Answer: 54:4
Step-by-step explanation:
Urn 1 contains 4 blue tokens and 9 red tokens; urn 2 contains 12 blue tokens and 5 red tokens. You flip a coin twice and if you see head two times, then you pick urn 2 else (if you see at least once the tail) you pick urn 1 and draw out a token at random from that urn. Given that the token is blue, what is the probability that the token came from urn 2
Answer:
0.433
Step-by-step explanation:
From the given information;
Let represent Urn 1 to be Q₁ ;
Urn 2 to be Q₂
and the event that a blue token is taken should be R
SO,
Given that:
Urn 1 comprises of 4 blue token and 9 red tokens,
Then, the probability of having a blue token | urn 1 picked is:
[tex]P(R|Q_1) = \dfrac{4}{4+9}[/tex]
[tex]= \dfrac{4}{13}[/tex]
Urn 2 comprises of 12 blue token and 5 red tokens;
Thus [tex]P(R| Q_2) = \dfrac{12}{12+5}[/tex]
[tex]=\dfrac{12}{17}[/tex]
SO, if two coins are flipped, the probability of having two heads = [tex]\dfrac{1}{4}[/tex]
(since (H,H) is the only way)
Also, the probability of having at least one single tail = [tex]\dfrac{3}{4}[/tex]
(since (H,T), (T,H), (T,T) are the only possible outcome)
Thus: so far we knew:
[tex]P(Q_2) = \dfrac{1}{4} \\ \\ P(Q_2) = \dfrac{3}{4}[/tex]
We can now apply Naive-Bayes Theorem;
So, the probability P(of the token from Urn 2| the token is blue) = [tex]P(Q_2|R)[/tex]
[tex]P(Q_2|R) = \dfrac{P(R \cap Q_2)}{P(R)} \\ \\ = \dfrac{P(R|Q_2) * P(Q_2)}{P(R|Q_2) \ P(R_2) + P(R|Q_1) \ P(Q_1)} \\ \\ \\ \\ = \dfrac{\dfrac{12}{17} \times \dfrac{1}{4} }{\dfrac{12}{17} \times \dfrac{1}{4} + \dfrac{4}{13} \times \dfrac{3}{4}} \\ \\ \\ = \dfrac{13}{30}[/tex]
= 0.433
A pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.90 bacteria colonies per field. Let r be a random variable that represents the number of bacteria colonies per field. Let O represent the number of observed bacteria colonies per field for throat cultures from healthy adults. A random sample of 100 healthy adults gave the following information:
r 0 1 2 3 4 5 or more
O 11 14 30 17 22 6
The pathologist wants to use a Poisson distribution to represent the probability of r, the number of bacteria colonies per field. The Poisson distribution is given below.
P(r) = e^−λλr / r!
Here λ = 2.90 is the average number of bacteria colonies per field.
Required:
Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more.
Answer:
P(0) = 0.055
P(1) = 0.16
P(2) = 0.231
P(3) = 0.224
P(4) = 0.162
P(5 or more) = 0.168
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Here λ = 2.90 is the average number of bacteria colonies per field.
This means that [tex]\mu = 2.90[/tex]
Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more.
[tex]P(0) = \frac{e^{-2.9}*(2.9)^{0}}{(0)!} = 0.055[/tex]
[tex]P(1) = \frac{e^{-2.9}*(2.9)^{1}}{(1)!} = 0.16[/tex]
[tex]P(2) = \frac{e^{-2.9}*(2.9)^{2}}{(2)!} = 0.231[/tex]
[tex]P(3) = \frac{e^{-2.9}*(2.9)^{3}}{(3)!} = 0.224[/tex]
[tex]P(4) = \frac{e^{-2.9}*(2.9)^{4}}{(4)!} = 0.162[/tex]
5 or more:
This is
[tex]P(X \geq 5) - 1 - P(X < 5)[/tex]
In which:
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.055 + 0.16 + 0.231 + 0.224 + 0.162 = 0.832[/tex]
[tex]P(X \geq 5) - 1 - P(X < 5) = 1 - 0.832 = 0.168[/tex]
So
P(5 or more) = 0.168
Suppose we want to choose 2 colors, without replacement, from the 3 colors red, blue, and green. (a) How many ways can this be done, if the order of the choices is relevant? X (b) How many ways can this be done, if the order of the choices is not relevant?
Number of ways to choose two colors of three colors when order of choice is relevant and relevant are 6 and 3 respectively.
What are permutations and combinations?Permutation refers to placing all members of a set in a particular order or choice of order. Combination is a way of selecting items from a collection, so the order of selection (unlike permutation) does not matter.
Given,
Three colors, red, blue and green
a) Number of ways of choosing 2 colors out of three colors when order matter
= ³p₂
= 3!/(3-2)!
