Probability of an event is the measure of its chance of occurrence. The probability that the family has 0,1 or 2 girls is 0.7504
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
What is the addition rule of probability for two events?For two events A and B, we have:
Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.
This can be written symbolically as:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
For three events, A, B and C:
[tex]P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A\cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)[/tex]
For the given case,
If the random variable X is such that:
X = number of girls born to a family which has two children.
Then, we can model this situation by Binomial distribution, where Bernoulli experiment is birth of child which either results in being girl(call it success), or boy( call it failure) (in this case, we assume that only two gender exist).
Since total there are 2 children, so n = 2
In that specified family, success in Bernoulli experiment = birth of girl, so probability of success = P(birth of girl) = 0.48 = p
and, failure in Bernoulli experiment = birth of boy, thus, probability of failure = P(birth of boy) = 0.52 = q = 1-p
Thus, X pertains binomial distribution (as it is count of successes), as:
[tex]X \sim B(n = 2,p = 0.48)[/tex]
Evaluating the needed probabilities:
Probability that the specified family gets 0 girl child = P(X = 0)Using the probability function for binomial distribution, we get:
[tex]P(X = 0) = \: ^2C_0(0.48)^0(0.52)^2 = 0.2704\\[/tex]
Probability that the specified family gets 1 girl child = P(X = 0)Using the probability function for binomial distribution, we get:
[tex]P(X = 0) = \: ^2C_1(0.48)^1(0.52)^1 = 0.2496\\[/tex]
Probability that the specified family gets 2 girl child = P(X = 0)Using the probability function for binomial distribution, we get:
[tex]P(X = 0) = \: ^2C_2(0.48)^2(0.52)^0 = 0.2304\\[/tex]
If we take three events as:
A = the specified family gets 0 girl child B = the specified family gets 1 girl child C = the specified family gets 2 girl childThen, their simultaneous occurrence isn't possible, so the probability of their intersection isn't possible.
The probability of event of getting 0, 1 or 2 girl child in that family is written as: [tex]P(A \cup B\cup C)[/tex]. Using the addition rule, and knowing that their intersection is having 0 chances, thus,
[tex]P(A \cup B \cup C) = P(A) + P(B) + P(C) =[/tex] [tex]0.2704 + 0.2496 + 0.2304 = 0.7504[/tex]
Thus, he probability that the family has 0,1 or 2 girls is 0.7504
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(x^5-y^5) divided (x-y)
See in the picture I have done till here but can anyone tell me next step
Answer:
[tex]\frac{x^6-yx-y^5}{x}[/tex]
Step-by-step explanation:
x^5-y^5 divided x-y
[tex]\frac{(x^5-y)x}{x} -\frac{y^5}{x}[/tex]
[tex]\frac{(x^5-y)x-y^5}{x}[/tex]
=> [tex]\frac{x^6-yx-y^5}{x}[/tex]
The output associated with an input of zero is known as the
Answer:
IO
Step-by-step explanation:
9514 1404 393
Answer:
y-intercept
Step-by-step explanation:
If the function is graphed as ...
y = f(x)
then y = f(0) is the y-intercept.
_____
Additional comment
Depending on the way the graph is created and labeled, any points or curve on the graph may cross the vertical axis at a point other than one that corresponds to an input of 0. In any event, it may not be called "y". It may be "sales" or "board feet" or "monkeys per acre". Then the name of the point may not be "y-intercept", but may be something else.
How much is 2 yd and 5 yd
Answer:
7 yards
Step-by-step explanation:
Answer:
7yd
ep-by-step explanat
Plz help me well mark brainliest if correct!
Answer:
The answer is B.
Step-by-step explanation:
The formula is Area = L x H
And remember perimiter is adding the legnth of all sides.
For A:
12 × 3 = 36
12 + 12 + 3 + 3 = 30
For B:
4 × 8 = 32
4 + 4 + 8 + 8 = 24
For C:
6 × 6 = 36
6 + 6 + 6 + 6 = 24
Hence, the answer is B, since B is the only one which meets the criteria.
hey guys in the middle of my final! help? 30 points going to mark the brainiest too!
Answer: 148
Step-by-step explanation: All the angles are the same and if you take 180-32 you get 148 and that is the answer.
