a shipment of 20 cameras includes 3 that are defective. what is the minimum number of cameras that must be selected if we require that p(at least 1 defective)≥0.8?
Answers
The minimum number of cameras that must be selected to ensure that p(at least 1 defective) ≥ 0.8 is either 0 (if selecting no cameras is allowed) or 1 (if at least one camera must be selected).
We can solve this problem using the complement rule:
p(at least 1 defective) = 1 - p(none defective)
Let X be the number of defective cameras selected. We want to find the minimum value of n (number of cameras selected) such that:
p(X ≥ 1) = 1 - p(X = 0) ≥ 0.8
If none of the cameras are defective, then we select 0 defective cameras out of 20, which can happen in C(20, 0) = 1 way. The probability of this is:
\(p(X = 0) = C(20, 0)\times (3/20)^0 \times (17/20)^{20\) ≈ 0.014
Using the complement rule, we have:
p(X ≥ 1) = 1 - p(X = 0) ≥ 0.8
1 - 0.014 ≥ 0.8
0.986 ≥ 0.8
This is already true, so we don't need to select any cameras. However, if we were required to select at least one camera, then the minimum number of cameras we would need to select would be 1, since selecting one camera and finding it defective would satisfy the requirement of having at least one defective camera.
Therefore, the minimum number of cameras that must be selected to ensure that p(at least 1 defective) ≥ 0.8 is either 0 (if selecting no cameras is allowed) or 1 (if at least one camera must be selected).
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Related Questions
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The sum of three numbers is 56. If the second number is equal to the first diminished by 4, and the third number is 3
times the first. What are the numbers?
If x represents the first number, then which of the following equations could be used to solve the problem?
x = 3x-4
56=4x4
56=3x-4
56-5x4
a
OX
e here to search
Answers
Answer:
56-5x4
Step-by-step explanation:
The reason you want to do it that way is because they will cansle eatch other out
7.3 right triangle and trigonometry homework 
Answers
Sine: the ratio of the length of the side opposite the angle to the length of the hypotenuse
Cosine: the ratio of the length of the adjacent side to the length of the hypotenuse
Tangent: the ratio of the length of the side opposite the angle to the length of the adjacent side
Cosecant: the reciprocal of the sine function
Secant: the reciprocal of the cosine function
Cotangent: the reciprocal of the tangent function
What is Trigonometry ?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Right triangles are particularly important in trigonometry because they have one angle that measures 90 degrees, which allows us to define the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent.
According to the question:
In a right triangle, the side opposite the 90-degree angle is called the hypotenuse, and the other two sides are called the legs. We can use the ratios of the lengths of the sides to define the six trigonometric functions as follows:
Sine: the ratio of the length of the side opposite the angle to the length of the hypotenuse
Cosine: the ratio of the length of the adjacent side to the length of the hypotenuse
Tangent: the ratio of the length of the side opposite the angle to the length of the adjacent side
Cosecant: the reciprocal of the sine function
Secant: the reciprocal of the cosine function
Cotangent: the reciprocal of the tangent function
Trigonometry is used in a wide range of fields, including physics, engineering, and navigation. It allows us to solve problems involving angles and distances, and to model periodic phenomena such as waves and oscillations.
Q: Explain about right angle and trigonometry ?
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Copy and complete the table for the graph
y = -2x - 3.
What values should replace A, B and C?
X
Y
-2 −1
1
A
0 1
B
-5
2
C
Answers
The values of A and B are 1 , 5 from the given equation y=2x+1.
What is linear Equation ?
linear equation can be defined as the equation in which the highest degree is one .
Given Equation ,
y = 2x+1
The values of x are -1,0,1,2,3
The values of y are -1,A,3,B,7.
put x= 0 and y = A in the equation
we get,
A = 2*0 + 1
A =1
put x = 2 and y = B
we get,
B = 2*2 +1
B = 4+1
B = 5
Hence, The values of A and B are 1 , 5 from the given equation y=2x+1.
