Using the hypergeometric distribution, it is found that the distribution is:
P(X = 0) = 0.0152
P(X = 1) = 0.1818
P(X = 2) = 0.4545
P(X = 3) = 0.3030
P(X = 4) = 0.0455
Hence:
A) There is a 0.0455 = 4.55% probability that all selected rats are female.
B) There is a 0.1818 = 18.18% probability that only one of the selected rats is female.
C) There is a 0.803 = 80.3% probability that at least two of the selected rats is female.
D) The mean of the probability distribution is of 2.18.
E) The standard deviation of the probability distribution is of 0.833.
The rats are chosen without replacement, hence the hypergeometric distribution is used to solve this question.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem:
There is a total of 11 rats, hence N = 11.6 of the rats are female, hence k = 6.4 rats are taken, hence n = 4.The distribution is the probability of each outcome, hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,11,4,6) = \frac{C_{6,0}C_{5,4}}{C_{11,4}} = 0.0152[/tex]
[tex]P(X = 1) = h(1,11,4,6) = \frac{C_{6,1}C_{5,3}}{C_{11,4}} = 0.1818[/tex]
[tex]P(X = 2) = h(2,11,4,6) = \frac{C_{6,2}C_{5,2}}{C_{11,4}} = 0.4545[/tex]
[tex]P(X = 3) = h(3,11,4,6) = \frac{C_{6,3}C_{5,1}}{C_{11,4}} = 0.3030[/tex]
[tex]P(X = 4) = h(4,11,4,6) = \frac{C_{6,4}C_{5,0}}{C_{11,4}} = 0.0455[/tex]
Item a:
P(X = 4) = 0.0455, hence:
There is a 0.0455 = 4.55% probability that all selected rats are female.
Item b:
P(X = 1) = 0.1818, hence:
There is a 0.1818 = 18.18% probability that only one of the selected rats is female.
Item c:
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.4545 + 0.3030 + 0.0455 = 0.803[/tex]
There is a 0.803 = 80.3% probability that at least two of the selected rats is female.
Item d:
The mean of the hypergeometric distribution is:
[tex]\mu = \frac{nk}{N}[/tex]
Hence:
[tex]\mu = \frac{4(6)}{11} = 2.18[/tex]
The mean of the probability distribution is of 2.18.
Item e:
The standard deviation of the hypergeometric distribution is:
[tex]\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}[/tex]
Hence:
[tex]\sigma = \sqrt{\frac{4(6)(11-6)(11-4)}{11^2(11-1)}} = 0.833[/tex]
The standard deviation of the probability distribution is of 0.833.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
Use Liam DeWitt's Flash Card statement and the credit calendar for Exercises a-e.
A) what is Liam’s average daily balance
B) what is Liam’s monthly periodic rate?
C) what is Liam’s finance charge?
D) what is Liam’s new balance?
E) what is Liam’s available credit?
The answers for this task are gotten in most cases by Careful Observation of Liam DeWitt's Bank Account Information.
What is a Bank Account Information?
A bank account information refers to all the details present on or which can be deduced from one's statement or record of banking activities..
Liam's Average Daily Balance is: Total sum of balance each day divided by the number of days. That is
(250+87+1300+470-200+34.76+102.71+45.90+84.60)/9
ADB= $241.66
B) Liam's Monthly Periodic Rate (MPR) is the Annual Interest Rate divided by the number of periods. In this case, that will be:
19.8%/12
MPR = 1.65%
C) Liam's Finance Charge is (Average Daily Balance * APR)/365.
That is (241.66 * 19.8)/365 = 13.11%
D) Liam's New Balance is calculated by removing new inflow from old balance. That is
(250+87.60+1,300+470.63+34.76+102.71+45+848.60)-3,240.5
= $-101.20
E) Liam's Available Line of Credit is clearly stated as $4,000.
See the link below for more about Bank Account Information:
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Suppose t and u are linear transformations from to such that t(ux)x for all x in. Is it true that u(tx)x for all x in ? why or why not?.
A linear transformation is used to illustrate a linear operator
It is true that U(T(x)) = x for all values of x
How to determine if the linear transformation is trueThe linear functions are given as:
U(x1) and U(x2)
Given that the function U(x) is a one-one-one function, then we have:
T(U(x1)) = T(U(x2))
This becomes
x1 = x2
The above equations mean that the function U is invertible
So, we have:
S(U(x)) = U(S(x)) = x for all values of x
Also, we have:
T(U(x)) = x for all values of x.