-Helper
The diagram shows a cylindrical tank.
The radius is 30 cm and the height is 80 cm.
(a) Calculate the area of the base of the tank.
(b) Calculate the volume of the tank in litres.
Step-by-step explanation:
a) A=π302=900π CM2 =2,827 CM 2
b) V=Ah=900=72000 π cm 3 = 226,195 cm3
What is the measure of m?
28
m
7
m
V[?]
Answer:
y geometric mean property,n² = 28 × 7 = 196n = 14.By pythagorean
Step-by-step explanation:
y geometric mean property,n² = 28 × 7 = 196n = 14.By pythagorean
2. The ordered pairs represent the ages of school
employees and the distance they drive to work
Which relation is a function?
A. {(26, 10), (31,9), (31, 12), (44, 18)}
B. {(29, 15), (29, 18), (33, 15), (33, 18)}
C. {(27, 11), (29,7), (34, 8), (34, 27)}
D. {(27, 11). (29, 11), (31, 11), (33, 11)}
(a)
Using a calculator, or otherwise, determine the value of:
(i) 5.25 - 0.015
Answer:
5.235
Step-by-step explanation:
Just use a calculator
Else
5.250
-0.015
______
5.235
Add 0 to make it equal. Carry 1 from 5 of 5.2'5'0 to 0 and make it 10. 10g5 is 5. Then 4 remains .4-1 is 3. Others are normally subtracted.
i give brainliest help
Answer:
B,F
i think
Step-by-step explanation:
Have a nice day
Karen finished watching a movie at 1:10 pm. The movie lasted 1 hour and 38 minutes. What is the time that karen started watching the movie
Answer:
11:32:00 AM
Step-by-step explanation:
Using elimination, what is the solution to the following system?
x+6y=32
-x-3y=-17
Answer:
x=2, y=5. (2, 5).
Step-by-step explanation:
x+6y=32
-x-3y=-17
---------------
3y=15
y=15/3
y=5
x+6(5)=32
x+30=32
x=32-30
x=2
We have considered a regression equation to predict life expectancy from percent of government expenditure on health care, using data for a sample of 50 countries in SampCountries. Using technology and this dataset, find a 95% prediction interval for each of the following situations.
(a) A country which puts only 3% of its expenditure into health care. Round your answers to one decimal place.
(b) A country which puts 10% of its expenditure into health care. Round your answers to two decimal places.
(c) A country which puts 50% of its expenditure into health care. Round your answers to two decimal places.
Country Health LifeExpectancy
Iceland 15.76 83.1
Kazakhstan 10.90 70.5
Lesotho 14.48 49.3
Uzbekistan 9.68 68.2
Peru 14.75 74.8
Iraq 5.99 69.5
Nicaragua 20.89 74.8
Zambia 12.57 58.1
Guinea-Bissau 7.79 54.3
Romania 12.17 74.5
United States 20.71 78.8
Sierra Leone 11.41 45.6
Malta 13.29 80.7
Luxembourg 13.64 81.8
Micronesia, Fed. Sts17.70 69.0
South Africa 14.02 56.7
Panama 12.79 77.6
Turkey 10.74 75.2
Nigeria 17.97 52.5
Hungary 10.23 75.3
Albania 9.85 77.5
Brunei Darussalam 7.42 78.6
Portugal 12.90 80.4
Comoros 7.55 60.9
Pakistan 4.73 66.6
Ethiopia 16.43 63.6
Belize 11.90 73.9
Sweden 14.98 81.7
Bulgaria 11.67 74.5
Botswana 8.75 47.4
Greece 11.66 80.6
Belarus 13.45 72.5
United Kingdom 16.18 81.0
Tunisia 13.33 73.6
Thailand 17.01 74.4
Croatia 12.67 77.1
Colombia 16.05 74.0
Samoa 17.00 73.3
Cuba 13.40 79.2
Guyana 13.87 66.2
South Sudan 4.00 55.2
Cote d'Ivoire 8.51 50.8
Burkina Faso 13.52 56.3
Malaysia 5.88 75.0
Australia 17.75 82.2
Indonesia 6.63 70.8
Kenya 5.85 61.7
Ireland 14.07 81.0
Grenada 9.56 72.7
Korea, Rep. 11.50 81.5
Answer:
(a) A country which puts only 3% of its expenditure into health care. = (41.8,85.2)