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Use centered finite difference to solve the boundary-value ordinary differential equation: dาน dx2 +607 – u = 2 with boundary conditions (0) = 10 and u(2)=1 Use discretization h = 0.5 and solve the resulting system of equations using Thomas algorithm. dx =
Answers
The Thomas algorithm is then applied to solve this system. The computed values of u are u(1) = 6.1111 and u(2) = 1, given a step size of h = 0.5 and boundary conditions u(0) = 10 and u(2) = 1.
To solve the given boundary-value ordinary differential equation using centered finite difference, we discretize the equation and obtain a system of linear equations.
Given,
The boundary-value ordinary differential equation is
d²u/dx² + 607 – u = 2,
with boundary conditions u(0) = 10 and u(2) = 1.
Discretization: h = 0.5
To solve the differential equation using centered finite difference,
we use the formula:
(u(i+1)-2u(i)+u(i-1))/h² + 607u(i) = 2
The above formula can be written in the following form as shown below:-u(i-1) + (607h²+2)u(i) - u(i+1) = -2
Discretizing the boundary conditions,
we getu(0) = 10 and u(2) = 1
As we know, the differential equation can be written in the form of
Ax = b, where A is a tri-diagonal matrix.
Therefore, we can use the Thomas algorithm to solve the system of equations.
The Thomas algorithm consists of two steps:
Forward Elimination and Backward Substitution.
Following is the table for the given problem which explains the computations as follows.
Central finite difference for 2nd derivative
d²u/dx²
evaluated at xi=ih
(u(i+1)-2u(i)+u(i-1))/h²
Right-hand side is b
(i)Left-hand side is represented as coefficients c(i), d(i) and e(i) for i=1,2,.....,m.Here, m=3/h.
Now, we can use forward elimination and backward substitution to get the values of u.
Therefore, the value of u can be calculated as given below:-
So, the value of u is,u(1) = 6.1111 and u(2) = 1
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A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 406,000 gallons. Tank cars with three different carrying capacities are available: 7,000 gallons, 14,000 gallons, and 28,000 gallons. How many of each type of tank car should be leased?
Let x1 be the number of cars with a 7,000 gallon capacity, x2 be the number of cars with a 14,000 gallon capacity, and x3 be the number of cars with a 28,000-gallon capacity.
Select the correct choice below and fill in the answer boxes within your choice.
a. The unique solution is x1=___ x2=___ , and x3=___(Simplify your answers.)
b. There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations
x1=___t+ (___), x2=___t+ (___), and 3=t for___? t ?___.
(Simplify your answers. Type integers or simplified fractions.)
c. There is no solution.
Answers
The solution is x1 = 14, x2 = 5, and x3 = 6. Hence, the correct choice is:
a. The unique solution is x1 = 14, x2 = 5, and x3 = 6.
To find the number of each type of tank car that should be leased, we can set up a system of equations based on the given information.
Let x1 be the number of cars with a 7,000-gallon capacity, x2 be the number of cars with a 14,000-gallon capacity, and x3 be the number of cars with a 28,000-gallon capacity.
Based on the carrying capacity information, we can write the following equations:
Equation 1: x1 + x2 + x3 = 25 (Total number of tank cars)
Equation 2: 7,000x1 + 14,000x2 + 28,000x3 = 406,000 (Total carrying capacity in gallons)
To solve this system of equations, we can use substitution or elimination methods.
Using the elimination method, we can multiply Equation 1 by 7,000 to match the units of Equation 2:
7,000(x1 + x2 + x3) = 7,000(25)
7,000x1 + 7,000x2 + 7,000x3 = 175,000
Now we have the following equations:
Equation 3: 7,000x1 + 7,000x2 + 7,000x3 = 175,000
Equation 2: 7,000x1 + 14,000x2 + 28,000x3 = 406,000
Subtracting Equation 3 from Equation 2, we get:
7,000x1 + 14,000x2 + 28,000x3 - (7,000x1 + 7,000x2 + 7,000x3) = 406,000 - 175,000
7,000x2 + 21,000x3 = 231,000
Now we have the following equations:
Equation 4: 7,000x2 + 21,000x3 = 231,000
Equation 1: x1 + x2 + x3 = 25
We now have a system of two equations with two unknowns (x2 and x3). By solving this system, we can find the values of x2 and x3, and then determine x1 using Equation 1.
Solving the system of equations, we find:
x2 = 5
x3 = 6
Substituting these values back into Equation 1:
x1 + 5 + 6 = 25
x1 = 14
Therefore, the solution is x1 = 14, x2 = 5, and x3 = 6.
Hence, the correct choice is:
a. The unique solution is x1 = 14, x2 = 5, and x3 = 6.
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Plss help i dont understand
Answers
Equation: 48=4x-12
Answer: x=15
Kennyhas$893inasavingsaccount.The interest rate is 8 1/5%, compounded annually.
To the nearest cent, how much interest will he earn in 5 years?
Answers
\( \sf \: I = P(1 + \frac{r}{n} {)}^{nt} - P \\ \sf = 893(1 + \frac{41}{500} ) ^{1 \times 5} - 893 \\ \sf= 893 \times ( \frac{541}{500} ) ^{5} - 893 \\ \sf= 1324.30 - 893 \\ \sf = 431.30\)
Answer:
$431.30(approximate value)
Hope you could get an idea from here.
Doubt clarification - use comment section.
The perimeter of the square and the equilateral triangle shown are the same. Write an equation to represent the situation, and solve for x. Then, find the perimeter of each shape. 7 2.5x type your answer... Perimeter: type your answer.... (DECIMAL) (Plug in x, then add all sides) anyone know please I need it done fast
Answers
Answer:
A side of a square is represented by 2.5x-3 and a side of an equilateral triangle is represented by 2x-2.
If the perimeter of the square and the equilateral triangle are the same, then we can set the perimeter of the square equal to the perimeter of the triangle:
4(2.5x-3) = 3(2x-2)
Expanding the equation and combining like terms we get:
10x - 12 = 6x - 6
Subtracting 6x from both sides we get:
4x - 12 = -6
Adding 12 to both sides we get:
4x = 6
Dividing both sides by 4 we get:
x = 3/2
With x = 3/2, we can find the perimeter of the square by plugging it back into the equation for the side of the square:
4(2.5(3/2) - 3) = 4(3.75 - 3) = 4(.75) = 3
And we can find the perimeter of the equilateral triangle by plugging it back into the equation for the side of the triangle:
3(2(3/2) - 2) = 3(3 - 2) = 3(1) = 3
So the perimeter of the square is 3 units and the perimeter of the equilateral triangle is also 3 units.
Which list orders the numbers from least to greatest?
O√13, 2.1, 5.4, √/17, T
OT, 3.2, 6.3, √/17, √20
√23, 2.6, 1.3, √30, π
T, √15, 4.1, 4. 85, √30 savvas
Answers
The list which orders the numbers from least to greatest is π, √15, 4.1, 4. 85, √30.
To find the list which orders the numbers from smallest to largest we need to find the values of the respective numbers,
In the first list, we have the numbers √13, 2.1, 5.4, √/17, π. The value of √13 = 3.6 and the next term is 2.1. As 2.1 < 3.6, the list does not arrange numbers in increasing order.
In the second list, we have the numbers π, 3.2, 6.3, √17, √20. The value of π is 3.14 and the next terms are 3.2 and 6.3 which are more than the former. But the value of √17 is 4.1 which is less than the previous number 6.3.
In the third list,√23, 2.6, 1.3, √30, π the numbers are not arranged in increasing order as √23's value is 4.8 more than the second number.
In the fourth list, π,√15, 4.1, 4. 85, √30 the numbers are arranged in increasing order when calculated. The value of π is 3.1, of √15 is 3.8, then there are 4.1 and 4.85, and at last, is √30 whose value is 5.5.