This means that,
T(x) = S(x) and U(T(x)) = x for all values of x, because U(S(x)) = x for all values of x
Hence, it is true that U(T(x)) = x for all values of x
Read more about linear transformations at:
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The perimeter of an equilateral triangle is 63 inches. If the length of each side is (4x-3) find the value of x
Answer:
X=6
Step-by-step explanation:
We know that the perimeter is the sum of all its sides.
[tex]P=63\\P=(4x-3)+(4x-3)+(4x-3)\\P=P\\(4x-3)+(4x-3)+(4x-3)=63\\12x-9=63\\12x=72\\x=\frac{72}{12} \\x=6[/tex]
Becky wants to make a giant cherry pie to try to break the world record. If she succeeds in making a pie with a 20 foot diameter, what will be the total distance around the pie? please round to the nearest tenth. Use 3.14 for pi.
The distance around would be the circumference.
Circumference formula = diameter x pi
circumference = 20 x 3.14 = 62.8 feet
Answer: 62.8 feet
One weekend Ella sells a total of 52 prints for a total of $2,975. Small prints cost $50 and large prints cost $75. How many of each size print did Ella sell?
Answer:
She soled 58 small prints and one big print
5(4x + 2) ÷ 7y
From the expression above, provide an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write "not present."
I HOPE THIS HELPS
The parts of the expression, 5(4x + 2) ÷ 7y,
are:Sum: 4x + 2
Term: 7y
Product: 5(4x + 2)
Factor: 5
Quotient: 5(4x + 2) ÷ 7y
Coefficient: 7
What are the Parts of an Expression?
- Sum means addition, therefore, an example of sum in the expression, 5(4x + 2) ÷ 7y, is: 4x + 2.
- An example of a term is in 5(4x + 2) ÷ 7y is: 7y.
- Product means multiplication. An example of a product is: 5(4x + 2).
- An example of a factor in 5(4x + 2) ÷ 7y, is 5.
- Quotient means division. An example is: 5(4x + 2) ÷ 7y.
- Coefficient is a number multiplying a variable. An example is: 7 or 4.
Therefore, the parts of the expression, 5(4x + 2) ÷ 7y, are:
Sum: 4x + 2
Term: 7y
Product: 5(4x + 2)
Factor: 5
Quotient: 5(4x + 2) ÷ 7y
Coefficient: 7
A salsa recipe uses green pepper, onion, and tomato in the extended ratio 4:5:6. What is the measure of the smallest angle?
Answer:
19.2 cups of onion
Step-by-step explanation:
Given a salsa recipe uses green pepper, onion, and tomato in the extended ratio 4:5:6, how many cups of onion are needed to make 72 cups of salsa?
4x + 5x + 6x = 72
⇒ 15x = 72
⇒ x = 72 ÷ 15
⇒ x = 4.8
Onion: 4x = 4 x 4.8 = 19.2 cups
Answer:
[tex]{\large{ \red{{{19.2 }}}}}[/tex]
Solution:
[tex]4x + 5x + 6x = 72[/tex]
[tex]⇒ 15x = 72[/tex]
[tex]⇒ x = \frac{72}{15}[/tex]
[tex]⇒ x = 4.8[/tex]
Onion: [tex]4x = 4 \times 4.8 = 19.2 cups[/tex]
The two-way table shows the distribution of book style to genre. Miguel claims that given that the book is paperback (PB) does not affect the outcome that the book is nonfiction (NF). A 4-column table has 3 rows. The first column has entries paperback, hardcover, total. The second column is labeled Fiction with entries 20, 10, 30. The third column is labeled nonfiction with entries 60, 30, 90. The fourth column is labeled total with entries 80, 40, 120. Is Miguel’s claim correct? Yes, the two events are independent because P(NF|PB) = P(NF). Yes, the two events are independent because P(PB|NF) = P(NF). No, the two events are not independent because P(PB|NF) ≠ P(PB). No, the two events are not independent because P(PB|NF) ≠ P(NF).
The claim of Miguel is correct, as the two events are independent because P(NF|PB) = P(NF).
What is conditional probability?The conditional probability is the happening of an event, when the probability of occurring of other event is given.
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
The probability of event A, given that the event B is occurred.
Independent events are those events whose occurrences do not depend on the other events.
The two-way table shows the distribution of book style to genre is given as,
The first column has entries paperback, hardcover, total.
The second column is labeled Fiction with entries 20, 10, 30.
The third column is labeled nonfiction with entries 60, 30, 90.
The fourth column is labeled total with entries 80, 40, 120.
Miguel claims that given that the book is paperback (PB) does not affect the outcome that the book is nonfiction (NF).