(b) A country which puts 10% of its expenditure into health care= (47.92,89.29)
(c) A country which puts 50% of its expenditure into health care= (63.33,132.17)
Explanation:
Country Health Life expectancy
1 Iceland 15.76 83.1
2 Kazakhastan 40.90 70.5
3 Lesotho 14.48 49.3
4 Uzbekistan 9.68 68.2
5 Peru 14.75 74.8
6 Iraq 5.99 69.5
mb=1m (life expectancy - Health, data=d1)
new data1 = data. frame (Health = 3)
new data2 = data. frame (Health = 10)
new data3= data. frame (Health = 50)
Predict (mb,newdata1, interval= "prediction)
fit owr upr
1 63.506 41.7298 85.2192
>Predict (mb,newdata2, interval = "prediction)\
fit owr upr
1 68.6062 47.9192 89.29321
>Predict (mb,newdata3, interval = "prediction)
fit owr upr
1 97.750 63.3292 132.1713
(a) A country which puts only 3% of its expenditure into health care. = (41.8,85.2)
(b) A country which puts 10% of its expenditure into health care= (47.92,89.29)
(c) A country which puts 50% of its expenditure into health care= (63.33,132.17)
Find the probability that the next student will select hamburger for lunch. You
must write your answer as a fraction.
Answer=3/10
Step wise =
Total number of student=40
student who eat Hamburger=12
now,
Probability of eating hamburger student = 12/40
=3/10
Let A and B be two disjoint events such that P(A) = .30 and P(B) = .60. What is P(A and B)? 0.18 0.72 0.90 0 none of the above
Answer:
0
Step-by-step explanation:
If two events are disjoing (aka mutually exclusive) that means that there is 0 overlap or the intersection equals 0
So the probability of A and B occuring is 0 (because P(A∩B)= 0)
Helpppppp pleaseeeeee !!!!!!!!! !!!!
Given:
The function is:
[tex]f(x)=6x-3[/tex]
To find:
The inverse of the given function, then draw the graphs of function and its inverse.
Solution:
We have,
[tex]f(x)=6x-3[/tex]
Step 1: Substitute [tex]f(x)=y[/tex].
[tex]y=6x-3[/tex]
Step 2: Interchange x and y.
[tex]x=6y-3[/tex]
Step 3: Isolate variable y.
[tex]x+3=6y[/tex]
[tex]\dfrac{x+3}{6}=y[/tex]
Step 4: Substitute [tex]y=g(x)[/tex].
[tex]\dfrac{x+3}{6}=g(x)[/tex]
Therefore, the inverse of the given function is [tex]g(x)=\dfrac{x+3}{6}[/tex] and the graphs of these functions are shown below.
find the area of the figure
area: units2
Find the measure of the angle, round to the nearest tenth: Sin X = .7547
Please help me solve this question
angle D = 92°
Step-by-step explanation:
Since the two figures are congruent.
angle D = angle K
20x + 12 = 25x - 8
5x = 20
x = 4
Substituting this value into angle D, we see that
angle D = 20x + 12
= 20(4) + 12
= 92°
PLEASE HELP ME FAST PLEASE HELP ME
The median for group 2 is "Less Or Greater"
Group 1 will likely "decrease or increase"
Group 2 and likely "Decrease or increase"
Fitzpatrick is "Correct or Incorrect"
Questions for 2nd Picture
PLEASE HELP ME FAST
HELP ME FAST I NEED HELP PLEASE
Answer:
The median for group 2 is greater.
Group 1 will likely decrease.
Group 2 and likely increase.
Fitzpatrick is correct.
About half of the haircuts cost less than $50.
Which of the following statements is true?
O 0.6 < 0.61 < 0.7
O 0.61 < 0.6 < 0.7
O 0.7 < 0.61 < 0.6
O 0.7 < 0.6 < 0.61
Answer: 0.06<0.61<0.7
Step-by-step explanation:
The numbers is 0.6< 0.61 <0.7.
It is required to find among the statements is true.
