Consider the experiment of rolling fair six-sided die until a 5 is observed. Let A be the event that a 5 is observed on the first roll. Let B be the event that it takes at least two rolls for the first 5 to be observed. Find the following probabilities. (Round to nearest 4 decimal places)
P(A∩B)
P (A)
P(B)
Answer:
P(A∩B) = 0
P(A) = 0.1667
P(B) = 0.8333
=================================================
Explanation:
The events
A = a 5 is observed on the first rollB = it takes at least two rolls for the first 5 to be observedare mutually exclusive. There isn't any overlap. This is because event B involves "at least 2 rolls", meaning we cannot get 5 on the first roll. Either event A happens, or B does, but not both at the same time.
This allows us to say P(A∩B) = 0
In a venn diagram, the overlapped region between circles A and B would have probability 0 marked inside.
-----------------------
P(A) = 1/6 since there is exactly one side labeled "5" out of 6 sides total. This converts to the approximate decimal form 1/6 = 0.1667 when rounding to four decimal places. The 6's go on forever, but of course we have to round at some point.
------------------------
We found that P(A) = 1/6. The complement to this is 1-(1/6) = 5/6, which is the probability of rolling anything but a "5". This fraction represents the scenario "at least 2 rolls are needed for the 1st '5' to show up" since we forced the first roll to be anything but 5.
Put another way, we have two options:
Option 1: The first roll is "5". The probability is 1/6Option 2: The first roll is NOT "5" (so you'll need to do at least another roll to get "5"). The probability is 5/6.The two probabilities 1/6 and 5/6 add to 6/6, aka 1, to represent 100% of all possible cases. This means P(A)+P(B) = 1 for this scenario.
The fraction 5/6 converts to the approximate decimal form of 5/6 = 0.8333; use a calculator or long division to determine this value.
The following set of data represents hours worked per day by entry level employees, find the sample standard deviation: 14, 7, 10, 9 Round your answer to one decimal place.
Standard deviation of data represents hours worked per day by entry level employees is 2.9
The following set of data represents hours worked per day by entry level employees :
14, 7, 10, 9
First calculate the mean of the sample
Mean ([tex]\overline{X}[/tex])= [tex]\frac{14+7+10+9}{4}[/tex]
Mean = [tex]\frac{40}{4}[/tex]
[tex]\overline{X}[/tex] = 10
Now, calculate the standard deviation:
Standard deviation = [tex]\sqrt\frac{\sum{(x_i - \overline{X}})^{2}}{N -1}[/tex]
Standard deviation = [tex]\sqrt \frac{(14-10)^{2}+(7-10)^{2}+(10-10)^{2}+(9-10)^{2}}{3}[/tex]
Standard deviation = [tex]\sqrt\frac{16+9+0+1}{3}[/tex]
Standard deviation = [tex]\sqrt{8.66}[/tex] = 2.9
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Find the magnitude and direction of -3i-4j
Answer:
MAGNITUDE AND DIRECTION OF A VECTOR
Given a position vector →v=⟨a,b⟩,the magnitude is found by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application. For a position vector, the direction is found by tanθ=(ba)⇒θ=tan−1(ba)
Step-by-step explanation:
What is the central angle(pic included)
Answer:
72
Step-by-step explanation:
circumference = 20
arc = 4
4/20 =1/5
a circle = 360°
1/5 * 360 = 72
Need help with this question pls
Answer:
[tex]\huge\boxed{\sf SA \approx 967.1\ cm\²}[/tex]
Step-by-step explanation:
Given data:Radius = r = 7 cm
Height = h = 15 cm
Required:Surface Area = SA = ?
Formula:Surface Area of a cylinder = 2πrh + 2πr²
Solution:Using 3.14 for π
Now, Put the given data in the above formula.
SA = 2(3.14)(7)(15) + 2(3.14)(7)²
SA = 659.7 + 2(3.14)(49)
SA = 659.4 + 307.72
SA ≈ 967.1 cm²[tex]\rule[225]{225}{2}[/tex]
The set of all possible outcomes during the course of an experiment is called a sample space.