Hence, π <√15 < 4.1 < 4. 85 <√30 is the list in the increasing order.
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Resuelve los siguientes triángulos rectángulos encontrando todos los datos faltantes
Answers
Respuesta:
A = 51,167
b = 28,5 pies
c = 45,4 pies
Explicación paso a paso:
C = 90 °
B = 38 ° 50 '
Convertir B a grado
1 ° = 60 '
x ° = 50 '
Multiplicar en cruz:
60x = 50
x = 50/60
x = 0,83333 °
Por lo tanto, 38 ° 50 '= 38 ° + 0.833 ° = 38.833 °
Recordar :
A + B + C = 180 ° (Suma de ángulos en un triángulo)
A + 38.833 + 90 = 180
A + 128.833 = 180
A = 180 - 128,833
A = 51,167 °
Usando identidades trigonométricas, podríamos encontrar byc
Para obtener b:
Tan B = opuesto / adyacente = b / 35.4
Tan 38,833 = b / 35,4
b = Tan 38,833 * 35,4
b = 28,5 pies
Para obtener c:
Podríamos usar:
Sin A = opuesto / hipoteno = 35,4 / c
Sin 51,167 = 35,4 / c
c * sin 51,167 = 35,4
c = 35,4 / sen 51,167
c = 45,4 pies
Can anyone help please and thanks
Answers
Answer:
7.02 ft
Step-by-step explanation:
Tan=opposite/adjacent
Tan(78)=x/33X×Tan(78)=334.70x=33do 33 divided by 4.70then you'll get 7.02 if your calculator is on Radian in modeAnswer:
7.02 ft
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your welcome have a good
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Step-by-step explanation:
A sample that does not represent the entire group of interest is called a _____ sample. Group of answer choices biased random bad partial
Answers
A sample that does not represent the entire group of interest is called a biased sample.
A biased sample is a sample that doesn't reflect the real-world population it is supposed to represent. It happens when the sample is chosen in such a way that some members of the population are less likely to be included than others.
Therefore, a biased sample may not be an accurate representation of the entire population.
For example, if a researcher wants to know how many people in a given area have access to the internet and chooses a sample of people from a high-income neighborhood, the results may be biased because people from low-income areas may have lower rates of internet access.
A biased sample can lead to inaccurate conclusions, and therefore, it's important to ensure that the sample is representative of the population. A random sample, on the other hand, ensures that all members of the population have an equal chance of being included in the sample.
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A 4-year project has an annual operating cash flow of $48,500. At the beginning of the project, $3,950 in net working capital was required, which will be recovered at the end of the project. The firm also spent $21,800 on equipment to start the project. This equipment will have a book value of $4,420 at the end of the project, but can be sold for $5,490. The tax rate is 21 percent. What is the Year 4 cash flow?
Answers
Answer: Cash flow = $58,680
Step-by-step explanation: You add $49,500 + 4,050 + 5,550 + .40($4,500 − 5,550)
I need help with this question . Please and thank you .
Answers
Angle A coincides with angle E.
Angle B coincides with angle D.
Segment AC coincides with segment EF.
Segment AB coincides with segment ED.
What is rigid motion?Any geometric transformation of a euclidean space that keeps the euclidean distance between every pair of points is referred to as a rigid transformation.
Rotations, translations, and reflections are some examples of rigid transformations.
If we observe the given preimage and image we can conclude that the triangle is rotated about 90° counterclockwise.
∴ Points, A = E, B = D , C = F from this we can conclude that
Angle A coincides with angle E.
Angle B coincides with angle D.
Segment AC coincides with segment EF.
Segment AB coincides with segment ED.
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using diagonals from a common vertex, how many triangles could be formed from a 21-gon?
Answers
Total 816 triangles that can be formed using diagonals from a common vertex of a 21-gon.
What are Diagonals?In mathematics, a diagonal is a line joining two vertices of a polygon or solid whose vertices do not lie on the same edge. Diagonals are generally defined as oblique lines or slanted lines connecting the vertices of a shape. A diagonal is defined as a horizontal shape with sides/edges and corners.
Solution of the given problem:
Firstly, choose 3 vertices of 21-gon which are not adjacent to each other.
Secondly, connect all three vertices to a common vertex.
Now, there are 18 vertices that are not adjacent to common vertex and there are now 18 diagonals that can be drawn to the common vertex up to these vertices.
To form a triangle using these diagonals, we need to choose 3 of these 18 vertices, this can be calculated using the binomial coefficient formula:
18 choose 3 = 18! / (3! * (18 - 3)!) = (18 * 17 * 16) / (3 * 2 * 1) = 816
Thus, total 816 triangles can be formed.
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I reallly badly need help
Answers
Answer:
You can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°
Step-by-step explanation:
The above is a cyclic quadrilateral.
What is a cyclic quadrilateral?A Cyclic quadrilateral is having all the vertices of a quadrilateral ( four sided figure) inside a circle, that is a quadrilateral inscribed in a circle.
To find either x or y, we should note:
The sum of opposite angles of a cyclic quadrilateral is 180° or Angles in opposite segment are supplementary.
Therefore,
2x + 2x + 4= 180
4x = 180 - 4
4x = 176
x = 44°
To find y
3y + 8 + y = 180°
4y = 180 - 8
4y = 172
y = 43°
Therefore, you can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°
If you want to buy an item in a store that costs $38 and is on sale for 10% off, then how much would the item actually cost you after the discount? Round to the nearest cent.
Answers
Flavia bought a pair of rollerblades. The regular price was 129.50. They were bought for 40% off and the sales tax was 15%. Show all the steps...
Answers
Answer:
Here u go
Step-by-step explanation:
1. 40/100 × 129.50 = 51.80
2. 129.50 - 51.80 = 77.70
3. 15/100 × 77.70 = 11.66
4. 77.70 + 11.66 = 66.04
The final cost of the roller blades is $ 89.66
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost of purchase be = A
Now , the initial cost of roller blades = $ 129.50
The discount percentage of roller blades = 40 %
So , the equation will be
The cost of the roller blades after discount = 129.50 - ( 40/100 ) x 129.50
= 129.50 - 51.8
= $ 77.7
Now ,
The sales tax percentage of roller blades = 15 %
So , the equation will be
The cost of roller blades after sales tax = 77.7 + ( 15/100 ) x 77.7
= 77.7 + 11.655
= $ 89.655
Therefore , the final cost is A = $ 89.66
Hence , The final cost of the roller blades is $ 89.66
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1/2(x-5)=2x+5. What’s the answer
Answers
Answer:
x = -5
Step-by-step explanation:
1/2(x-5)=2x+5
Multiply each side by 2
2(1/2(x-5))=2(2x+5)
x-5 = 4x+10
Subtract x from each side
x-5-x = 4x+10-x
-5 = 3x+10
Subtract 10 from each side
-5-10 = 3x+10-10
-15 =3x
Divide by 3
-15/3 = 3x/3
-5 =x
One seventh of a number is 12.
What is the number?
Answers
Answer:
84
Step-by-step explanation:
12 x 7 = 84
Answer:
84
Step-by-step explanation:
12÷ 1/7=84
For every household in a particular county, the water use in thousands of gallons over the course of a year was recorded. The mean water use for the households in the county was found to be 162 and the standard deviation was 140.a) based on the information given above, could the distribution of household water use for that county be approximately normal? Explain.b) A random sample of 50 households will be selected, and the mean water use will be calculated for the households in the sample. Is the sampling distribution of the sample mean for random samples of size 50 approximately normal? Explain.
Answers
The probability of x' bar to be greater than 59 is equal to 0.1193.
What is Mean value?
Apart from mode and median, mean is the one of the measures of central tendency. When we do the average of given set of values, it is called mean. Here in this question we need to check if the data meets the criterion for a normal distribution. One of these criterion is that data should be symmetric & bell shaped and another one is that mean and median should be approximately equal. By adding the total values given in the datasheet and dividing the sum by total no of values we will get the value of mean.
Here, the mean is = 162 point, the standard deviation = 140 point and x is considered as a variable for household water use in the country
μ=162
σ=140
X:- household water use for country
i.e., approx. Normal
(b) n=50
n>30
i.e., approx. normal
(c) P(X'>59) = 1 - P(X'≤59)
= 1- P((X'-μ)/(σ/√n)≤59-57/(12/√50))
= 1- P(z ≤ 1.178)
= 1-0.8807
P(X'>59)= 0.1193
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Angie Kenny play online video games Angie buys one software package in one month of gameplay Kenny buys two software packages and five months of gameplay each software package is cost $45 if their total cost is $207 what is the cost of one month of gameplay
Answers
Answer:
8 dollars
Step-by-step explanation:
2s+5m+s+m=207
s=45
2(45)+5m+45+m=207
135+6m=207
subtract 135 from both sides
6m = 72
divide both sides by 6
m=8 dollars per month of gameplay
If one angle of a linear pair is acute, then the other angle must be obtuse. Explain why.
Answers
Help me pls
A dance team is going to spend $1,440 to Purchase all sweatshirts or all jackets for the team members. Sweatshirts cost $24 each. Jackets cost $32 each. What is the greatest number of sweatshirts or jackets th team can Purchase?
The team can Purchase ___________ sweatshirts or ___________ jackets.
Answers
Answer:
They can get 60 sweatshirts or 45 jackets
Step-by-step explanation:
1440/24 for sweatshirts and 1440/32 for jackets.
Answer: 60 sweatshirts or 45 jackets
Step-by-step explanation:
Type the correct answer in the box.
Write one trigonometric expression that can be used to find the value of x by replacing the variable a with the correct value.
Answers
Answer:
put 3/5 for (a)
Step-by-step explanation:
The trigonometric expression that represents the value of x is sin⁻¹(3/5), which is equal to 36.87°.
What are trigonometric expressions?Trigonometric expressions are ratios of the sides of a right triangle.
How to solve the question?In the question, we are asked to write the trigonometric expression expressing the value of x.
We know that in the given right triangle,
sin x = 3/5 {∵ sin θ = perpendicular/hypotenuse}
Therefore, we can write x = sin ⁻¹ (3/5).
or, x = 36.87°.
Thus, the trigonometric expression that represents the value of x is sin⁻¹(3/5), which is equal to 36.87°.
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If the product of two integers is 27 x 38 × 52 × 711 and their greatest common divisor is 23 x 34 x 5, what is their least common multiple?
Answers
The least common multiple of the given two integers is 24804834 if the product of two integers is 27 x 38 × 52 × 711 and their greatest common divisor is 23 x 34 x 5.
We can use the formula
LCM(a, b) = (a * b) / GCD(a, b)
where LCM(a, b) is the least common multiple of a and b, and GCD(a, b) is their greatest common divisor.
We are given that the product of the two integers is
27 x 38 x 52 x 711
We can factor this into its prime factors
27 x 38 x 52 x 711 = 3^3 x 2 x 19 x 2^2 x 13 x 3 x 59 x 79
The greatest common divisor of the two integers is
23 x 34 x 5 = 2^2 x 5 x 23 x 17
We can now use the formula to find the least common multiple
LCM = (27 x 38 x 52 x 711) / (23 x 34 x 5)
LCM = (3^3 x 2 x 19 x 2^2 x 13 x 3 x 59 x 79) / (2^2 x 5 x 23 x 17)
Simplifying, we can cancel out the common factors of 2, 5, 23, and 3
LCM = 3^2 x 2 x 19 x 13 x 59 x 79 x 17
LCM = 24804834
Therefore, the least common multiple of the two integers is 24804834.
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What is the value of K roots of a quadratic equation?
Answers
When k is o doesn't satisfy the equation.
What is quadratic equation?We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. The formula (-b(b2-4ac))/(2a) is then used to enter these coefficients. A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0 The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible. To put it another way, if you have an equation with the form a squared by the expression after b plus b squared by the same expression but not squared plus c equal to 0, you have a quadratic equation.Value of \($\mathrm{k}=(?)$\), equation \($\mathrm{kx}(\mathrm{x}-2)+6=0$\) has equal roots.
\(& \Rightarrow \mathrm{kx}(\mathrm{x}-2)+6=0 \\\)
\(& \mathrm{kx} x^2-2 \mathrm{kx}+6=0 \\\)
two roots of quadratic equation
\(& \alpha, \beta= \frac{-\mathrm{b} \pm \sqrt{\mathrm{b}^2-4 \mathrm{ac}}}{2 \mathrm{a}} \\\)
\(& \alpha, \beta= \frac{+2 \mathrm{k} \pm \sqrt{(-2 \mathrm{k})^2-4 \times 6 \times \mathrm{k}}}{2 \times \mathrm{k}} \\\)
\(& \alpha, \beta=2 \mathrm{k} \frac{\pm \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\\)
\(\alpha=\beta \\\) The roots are qual
\(& \Rightarrow \frac{2 \mathrm{k}+\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}}=\frac{2 \mathrm{k}-\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\\)
\(& \Rightarrow 2 \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}=0 \\\)
\(& \Rightarrow 4 \mathrm{k}^2-24 \mathrm{k}=0 \\\)
\(& \Rightarrow 4 \mathrm{k}(\mathrm{k}-6)=0 \\\)
\(& \Rightarrow \mathrm{k}=0 \text { or } \mathrm{k}=6\)
\($\Rightarrow \mathrm{k}=6[\because \mathrm{k} \equiv 0]$\) as\($\mathrm{k}=0$\) doesn't satisfy the equation.
The complete question is,
For what value of \($\mathrm{k}$\), are the roots of the quadratic equation, \($\mathrm{kx}(\mathrm{x}-2)+6=0$\) equal?
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If you roll a six-sided die 12 times, what is the probability that you get all six numbers at least once?.
Answers
The probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.
To calculate the probability of rolling all six numbers at least once when rolling a six-sided die 12 times, we can use the concept of permutations.
The total number of possible outcomes when rolling a six-sided die 12 times is 6^12 since each roll has six possible outcomes. This represents the denominator of our probability calculation.
Now, let's calculate the numerator, which represents the number of favorable outcomes where we get all six numbers at least once. We can use the concept of derangements (or the principle of inclusion-exclusion) to determine this.
A derangement is a permutation in which none of the elements appear in their original position. In our case, we want to find the number of derangements for a set of six elements (the six numbers on the die).
The formula to calculate the number of derangements for a set of n elements is given by n! * (1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!).
Using this formula, we can calculate the number of derangements for six elements:
Number of derangements = 6! * (1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!) = 265
Therefore, the numerator of our probability calculation is 265.
Finally, we can calculate the probability by dividing the numerator by the denominator:
Probability = Number of favorable outcomes / Total number of possible outcomes = 265 / 6^12
Calculating this value:
Probability ≈ 0.0263
So, the probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.
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The sampling distribution of the sample mean will always have the same _________ as the original distribution.
Answers
The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.
What is distribution?
Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.
Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.
Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.
So we need to use the mean of non-normal distribution.
Hence the answer will be the mean of the original non-normal distribution.
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2) Rachel wanted to drink exactly three bottles of water each day, so she bought twenty-six
bottles when they were on sale. How many more bottles will she need to buy on the last
day?
Answers
Answer:
1
Step-by-step explanation:
Twenty-Six is not a multiple of three so you know it won't be 26. Counting by threes goes 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Twenty-seven is the closest number to 26 which is higher than 26. Twenty-six + 1 = 27. That means that 1 is the answer.
Answer:
1 bottles and the last day