What is integer?An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Given that:
0.7 is largest number among the given integer.
0.61 is 2nd largest number among the given integer.
0.6 is lowest number among the given integer.
∴0.6< 0.61 <0.7.
So, the numbers is 0.6< 0.61 <0.7.
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Which statement is most likely to be true for this distribution?
1
A. The mean is less than the median.
B. The mean is greater than the median.
O C. The mean is the same as the median.
Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .
I need the answer step by step
Answer:
The family of all prime numbers such that [tex]a^{2} + b^{2} + c^{2} -1[/tex] is a perfect square is represented by the following solution:
[tex]a[/tex] is an arbitrary prime number. (1)
[tex]b = \sqrt{1 + 2\cdot a \cdot c}[/tex] (2)
[tex]c[/tex] is another arbitrary prime number. (3)
Step-by-step explanation:
From Algebra we know that a second order polynomial is a perfect square if and only if [tex](x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}[/tex]. From statement, we must fulfill the following identity:
[tex]a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}[/tex]
By Associative and Commutative properties, we can reorganize the expression as follows:
[tex]a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}[/tex] (1)
Then, we have the following system of equations:
[tex]x = a[/tex] (2)
[tex](b^{2}-1) = 2\cdot x\cdot y[/tex] (3)
[tex]y = c[/tex] (4)
By (2) and (4) in (3), we have the following expression:
[tex](b^{2} - 1) = 2\cdot a \cdot c[/tex]
[tex]b^{2} = 1 + 2\cdot a \cdot c[/tex]
[tex]b = \sqrt{1 + 2\cdot a\cdot c}[/tex]
From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, [tex]a, b, c > 1[/tex]. If [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] are prime numbers, then [tex]2\cdot a\cdot c[/tex] must be an even composite number, which means that [tex]a[/tex] and [tex]c[/tex] can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.
In addition, [tex]b[/tex] must be a natural number, which means that:
[tex]1 + 2\cdot a\cdot c \ge 4[/tex]
[tex]2\cdot a \cdot c \ge 3[/tex]
[tex]a\cdot c \ge \frac{3}{2}[/tex]
But the lowest possible product made by two prime numbers is [tex]2^{2} = 4[/tex]. Hence, [tex]a\cdot c \ge 4[/tex].
The family of all prime numbers such that [tex]a^{2} + b^{2} + c^{2} -1[/tex] is a perfect square is represented by the following solution:
[tex]a[/tex] is an arbitrary prime number. (1)
[tex]b = \sqrt{1 + 2\cdot a \cdot c}[/tex] (2)
[tex]c[/tex] is another arbitrary prime number. (3)
Example: [tex]a = 2[/tex], [tex]c = 2[/tex]
[tex]b = \sqrt{1 + 2\cdot (2)\cdot (2)}[/tex]
[tex]b = 3[/tex]
What is the volume of a regular triangular pyramid with an apothem of 2.3ft, a side length of 8ft and a height of 25 feet
230FT
Regular tetrahedron
Solve for volume
V≈1.15×107
Use the formula for the volume of a triangular pyramid: V=13Ah , where A = area of the triangular base, and H = height of the pyramid.
how much must be added to 750 metres to make 2 km
Answer:
1250 meters because 2 km is 2000 meters
2000 - 750
= 1250
Answer:
you need to add 1250 to 750 in order to make 2 km
Step-by-step explanation:
We know that:
1 KM = 1000 meters
and out of those 1000, we already have 750, therefore:
1000-750 = 250
Which completes 1 km now, since there are 2 km, add 1000 to 250:
1000+250 = 1250
So you need to add 1250 meters to make 2 km
Hope this helps!
Gretchen is refinishing her gazebo that is in the shape of a regular octagon. The length of one side is 3 feet and the apothem is 3.5 feet. What is the area that Gretchen will be refinishing? Need help fast
The area that Gretchen will be refinishing is 42 square feet.
What is a polygon?A polygon is a closed more than two-sided and can be made up of a finite number of straight line segments and is a type of planar figure in geometry.
Each line of the polygonal circuit's segments is referred to as its edges or sides.
An octagon has 8 sides.
We know, Apothm is the distance from the center to its side.
We also know that an octagon can be divided into 8 similar triangles.
