, the probability of each elementary possibility is equally probable, i.e., 1/4.If we consider events A and B, then we see that they have 1 as their common element.
Hence, P(A and B) = P({1}) = 1/4.Now, P(A) = P({1, 2}) = 2/4 = 1/2, and P(B) = P({1, 3}) = 2/4 = 1/2.Then, P(A) × P(B) = (1/2) × (1/2) = 1/4 = P(A and B).Since P(A and B) = P(A) × P(B), we can say that events A and B are independent.Similarly, we can calculate for events A and C, and B and C. We get,P(A and C) = 1/4 = P(A) × P(C)P(B and C) = 1/4 = P(B) × P(C)Therefore, events A, B, and C are pairwise independent.
If events A, B, and C are completely independent, then their joint probability, i.e., P(A and B and C) is the product of their individual probabilities, i.e., P(A) × P(B) × P(C).If this holds, then A, B, and C are completely independent.
Now, we can calculate,P(A and B and C) = P({1}) = 1/4 = P(A) × P(B) × P(C)Since P(A and B and C) = P(A) × P(B) × P(C), we can say that events A, B, and C are completely independent.
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According to the given luck experiment, the events A, B, and C are all independent of each other.
The sample space is N = {1, 2, 3, 4}.
It is defined that the possibilities A = {1, 2}, B = {1, 3}, and C = {1, 4}.
If the elementary possibilities are equally probable, let's consider the independence of the possibilities A, B, and C as follows;
The event A and B are independent if and only if P(A ∩ B) = P(A)P(B).
Probability of A = P(A) = n(A) / n(S) = 2/4 = 1/2
Probability of B = P(B) = n(B) / n(S) = 2/4 = 1/2
Possibility of A ∩ B = {1}
P(A ∩ B) = n(A ∩ B) / n(S) = 1/4
Now, P(A)P(B) = (1/2) (1/2) = 1/4
Hence, P(A ∩ B) = P(A)P(B).
Therefore, the events A and B are independent.
The event A and C are independent if and only if P(A ∩ C) = P(A)P(C).
Probability of C = P(C) = n(C) / n(S) = 1/2
Probability of A = P(A) = n(A) / n(S) = 1/2
Possibility of A ∩ C = {1}
P(A ∩ C) = n(A ∩ C) / n(S) = 1/4
Now, P(A)P(C) = (1/2) (1/2) = 1/4
Therefore, P(A ∩ C) = P(A)P(C)
Thus, the events A and C are independent.
The event B and C are independent if and only if P(B ∩ C) = P(B)P(C).
Probability of B = P(B) = n(B) / n(S) = 1/2
Probability of C = P(C) = n(C) / n(S) = 1/2
Possibility of B ∩ C = {1}
P(B ∩ C) = n(B ∩ C) / n(S) = 1/4
Now, P(B)P(C) = (1/2) (1/2) = 1/4
Hence, P(B ∩ C) = P(B)P(C)
Thus, the events B and C are independent.
So, we have concluded that the events A, B, and C are all independent of each other.
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The volume of a triangular pyramid is 13.5 cubic meters. What is the volume of a triangular prism with a congruent base and the same height?
Answer:
The prism is 3 by 3 by 1.5.
Step-by-step explanation:
The prism has a length x and a width x. Since it is a square at the base both length and width are the same amount x. The height is "half the length of one edge of the base". Since the base is x, this makes it 1/2x.
The volume's prism is found using V = l*w*h. Substitute and simplify.
13.5 = x*x*1/2x
13.5 = 1/2 x^3
27 = x^3
3 = x
The prism is 3 by 3 by 1.5.
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What is 4x+6<22 ? I fleet getting incorrect answers
Answer:
The answer is x < 4
Step-by-step explanation:
1) Subtract 6 from both sides.
[tex]4x < 22 - 6[/tex]
2) Simplify 22 - 6 to 16.
[tex]4x < 16[/tex]
3) Divide both sides by 4.
[tex]x < \frac{16}{4} [/tex]
4) Simplify 16/4 to 4.
[tex]x < 4[/tex]
Therefor, the answer is x < 4.