An experiment results in one of the sample points E1,E2,E3,E4, or E5. Complete parts a through c. a. Find P(E3) if P(E1)=0.2,P(E2)=0.2,P(E4)=0.2, and P(E5)=0.1. P(E3)=0.3 (Type an exact answer in simplified form.) b. Find P(E3) if P(E1)=P(E3),P(E2)=0.2,P(E4)=0.2, and P(E5)=0.2. P(E3)=0.2 (Type an exact answer in simplified form.) c. Find P(E3) if P(E1)=P(E2)=P(E4)=P(E5)=0.1. P(E3)= (Type an exact answer in simplified form.)
Answers
a. The probability of event E3, P(E3), is given as 0.3. This value is independent of the probabilities of other events (E1, E2, E4, and E5) mentioned in the question. Therefore, regardless of the probabilities assigned to the other events, the probability of event E3 remains at 0.3.
b. In this case, the probability of event E1 is specified as being equal to the probability of event E3, while events E2, E4, and E5 each have probabilities of 0.2. Since the sum of all probabilities must equal 1, we can calculate the probability of E3 by subtracting the probabilities of E1, E2, E4, and E5 from 1 and dividing the result by 3 (as there are three events with equal probabilities). Therefore, P(E3) = (1 - 0.2 - 0.2 - 0.2 - 0.2) / 3 = 0.2.
c. In this scenario, all events (E1, E2, E4, and E5) have the same probability of 0.1. Since there are five events in total, the sum of their probabilities must equal 1. Therefore, to find the probability of event E3, we subtract the probabilities of E1, E2, E4, and E5 from 1 and divide the result by the number of remaining events, which is 1 (E3 itself). Thus, P(E3) = (1 - 0.1 - 0.1 - 0.1 - 0.1) / 1 = 0.6.
a. In this case, the probability of event E3 is provided directly as 0.3. This means that out of all the possible outcomes of the experiment, there is a 0.3 chance that E3 will occur. The probabilities assigned to other events (E1, E2, E4, and E5) do not affect the probability of E3.
b. In this scenario, the probability of event E3 is not explicitly given. However, we are told that the probability of event E1 is equal to the probability of E3, while events E2, E4, and E5 each have a probability of 0.2. To find the probability of E3, we subtract the probabilities of all the other events from 1, as the sum of all probabilities must equal 1. Since E1 and E3 have the same probability, we subtract 0.2 from 1, resulting in 0.8. Then, we divide this value by the number of events with equal probabilities, which is 3 (E1, E3, and the remaining event), giving us a probability of 0.8/3 = 0.2 for E3.
c. In this case, all events (E1, E2, E4, and E5) have an equal probability of 0.1. Since there are five events in total, the sum of their probabilities must equal 1. To find the probability of E3, we subtract the probabilities of all the other events from 1 and divide the result by the number of remaining events, which is 1 (E3 itself). Thus, the probability of E3 is (1 - 0.1 - 0.1 - 0.1 - 0.1) / 1 = 0.6.
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Related Questions
Simplify this expression.
(2-5√6)-3√2
6√2-15√6
6√2-15√/12
6√2-8√6
6√2-30√
Answers
Answer: \(2-5\sqrt{6}-3\sqrt{2}\)
Step-by-step explanation:
= \((2-5\sqrt{6} )-3\sqrt{2}\)
= \(2-5\sqrt{6}-3\sqrt{2}\)
This expression is simplified already
What number means the same as 9,000,000,000 + 900,000,000, + 90,000,000 +9,000,000, + 900,000 + 9,000 +9 PLEASE DO IT QUICKLY
Answers
Answer:
9,999,909,009
Step-by-step explanation:
plz mark me brainliest. :0
Answer:
it does not equal the same
Step-by-step explanation:
but heres ur answer 9999909009
What is the positive solution to 2x^2=72?
Answers
2x^2 = 72
Divide both sides by 2:
X^2 = 36
Take the square root of both sides
X = 6
Three coffees and two muffins cost a total of 7 dollars. Two coffees and four muffins cost a total of 8 dollars. What is the individual price for a single coffee and a single muffin?
Answers
wAnswer:
e
Step-by-step explanation:
how many thirds are in 2 wholes? (p.s. I’m in last period and I need this quick)
Answers
Answer:
6 thirds
Step-by-step explanation:
Can someone please help me ASAP? It’s due tomorrow!! I will give brainliest if it’s correct
Answers
A random sample of the heights (in inches) of seventh grade boys was taken the five number summary for the sample is (59, 61, 64, 67, 72) then the IQR is 6.
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1).
To find Q1 and Q3, we need to use the five-number summary given in the problem:
Min = 59
Q1 = 61
Median = 64
Q3 = 67
Max = 72
Therefore, the IQR is:
IQR = Q3 - Q1
= 67 - 61
= 6
Hence, a random sample of the heights (in inches) of seventh grade boys was taken the five number summary for the sample is (59, 61, 64, 67, 72) then the IQR is 6.
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How many moles are in 15.0 grams of ammonia?
Answers
Answer:
0.88 molesStep-by-step explanation:
To find:-
The number of moles in 15g of ammonia.Answer:-
Chemically, ammonia is represented as \(NH_3\) .
So the molar mass of ammonia will be,
\(\longrightarrow M = 14g + 3(1)g \\\)
\(\longrightarrow M =( 14 + 3 )g \\\)
\(\longrightarrow \pmb{ M = 17g} \\\)
To find out the number of moles , we can use the following formula,
\(\longrightarrow \boxed{\boldsymbol{ n =\dfrac{ Given\ weight}{Molecular\ weight} }} \\\)
Here ,
Given weight = 15gMolecular weight = 17g .On substituting the respective values, we have;
\(\longrightarrow n =\dfrac{15\ g}{17\ g} \\\)
\(\longrightarrow \underline{\boxed{\boldsymbol{ n = 0.88 \ moles }}} \\\)
Therefore there are 0.88 moles in 15g of ammonia .
The molar mass of ammonia (NH3) is approximately 17.03 g/mol.
To find the number of moles in 15.0 grams of ammonia, we can use the formula:
moles = mass / molar mass
Substituting the given values, we get:
moles = 15.0 g / 17.03 g/mol
moles = 0.8817 mol (rounded to four significant figures)
Therefore, there are approximately 0.8817 moles in 15.0 grams of ammonia.
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If a total of 1,176 dancers at a beyonce music video audition are divided into 6 equal sized teams how many dancers are on each team
Answers
Answer:
196
Step-by-step explanation:
1176/ 6
= 196 dances are on each team
two angles that add up to 90 degrees are called ________ angles.
Answers
Answer: Right/complementary angles
Step-by-step explanation:
Two angles that add up to 90 degrees are called complementary angles.
Complementary angles are a pair of angles that, when added together, equal a right angle, which measures 90 degrees.
In other words, the sum of the measures of complementary angles is always 90 degrees.
Complementary angles often arise in geometry and trigonometry, and understanding their properties is important when working with angles and solving problems involving right triangles.
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You run Colgate and sell toothpaste. You are trying to forecast demand for 2022 , and you have sales data for the past 5 years, in \$M:
2017: 55
2018: 45
2019: 100
2020: 50
2021: 100
First, generate 4 forecasts using the following methods: naive, simple mean method, 3 period moving average, 2 period weighed moving average (with weights of 0.8 and 0.2 for the the most recent and second most recent period, respectively. Anthony is in marketing, and he's very worried about being understocked, so he picks his favorite 2022 forecast based on this worry. Bria, on the other-hand is really worried about big forecasting errors in either direction, and she picks her favorite 2022 forecast using her preferred metric. What is the absolute difference in Anthony's favorite forecast and Bria's favorite forecast? Round to the nearest $M. For example, if your answer is $4.39M, enter 4 in the box.
Answers
The absolute difference between Anthony's favorite forecast and Bria's favorite forecast is $22 million.
To find Anthony's favorite forecast, we need to compare the forecasts generated using different methods and choose the one that suggests a higher demand for 2022.
Bria's favorite forecast, on the other hand, is based on minimizing forecasting errors, so she will choose the forecast with the smallest absolute difference from the actual sales data.
Using the given sales data, we can calculate the forecasts using the four methods mentioned. The naive forecast for 2022 is simply the sales value from the most recent year, which is $100 million.
The simple mean method calculates the average of the past 5 years' sales, resulting in a forecast of $70 million. The 3-period moving average takes the average of the sales from the three most recent years, giving a forecast of $83.33 million.
The 2-period weighted moving average assigns weights of 0.8 and 0.2 to the most recent and second most recent years, respectively, resulting in a forecast of $85 million.
Anthony's favorite forecast would be the one with the highest value, which is $100 million (the naive forecast). Bria's favorite forecast would be the one with the smallest absolute difference from the actual sales data, which is $85 million (the 2-period weighted moving average forecast).
The absolute difference between these two forecasts is $15 million, rounded to the nearest million, resulting in an absolute difference of $22 million.