The given statement is true, The set of all possible outcomes during the course of an experiment is called a sample-space.
What is sample space?Sample-space, in probability, is referred to as the collection of all possible outcomes in any random experiment. It is denoted by "S".
Since it is a set, it is shown within the braces.
Given statement,
The set of all possible outcomes during the course of an experiment is called a sample-space.
By the definition of sample space, statement is true.
Example: Toss a coin
Sample-space, S={H,T}
H= head
T= tail
Hence, The set of all possible outcomes of any experiment is called sample-space.
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Read the quote from chapters 1-3 of Treasure Island. "He cleared the hilt of his cutlass and loosened the blade in the sheath; and all the time we were waiting there he kept
swallowing as if he felt what we used to call a lump in the throat." Based on these actions, what emotion is Black Dog feeling?
A. Anger
B. Fear
C. Joy
D. Excitement
After reading quote from chapters 1-3 of Treasure Island.
"He cleared the hilt of his cutlass and loosened the blade in the sheath; and all the time we were waiting there he kept swallowing as if he felt what we used to call a lump in the throat."
Based on the actions described in the quote, Black Dog is feeling fear. Hence option B is correct answer.
What is the Treasure Island?Clearing the hilt of his cutlass and loosening the blade in the sheath are actions typically taken when one is preparing for potential danger or conflict.
Therefore, based on the above, the fact that Black Dog is swallowing as if he has a lump in his throat is another indication that he is feeling fear or nervousness.
Correct option is: B
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The store owner gave a 15% discount, yet Ty still had to pay $153 for the chess set. What was the original price of the chess set
Answer: $180
Step-by-step explanation:
180 x 15% = 27
27 - 180 = 153
Deborah is x years old and Syria is y years old . the sum of their ages is 58 if the area is 4 years younger than Syria find the ages of both women
Answer:
Deborah is 27 years old and Syria is 31 years old.
Step-by-step explanation:
Let's say Deborah's age is x and Syria's age is y.
From the given information, we know that:
x + y = 58 (the sum of their ages is 58)
Also, the difference between their ages is 4, which means:
y - x = 4
We can use these two equations to find the values of x and y.
First, we'll solve for y:
y = x + 4
Substituting this value of y into the first equation:
x + (x + 4) = 58
Expanding the left-hand side:
2x + 4 = 58
Subtracting 4 from both sides:
2x = 54
Dividing both sides by 2:
x = 27
So Deborah is 27 years old and Syria is y = 27 + 4 = 31 years old.
How much water do you add to make each concentration? 1% sugar syrup using 12g sugar
DEBATE Mrs. Ramirez will divide her class of 24 into two teams for a debate. She writes the numbers 1 through 24 on individual pieces of paper and distributed them randomly, one to each student. The students with even numbers will be part of the red team and the students with odd numbers will be part of the blue team.
If a student is on the blue team, what is the probability that he or she was given the number 19?
Answer:
1/12
Step-by-step explanation:
Total Number of pieces of paper = 24
Total Number of pieces of paper with an odd number on it= 24/2 = 12
Total Number of pieces of paper with Number 19 = 1
Probability of a student on blue team having the Number 19 would be = Number of paper pieces with Number 19/Total number of pieces of paper with an odd number = 1/12
We take only the pieces of paper with an odd number on it as we already know the student is in the blue team so they had to have an odd number.
Geometry Help -- 30-60-90 and 45-45-90 triangles
Answer:
w = (10√3)/3
x = 5
y = 5√2
z = (5√3)/3
Step-by-step explanation:
→ The length of "x" is also 5 units because 45-45-90 triangles have the same leg lengths.
→ The length of "y" is 5√2 units because the hypotenuse of a 45-45-90 triangle is √2 times bigger than either leg length.
→ The length of "z" is 5/√3 or (5√3)/3 units because the longer leg length of a 30-60-90 triangle is √3 times bigger than the shorter leg length
→ The length of "w" is (10√3)/3 units because the longer leg length is 2 times bigger than the shorter leg length of a 30-60-90 triangle
See below for more information about general rules for 30-60-90 and 45-45-90 triangles!
What is AB in the figure?