Suppose that two events are denoted by A and B. They are said to be an independent event if and only if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Put the values as,
[tex]\dfrac{60}{120}=\dfrac{80}{120}\times\dfrac{90}{120}\\\dfrac{1}{2}=\dfrac{1}{2}[/tex]
As both the values are equal. Thus, the claim of Miguel is correct because the two events are independent because P(NF|PB) = P(NF).
Learn more about the probability here;
https://brainly.com/question/24756209
Learn more about the independent events here;
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Answer:
The correct answer is option A. :)
Step-by-step explanation:
Just got it right on edge - the above answer helped and is correct :D
Brainliest would be greatly appreciated!
identify the triangle
Answer:
scalene right
Step-by-step explanation:
it has a right angle in it and all the sides are different.
Simon put $15000 in an account with a simple interest rate of 4.5%. How much interest will be earned after 8 years?
Answer:
The interest earned at the end of 8 years is $5400, hope this helps!
Step-by-step explanation:
The interest earned at the end of 8 years is $5400.The fee you pay to borrow money or the fee you charge to lend money is called interest.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
It is given that, Simon put $15000 in an account with a simple interest rate of 4.5% for the time period of 8 years.
Principal,P = $15000
Rate,R = 4.5% per annum
Time period, T =8 years
The simple interest is found as,
SI = (P×R×T) / 100
Where P is the principal, T is the rate and T is the period.
SI = ( $15000×4.5× 8 ) / 100
SI = $540000/100
SI = = $5400
Thus, the interest earned at the end of 8 years is $5400.
Learn more about the simple interest here:
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PLEASEEEE HELP!!!!!!!!!!
DEF and GHI are shown below.
Which statement is true?
Answer:
They are not similar,
the reason why is because 56 degrees is given and the two sides that form the angle are the same length whilst the other triangle has two uneven sides that form a 56 degree angle.
what is an equation with a difference of 6
Element X decays radioactively with a half life of 9 minutes. If there are 890 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 238 grams?
Answer:
13.18651685
13.9
Explain:
890-238=652
652/890=0.7325842697 (Find out the percentage)
We know that 1 gram of Element X will be fully decayed in 18 minutes and half of it in 9 minutes.
0.7325842697x18=13.18651685
As you see 18/13.18651685 will equal to 18 (not exactly since it is rounded)
And of course we need to round it to nearest tenth. So the answer would be 13.9!
The time taken for the element to decay to 238 grams is 13.9 minutes.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that element X decays radioactively with a half-life of 9 minutes. If there are 890 grams of Element X,
The time taken will be calculated as,
890-238=652
652/890=0.7325842697 (Find out the percentage)
We know that 1 gram of Element X will be fully decayed in 18 minutes and half of it in 9 minutes.
0.7325842697x18=13.18651685
Therefore, the time taken for the element to decay to 238 grams is 13.9 minutes.
To know more about expression follow
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Click and drag the steps in the order they are performed if you use the algorithm devised in the previous question to sort the list 3, 2, 4, 5, 1, 6 in ascending order.
Sorting involves arranging a set of elements in a particular order (ascending or descending)
How to sort the list elementsThe list elements are given as:
3, 2, 4, 5, 1, 6
To sort the list in ascending order, the adjacent elements are compared, and the smaller element is pushed to the left.
So, we have the following steps
Begin with 3, 2, 4, 5, 1, 6Compare 3 and 2. 2 is less than 3. So, we have: 2, 3, 4, 5, 1, 6Compare 4 and 3. 4 is greater than 3. So, we have: 2, 3, 4, 5, 1, 6Compare 5 and 4. 5 is greater than 4. So, we have: 2, 3, 4, 5, 1, 6Compare 1 all the way to the first element. So, we have: 1, 2, 3, 4, 5, 6Compare 6 and 5. 5 is less than 6. So, we have: 1, 2, 3, 4, 5, 6See attachment for the complete step that sorts the list
Read more about sorting techniques at:
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Is c = 7 a solution to the inequality below?
3 < 9− c
Answer:
NoStep-by-step explanation:
Where 'c' is, plug its value into the equation:
3 < 9 - 7
Simplify (9-7)
9 - 7 = 2
"The crocodile ALWAYS eats the bigger umber" in true equations
3 < 2 reads: 3 is less than 2
Is 3 less than 2?
No, 3 is greater than 2.
Your answer is 'no'.
9. A ladder of length 23 feet leans against the side of a building. The angle of elevation of the ladder is 76. Find the distance from the top of the ladder to the ground. Round your answer to two decimals.
