Using the hypergeometric distribution, it is found that there is a 0.0002 = 0.02% probability that 4 of those containers are the same flavor.
The flavors are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
[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 are 52 containers, hence [tex]N = 52[/tex]For each flavor, there are 4 containers, hence [tex]k = 4[/tex]5 containers are chosen, hence [tex]n = 5[/tex]The probability of choosing all containers of one flavors is P(X = 4).
There are 13 containers, hence, the probability is multiplied by 13.[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 = 4) = h(4,52,5,4) = \frac{C_{4,4}C_{48,1}}{C_{52,5}} = 0.000018469[/tex]
13 x 0.000018469 = 0.0002
0.0002 = 0.02% probability that 4 of those containers are the same flavor.
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The probability that 4 of those containers are the same flavor is 0.02% and this can be determined by using the Hypergeometric distribution.
Given :
Fido ate 52 containers of ice cream in 13 different flavors, with 4 containers containing each flavor. The first 5 containers were chosen at random, without replacement.The probability according to the Hypergeometric distribution is given by:
[tex]\rm P(X=x) = h(x,N,n,k)=\dfrac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex] --- (1)
where the total number of successes is 'x', population size is 'N', the sample size is 'n', and the total number of desired outcomes is 'k'.
Now, substitute the values of known terms in the expression (1).
[tex]\rm P(X=4) = h(4,52,5,4)=\dfrac{C_{4,4}C_{48,1}}{C_{52,5}}[/tex]
[tex]\rm P(X=4) =0.000018469[/tex]
Now, multiply the above result by 13.
[tex]13\times 0.000018469=0.0002[/tex]
So, the probability that 4 of those containers are the same flavor is 0.02%.
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What is the probability of grabbing a blue marble from a bag that contains 4 black, 5 white, 3 red, and
2 blue marbles?
Answer: 1/7
Step-by-step explanation:
You can add 4+5+3+2 to get 14, and 2/14 can be simplified to 1/7
A couch and coffee table cost a total of $1272. The cost of the couch is two times the cost of the coffee table. Find the cost of each item.
Answer:
318+954
Step-by-step explanation:
divide 1272 by 2 to get what they would cost if they were the same amount then divide that by 2 to get 318 times that by 3 to get 954 and add 318 to get 1272
The required cost of the couch and coffee table is $848 and $424 respectively.
Given that,
A couch and coffee table cost a total of $1272. The cost of the couch is two times the cost of the coffee table.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
let the cost of the coffee table be x,
Now the cost of the couch = 2x
According to the question,
2x + x = 1272
x = 424
now,
Cost of the couch = 424 [2] = 848
Thus, the required cost of the couch and coffee table is $848 and $424 respectively.
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Serious help needed what is the domain and range
Answer:
domain: all real numbersrange: -1 ≤ y ≤ 5 or -1 ≤ y < ∞Step-by-step explanation:
The arrows on the ends of the graph mean the graph extends indefinitely left and right. The domain is the horizontal extent of the graph, so it extends from -∞ to +∞, all real numbers.
__
The upward slant of the graph at the ends is ambiguous regarding the vertical extent of the graph. It could mean either of ...
the graph oscillates indefinitely between the values -1 and +5, orthe graph continues upward toward +∞We expect the latter case would be drawn with the ends of the arrows above the peak value shown. However, oscillation tends to involve a certain symmetry, and the graph has no symmetry about the local minimum points. In short the usual clues to the vertical extent are missing. Your guess is as good as mine.
The range could be [-1, 5], or it could be [-1, ∞). We cannot tell from this graph.
_____
Additional comment
The shape of the graph does not seem to match that of a 4th-degree polynomial, so we're not at all certain what sort of function is being plotted here. (A 4th-degree polynomial gets steeper beyond the outside zeros, rather than flatter, as shown here.) A couple of different functions with the approximate characteristics shown are graphed in the attachment.
What is the measure of the angle in the polygon shown below?A.B.C.D.
C.130°
Answer:
Solution given:
no of sides(n)=6
now
total interior angle of polygon having 6 sides is
(n-2)*180=(6-2)*180=4*180=720°
we have
Sum of interior angle of polygon: 720°
130°+100°+130°+130°+100°+?=720°
590°+?=720°
?=720°-590°
?=130°
Please help.
I) Determine the remainder when f(x)= 2x³+bx²+2x+5 is divided by x+1.
