Answer:
0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.
Step-by-step explanation:
The buckets are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses 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 sucesses.
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:
8 covered buckets, so N = 8.
4 buckets are selected, so n = 4.
2 contain a ball, which means that k = 2.
Find the probability that a contestant wins the game if he/she gets to select 4 of the buckets.
This is P(X = 2). So
[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 = 2) = h(2,8,4,2) = \frac{C_{2,2}*C_{6,2}}{C_{8,2}} = 0.2143[/tex]
0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.
Use mathematical induction to prove the following statement:
The sum of the first n even positive integers is (n2 + n). That is, 2 4 6 8 .... 2n
Answer:
Step-by-step explanation:
To prove that the sum of the first n even +ve integers is:
[tex]\mathsf{2+4+6+8+ . . . +2n = n^2+ n }[/tex]
By using mathematical induction;
For n = 1, we get:
2n = 2 × 1 = 2
2 = 1² + 1 ----- (1)
∴ the outcome is true if n = 1
However, let assume that the result is also true for n = k
Now, [tex]\mathsf{2+4+6+8+. . .+2k = k^2 + k --- (2)}[/tex]
[tex]\mathsf{2+4+6+8+. . .+2k+2(k+1)}[/tex]
we can now say:
[tex]\mathsf{= (k^2 + k) + 2(k + 1)} \\ \\ \mathsf{= k^2 + k + 2k + 1}[/tex]
[tex]\mathsf{= (k^2 + 2k + 1) + (k + 1)}[/tex]
[tex]\mathsf{= (k + 1)^2 + (k + 1)}[/tex]
∴
[tex]\mathsf{2 + 4 + 6 + 8 + . . . + 2k + 2(k + 1) = (k + 1)^2 + (k + 1)}[/tex]
Thus, the result is true for n = m+1, hence we can posit that the result is also true for each value of n.
As such [tex]\mathsf{2+4+6+8+. . .+2n = n^2 + n }[/tex]
Find the volume of the prism.
The volume of the prism is (B) 864 mm3
Csikszentmihalyi & Figurski (1982) conducted a study to determine the degree to which people find out about themselves through the process of introspection (thinking about themselves). They gave people beepers and asked them to write down what they were thinking about when the beepers went off randomly throughout the day. The results indicated that:
Answer:
We think about ourselves way less than we think 8% of the time.
Step-by-step explanation:
In a self-awareness: introspection research study conducted by Mihaly Csikszentmihalyi and Thomas Figurski in 1982, to determine the degree to which people find out about themselves through the process of introspection (thinking about themselves).
The research involved an arrangement where participants were given beepers and asked to write down what they were thinking about when the beepers went off randomly throughout the day. The results indicated that "We think about ourselves way less than we think 8% of the time."
21.5 sq. Cm
43 sq. Cm
100 sq. Cm
68.6 sq. Cm
[tex] \large \boxed{ \boxed{ \mathrm{21.5 \: \: cm {}^{2}} }}[/tex]
Solution :By Observing the Above figure, we can conclude that the area of shaded region is equal to the Area of Square minus the sum areas of two equal semicircles (since their diameters are equal)
let's solve for area of square :
[tex]\longrightarrow \: \mathrm{side {}^{2} }[/tex]
[tex]\longrightarrow10 {}^{2} [/tex]
[tex]\longrightarrow \mathrm{100 \: cm {}^{2} }[/tex]
Now,
Radius of the both semicircles measure :
[tex]\longrightarrow \dfrac{10}{2} [/tex]
[tex]\longrightarrow5 \: cm[/tex]
now, let's solve for their area
[tex] \longmapsto 2 \times \dfrac{\pi {r}^{2} }{2} [/tex]
(Since, there are two semicircles)
[tex]\longrightarrow3.14 \times 5 \times 5[/tex]
[tex]\longrightarrow78.5 \: cm {}^{2} [/tex]
Area of Shaded region = Area of Square - Area of Semicircles, that is
[tex]\longrightarrow100 - 78.5[/tex]
[tex]\longrightarrow \mathrm{21.5 \: cm {}^{2} }[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{hope \: it \: helps \: you \: }}{\orange{.....}}}}}[/tex]
6!3! divided by 2!5!
Simplify the answer as much as possible.
Answer:
3/20
Step-by-step explanation:
Set up the quotient:
6!3!
------
2!5!
6! is equivalent to 6*5!, and so we have:
6*5!3! 6*5!3! 6*3*2*1 6
------------ which reduces to ------------- or ------------------- or ------------
2!5! 2!5! 2*5*4*3*2*1 (2)*5*4
3
This final result simplifies further to ---------------
20
Which set of values could be the side lengths of a 30-60-90 triangle? A. {5, 10, 10-2} B. {5,5,12,10) O C. {5,5,5, 10) D. {5, 10, 10.5)
Answer:
The hypotenuse is twice the length of the shortest side so;
A could be the answer as when 5 is shortest and 10 is hypotenuse we get 5√3 for the other side which = 8.6
It cannot be B, C or D as the numbers cannot be 2 values same as hypotenuse (the longer length) as 5 + 5 = 10 and we cant use 4 lengths in one triangle and either of 3 out of 4 values do not show ratio of lowest side any value middle value = LV +√3 and hyp LV(2)
so A is the answer.