A)
5.73 feet
B)
22.32 feet
C)
5.56 feet
D)
18.96 feet
E)
13.02 feet
Answer:B) 22.32 feet
[tex] \quad\rule{300pt}{1pt}[/tex]
Solution:
we are given that , a ladder is placed against a side of building , which forms a right angled triangle . We wre given one side of a right angled triangle ( hypotenuse ) as 23 feet and the angle of elevation as 76 ° . We can find the Perpendicular distance from the top of the ladder go to the ground by using the trigonometric identity:
[tex] \qquad\quad\bull ~{\boxed{\bf{ Sin\theta =\dfrac{Perpendicular}{Hypotenuse}}} }~\bull[/tex]
Here,
hypotenuse = 23 feet[tex]\theta [/tex] = 76°Value of Sin[tex]\theta [/tex] = 0.97Perpendicular = ?[tex] \quad\dashrightarrow\quad \sf { sin\theta =\dfrac{P}{H}}[/tex]
[tex] \quad\dashrightarrow\quad \sf { sin76° =\dfrac{P}{23}}[/tex]
[tex] \quad\dashrightarrow\quad \sf { 0.97=\dfrac{P}{23}}[/tex]
[tex] \quad\dashrightarrow\quad \sf {P = 0.97 \times 23 }[/tex]
[tex] \quad\dashrightarrow\quad \sf { P = 22.32}[/tex]
ㅤㅤㅤ~Hence, the distance from the top of the ladder to the ground is 22.32 feet !
[tex] \rule{300pt}{2pt}[/tex]
Question 4 of 5
What is the approximate radius of a sphere with a volume of 3052 cm3?
A. 27 cm
o
B. 18 cm
C. 54 cm
D. 9 cm
SUBMIT
Answer:
D. 9 cm
Step-by-step explanation:
The radius of the sphere can be found by solving the volume equation for the radius.
V = 4/3πr³
3V/(4π) = r³
r = ∛(3V/(4π)) = ∛(3×3052/(4×π)) ≈ ∛728.611
r ≈ 9.0 cm
The radius of the sphere is about 9 cm.
i need help with my homework and thx
Answer:
Step-by-step explanation:
300.364 us liquid gallonsgallons
Which point is located at (-2, 5)?
point C
point D
point B
point A
Image below
Answer:
point B
Step-by-step explanation:
point B is located at (-2, 5).
Hope it helps you in your learning process.
Answer:
B
Step-by-step explanation:
It is on the -2 5 so therefore your answer is B.
D is on 2 and -5
C is on 5 and -2
A is on -5 and 2
Therefore, it's B confirmed.
David’s favorite restaurant adds a 42% markup on top of what it costs it to make a dish. At what price would the restaurant sell a dish that costs $15 to make?
Answer:
Revenue
$21.30
Profit:
$ 6.30
Step-by-step explanation:
solve and simplify 5/6 x 3/4
Answer: 5/8
Step-by-step explanation:
find common denominator:
Multiple: 3/4 * 5/6 = 3 · 5/4 · 6= 15/24 = 5 · 3/8 · 3 = 5/8 Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(15, 24) = 3. In the following intermediate step, cancel by a common factor of 3 gives 5/8. In other words - three quarters multiplied by five sixths = five eighths.
I would very appreciate help with this pretty soon.
Answer:
Step-by-step explanation: Hi there.
We can treat this problem just like a simple subtraction problem, like 3-2
It helps to form the equation like this:
x^2+9x+18
- (1x+06)
Remember that the operation changes the sign: -1x-6
The result is x^2+8x+12, and it is already in standard form.
Have a nice day! :)
Answer:
x² + 8x + 12
Explanation:
given:
f(x) = x² + 9x + 18g(x) = x + 6solve function:
→ f(x) - g(x)
→ x² + 9x + 18 - (x + 6)
→ x² + 9x + 18 - x - 6
→ x² + 9x -x + 18 - 6
→ x² + 8x + 12
Evaluate the following expression.
4 – (3 – 2)(exponent 2
Answer: 3
Step-by-step explanation:
3 minus 2 is 1.
1 to the power of 2 is still 1.
4 minus 1
= 3
Please help in the photo shown!
Given that angle
a
= 40° and angle
b
= 15°, work out
x
.
The diagram is not drawn accurately.