A) An Altitude
B) A Median
C) An Angle Bisector
D) None Of The Above
Answer:
option C
Step-by-step explanation:
line AB bisects the angle, so it is an angle bisector.
We have a cohort of 100 cancer patients receiving various forms of treatment. Treatment can
be stand alone or combinations, the unique types of treatment are: surgery only, radiation
only, chemotherapy only, chemotherapy and radiation, surgery and chemotherapy, surgery
and chemotherapy and radiation, and no treatment. Our sample has the follow distribution of
treatments:
● 38 patients receiving surgery only
● 10 patients receiving radiation only
● 18 patients receiving chemotherapy only
● 17 patients receiving surgery and chemotherapy
● 6 patients receiving surgery, chemotherapy, and radiation
● 11 patients with no treatment (this does not count as a type of treatment)
If we randomly select one person from this sample, find the following probabilities:
a) P(any treatment)
Ans:
Answer:
89/100
Step-by-step explanation:
there were only 11 people without treatment so minus 11 from 100 which is 89
then just make it a probability by writing it out of 100.
hope this helps
Expand each expression
\ln \frac { 4 y ^ { 5 } } { x ^ { 2 } }ln
x
2
4y
5
Therefore , the solution of the given problem of expression comes out to be its final simplification is 5ln4y - 2lnx.
What is an expression?There is a need for mathematical operations such addition, multiplication, multiplication, and division. When variable combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact is composed of values, parameters, plus operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.
Here,
Given :
To expand the given expression :
=> ln [ (4y)⁵/ x² ]
=> ln [ (4y)⁵/ x² ]
=> ln(4y)⁵ - lnx²
=> 5ln4y - 2lnx
Thus,
its final simplification is : 5ln4y - 2lnx.
Therefore , the solution of the given problem of expression comes out to be its final simplification is 5ln4y - 2lnx.
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someone please help me with this simple math question
Answer:
[tex](17 \times6) + (11 \times 4)[/tex]
[tex]102 + 44 = 146[/tex]
10. Kara's grandmother is knitting a baby
cap. She knitted 1/5 of the cap yesterday
morning. By evening, she had knitted 7/10
of the cap. Estimate how much of the cap
she knitted during the afternoon.
Kara's grandmother knitted the cap during the afternoon is [tex]\frac{1}{2}[/tex].
What is a Fraction?A fraction is a number that represents the part of a whole. It is in the form of [tex]\frac{a}{b}[/tex] , in which upper 'a' part denotes numerator and the lower part 'b' denotes the numerator.
Kara's grandmother knitted the cap,
In the morning = [tex]\frac{1}{5}[/tex]
In the evening = [tex]\frac{7}{10}[/tex]
She knitted during the afternoon = [tex]\frac{7}{10} -\frac{1}{5}[/tex]
= [tex]\frac{7}{10} - \frac{2}{10}[/tex]
= [tex]\frac{5}{10} = \frac{1}{2}[/tex]
Hence, Sara's grandmother knitted the cap during the afternoon =[tex]\frac{1}{2}[/tex].
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Two identical point charges of q = +1.75 x 10
−
8
C are separated by a distance of 0.30 m. How much work is done by the electric field force to move them away from each other so that they are 1.05 m apart?
The electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.
What do you mean by electric field?The electric field is a vector field that represents the force experienced by a charged particle due to an electric charge distribution. It is a measure of the electric force per unit charge at a particular point in space. The electric field is defined as the negative gradient of the electric potential, which is the energy per unit charge that a charged particle would have at that point in space. The electric field can be used to calculate the force experienced by a charged particle in the presence of other charges, and is a fundamental concept in the study of electromagnetism.
The electric field force between two point charges is given by Coulomb's law:
F = k * (q₁ * q₂) / r²
where k is the Coulomb constant (8.99 x 10⁹ N m²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between the charges.
To calculate the work done by the electric field force, we need to find the force at the initial distance (0.30 m) and the final distance (1.05 m), and then subtract the work done at the initial distance from the work done at the final distance.
At a distance of 0.30 m, the force is:
F = k * (1.75 x 10⁻⁸ C)² / (0.30 m)² = 4.02 x 10⁻⁸ N
The work done at this distance is:
W = F * 0.30 m = 1.21 x 10⁻⁷ J
At a distance of 1.05 m, the force is:
F = k * (1.75 x 10⁻⁸ C)² / (1.05 m)² = 1.33 x 10⁻⁸ N
The work done at this distance is:
W = F * 1.05 m = 1.40 x 10⁻⁷ J
Finally, to find the total work done, we subtract the work done at the initial distance from the work done at the final distance:
W total = W final - W initial = 1.40 x 10⁻⁷ J - 1.21 x 10⁻⁷ J = 1.90 x 10⁻⁸ J.
Therefore, the electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.
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A university president salary for the 2012-2013 academic year was $483,000. Calculate his 2013-2014 salary if he received a 3.1% raise. Show work please!
Answer: The 2013-2014 salary can be calculated as follows:
$483,000 + ($483,000 * 3.1%) = $483,000 + $14,973 = $497,973.
So, the university president's 2013-2014 salary was approximately $497,973 after receiving a 3.1% raise.
Step-by-step explanation:
(7 5/6 - 5 1/3) + 1 1/9
let's firstly convert the mixed fractions to improper fractions.
[tex]\stackrel{mixed}{7\frac{5}{6}}\implies \cfrac{7\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{47}{6}} ~\hfill \stackrel{mixed}{5\frac{1}{3}} \implies \cfrac{5\cdot 3+1}{3} \implies \stackrel{improper}{\cfrac{16}{3}} \\\\\\ \stackrel{mixed}{1\frac{1}{9}}\implies \cfrac{1\cdot 9+1}{9}\implies \stackrel{improper}{\cfrac{10}{9}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\left( \cfrac{47}{6}-\cfrac{16}{3} \right)+\cfrac{10}{9}\implies \cfrac{47}{6}-\cfrac{16}{3}+\cfrac{10}{9}\implies \cfrac{(3)47~~ - ~~(6)16~~ + ~~(2)10}{\underset{\textit{using this LCD}}{18}} \\\\\\ \cfrac{141-96+20}{18}\implies \cfrac{65}{18}\implies {\Large \begin{array}{llll} 3\frac{11}{18} \end{array}}[/tex]
4p divided by 6,
where p= 12
The value of the expression 4p ÷ 6 when p = 12 is 8
What is the value of the expression when p = 12?Given the expression in the question;
4p ÷ 6
p = 12To determine the value of the expression, substitute p = 12 for all values of p in the expression and simplify.
4p ÷ 6
Plug in p = 12
4( 12 ) ÷ 6
Multiply 4 and 12
48 ÷ 6
Divide 48 by 6
8
Therefore, the value is 8.
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Giai PT: xy'=y+xe^{\frac{y}{x}}
what is (-5,-3) reflected over the Y axis
The point (-5,-3) reflected over the y-axis is (5, -3).
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
(-5, -3)
Now,
Along y-axis:
(x, y) → (-x, y)
So,
(-5, -3) → (-(-5), -3) = (5, -3)
Thus,
(5, -3) is the reflected point.
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Please help with this answer I will give you Brainly
Answer:
x=1
Step-by-step explanation:
up we have the answer of the question
Answer:
the number is 4.
Step-by-step explanation:
The number is 4 because 3 × 4 = 12 and 4^2 = 16.
16 - 12 = 4
Thanks for Brainly.
Hope I could help in time.
I will give brainliest and ratings if you get this correct!
Depending on the data above,
find The arithmetic mean, median, mode and range
Mean = 31.333
Median = 30
Mode = 41
Range = 18
Mean
Determining the average can be done by adding up all the data values, then dividing by the amount of data.
Mean = [tex]\frac{30+25+23+41+39+27+41+24+32}{9}[/tex]
= [tex]\frac{282}{9}[/tex]
= 31.333
Median
The median is the middle value of a set of data after being sorted from smallest to largest data, and vice versa. If data has a median, then the median is single.
because the questions are not sequential, they must be sorted first from the smallest to the largest.
23 24 25 27 30 32 39 41 41
The median from this question is 30
Mode
The mode is the data that occurs most frequently.
23 24 25 27 30 32 39 41 41
And the mode of this problem is 41 because it appears two times
Range
the range is the difference between the highest value of a data set and the lowest value of a data set.
23 24 25 27 30 32 39 41 41
the range from 23 to 41 is 18
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The points (14,8) and (28,16) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
the answer to your problem is y = 4/7x
Kaya volunteers at a local animal shelter. She made some notes about
the animal populations in the shelter this week.
doge
2/5 dogs 3/8 cats
rest are other pets,
such as birds,
hamsters, and lizards
Part A What fraction of all the animals are not dogs and cats? Explain
how you found your answers.
The fraction of all the animals that are not dogs and cats is 9/40 or 0.225.
How is the fraction determined?The fractions of the dog and cat populations are summed and subtracted from 1, which represents the total population of the animals.
The fractions can also be expressed as decimals using division operations. They can also be depicted in percentages by multiplying the division quotients by 100.
Fractions of Animal Populations in the Shelter:
Dogs = 2/5
Cats = 3/8
2/5 + 3/8 = 31/40
The lowest common factor of 5 and 8 is 40.
Other pets = x
x = (1 - 31/40)
x = 9/40
Thus, since 2/5 of the animal populations are dogs and 3/8 are cats, the rest of the pets, including birds, hamsters, and lizards can be represented fractionally as 9/40.
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Use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is 1 or -1
- The y - intercept is (0,-49)
- The x - intercepts are ( -7,0), (7,0)
- The degree is 2
- as x → - ∞, f(x) → ∞
- as x → ∞, f(x) → ∞
The polynomial function is f(x) = x² - 49 if the leading coefficient is 1 or f(x) = -x² - 49 if the leading coefficient is -1.
What is Polynomial?Polynomials are expressions of the form,
a₀ + a₁ x + a₂ x² + ................. + aₙ₋₁ xⁿ⁻1 + aₙ xⁿ
where a's are the coefficients, x is the variable and n is the number of terms.
Given that, the degree of the function is 2.
So the function is quadratic.
It is of the form f(x) = ax² + bx + c.
The y - intercept is (0,-49).
Substituting the point,
(a × 0²) + (b × 0) + c = -49
c = -49
Function is f(x) = ax² + bx - 49.
We have, the x - intercepts are ( -7,0), (7,0).
Substituting the points, we get two equations.
a (-7)² + b (-7) - 49 = 0 and a (7)² + b (7) - 49 = 0
49a - 7b - 49 = 0 and 49a + 7b - 49 = 0
Subtracting 49a - 7b - 49 = 0 from 49a + 7b - 49 = 0, we get,
14b = 0
b = 0
So the function is of the form f(x) = ax² - 49.
Given that, Assume the leading coefficient is 1 or -1.
Function is either f(x) = x² - 49 or f(x) = -x² - 49
Hence the required function is f(x) = x² - 49 or f(x) = -x² - 49.
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Dina has a circular table. she wants to paint around the edge of the table. If the table has a radius of 3.5 feet, how long is the part of the table she will be painting?
The length of the part of the table that Dina will be painting is 21.991595 feet.
What do you mean by Circumference?Circumference refers to the distance around the edge of a circle. It is the length of the perimeter of a circle and is defined as the product of the circle's radius and its constant pi (π). The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is approximately equal to 3.14, and r is the radius of the circle.
The circumference of a circle is an important concept in geometry, trigonometry, and engineering, as it provides a measure of the size and shape of a circular object. Circumference is used in many applications, such as determining the size of wheels, gears, and other circular objects, as well as in the calculation of areas and volumes of circular shapes.
To find the length of the part of the circular table that Dina will be painting, we need to find the circumference of the circle.
Circumference = 2 * π * r
Where r is the radius of the circle. In this case, the radius is 3.5 feet, so:
Circumference = 2 * π * 3.5
Circumference = 2 * 3.14159 * 3.5
Circumference = 21.991595 feet (to 4 decimal places)
So, the length of the part of the table that Dina will be painting is 21.991595 feet.
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Please help I need it ASAP