= (3×2×1)
= 6
b) a) Number of ways of choosing 2 colors out of three colors when order does not matter
= ³C₂
= 3!/(3-2)!2!
= (3×2×1)/(2×1)
= 3
Hence, when 6 and 3 are the number of ways to choose 2 colors from three colors when order matter and dose not matter respectively.
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The area of a rectangle is 93.6 square inches. If the length of one of its sides is 5.2 in. what is its perimeter?
the area of a rectangle is the product of its length and width.
A storage tank contains a liquid radioactive element with a half-life of 96 years. It will be relatively safe for the contents to leak from the tank when 0.02% of the
radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?
The tank must remain intact for years.
(Round the base of the exponential function to four decimal places. Then round the final answer to the nearest year as needed.)
Answer:
The tank must remain intact for 1183 years.
Step-by-step explanation:
Exponential equation for decay:
The amount of a substance after t years is given by:
[tex]A(t) = A(0)e^{rt}[/tex]
In which A(0) is the initial amount and r is the decay rate.
A storage tank contains a liquid radioactive element with a half-life of 96 years.
This means that [tex]A(96) = 0.5A(0)[/tex], and we use this to find r.
[tex]A(t) = A(0)e^{rt}[/tex]
[tex]0.5A(0) = A(0)e^{96r}[/tex]
[tex]e^{96r} = 0.5[/tex]
[tex]\ln{e^{96r}} = \ln{0.5}[/tex]
[tex]96r = \ln{0.5}[/tex]
[tex]r = \frac{\ln{0.5}}{96}[/tex]
[tex]r = -0.0072[/tex]
So
[tex]A(t) = A(0)e^{-0.0072t}[/tex]
It will be relatively safe for the contents to leak from the tank when 0.02% of the radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?
This is t for which [tex]A(t) = 0.0002A(0)[/tex]. So
[tex]A(t) = A(0)e^{-0.0072t}[/tex]
[tex]0.0002A(0) = A(0)e^{-0.0072t}[/tex]
[tex]e^{-0.0072t} = 0.0002[/tex]
[tex]\ln{e^{-0.0072t}} = \ln{0.0002}[/tex]
[tex]-0.0072t = \ln{0.0002}[/tex]
[tex]t = -\frac{\ln{0.0002}}{0.0072}[/tex]
[tex]t = 1183[/tex]
The tank must remain intact for 1183 years.
Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of 0.5 ft^3/s. Initially, the balloon has 4 ft^3 of hydrogen. Initially, the balloon has 2 ft^3 of hydrogen.
Required:
a. Find a linear function V that models the volume of hydrogen in the balloon at any time t.
b. If the balloon has a capacity of 15 ft^3, how long does it take to completely fill the balloon?
Answer:
a) The linear function that models the volume of hydrogen in the balloon at any time [tex]t[/tex] is [tex]V(t) = 2 + 0.5\cdot t[/tex].
b) 26 seconds are needed to completely fill the balloon.
Step-by-step explanation:
The statement has a mistake, the correct form is described below:
Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of [tex]0.5\,\frac{ft^{3}}{s}[/tex]. Initially, the balloon has [tex]2\,ft^{3}[/tex] of hydrogen.
a) The volume of weather balloons is increasing linearly in time ([tex]t[/tex]), in seconds, since the rate of change of volume ([tex]\dot V[/tex]), in cubic feet per second, is stable. The linear function of the volume of the weather balloon in terms of time is:
[tex]V(t) = V_{o} + \dot V\cdot t[/tex] (1)
Where:
[tex]V(t)[/tex] - Current volume, in cubic feet.
[tex]V_{o}[/tex] - Initial volume, in cubic feet.
If we know that [tex]V_{o} = 2\,ft^{3}[/tex] and [tex]\dot V = 0.5\,\frac{ft^{3}}{s}[/tex], then the volume as a function of time is:
[tex]V(t) = 2 + 0.5\cdot t[/tex]
b) If we know that [tex]V(t) = 2 + 0.5\cdot t[/tex] and [tex]V(t) = 15\,ft^{3}[/tex], then the time taken to fill the balloon is:
[tex]V(t) = 2 + 0.5\cdot t[/tex]
[tex]V(t) - 2 = 0.5\cdot t[/tex]
[tex]t = \frac{V(t) - 2}{0.5}[/tex]
[tex]t = \frac{15-2}{0.5}[/tex]
[tex]t = 26\,s[/tex]
26 seconds are needed to completely fill the balloon.
What are the solutions of this quadratic equation?
Please help
Answer:
B
Step-by-step explanation:
Use quadratic formula
I rly need help this is a diagnostic test and if I fail it I will be in sooo soo much trouble? Plz help
Answer:
1/3P
Step-by-step explanation:
P/3 is equal to 1/3P
HELP PLZ MATH IM FAILING
Answer:
Hello! In this picture I marked the new dot for that point and reflected it across the x axis!