(Triangle)
Answer:
125°
Step-by-step explanation:
a+b+c=180° (sum of a triangle is 180°
40°+15°+x = 180°
55°+x = 180°
x = 180°-55°
=125°
what is the answer? :D
Answer:
6/9, 12/18 (just 6 then 12)
Step-by-step explanation:
Please mark brainlest
Answer:
6/9
12/18
Step-by-step explanation:
Hopefully this is correct
Jason is bungee jumping in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function y = x² - 18x, where x is the time in seconds and y is the height in feet.
A) How long did it take for Jason to reach his minimum height?
B) What was the lowest point that Jason reached?
C) Jason returned to the top of the bungee jump at what time?
Answer:
A) 9 seconds
B) lowest point is -81 ft, or 81 ft below the top of the bungee jump
C) 18 seconds
Step-by-step explanation:
A) To find the x-value of the turning point (minima/maxima) differentiate, then set to zero and solve for x:
[tex]\dfrac{dy}{dx}=2x-18\\\\\implies \dfrac{dy}{dx}=0\\\\\implies 2x-18=0\\\\\implies x=9[/tex]
Therefore, it took 9 seconds to reach the minimum height
B) lowest point is when x = 9:
⇒ y = (9)² -18(9) = -81
Therefore, lowest point is -81 ft, or 81 ft below the top of the bungee jump
C) find x when y = 0
⇒ x² - 18x = 0
⇒ x(x - 18) = 0
⇒ x = 0 and x - 18 = 0
⇒ x = 0 and x = 18
So he returned to the top of the bungee jump at 18 seconds
Answer:
A) 9 s
B) -81 feet
C) 18 feet
step by step explanation:
A)
[tex]\sf y = x^2 - 18x[/tex]
use the vertex formula: [tex]\sf \frac{-b}{2a}[/tex]
Here a = -18 and a = 1, these are coefficients from ax² + bx + x
solve:
[tex]\hookrightarrow \sf \frac{--18}{2(1)}[/tex]
[tex]\hookrightarrow \sf \frac{18}{2}[/tex]
[tex]\hookrightarrow \sf 9[/tex] s
It takes 9 s for Jason to reach his minimum height.
B)
if taken 9 s then put it in x and find the height reached
[tex]\sf \hookrightarrow \sf h(9) = 9^2 - 18(9)[/tex]
[tex]\sf \hookrightarrow h(9) = 81 - 162[/tex]
[tex]\hookrightarrow \sf h(9) = -81[/tex]
The lowest point is - 81 feet, as it says lowest.
C)
solve for when the height, y is 0
[tex]\hookrightarrow \sf 0 = x^2 -18x[/tex]
[tex]\hookrightarrow \sf 0 = x(x -18)[/tex]
[tex]\hookrightarrow \sf x = 0, \ x -18 = 0[/tex]
[tex]\hookrightarrow \sf x = 0, \ x = 18[/tex]
[tex]\hookrightarrow \sf\ x = 18[/tex]
Jason returned to the top of the bungee jump at 18 s.
Which type of graph would you use to show the percentage of students who have blond, brown, black, or red hair?
Answer: Pie chart!
Step-by-step explanation: It is pefect for seperating things or people into sections that show how much % it takes of the whole. You would be able to have a section of each hair color in a pie chart. hope it helps! ^w^
Are my answers correct??
Math class, last chance to take it!
Answer:
[tex]\sf x=-4[/tex] [tex]\sf \ and[/tex] [tex]\sf y=45[/tex]
Step-by-step explanation:
given:
[tex]\sf{-\frac{1}{2} x+\frac{1}{5} y=11}[/tex]
[tex]\sf{3 x+\frac{1}{4} y=-\frac{3}{4} }[/tex]
make x subject:
[tex]\sf{-\frac{1}{2} x+\frac{1}{5} y=11}[/tex]
[tex]\sf{-\frac{1}{2} x =11-\frac{1}{5}y}[/tex]
[tex]\sf{- x =22-\frac{2}{5}y}[/tex]
[tex]x =-22+\frac{2}{5}y}[/tex]
solve using substitution method:
[tex]\sf{3 x+\frac{1}{4} y=-\frac{3}{4} }[/tex]
[tex]\sf{3 (-22+\frac{2}{5}y) +\frac{1}{4} y=-\frac{3}{4} }[/tex]
[tex]\sf-66 +\frac{6}{5} y+\frac{1}{4} y = -\frac{3}{4}[/tex]
[tex]\sf 1.45y = 65.25[/tex]
[tex]\sf y=45[/tex]
then x will be:
[tex]x =-22+\frac{2}{5}y}[/tex]
[tex]x =-22+\frac{2}{5}(45)}[/tex]
[tex]\sf x=-4[/tex]