If the remainder when f(x) is divided by (x-2) is equal to the remainder in I) calculate the value of b.
Here is the remainder for both. No the remainders are not equal.
determine which graph shows Y is a function of x PLEASE HELP ASAPPP
Answer: The Horizontal line at 5
Step-by-step explanation: For Y to be a function, there cannot be different points on the same x value. The horizontal line is the only one that has one y value per x value.
Hope this helps!
Answer: C
Step-by-step explanation:
Emily makes 75 pins to sell at the school craft fair. She has two designs: a star and
a bumblebee. She makes 2 star pins for every 3 bumblebee pins. How many pins
of each type does Emily make? Show your work.
Answer:
45 bumblebee, 30 star.
Step-by-step explanation:
2:3 = 5
75/5 = 15
15 X 2= 30
15 X 3= 45
Solving quadratic formulas
8y²-30y+27=2
Help! Will give brainliest!
Answer:
The domain of "Per Night Stay" would amount to $125 surcharge by day amounting to $3000 total cost function
Step-by-step explanation:
PLS ANSWER URGENT
1. Larry writes a list of numbers that has average 14, median 21 and mode 11
(a) Moe creates a list by adding 12 to each number in Larry’s list. What is the average, median and mode of Moe’s list?
(b) Curly creates a list by multiplying each number in Larry’s list by 2, what are the average, median and mode of Curly’s list?
Answer:
See step-by-step below!
Step-by-step explanation:
a) Moe's list:
Average=26
Median=33
Mode= 23
b) Curly's list
Average= 28
Median= 42
Mode= 22
Two angles are supplementary. The measure
of one angle is 9º more than twice the measure
of the other angle. What is the measure of the
smaller angle?
Answer:
57°
Step-by-step explanation:
Let's assume the measurement of the second angle is x.
so, following the problem
(2x + 9) + x = 180
2x + x = 3x
=> 3x + 9 = 180
=> 3x = 180 - 9
3x = 171
x = 171/3
x = 57°
57° is the smallest angle
3. Write the equation of the altitude from B for A(-7,-5) B(-5,5), C(2, 1).
Answer:
y -5 = -3/2(x +5)
Step-by-step explanation:
The altitude from B is perpendicular to segment AC. The slope of segment AC is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-5))/(2 -(-7)) = 6/9 = 2/3
The slope of the altitude line will be the opposite reciprocal of this, so is ...
-1/m = -1/(2/3) = -3/2
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -5 = -3/2(x +5) . . . . . line with slope -3/2 through B(-5, 5)
_____
Additional comment
The equation can be put in other forms, as you may wish. Solving for y gives the slope-intercept form.
y = -3/2x -5/2 . . . . . slope-intercept form
3x +2y = -5 . . . . . . . standard form
The graph of a proportional relationship passes through the given point and (1, y). Find y.
Given point: (19, 342)
Answer: 4/3
Step-by-step explanation:
A 7-pound bag of cat food costs $13.93. What is the unit price?
Answer:
$1.99 is the unit price
Step-by-step explanation:
13.93 divided by 7 determines the unit price
Help help help help help math
Answer:
8
Step-by-step explanation:
Give me answer plz !!!
Answer:
c.-2.5 ,because[2.5]=2.5
Step-by-step explanation:
I hop this is fine
Answer:
B part
Step-by-step explanation:
2.5 because |2.5| = 2.5 and it's never negative.
Hope it helps :)
PLEASE ANSWER!!!!!!!!!! I'LL GIVE BRAIN !!!!!!!!!!!!!!!!!!!!!! A _______ is a ratio that compares two things with different units of measurement.
rate
coordinate
cross
unit
Answer:
RATE
Step-by-step explanation:
Answer:
A. Rate
Step-by-step explanation:
A rate is an example of comparing two different units of measure. For example, miles per hour is a rate because it compares miles, which is a unit of distance, to hours, which is a unit of time.
Hope this helps.
G and F are supplementary angles. If F is fifteen less then four times the measure of G find the measure of both angles
Answer:
G=39, F=141
Step-by-step explanation:
Let us set up equations, with G and F as variables.
Since G and F are supplementary, they must add up to 180.
G+F=180
Given the equation, we can set it up too
F = 4 * G - 15
Here, we can solve for this equation by plugging the second equation into the first one with substitution
G+4*G-15=180
simplify and solve
5G=195
G=39
Plug this into the first equation to solve for F:
39+F=180
F=141
We can plug both answers into the second equation to check and find that we are indeed right.
HELP please it’s due in a hour
Answer:
5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.
Step-by-step explanation:
First find the length of the 2 missing sides. Remember that the picture is WAY out of proportion, so the sides won't be what they look like.
Since the left side is 4 and the right side is 8 cm, the missing left side is 4 cm.
Since the top side is 5 and the bottom side is 10 cm, the missing top piece is 5 cm.
So the sides starting at the bottom right and going clockwise are 10, 4, 5, 4, 5, 8 cm. Multiply each of these * 0.5 and call them meters.
5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.
Your class is learning to tie knots. Each student needs a piece of rope that is 3/4 yard long. How many yards of rope are needed for the 20 students in your class?
Answer:
15
Step-by-step explanation:3/4*20=15
An education website has 434,206 daily unique visitors. An e-commerce website gets double the number of visitors. How many visitors does the e-commerce website get? Show Your Work
Answer:
868412
Step-by-step explanation:
434206x2=868412
A triangle has sides with lengths of 4 meters , 5 meters, and 7 meters . Is it a right angle ?
Answer:
No
Step-by-step explanation:
720 inches per second to miles per minute
Answer:
0.681818 miles per min
Step-by-step explanation:
pls answer quickly
which of the following measurement is the smallest?
A) kilogram
B) Gram
C) centigram
D) milligram
Answer:
D, milligram.
Step-by-step explanation:
In latin prefixes, kilo- means 1000, cent- means 1/10, and milli- means 1/1000. This means milli- is the shortest and therefore milligrams are the smallest measurement.
Answer:
Milligram I think
Step-by-step explanation:
I could be wrong however
Find the magnitude of the vector (4,9).
Write your answer in simplified radical form.
Step-by-step explanation:
4^2+9^2=97
Magnitude=sqrt(97)
In simplified radical form, the magnitude of the vector (4, 9) is represented as √97.
How to find the magnitude of a vector?To find the magnitude of a vector (a, b), you can use the formula which is expressed as:
Magnitude = √(a² + b²)
Given the vector (4, 9), let's calculate its magnitude as shown below:
Magnitude = √(4² + 9²)
Magnitude = √(16 + 81)
Magnitude = √97
So, the magnitude of the vector (4, 9) is √97 in simplified radical form.
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HELP PLEASEEEE what is the range of 0,5,10,15,20,25
5
11
20
25
Answer:
25!
Step-by-step explanation:
Subtract the highest and lowest so its 25:)
Answer:
25
Step-by-step explanation:
Range is the largest number minus the lowest
mr John wants to put a fence around his farm. if the length of one side is 25m and the width is the same length what would be the amount of fencing needed?
Answer:
100 meters
Step-by-step explanation:
4 sides
1 side = 25 m
25m = width as well
so just multiply 25 by 4 to get your answer
Mr John needs to focus on outlining the width and length of the farm. Based on the length and width being the same length, the shape of the farm is a square. To make things simple, multiply the length of one side by four and you will have the exact amount needed to place a fence.
25m x 4 = 100m
So, Mr John needs about 100m of fencing to complete the construction of the fence surrounding his farm.
helpppppppppppppppppppppp plzzzzzzzzzzzzzz
Answer: x= -2, y= 3
Step-by-step explanation:
3x+5y=9
X-y=-5
Multiply bottom equation by 5
3x+5y=9
5x-5y=-25
3x + 5x=8x
5y-5y cancels out
9-25= -16
8x= -16
X= -2
Plug -2 back into equation of choice to find y
3(-2)+5y=9
-6+5y=9
Add -6 to both sides
-6+6 cancels
9+6=15
5y=15
Y=3
2+2×4 that is my question i need help
Answer:
10
Step-by-step explanation:
2+(2x4)
2x4=8
2+8=10
Answer:
10
Step-by-step explanation:
so we need to use PEMDAS
2×4=8
8+2=10
What percent of 55 is 44?
The number 44 is 80% of the number 55.
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the numbers are 55 and 44. The percentage will be calculated below,
55 x X% = 44
X% = ( 44 x 100 ) / 55
X% = 80%
Therefore, the number 44 is 80% of the number 55.
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