Answers
Using integrals, the probabilities and desired measures are given as follows:
a) P(0 < X) = 0.5.
b) P(0.6 < X) = 0.392.
c) P(-0.5 ≤ X ≤ 0.5) = 0.125.
d) P(X < -2) = 0.
e) P(X < 0 or X > -0.5) = 1.
f) x = 0.965.
What is the probability distribution?
The distribution is given by:
f(x) = 1.5x², -1 < x < 1.
The integral of this function will be used to find the probabilities.
In item a, the probability is given by:
\(P(0 < X) = \int_{0}^{1} f(x) dx\)
\(P(0 < X) = \int_{0}^{1} 1.5x^2 dx\)
\(P(0 < X) = 0.5x^3|_{x = 0}^{x = 1}\)
Applying the Fundamental Theorem of Calculus:
P(0 < X) = 0.5(1)³ - 0.5(0)³ = 0.5 - 0 = 0.5.
Item b is similar as item a, just with lower limit 0.6, hence:
P(0.6 < X) = 0.5(1)³ - 0.5(0.6)³ = 0.5 - 0.108 = 0.392.
For item c, the lower limit is -0.5 and the upper limit is of 0.5, hence:
P(-0.5 ≤ X ≤ 0.5) = 0.5(0.5)³ - 0.5(-0.5)³ = 0.125.
For item d, values of -2 and less are not on the range of the distribution, which is between -1 and 1, hence the probability is of 0.
For item e, the intersection of the intervals is the entire range of the function, hence the probability is of 1.
For item f, we have that:
0.5(1)³ - 0.5(x)³ = 0.05
0.5x³ = 0.45
x³ = 0.9.
x = (0.9)^(1/3) -> cubic root
x = 0.965.
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Related Questions
Which one of the colors do I choose to pick
Answers
Answer:
you should pick green colour
Suppose $30,000 is deposited into an account paying 3.5% interest, compounded annually.How much money is in the account after ten years if no withdrawals or additional deposits aremade?
Answers
Ok, so
We know that the initial amount which is deposited is $30,000.
For this problem, it is useful to use an exponential function because we know that we're working with a compounded interest.
So, we'll write:
Now, the question ask to us to find how much money is in the ccount after ten years. For this, we just replace t=10 in our equation. Like this,
Therefore, there will be $42317.96 in the account.
please help (question above)
Answers
The solution of the line is, (3, 2), (-1, 1), (1, 3/2), and the equation of the line is y = 1 / 4 x + 5 / 4, so options A, B, C, E, and F are correct.
What is a line?A line is a shape with an infinite length but no width, depth, or curvature. Lines are one-dimensional objects even though they can exist in two, three, or higher-dimensional contexts.
Given:
The graph of linear equation,
As you can see from the graph the line has coordinates of (3, 2), (-1, 1), (1, 3/2).
Calculate the equation of the line by using the coordinates as shown below,
\(y - y_1 = [y_2 - y_1 / x_2 - x_1] (x- x_1)\)
y - 1 = [1 - 2 / -1 - 3] [x-(-1)]
y - 1 = -1 / (-4) (x + 1)
4y - 4 = x + 1
y = 1 / 4 x + 5 / 4
And line can have many solutions, as it can have more than two values.
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The lowest temperature ever
recorded on earth was -89°C
in Antarctica. The average
temperature on Mars is about
-55°C. Which is warmer?
Write an inequality to support
your answer
Answers
Answer:
Mars
Step-by-step explanation:
America
what is the soulution of the system? use any method
3y = –1/2x+2
y = –x + 9
(20, –4)
(3, 6)
(10, –1)
(–1, 8)
Answers
Answer:
c
Step-by-step explanation:
10,-1
your welcome
thats the right answer
Find the GCF and LCM for 16 and 24.
Answers
Greatest Common Factors (GCF) of 16 and 24 = 8
Least Common Multiple of 16 and 24 = 48
GCF means Greatest Common Factors
Factors of 16 = 1, 2, 8, 4, and 16
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24
Common Factors of 16 and 24 = 1, 2, 4, and 8
Greatest Common Factors (GCF) of 16 and 24 = 8
LCM means Least Common Multiples
Multiples of 16 = 16, 32,48, 54.....