The original coordinates are: 5, -3
and the new coordinates are: 5, 3
Hope that helps!
What is the y-intercept of y= 2/3x+2
1.(2,3)
2.(3,2)
3.(0,2)
4.(-3,0)
Four customers came into a bakery. The first one said, "give me half of all the donuts you have left, plus half a donut more." The second customer said, "give me half of all the donuts you have left, plus half a donut more." The third customer said, "give me three donuts." The last customer said, "give me half of all the donuts you have left, plus half a donut more." This last transaction emptied the display case of donuts. How many donuts were there to start with?
Step-by-step explanation:
For each of the following variables, identify the type of variable (categorical vs. numerical).
(I) Fuel economy (miles per gallon) of used car
(II) Number of auto insurance claims in a month
1) (I) Categorical , and (II) Categorical
2) (I) Categorical , and (II) Numeric
3) (I) Numeric , and (II) Numeric
4) There is no correct match.
5) (I) Numeric , and (II) Categorical
Answer:
3) (I) Numeric , and (II) Numeric
Step-by-step explanation:
Numeric variable:
The variable assume number values.
Categorical values:
The variable assumes labels. Examples are yes/no, good/bad.
(I) Fuel economy (miles per gallon) of used car
(II) Number of auto insurance claims in a month
Both of these variables are numbers, none have labels, so they are both numeric. The correct answer is given by option 3).
If a conversion rate of 8 dollars is worth 13 euros, how many euros do you get
when you convert 500 dollars?
Find the area of the triangle in the picture.
Answer:
A =16.25 cm^2
Step-by-step explanation:
The area of a triangle is given by 1/2 bh where b is the base and h is the height
A = 1/2 (5) * 6.5
A =16.25 cm^2
Do-Nothing #1 paid $8 for 2 paddle ball
paddles and 4 jigsaw puzzles. Do-Nothing #2
paid $18 for 3 paddle ball paddles and 10
jigsaw puzzles.
a.) How much did each jigsaw puzzle cost?
b.) How much did each paddle ball paddle cost?
If you came for a short answer
A=1.50
B=1
a) Each jigsaw puzzle costs $1.5.
b) Each paddle ball paddle costs $1.
Given that Do-Nothing #1 paid $8 for 2 paddle ball paddles and 4 jigsaw puzzles.
Do-Nothing #2 paid $18 for 3 paddle ball paddles and 10 jigsaw puzzles.
We need to find how much each cost.
Let's solve the problem step by step.
Let's assume the cost of each jigsaw puzzle is 'x' dollars, and the cost of each paddle ball paddle is 'y' dollars.
According to the given information:
The first person paid $8 for 2 paddle ball paddles and 4 jigsaw puzzles. So, we can write the equation as:
2y + 4x = 8............. eq(i)
The second person paid $18 for 3 paddle ball paddles and 10 jigsaw puzzles. So, we can write the equation as:
3y + 10x = 18............. eq(ii)
Now, we can solve these two equations to find the values of 'x' and 'y'.
To do so, we can multiply Equation 1 by 3 and Equation 2 by 2 to eliminate the 'y' term:
6y + 12x = 24............. eq(iii)
6y + 20x = 36............. eq(iv)
Subtracting Equation 3 from Equation 4, we get:
6y + 20x - (6y + 12x) = 36 - 24
6y + 20x - 6y - 12x = 12
8x = 12
x = 12/8
x = 1.5
Now, substitute the value of 'x' back into Equation 1 to find 'y':
2y + 4(1.5) = 8
2y + 6 = 8
2y = 8 - 6
2y = 2
y = 2/2
y = 1
So, the cost of each jigsaw puzzle is $1.5, and the cost of each paddle ball paddle is $1.
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1.
Which of the following is acute angle?
The function, f(x), is plotted below.
On a coordinate plane, a function curves up to (StartFraction pi Over 4 EndFraction, 0), curves down through (0, negative 0.5) to (StartFraction 3 pi Over 4 EndFraction, negative 4) and then curves back up.
What is reasonable estimate for the limit?
Limit of f (x) as x approaches StartFraction pi Over 4 EndFraction f(x) =
Answer:
-2
Step-by-step explanation:
Determining the limit from a graph edge
Answer:
-2
Step-by-step explanation:
click image to see it all:))))
9514 1404 393
Answer:
16 miles
Step-by-step explanation:
The problem can be modeled by a right triangle with one angle of 7° and the side opposite being 10,000 ft. The distance needed is the hypotenuse of the triangle, so the relevant trig relation is ...
Sin = Opposite/Hypotenuse
Hypotenuse = Opposite/Sin
air distance = (10,000 ft)/sin(7°) ≈ 82,055 ft
At 5,280 ft per mile, that is ...
(82,055 ft)/(5,280 ft/mi) ≈ 15.54 mi
The plane's air distance to the airport is about 16 miles.
MATHS
1. Caleulate the area of a rectangle of length
250cm and width 200cm.
2. A square room is 650cm long. Find the area in:
(i) square centimeter (ii) square metres
Answer:
1. 50000
2.
i 274625000cm
ii 274.625m
Step-by-step explanation:
1. Area of a rectangle: length*width
250*200=50000cm
2. Volume of a cube: length^3
i 650^3=274625000cm
ii 650 cm=6.5m; 6.5^3=274.625m
The diameter of a circle is 4 meters. What is the circles circumference
Answer:
12.56m²
Step-by-step explanation:
So the formula for the circumference of a circle is π x diameter, so we just have to plug into our equation (we're using 3.14 as π):
3.14 x 4 = 12.56
So the circumference of your circle is 12.56 meters²
hope this helps:)
The baseball field is 9/10 of a mile from Benson’s house. Benson runs 3/10 of a mile and walks 4/10 of a mile on his way to the field. How much farther does Benson need to go to get to the baseball field?
Answer:
2/10 I believe
Step-by-step explanation:
3/10 + 4/10= 7/10
9/10 - 7/10 = 2/10
The perimeter of a rectangular field is 238 yards. If the length of the field is 65 yards, what is its width?
Answer:
54 is the width
Step-by-step explanation:
65+65=130
238-130=108
108÷2=54
Answer:
The width of the rectangular is 54yards
Step-by-step explanation:
please mark me brainliest
A bag of M&Ms contains 13 blue, 5 brown, 10 orange, 8 yellow, 8 red, and 4
green. Reaching into the bag, a person grabs 5 M&Ms.
What is the probability of getting no browns? Round to 3 decimal places.
Answer:
0.5622 = 56.22% probability of getting no browns.
Step-by-step explanation:
The M&Ms are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
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.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
13 + 5 + 10 + 8 + 8 + 4 = 48 total M&Ms, which means that [tex]N = 48[/tex]
Sample of 5 means that [tex]n = 5[/tex]
5 browns means that [tex]k = 5[/tex]
What is the probability of getting no browns?
This is P(X = 0).
[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(0,48,5,5) = \frac{C_{5,0}*C_{43,5}}{C_{48,5}} = 0.5622[/tex]
0.5622 = 56.22% probability of getting no browns.
Which pair of functions are inverses of each other?
Answer:
D.f(x)=2x-9and g(x)=X+9/2
lus
Find the expected value of a
random variable x having the
following probability distribution.
5
1
0
1
8
Probability
12
16
U22
112
1
2
Well formatted version of question:
Find the expected value of a random variable x having the following probability distribution.
x (-5,-1,0,1,5,8)
Probability (.12, .16, .28, .22, .12, .1)
Answer:
0.86
Step-by-step explanation:
The expected value E(X) is calculated as :
E(X) = Σ(x * p(x))
(-5)(0.12) + (-1)(0.16) + (0)(0.28) + 1(0.22) + 5(0.12) + 8(0.10)
-0.6 + -0.16 + 0 + 0.22 + 0.6 + 0.8
= 0.86
Oak Street and Elm Street run parallel to each other. When Main Street
intersects them, it forms exterior 28, measuring 60°. What is the-
measure of
22?
Answer:
100degrees
Step-by-step explanation:
From the given diagram;
<2 = <6 (corresponding angle)
Since <6 + 80 = 180
<6 = 180 - 80
<6 = 100 degrees
Since <2 = <6, hence <2 = 100degrees
I would appreciate it if someone could help answer this problem:)
Answer:
sum of exterior angles of a polygon=360
Step-by-step explanation:
4x+2x+x+4+x+4x+2=360
12x+6=360
2x+1=60
x=59/2
29.5
Write the log equation as an exponential equation. You do not need to solve for x.
log (x-6) (6) = 3x – 5
Answer:
(x-6)^3x-5 =6
Step-by-step explanation:
logb a=c ------> b^c =a
One number exceeds another by 9. The sum of the numbers is 35. What are the numbers? The numbers are (Use a comma to separate answers.
9514 1404 393
Answer:
13, 22
Step-by-step explanation:
Let s represent the smaller. The sum of the numbers is ...
s + (s+9) = 35
2s = 26 . . . . . . subtract 9
s = 13
s+9 = 22
The two numbers are 13 and 22.
_____
Additional comment
As you can see, the smaller number is half the difference of the sum and difference: s = (35-9)/2. This is the generic solution to a "sum and difference" problem.
Help please! I think I wrote the rectangle right but I do not get the questions!
Step-by-step explanation:
perimeter = 2×(7+5) = 2×12= 24 units
area = 7×5 = 35 sq. units