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Determine the equation of the line with slope 3 that passes through the point M (1,2) 1) 3x + y = 1 2) 3x - y = -1 3) 3x - y = 1 4) x- 3y = -1
Answers
Answer:
3) 3x - y = 1
Step-by-step explanation:
m=3
(y-2) / (x-1) = 3
y-2 = 3(x-1)
y = 3x - 1
If lindley requests an extension to file her individual tax return in a timely manner, the latest she could pay her tax due without penalty is::_________
Answers
If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
What is an individual tax return?A person or married couple must submit an official form known as an individual tax return to a federal, state, or local taxing authority in order to record any taxable income they received within a certain time period, typically the previous year.
This document is used to determine how much tax was paid in excess of what was required during that time period.
In this case, if Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
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If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is:
April 15th.
October 15th.
August 15th.
November 15th.
None of the choices are correct.
please can someone help me i dont know how to do this
Answers
9514 1404 393
Answer:
B, D = yes; others = no
Step-by-step explanation:
Recognize that "at most" means "less than or equal to." Sarah's spending must satisfy ...
3.50 + a ≤ 9.00
Subtracting 3.50 from both sides gives ...
a ≤ 5.50 . . . . . . . . . matches the second inequality shown
__
The graph of this will be shaded to the left, where 'a' values are less than the limit. The graph will have a solid dot at 5.50, where a = 5.50 is an allowed solution. This description matches the first number line shown.
_____
Point of clarification
We have used a red X to indicate that the corresponding inequality or graph is not an appropriate choice. It does not mean that the "NO" answer is incorrect. Rather, it means the answer is "NO."
The smaller triangle was dilated to form the larger triangle. What is the value of x? A smaller triangle has side lengths of 5, 13, 12. A larger triangle has side lengths of x, blank, 18. 6. 9 7. 5 10 11.
Answers
The value of x is 7.5.
DilationDilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.
Given
The smaller triangle was dilated to form the larger triangle.
A smaller triangle has side lengths of 5, 13, 12. A larger triangle has side lengths of x, blank, 18.
To findThe value of x.
How to find the value of x?We know the formula.
Side of a large triangle = Dilation x Side of a small triangle
Then we have,
18 = Dilation x 12
Dilation = 1.5
So the blank side will be
Blank side = 1.5 x 13
Blank side = 19.5
And x will be
x = 1.5 × 5
x = 7.5
Thus, the value of x is 7.5.
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if a is an approximate value for a quantity whose true value is t, and a has relative error r, prove from the definitions of these terms that a=t(1 r).
Answers
Given that "a" is an approximate value for a quantity with a true value of "t" and a relative error of "r," we need to prove that "a" can be expressed as "t(1+r)" using the definitions of these terms.
The relative error "r" is defined as the absolute difference between the true value "t" and the approximate value "a," divided by the true value "t." Mathematically, this can be expressed as r = |t - a| / t.
To prove that a = t(1 + r), we start by rearranging the definition of relative error:
r = |t - a| / t
Multiply both sides by t:
rt = |t - a|
Since the absolute value of t - a is equal to a - t (as the true value "t" is assumed to be larger than the approximate value "a"), we can rewrite the equation as:
rt = a - t
Rearranging the equation, we have:
a = t + rt
Factoring out t, we get:
a = t(1 + r)
Thus, we have proven that "a" can be expressed as "t(1 + r)" based on the definitions of "a," "t," and "r." This equation shows the relationship between the approximate value "a," the true value "t," and the relative error "r."
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what is the term for the rotational movement of the nose of the plane
Answers
The volume of a cone can be calculated using the formula \(V = (1/3) * * r2 * h\), where V is a constant roughly equal to 3.14159, r is the radius, and h is the height.
When the required values are substituted, the answer is \(V = (1/3) * 3.14159 * (1.75 feet)2 * 2.1\) feet.
The assessment of this expression yields V = 5.6688 cubic feet. The cone has a radius of 1.75 feet, a height of 2.1 feet, and a volume of approximately 5.6688 cubic feet."Pitch" is the technical word for the rotating movement of an airplane's nose. Pitch describes the rotation of the aircraft's nose around its lateral axis, either upward or downward. A plane is said to be in a positive pitch attitude when its nose is pointing up, and a negative pitch attitude when it is pointing down. Pitch control is essential for maintaining the correct flying path and managing the aircraft's height.
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The larger of two numbers is eight more than the smaller. If the sum of the two numbers is 32, what are the two numbers
Answers
The two numbers are 12 and 20
How to determine the numbers
Let the small number be x
Let the large number be y
We have that;
y = 8 + x (1)
But;
x + y = 32 (2)
Now, substitute the value of y as 8 + x in equation (2)
x + 8 + x = 32
collect like terms
2x + 8 = 32
2x = 32 - 8
2x = 24
Make 'x' the subject
x = 24/ 2
x = 12
But;
y = 8 + x
y = 8 + 12
y = 20
Thus, the two numbers are 12 and 20
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10 + 4a = a -23 i need to solve for a please help
Answers
Answer:
a = -11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
10 + 4a = a - 23
Step 2: Solve for a
Subtract a on both sides: 10 + 3a = -23Isolate a term: 3a = -33Isolate a: a = -11Step 3: Check
Plug in a into the original equation to verify it's a solution.
Substitute in a: 10 + 4(-11) = -11 - 23Multiply: 10 - 44 = -11 - 23Subtract: -34 = -34Here we see that -34 does indeed equal -34.
∴ a = -11 is the solution to the equation.
\(\sf{\bold{\green{\underline{\underline{Given}}}}} \)
⠀⠀⠀
10 + 4a = a - 23 ______________________\(\sf{\bold{\green{\underline{\underline{To\:Find}}}}} \)
⠀⠀
Value of a = ?? ______________________\(\sf{\bold{\green{\underline{\underline{Solution}}}}} \)
⠀⠀⠀⠀
For solving such problems we must have a glance at BODMAS rule .
⠀⠀⠀⠀
Firstly , putting all the variables at left and putting all the constants at right
⠀⠀⠀⠀
4a - a = - 23 - 10
⠀⠀⠀⠀
Secondly , solving the variable side
⠀⠀⠀⠀
3a = -23 - 10
⠀⠀⠀⠀
Now , solving the constant side
⠀⠀⠀⠀
3a = - 33
⠀⠀⠀⠀
Thirdly isolating the variable
⠀⠀⠀⠀
a = -33 / 3
⠀⠀⠀⠀
a = - 11
______________________\(\sf{\bold{\green{\underline{\underline{Answer}}}}} \)
⠀⠀⠀⠀
Value of a is -11Answer this for me please! thanks very much <3
Answers
the answer is b lil boy ggggggg
The population of fish in an aquarium can be modeled after exponential growth. If there were originally 3 fish and after 6 weeks there were 31 fish, how many fish would there be after 14 weeks?
Answers
Answer:
The population in 14 weeks is 232 fishes
Step-by-step explanation:
The equation for exponential growth is f(x) = a·(1 + r)ˣ
Where;
a = The starting population size = 3
r = The rate at which the population of grows
x = The number of periods to of change of the population
Therefore, we have;
f(6) = 31 = 3 × (1 + r)⁶
31/3 = (1 + r)⁶
㏑(31/3) = 6㏑(1 + r)
(㏑(31/3))/6 =㏑(1 + r)
1 + r = e^((㏑(31/3))/6) ≈ 1.476
1 + r ≈ 1.476
Therefore, the population in 14 weeks is given as follows;
f(14) = 3 × (1.467)¹⁴ ≈ 232.574
Given that we the information is with regard of living things, such that there are no fractions, we round down to the nearest whole number as follows;
f(14) ≈ 232
The population in 14 weeks = 232 fishes.
Find the value of y
A. 65
B. 70
C. 35
Answers
Answer: 35
Step-by-step explanation:
Assuming the triangles are congruent, then by CPCTC,
\(65=2y-5\\\\70=2y\\ \\ y=35\)
help, thank youu
A: 75
B: 61
C: 48
D: 80
Answers
Answer:
The answer is C, 48
Step-by-step explanation:
Its the only answer that makes sense
Answer:
75
Step-by-step explanation:
1. Eliminate wrong answers
a. (boys 5 & girls 4) meaning the boys should have a higher number than girls (which is 60) this meaning that 48 and 61 can not be the correct answer.
5/4=x/60
x=(5/4)*60
x=75
Math rocks
Leaving it to the obvious chose(The answer is 75)
Hope this helps
Write y=-11x-4 in standard form
Answers
Step-by-step explanation:
y = -11x - 4
y + 11x = -4
y + 11x + 4 = 0
I'm pretty sure that's the standard form
(20,8),(9,16). Can u do a step by step
Answers
Answer: [20x, 8y] [9x, 16y]
Step-by-step explanation:
Go on x value 20 and go up to 8 on y value.
Go on x value 9 and go up 16 on y value.
Which coordinate comes first?
Answers
While writing the coordinates in the coordinate plane the coordinate that comes first coordinate is represented by x-coordinate.
As given in the question,
In the coordinate plane:
We draw two axis named as x-axis and y-axis.x-axis and y-axis intersect at origin with coordinate ( 0,0 ).x-axis is represented by the horizontal axis.y - axis is represented by the vertical axis.First coordinate is of horizontal axis and second one is of vertical axis.Coordinates in the coordinate plane are represented by ( x ,y )First coordinate is represented by x -coordinate.Therefore, the first coordinate in the coordinate plane is represented by x-coordinate.
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6. Given that AD= 61, CD= 61, and m< ABC= 48,
find m < CBD.
Answers
Answer:
m∠CBD=24
Step-by-step explanation:
The angle measure of m∠CBD = 24°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
AD= 61,
CD= 61,
and m∠ABC= 48°.
The diagram is given in the attached image.
Converse of Angle Bisector Theorem's
If a triangle's interior point is equally spaced from its two sides, that point will be on the angle bisector created by the two line segments.
That means,
angle measure of m∠CBD = 48/2 = 24°.
Therefore, m∠CBD = 24°.
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The temperature in a room changes at a rate of r(t) =ln(t+1) sint degrees celsius per hour (where t is the time in hours). At t=1 hour, the temperature is 18 degrees celsius. What is the room's temperature at time t =3 hours?
Answers
The room's temperature at time t =3 hours is 18.2 degrees celsius
Calculating the room's temperature at time t =3 hours?From the question, we have the following parameters that can be used in our computation:
Rate, r(t) = ln(t + 1) sin(t)
The room's temperature at time t =3 hours is calculated as
Temperature = Temperature at t = 1 + Rate at t = 3
So, we have
Temperature = 18 + ln(3 + 1) sin(3)
Evaluate
Temperature = 18.2
Hence, the room's temperature at time t =3 hours is 18.2 degrees celsius
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Match each sequence with the position of its first term that is out of increasing order.
1. 1 5 78 99 101 202 400
2. 5 2 7 90 85 80 72
3. 5 6 9 10 14 21 20
4. 3 7 10 9 8 14 17
5. 5 77 25 45 22 94 58 99
Answers
In summary: Sequence 1 has no term out of increasing order. Sequence 2 has the first term out of increasing order at position 2. Sequence 3 has the first term out of increasing order at position 7. Sequence 4 has the first term out of increasing order at position 4. Sequence 5 has the first term out of increasing order at position 3.
1 5 78 99 101 202 400: This sequence is in increasing order throughout, so there is no term that breaks the increasing pattern.
5 2 7 90 85 80 72: The sequence starts with 5, then decreases to 2 (out of increasing order) at position 2.
5 6 9 10 14 21 20: The sequence is increasing until position 6, where it reaches 21. However, the next term, 20, is lower than the previous term, 21 (out of increasing order) at position 7.
3 7 10 9 8 14 17: The sequence starts with 3 and increases until position 3 (10). However, at position 4, the next term, 9, is lower than the previous term, 10 (out of increasing order).
5 77 25 45 22 94 58 99: The sequence is increasing until position 2, where it reaches 77. However, at position 3, the next term, 25, is lower than the previous term, 77 (out of increasing order).
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What are the four steps to solve a radical equation? The four steps to solving a radical equation are as follows: 1. Isolate the radical expression on one side of the equation. 2.Raise both sides to an exponent equal to the radical expression's order. 3.Solve the simplified equation. 4.Check each answer for extraneous solutions
Answers
The four steps to solve a radical equation are: Isolate the radical, square both sides, solve the resulting equation, and check for extraneous solutions.
To solve a radical equation, follow these four steps:
1. Isolate the radical: Move any terms that don't contain the radical to the other side of the equation. This step ensures that the radical term is alone on one side of the equation.
2. Square both sides: Raise both sides of the equation to the power that eliminates the radical. If you have a square root, square both sides. If you have a cube root, cube both sides, and so on. This step helps eliminate the radical.
3. Solve the resulting equation: Once you've eliminated the radical, solve the resulting equation for the variable. At this stage, you should have an equation without any radicals.
4. Check for extraneous solutions: After finding a potential solution, substitute it back into the original equation and verify if it satisfies the equation. Sometimes, in the process of eliminating the radical, you may introduce extraneous solutions that don't actually satisfy the original equation. If the substituted solution doesn't satisfy the equation, discard it as an extraneous solution.
By following these four steps, you can solve radical equations systematically and ensure that you find all valid solutions.
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Find the volume of the rectangular pyramid.
6 ft
2 ft
7 ft
Figure not drawn to scale.
Answers
Answer:
28
Step-by-step explanation:
V = (1/3)Bh
V = (1/3)(7 ft)(2 ft)(6 ft)
V = 28 ft^3