Multiples of 24 = 24, 48, 72....
The Least Common Multiple of 16 and 24 = 48
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Find the angle θ between a = 3i − k, b = 2i + 2k
Answers
a · b = ||a|| ||b|| cos(θ)
where ||a|| and ||b|| are the magnitudes of the vectors a and b, respectively.
First, we need to find the magnitudes of the vectors:
||a|| = sqrt(3^2 + 0^2 + (-1)^2) = sqrt(10)
||b|| = sqrt(2^2 + 0^2 + 2^2) = 2sqrt(2)
Then, we can calculate the dot product:
a · b = (3i - k) · (2i + 2k)
a · b = 6 + 0 - 2
a · b = 4
Now we can solve for the angle θ:
a · b = ||a|| ||b|| cos(θ)
4 = sqrt(10) * 2sqrt(2) cos(θ)
cos(θ) = 4 / (sqrt(10) * 2sqrt(2))
cos(θ) = 2 / sqrt(5)
Finally, we can calculate the angle θ:
θ = cos^-1(2 / sqrt(5))
θ ≈ 54.7 degrees
Therefore, the angle between a and b is approximately 54.7 degrees.
Answer these questions please for 59 points
Answers
In this case, the amount of the paint that she used to paint her room is 4 1/2 of the paint
How do you form an equation from a word problem?Here are the general steps to follow when forming an equation from a word problem:
Read the problem carefully and identify the quantities and variables involved. Look for keywords that indicate the mathematical operation to be performed, such as "sum", "difference", "product", "quotient", "is", "was", "will be", "more than", "less than", "equal to", etc.
Translate the words into mathematical expressions and equations. Use the quantities and variables identified in step 1 to form equations. Assign variables to unknown quantities, and use algebraic symbols and operations to represent the relationships between the quantities.
Solve the equations to find the answer to the problem. Simplify the equations and solve for the unknown variable. Check your answer to make sure it makes sense in the context of the problem.
1) 5 * 19/4
= 95/4
23 3/4
2) Total weight = 3(14/3) + 5(15/2)
14 + 75/2
28 + 75/2
= 51 1/2 pounds
3) x = 45/8 * 4/5
= 9/2
= 4 1/2
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A doctor would like to estimate the proportion of adults who eat an apple a day.
To learn more about this, she selects a random sample of 200 adults and finds that 24 of them eat an apple a day.
She would like to construct a 98% confidence interval for the true proportion of adults who eat an apple a day.
Random condition:
10% condition:
Large counts condition:
Are the conditions for inference met?
Answers
All three conditions for inference are met, the doctor can proceed with constructing a confidence interval for the true proportion of adults who eat an apple a day.
What is 98% confidence interval?An interval with a 98% confidence level suggests that if the doctor repeated the sampling procedure numerous times and created a confidence level with each sample, around 98% of those intervals would contain the actual percentage of adults who eat an apple every day. With a sample of 200 persons, the doctor can be 98% confident that the actual proportion of adults who eat an apple every day falls between 0.046 and 0.194. While the true proportion is a fixed figure, it is crucial to highlight that this interpretation does not imply that there is a 98% likelihood that it is within this range (although unknown).
The reference conditions for the given situation are:
Random condition: This requirement is satisfied because the doctor chose a random sample of 200 adults.
10% condition: As the sample size is substantially less than 10% of the population (200), this requirement is also satisfied.
High numbers requirement: The doctor must determine whether both the success rate (the proportion of adults who eat an apple every day) and the failure rate (the proportion of adults who don't) are at least 10. In this instance, there were 24 successes and 200 failures, which equals 176. As both of these sums are more than 10, the requirement for big counts is likewise satisfied.
Since all three conditions for inference are met, the doctor can proceed with constructing a confidence interval for the true proportion of adults who eat an apple a day.
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Answer:
Met
Met
Met
Yes
Step-by-step explanation:
Someone help ASP YOU GET 30 points and more show work so I’ll be able to understand THANK YOU!!
Answers
Answer: 1. x=4
2. x=12
3. x=-1
Step-by-step explanation:
1. 2(3x-5)=-4x+30
6x-10=-4x+30
6x+4x-10=-4x+4x+30
10x-10=30
10x-10+10=30+10
10x=40
10x/10=40/10
x=4
2. 5x-6-3x=18
5x-3x-6=18
2x-6=18
2x-6+6=18+6
2x=24
2x/2=24/2
x=12
3. -11-5x=6(5x+4)
-11-5x=30x+24
-11-5x+5x=30x+5x+24
-11=35x+24
-11-24=35x+24-24
-35=-35x
x=-1
Find the value of x
Answers
Since they are vertical angles:
\(x=90\)
si ABCD son los vertices de un cuadrado y A(2,2) y C (10,8) 2 vertices opuestos. Hallar los otros dos vertices, dar como respuesta la mayor de las ordenadas
Answers
The area of the square is given as 100 square unit
How to determine the area of square?You should be aware that the square has all its sides equal
The perpendicular from opposite vertices represent distance
The given vertices are
(2,2) and (10,8)
Using the formula for distance between two points
d=√(10-2)²+(8-2)²
d=√8²+6²
d = √64+36
d=√100
This implies that d=10
The area of a square is given as s²
Area = 10²
Atrea = 100 square units
In conclusion, the area of the square is 100 square units
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Translated question:
The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square
-b-
Note: Figure is not drawn to scale.
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
OA.
21 m
OB.
32 m
29 m
34 m
OC.
OD.
6 of 10 Answered
Reset
Submit
Session Timer: 78:05
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C
Answers
After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.
The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted measurement regarding the distance around the outside of a two-dimensional shape. In this system the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m
100 points and will mark bralist
Answers
b divided by 3 +17=48
Answers
Answer:
How are we supposed to answer this?
The value of b that satisfies the equation B/3 + 17 = 48 is 93.
To find the value of b in the equation B/3 + 17 = 48, we need to isolate the variable b.
First, we subtract 17 from both sides of the equation to get rid of the constant term:
B/3 = 48 - 17
Simplifying, we have:
B/3 = 31
To isolate B, we multiply both sides of the equation by 3:
3 * (B/3) = 3 * 31
This simplifies to:
B = 93
By subtracting 17 from both sides of the equation, we eliminate the constant term on the left side. This leaves us with B/3 on the left side. Next, multiplying both sides by 3 allows us to cancel out the denominator and isolate B. Finally, simplifying the expression gives us the value of b, which is 93.
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Complete question is:
B divided by 3 +17=48
find value of b
Use linear approximation, i.e. the tangent line, to approximate 3√ 125.2 as follows: Let f(x)=√x. The equation of the tangent line to f(x) at x = 125 can be written in the form
y=mx+b
Answers
Using linear approximation, the expression √125.2 can be approximated as approximately 10.02.
How to find linear approximation?To find the equation of the tangent line to the function f(x) = √x at x = 125, determine the slope (m) and the y-intercept (b) of the tangent line.
First, find the slope (m) using the derivative of the function f(x) = √x:
f'(x) = 1 / (2√x)
Evaluate the derivative at x = 125:
f'(125) = 1 / (2√125) = 1 / (2 × 5) = 1/10
Now, find the y-coordinate of the point on the function f(x) at x = 125:
f(125) = √125 = 5
So, the tangent line at x = 125 passes through the point (125, 5) and has a slope of 1/10.
Using the point-slope form of a linear equation, the equation of the tangent line can be written as:
y - 5 = (1/10)(x - 125)
To simplify, multiply through by 10:
10y - 50 = x - 125
Rearranging the equation, express it in the form y = mx + b:
y = (1/10)x - 75/10 + 5
Simplifying further:
y = (1/10)x - 75/10 + 50/10
Combining the terms:
y = (1/10)x - 25/10
Therefore, the equation of the tangent line to f(x) = √x at x = 125 is y = (1/10)x - 25/10.
Now, use this tangent line to approximate the value of √125.2:
Substitute x = 125.2 into the equation:
y = (1/10)(125.2) - 25/10
y = 12.52 - 2.5
y ≈ 10.02
So, using linear approximation, approximate √125.2 as approximately 10.02.
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Please help my math question. I'll be giving brainly.
DO NOT, PUT RANDOM ANSWERS, YOU HAVE BEEN WARNED.
Answers
Answer:
80
Step-by-step explanation:
80
angle a = angle s
amr and msr are similar triangles
Answer:
Simple question!
Step-by-step explanation:
I'm never challenged in school, could you send me your hw each day?
Email ivaliu2008+outlook.com
Also, what grade are you?
Thanks!
In a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If 2/7 of
the drink is apple juice and 1/2 is orange juice then write the ratio of cranberry juice to apple
juice to orange juice in its simplest form,
Answers
Answer:
3 : 4 : 7
Step-by-step explanation:
apple juice - 2/7 = 4/14
orange juice - 1/2 = 7/14
AJ + OJ = 11/14
this means that 3/14 of the punch is cranberry juice.
cranberry : apple : orange
3 : 4 : 7
In triangle ABC, angle A = 2x + 5, angle B = 4x + 10 and angle C = x - 31. Find the value of x.
Answers
Answer:
x=28
Step-by-step explanation:
sum of all angles im a triangle = 180°
(2x+5) + (4x+10) + (x-31) = 180
7x=196
x=28
Answer:
x = 28°
Step-by-step explanation:
Sum of a triangle is equal to 180°. Firstly you need to form an equation. Add all the angles which equals to 180°.
2x + 5 + 4x + 10 + x - 31 = 180°
Now simply and find the value of x. Add all the x terms and whole numbers.
7x + 5 + 10 - 31 = 180°
7x + 15 - 31 = 180°
7x - 16 = 180°
7x = 180° + 16
7x = 196
x = 196 ÷ 7
x = 28°
So the angles are:
Angle A = 2x + 5
2 x 28 + 5 = 61°
Angle B = 4x + 10
4 x 28 + 10 = 122°
Angle C = x - 31
28 - 31 = -3°
PLEASE HELP
Polygon ABCD with vertices at A(1,-1) B(3,-1), C(3,-2) and D(1-2) is dilated to create polygon ABCD with vertices at A’(2,-2), B(6,-2), C’(6,-4) and D’(2,-4). Determine the scale factor used to create the image
A. 3
B. 2
C. 1/2
D. 1/3
Answers
The scale factor of the image after the dilation is k = 2
Given data ,
Polygon ABCD with vertices at A(1,-1) B(3,-1), C(3,-2) and D(1-2)
Now , the dilated polygon is represented as A'B'C'D'
where the coordinates are A’(2,-2), B(6,-2), C’(6,-4) and D’(2,-4).
Now , we can compare the corresponding side lengths of the two polygons to determine the scale factor:
Scale factor = (corresponding side length of dilated polygon) / (corresponding side length of original polygon)
So, A'/A = 2 / 1
A' = 2A
So, the scale factor is k = 2
Hence , the dilation is solved.
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34 miles
30 mph
How much time will it
take for these two
vehicles to meet?
55 mph
[?] hours
![34 miles30 mphHow much time will ittake for these twovehicles to meet?55 mph[?] hours](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/lJao5IqrAPJR8grB8BLa8305HMimCTar.png)
Answers
Answer:
0.4 hours
Step-by-step explanation:
or 24 minutes :D
How does the graph of g(x) = (x − 2)3 + 6 compare to the parent function of f(x) = x3?
g(x) is shifted 2 units to the right and 6 units down.
g(x) is shifted 2 units to the right and 6 units up.
g(x) is shifted 2 units to the left and 6 units down.
g(x) is shifted 6 units to the left and 2 units down.
Answers
The relationship of the graph g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3 is that g(x) is shifted 2 units to the right and 6 units up.
Translation of coordinatesTranslations is a transformation technique that changes the position of an object from one point on the plane to another.
Given the function below
g(x) = (x − 2)^3 + 6
The function compared to f(x) = x^3, shows a translation of f(x) by 2 unit to the right along the horizontal and vertical translation of the function 6 units up
Hence the relationship of the graph g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3 is that g(x) is shifted 2 units to the right and 6 units up.
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Answer:
g(x) is shifted 6 units to the left and 2 units down.
Step-by-step explanation:
took the test
what is the slope of the line -3y=12x+6
Answers
Answer:
Step-by-step explanation:
uhh
he button provides an automatic means of checking for mathematical errors within formulas of a worksheet.
Answers
The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.
The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled.
Arrows pointing from the selected cell to cells that depend on the selected cell are generated by using the Trace dependents button of the Formula Auditing group.
nodes in an influence diagram represent part of the model
The Trace Precedents button, located in the Formula Auditing group, creates arrows pointing to the selected cell from cells that are part of the formula in that cell
The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.
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Simplify
a+b
a-b
a=5 and b= 3
Answers
Answer:
Step-by-step explanation:
The value of the given expression will be 4.
pls ANSWER if you actually know the answer
Answers
Answer:
The rate's aren't equivalent.
Step-by-step explanation:
If you find a common number of hours between the two expressions such as 24 hours you will see that the pay isn't the same. $24 for 6 hours of work ($4:1hr) can be turned into $96 for 24 hours of work and $36 hours for 8 hours of work ($4.5:1) turns into $108 for 24 hours of work.
36/(x-3)=4 thank uu :>
Answers
Answer:
12
Step-by-step explanation:
36 / (x - 3) = 4
multiply both sides by (x - 3):
(x - 3)(36 / (x - 3)) = 4(x - 3)
36 = 4(x - 3)
expand right side:
36 = 4x - 12
add 12 to both sides:
36 + 12 = 4x - 12 + 12
48 = 4x
divide both sides by 4:
48/4 = 4x/4
x = 12
What is the meaning of "The usual notation makes this identification transparent by writing every sequence (x1, x2, ..., xn) as a product or word x1x2· · · xn in the alphabet X"?
Answers
The statement refers to the way that symbols are represented in sequences, a common practice in formal language theory, by employing a notation that makes symbols a part of the sequence.
How is sequence notation and language related?In formal language theory, a language is often defined as a set of strings over an alphabet. By representing any alphabetic sequence of symbols as a single string using the notation outlined in the statement, we are able to recognise the language that comprises that sequence as a collection of strings. A subset of the language having all possible strings over the alphabet (a, b, and c) is the set of strings abc, which may be used to represent the language including the sequence (a, b, and c). So, this notation offers an easy approach to discuss languages and the sequences that make up such languages.
Hence, the statement relates the symbols and sequences.
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for each of the initial conditions below, determine the largest interval on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.
Answers
The existence of a unique solution is guaranteed by y(a) = \( c_{0} \), y' (a) = \( c_{1} \), . . . . \( y_{n-1}(a) \) = \( c_{n-1} \).
Consider the differential equation
\( a_{0}(x) {y}^{n} \) + \( a_{1}(x) {y}^{n} \) + . . . . + \( a_{n-1}(x) {y}^{'} \) + \( a_{n}(x) {y} \) = F (x)
Now, for each x ∈ [a, b]
\( a_{0}(x) \) ≠ 0, F(x), \( a_{1}(x) \), \( a_{2}(x) \), . . . . \( a_{n}(x) \) all are continuous function of x in [a,b] and
y(a) = \( c_{0} \), y' (a) = \( c_{1} \), . . . .
\( y_{n-1}(a) \) = \( c_{n-1} \)
Then given differential equation has a unique solution
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mean number of cell phone calls made or received per day by cell phone users. in a survey of 1917 cell phone users, the mean was 13.10 phone calls a day. give the correct notation for the quatity descrobed
Answers
This sample's notation is indicated by \(\bar x\).
The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole. A population in research doesn't usually refer to humans.
What distinguishes the sample from the population?A population is the total group about which you want to draw conclusions.
A sample is the specific group from which you will collect data. Always, the sample size is less than the whole population.
Provided, The mean number of calls made per day by cell phone users in a survey of 1917 people was 13.10.
Since this is a sample, the mean is denoted by the symbol \(\bar x\)
If it were for a population, the mean would have been written as μ.
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Complete question -
Give the correct notation for the quantity described and give its value.
Mean number of cell phone calls made or received per day by cell phone users. In a survey of
1917 cell phone users, the mean was 13.10 phone calls a day.¹