Step-by-step explanation:
Mona wants to buy carpet for a floor in her house.
The floor is rectangular with a width of 8 m and a length of 9 m.
Two shops sell carpet with the prices shown below.
How much will Mona save by going to Carpet World ?
There are 90 girls in fourth form 25 of whom study biology what percentage of fourth form girl study biology?
11-11×11+11 =?????
Answer:
-99
Step-by-step explanation:
Answer:
- 99
Step-by-step explanation:
11 - 11 × 11 + 11
➛ 0 × 11 + 11
➛ - 110 + 11
➛ - 99
50 POINTS! SHOW WORK OR ILL REPORT! Multiplying mixed numbers
Answer:
15/2 = 7 1/2
Step-by-step explanation:
3 1/3 * 2 1/4 =
= (3 * 3 + 1)/3 * (2 * 4 + 1)/4
= 10/3 * 9/4
= 90/12
= 45/6
= 15/2
= 7 1/2
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
See this attachment
Nevaeh is going to drive from her house to City A without stopping. Let DD represent Nevaeh's distance from City A tt hours after leaving her house. The table below has select values showing the linear relationship between tt and D.D. Determine the distance from Nevaeh's house to City A, in miles.
t d
1 195
2 130
2.5 97.5
Answer:
Step-by-step explanation:
Answer:
260
Step-by-step explanation:
What is the probability that out of 125 babies born, at least 70 will be girls?
Assume that boys and girls are equally probable, and round your answer to
the nearest tenth of a percent.
O A. 70.4%
B. 10.5%
C. 51.2%
D. 99.0%
Answer:
Well just looking at the choices can lead you to the answer right away.
Well since the probability of boys and girls are equal, its 50/50. And since 125 in half well about is about 60-62 and the minimum amount of girls has to be 70. It can’t be higher then half and the choices remain to less then half not including 50%. So that eliminates all 3 choices except B.
The probability that out of 125 babies born, at least 70 will be girls is 10.5%. So, option B is correct.
What is meant by probability ?Probability is defined as the chance for an event to occur. The value of probability is expressed from zero to one.
Here,
Let X be the number of girls born among the babies.
Let the number of babies born be n = 125
Let the probability of girls being born be P
Since, boys and girls are equally probable, P = 1/2 = 0.5
The probability that at least 70 girls will be born is P(X ≤ 70)
P(X ≤ 70) = P(70) + P(71) + P(72) + P(73) + P(74) +....P(125)
Applying the binomial probability equation,
P(X) = {n!/[X!(n - X)!} Pˣ (1 -P)ⁿ⁻ˣ
So,
P(70) = {125!/[70!(125-70)!]}x 0.5⁷x (1 - 0.5)⁵⁵
We get P(70) = 0.02913
Using cumulative probability function, we get the probability upto X=125.
By adding all the values, we get,
P(70) = 0.1051
Therefore probability that at least 70 girls are born = 0.1051 x 100 = 10.5%
Hence,
The probability that out of 125 babies born, at least 70 will be girls is 10.5%.
To learn more about probability, click:
https://brainly.com/question/14210034
#SPJ7
Classify the quadrilateral.
Answer:
Trapezoid
Step-by-step explanation:
It has two opposite parallel lines and the other two are not parallel
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
100, 20, 4, ...
Answer:
its a geometric progression. r=1/5 or 0.2
pls help me I been in this question for hr pls help
Question 7 of 21
Which of the following expressions is equivalent to the one shown below?
(-5. 43
A. –158.12
B. (-5)9.4
C.-15.12
D. -8.7
SUBMIT
Answer:
C-15.12. That is the most suitable answer
Find the area of the circle. Round your answer to the nearest tenth.
Answer:
254.47 mm
Step-by-step explanation:
For this graph, mark the statements that are true.
A. The domain is the set of all real numbers greater than or equal to zero.
B. The range is the set of all real numbers.
C. The range is the set of all real numbers greater than or equal to zero.
D. The domain is the set of all real numbers.
Given:
The graph of function.
To find:
The correct statement for the domain and range of the given graph.
Solution:
Domain: The set of input values.
Range: The set of output value.
From the given graph it is clear that the graph represents a polynomial function.
The given graph of a polynomial function is defined for all real values of x. So, the domain is the set of all real numbers.
The graph of the function approaches from negative infinite to positive infinite. So, the output the given graph is set of all real numbers. It means the range is the set of all real numbers.
Therefore, the correct options are B and D.
The true statements are:
B. The range is the set of all real numbers.
D. The domain is the set of all real numbers.
From the figure, we can see that the graph extends in all directions without any end.
This means that, the graph of the function can take any real value as its input, and output
Hence, the domain and the range of the graph are set of all real numbers
Read more about domain and range at:
https://brainly.com/question/10197594
9)
10)
22x - 2
8x + 2
A) 5
B) 6
D 2
C) 8
A 5
C) -10
Answer:
I don't know
Step-by-step explanation:
could you screenshot your question or reword it. I don't know what you're asking. Sorry.
Is w = 8 a solution to the equation 5 + w = 58? Explain
No.
Since w = 8, you must replace the variable with the number associated to it.
So, it would be 5 + 8 = 58
5 + 8 is not equal to 58, it is equal to 13.
If you wanted to find out what w was, simply subtract 5 on both sides.
w = 58 - 5
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 82 m long and 53m wide. What is the length of a training track running around the field? (Use the value 3.14 and do not round your answer. Be sure to include the correct unit in your answer.)
Answer:
436.42 m
Step-by-step explanation:
We are to determine the perimeter of the field
perimeter = perimeter of rectangle + perimeter of the two semicircles
Perimeter of a rectangle = 2 x (length + breadth)
2 x (82 + 53) = 270m
Perimeter of a semicircle = 1/2πD
perimeter of the 2 semicircles = 2 x (1/2 x 3.14 x 53) = 166.42
Perimeter = 270 + 166.42 = 436.42 m
What is the scale factor in the dilation? A.2/5
B.1/2 C.2 D.2 1/2
Answer:
d
Step-by-step explanation:
it is
What can you tell about a triangle when vibe three side lengths
Answer:All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle.
Hope it helps...
A marine biologist wanted to construct a t interval to estimate the mean weight of marine otters using 98% confidence. They took a random sample of n = 8 marine otters to measure their weights. These weights were roughly symmetric with a mean of 2 = 4.5 kg and a standard deviation of sx = 1.1 kg.What critical value t* should they use?
Answer:
CI 98 % = ( 3.332 ; 5.668 )
t(c) = 2.9979
Step-by-step explanation:
Confidence Interval CI 98 % then α = 2 % α = 0,02 α/2 = 0.01
Sample information:
Sample size n = 8
sample mean x = 4.5
standard deviation of sample s = 1.1 kg
degree of freedom df = n - 1 df = 8 - 1 df = 7
With α/2 0.01 and df = 7 from t-studente table we find t(c)
t(c) = 2.9979
CI 98 % = ( x ± t(c) * s/√n )
CI 98 % = ( 4.5 ± 2.9979 * 1.1/ √8 )
CI 98 % = ( 4.5 ± 3.2976/2.8228 )
CI 98 % = ( 4.5 ± 1.168 )
CI 98 % = ( 3.332 ; 5.668 )
Graph (x-4)^2/4 + y^2/9 = 1
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Compare the equation to that of an ellipse with center (h, k) and axes of lengths 2a and 2b.
((x -h)/a)^2 +((y -k)/b)^2 = 1
We see that (h, k) = (4, 0) and a=2, b=3.
This tells us the center of the ellipse is (4, 0), the major axis is parallel to the y-axis, and the minor axis is parallel to the x-axis. The ellipse extends ±2 units from its center in the x-direction and ±3 units from its center in the y-direction.
Answer:
It is graph C on edge.
Step-by-step explanation:
Tell me a some basic terms related bijective.
1:A function of F:R --->is defined by f(x)=x²-1,is f one to one an onto.
Answer:
NoStep-by-step explanation:
The answer is no since f(-x) = f(x)
Example:
f(-1) = 1 - 1 = 0f(1) = 1 - 1 = 0It is not one-to-one, it is two-to-one
A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday’s lunch.
Answer:
20%
Step-by-step explanation:
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need help again thank you
<3
a.
Answer:
240 cm^3
b.
Answer:
208cm^2
Astronomers sometimes use angle measures divided into degrees, minutes, and seconds. One degree is equal to 60 minutes, and one minute is equal to 60 seconds. Suppose that angleJ and angleK are complementary, and that the measure of angleJ is 49 degrees, 28 minutes, 21 seconds. What is the measure of angleK?
The measure of angleK is degrees, minutes, and seconds.
9514 1404 393
Answer:
40° 31' 39"
Step-by-step explanation:
Base-60 arithmetic is just like base-10 arithmetic in that you borrow the value of the base from the next-higher "digit" when you need to subtract a larger number from a smaller number.
90 : 00 : 00 - 49 : 28 : 21 . . . . . we used a colon (:) to separate "digits"
= 89 : 59 : 60 -49 : 28 : 21
= 40 : 31 : 39
The measure of angle K is 40° 31' 39".
10) -2(n - 6) = 20
please help!
Answer:
n = 1
Step-by-step explanation:
Answer:
n = -4
Step-by-step explanation:
Let's solve your equation step-by-step.
−2(n − 6) = 20
Step 1: Simplify both sides of the equation.
−2(n − 6) = 20
(−2)(n) + (−2)(−6) = 20(Distribute)
−2n + 12 = 20
Step 2: Subtract 12 from both sides.
−2n + 12 − 12 = 20 − 12
−2n = 8
Step 3: Divide both sides by -2.
[tex]\frac{-2n}{-2} = \frac{8}{-2}[/tex]
n = -4
Hope this helps, please mark brainliest if possible. Have a great day.