Therefore, The area of the octagon will be,
= 8×(1/2)×3×3.5 square feet.
= 4×10.5 square feet.
= 42 square feet.
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What’s the answer ?
Answer:
c
Step-by-step explanation:
I cannot see the whole picture. some numbers are cut off.
but just by making the calculating for the top-left corner we can see the only possible right answer.
so, top-left corner of A = 4 and of B = 7.
therefore, the top-left corner of the result matrix is then according to -2×A + 7×B
-2×4 + 7×7 = -8 + 49 = 41
the only solution option with 41 in the top-left corner is c.
Offering brainliest if answered with explanation
Answer:
Step-by-step explanation:
we know that the 3 sides add up to the perimeter of 18cm. We can use this to find the length of the 3rd side, CA.
AB + BC + CA = 18
7 + 3 + CA = 18
10 + CA = 18
CA = 8
The pythagorean theorem states that in a right triangle a2 + b2 = c2, where c is the length of the hypotenuse (the longest side opposite to the right angle) and a and b are the lengths of the other two sides.
In this problem we can replace a with 7, the length of AB, b with 3, the length of BC, and c with 8, the length of CA.
a2 + b2 = c2
72 + 32 = 82
49 + 9 = 64
58 = 64
Since the equation is not true, we can deduce that ABC is NOT a right triangle start, we know that the 3 sides add up to the perimeter of 18cm. We can use this to find the length of the 3rd side, CA.
AB + BC + CA = 18
7 + 3 + CA = 18
10 + CA = 18
CA = 8
The pythagorean theorem states that in a right triangle a2 + b2 = c2, where c is the length of the hypotenuse (the longest side opposite to the right angle) and a and b are the lengths of the other two sides.
In this problem we can replace a with 7, the length of AB, b with 3, the length of BC, and c with 8, the length of CA.
a2 + b2 = c2
72 + 32 = 82
49 + 9 = 64
58 = 64
Since the equation is not true, we can deduce that ABC is NOT a right triangle start, we know that the 3 sides add up to the perimeter of 18cm. We can use this to find the length of the 3rd side, CA.
AB + BC + CA = 18
7 + 3 + CA = 18
10 + CA = 18
CA = 8
The pythagorean theorem states that in a right triangle a2 + b2 = c2, where c is the length of the hypotenuse (the longest side opposite to the right angle) and a and b are the lengths of the other two sides.
In this problem we can replace a with 7, the length of AB, b with 3, the length of BC, and c with 8, the length of CA.
a2 + b2 = c2
72 + 32 = 82
49 + 9 = 64
58 = 64
Since the equation is not true, we can deduce that ABC is NOT a right triangle
Answer:
ABC is not a right triangle.
Step-by-step explanation:
The perimeter of a triangle is the sum of all its sides(easier to see if you draw it):
P = AB + BC + AC
We can substitute the values we have:
18 = 7 + 3 + AC
18 = 10 + AC
AC = 8
In a right triangle, the hypotenuse is always the largest side and is equal to the square root of the squares of the legs by the pythagorean theorem(a^2 + b^2 = c^2). Our largest side is 8, so we would set that as equal to the hypotenuse:
8^2 = 7^2 + 3^2
64 = 49 + 9
64 = 58
64 is not equal to 58, so triangle ABC is not a right triangle.
lent receives per day?
A patient is receiving a normal saline solution, infusing continuously at 80 ml/hr IV, and a tube feeding formula,
Glucerna, infusing continuously at 50 ml/hr. What is the total amount of fluids infused per day?
Answer:
The total amount of fluids infused per day is 3,120 ml.
Step-by-step explanation:
Given that a patient is receiving a normal saline solution, infusing continuously at 80 ml / hr, and a tube feeding formula, Glucerna, infusing continuously at 50 ml / hr, to determine what is the total amount of fluids infused per day the following calculation must be done:
(80 x 24) + (50 x 24) = X
1,920 + 1,200 = X
3.120 = X
Therefore, the total amount of fluids infused per day is 3,120 ml.
there are 32 students at a pizza party. each students ate 1/4 pizza how many whole pizzas did the students eat altogether?
Answer:
8
Step-by-step explanation: