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The probability of landing heads exactly 11 times when a coin is tossed 20 times is option a) 0.1602

The repeated tossing of a coin follows a binomial distribution

P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ ⁻ ˣ⁾

where,

n = No. of times the experiment was repeated

x = random variable defining the number of "successes"

p = probability of "success"

Here

"succeess" is the event of landing a head.

n = 20

x = no. of times heads should show, i.e 11

p = probability of landing a head in a single toss

= 1/2

Hence, putting all this in the formula above we get

P(X = 11) = ²⁰C₁₁ 0.5¹¹ (1 - 0.5)⁽²⁰ ⁻ ¹¹⁾

= ²⁰C₁₁ 0.5¹¹ 0.5⁹

= ²⁰C₁₁ 0.5²⁰

= 20!/ 11! (20 - 11)! X 0.5²⁰

= a) 0.1602

Complete Question

An unbiased coin is tossed 20 times.

Find the probability that the coin lands heads exactly 11 times

a. 0.1602

b. 0.5731

c. 0.2941

d. 0.1527

e. 0.6374

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a. The magnitude of the magnetic field at a distance x from the middle of the dipole along the axis connecting the north and south poles is given by \(\[ B = \frac{{\mu_0}}{{4\pi}} \frac{{2p}}{{(x^2 + d^2)^{3/2}}} \]\).

b. The magnetic flux Φ through the area of the coil in the one-dimensional solenoid is \(\[ \Phi = \frac{{\mu_0 N^2 A}}{{2a}} \]\)), where N is the number of loops, A is the cross-sectional area, and a is the half-length of the solenoid.

a. To determine the magnitude of the magnetic field at a distance x from the middle of the dipole along the axis connecting the north and south poles, we can use the formula for the magnetic field due to a magnetic dipole.

The magnitude of the magnetic field B at that point is given by:

\(\[ B = \frac{{\mu_0}}{{4\pi}} \frac{{2p}}{{(x^2 + d^2)^{3/2}}} \]\)

where p is the magnetic strength of each pole, d is the distance between the poles, and μ0 is the permeability of free space.

b. For the solenoid, to calculate the magnetic flux Φ through the area of the coil, we can use the formula for the magnetic flux through a solenoid.

Assuming one-dimensional geometry along the x-axis, the magnetic flux Φ is given by:

\(\[ \Phi = \frac{{\mu_0 N^2 A}}{{2a}} \]\)

where N is the number of loops, A is the cross-sectional area of the solenoid, a is the half-length of the solenoid, and μ0 is the permeability of free space.

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X = [1, α_1, α_2, ..., α_a, β_1, β_2, ..., β_b],hthe first column represents the intercept term μ .θ_hat = (X^T X)^(-1) X^T Y, where X^T represents the transpose of X.  rank of X is equal to the number of linearly  independent columns in X. Based on the rank of matrix X, we can impose constraints on α_i's and β_j's to ensure the uniqueness of the LSE of θ.

(a) To express the data in a linear model, we can stack the observations Y_ij in a column vector Y and express it as Y = Xθ + ε, where Y is a (ab x 1) vector, X is a (ab x (a + b + 1)) matrix, θ is a ((a + b + 1) x 1) parameter vector, and ε is a (ab x 1) error vector.

The matrix X is constructed by combining the variables μ, α_i, and β_j in a way that each observation Y_ij is represented by a linear combination of these variables. We can define X as follows:

X = [1, α_1, α_2, ..., α_a, β_1, β_2, ..., β_b],

where the first column represents the intercept term μ, the next a columns represent the α_i terms, and the remaining b columns represent the β_j terms.

(b) To obtain the least squares estimate (LSE) of θ, we can minimize the sum of squared errors. The LSE of θ, denoted as θ_hat, can be calculated as:

θ_hat = (X^T X)^(-1) X^T Y,

where X^T represents the transpose of X.

(c) The rank of the matrix X can be determined by analyzing its linearly independent columns. Since X has a column of 1's as the first column and each subsequent column represents a different α_i or β_j term, the rank of X is equal to the number of linearly independent columns in X.

(d) Based on the rank of matrix X, we can impose constraints on α_i's and β_j's to ensure the uniqueness of the LSE of θ. If the rank of X is less than (a + b + 1), it means that there is linear dependence among the columns of X. In such cases, we need to impose constraints on the α_i's and β_j's to eliminate this dependence and make the LSE of θ uniquely defined.

One common constraint is to set the sum of the α_i's or β_j's to zero. For example, we can impose the constraint ∑α_i = 0 or ∑β_j = 0. This constraint removes the ambiguity in the estimation of θ caused by the linear dependence among the columns of X.

By imposing such constraints, we can ensure that the LSE of θ is unique and can be obtained by minimizing the sum of squared errors in the linear model Y = Xθ + ε.

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Answer:

Mean: 9.2857142857143

Median: 9

Range: 11

Step-by-step explanation:

The mean is the average of the data set. Add all the numbers up then divide by the amount of numbers you had to start with.

The median of a set of data is the middlemost number. Order your set into least to greatest order then count inwards. If you have an even set or number then add both middle numbers and divide by 2.

The range of a set of data is the difference between the highest and lowest values in the set. Find your lowest and highest value numbers and subtract the lowest number form the highest one.

Answer:

I Think the answer is D, it should be a positive number

The equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

If we assume that the growth rate of the world population was constant from 1997 to 2017, then we can use the following equation:

Population in 2017 = Population in 1997 × (1 + r)²⁰

where r is the annual growth rate, and the exponent 20 represents the number of years between 1997 and 2017.

We can rewrite this equation to solve for r:

(7.53 ) = (5.88 ) × (1 + r)²⁰

Divide both sides by (5.88 ):

(7.53 ) / (5.88 ) = (1 + r)²⁰

Take the 20th root of both sides:

\((7.53 / 5.88 )^{(1/20)} = 1 + r\)

Subtract 1 from both sides:

\(r = (7.53 / 5.88 )^{(1/20)} - 1\)

Therefore, the equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

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Checking the given predicates, there are unifiers in (i), (ii), (iii) and (iv) but not in (v).

Unifier is a substitution that allows two expressions or terms to be made equal by replacing variables with suitable values. A unifier is used to find a common instance or solution to a set of logical expressions or predicates.

A unifier is useful in fields like natural language processing, and artificial intelligence.

From the given question, to know if Unifier exists,

i. Yes, a unifier exists. One possible unifier is:

x = Bob, y = John

ii. Yes, a unifier exists. One possible unifier is:

x = Bob, y = x

iii. Yes, a unifier exists. One possible unifier is:

x = Mary

iv. Yes, a unifier exists. However, there are multiple possible unifiers, since the predicates do not constrain any variables to specific values. For example:

x = y, z = Bob

v. No, a unifier does not exist, since the predicates are contradictory. One predicate states that Bob is shorter than John, while the other states that Bob is shorter than Mary. These two statements cannot be true at the same time, so the predicates cannot be unified.

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Answer:

(3, 6)

Step-by-step explanation:

Opposite of neg3 and 6, which is 3 and 6.

Answer: $310.31

Step-by-step explanation:

Invested amount (P) = $302

Interest rate (r) = 3.3% per year

Period = 10 months

Recall, simple interest formula :

A = P(1 + rt) where ; A = final amount

Interest = 3.3% = 3.3/ 100 = 0.033

A = $302 ( 1 + 0.033(10/12))

A = $302 (1 + 0.033(0.8333333))

A = $302 ( 1 + 0.0275)

A = $302 ( 1. 0275)

A = $310.305

A = $310.31

Answer: here

Step-by-step explanation:

Math is used in various careers such as construction. You will need to know the dimensions to make sure whatever it is being constructed is stable.

Math can help you financially. It can help you budget and prevent you from going into debt.

Math can help you understand real world problems better even if you may not use everything that you learn.

Answer:

Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art. It gives us a way to understand patterns, to quantify relationships, and to predict the future. Math helps us understand the world — and we use the world to understand math. The world is interconnected. Everyday math shows these connections and possibilities.

Step-by-step explanation:

1.we use mathematics for our daily living

2.from day care of school we started our mathematics lesson

3.mathematics is the most important specially when your in business 1.our daily living needs  simple mathematics to calculate. example; I buy a goods amounted 100 pesos then I have 500 pesos in my pocket so i am sure   400 pesos is my change.

2.From the very beginning or the early stage of our education we have to     start learning mathematics so the as we grow older math is in our brain system.

3.In business we know that math is very important because we calculate the capital, expenses, equals the profit.

Answer:

7×7+7

49+7

=56

order of operations multiply first then add

Answer:

All have the same angle

Step-by-step explanation:

Answer:

i think its 230cm but i could be wrong let me know

Step-by-step explanation:

Out of the given figures, namely, a square, triangle, a trapezoid, a regular pentagon, and a rhombus, a test would require selecting a figure among these figures.

However, we can understand the nature of each of these figures, their characteristics, properties, and formulas related to them, and determine how to select a figure for the test.The square has four sides and four right angles, with all sides of equal length.

Its formula for area is A = s²,

where s is the length of the sides.

The triangle is a polygon with three sides, with its area calculated as A = (1/2)bh,

where b is the base and h is the height of the triangle.A trapezoid is a quadrilateral with only one pair of parallel sides. Its formula for area is A = [(b1+b2)/2]h,

where b1 and b2 are the lengths of the parallel sides, and h is the height of the trapezoid.

A regular pentagon is a polygon with five sides, with all sides of equal length. Its area formula is A = (1/4)s²√(25+10√5), where s is the length of the sides.

The rhombus has four equal sides, with opposite angles being equal.

Its area formula is A = (1/2) d1d2, where d1 and d2 are the lengths of the diagonals.

Depending on the nature and level of the test, the selection of any of the figures can vary. For example, if the test is related to the calculation of areas, the selection of square, triangle, trapezoid, and rhombus would be more appropriate, while the selection of a regular pentagon can be suitable for a more advanced test.

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Answer:

I this a question of some sort?

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

b. Linear programming model is the correct option.

A linear programming model is a mathematical technique used to find the best outcome in a given set of constraints. In this case, Manders Manufacturing Corporation is trying to determine the optimal product mix for its two products, metal (M) and scrap metal (S), based on certain constraints. The objective is to maximize the profit, represented by the function Z = $30M + $70S.

The constraints are represented by the inequalities:

3M + 2S ≤ 15

2M + 4S ≤ 18

These constraints define the limitations on the production of metal and scrap metal. The model aims to find values of M and S that satisfy these constraints while maximizing the objective function.

Using linear programming techniques, the corporation can solve this model to find the optimal values for M and S that will maximize their profit. This approach allows them to make data-driven decisions and allocate their resources efficiently. By formulating the problem as a linear programming model, Manders Manufacturing Corporation can make informed choices about the optimal product mix to achieve their business objectives.

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The possible triangle whose vertices are given by the lattice points with positive integer coordinates less than 5 is 20.

To solve this, we apply principles of permutation and combination to count the number of possible triangles that can be formed from the given set of lattice points.

Here are the different ways of arranging the lattice points with lattice point coordinates less than 5:

If we want to choose any three lattice points, we can pick the first point from the 20 given in the table above.

Then, we can pick the second point from those lattice points that lie strictly above and strictly to the right of the first point.

For the third point, we can only pick lattice points lying above and to the right of the line segment connecting the first two points.

So, there are 20 possible triangles whose vertices are positive integer coordinates less than five.

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Answer:123

Step-by-step explanation:123

Based on the calculation of the index of the 65th percentile using the formula and the ordered list of bills, the 65th percentile of the bills for the sample of 20 couples at the restaurant is 63 dollars.

We must arrange the bills in ascending order in order to determine the sample's 65th percentile:

6, 15, 21, 21, 23, 23, 24, 26, 27, 30, 30, 31, 37, 56, 61, 62, 63, 63, 64, 65

The formula for calculating the index of the 65th percentile is as follows:

Index = (Percentile / 100) * (N + 1)

where N is the sample size (which is 20 in this case).

So, for the 65th percentile, we have:

Index = (65 / 100) * (20 + 1) = 13.65

We require the index of the bill that is more than or equal to the 65th percentile, so we must round up this value to the nearest integer.

Therefore, the 65th percentile is the 14th bill in the ordered list:

6, 15, 21, 21, 23, 23, 24, 26, 27, 30, 30, 31, 37, 56, 61, 62, 63, 63, 64, 65

So, The 14th banknote on the ordered list, with a value of 63 dollars, represents the 65th percentile.

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Answer: The answer for this question is x=1

Step-by-step explanation: -3(2x-3)=-6x+9 first you multiply -3x with 2x and -3 to get -6x+9=-6x+9 then subtract nine from both sides to leaves -6x=-6x then you divide -6 on both sides and you get x=1.

Any value of x makes the equation true. All real numbers

Interval Notation: (−∞,∞)

Because if you solve it

-3(2x-3)=-6x+9

distribute

-6x + 9 = -6x + 9

subtract 9 from both sides

-6x = -6x

simplify

0 = 0

Answer:

Step-by-step explanation:

Upper box in the diamond: Add the two numbers  ⇒ (-2) + 3 = -1

Bottom box in the diamond : Multiply the two numbers ⇒ (-2) * 3 = -6

3) Upper box = (-6) +  (-3)  = (-9)

Bottom box = (-6) *(-3) = 18

4) Upper box  = 1 +(-11) = -10

 Bottom box = 1 *(-11) = -11

5) Upper box = 7+8 = 15

Bottom box = 7*8 = 56

Answer:

I don't know ‍♀️

Step-by-step explanation:

Answer:

h(x)=6^x/3 is what I got hope I could help

Answer:

Below

Step-by-step explanation:

To complete the square, the leading x^2 coefficient needs to be = 1 , so factor out a 3 to get

y = 3 ( x^2 + 5/3x )   +3                (I assumed it was a + sign between the terms)

 Then take 1/2 of the 5/3   ( 5/6 )  , square it  (25/36) , add it to the parentheses.... then subtract the amount you added (3 * 25/36) by doing this.....  to have this :

y = 3 ( x^2 + 5/3 x + 25/36)  -   3 * 25/36   +3      then simplify to

y = 3 ( x + 5/6)^2  + 11/12               Done.

Answer:

JK = 42

KL = 78

Step-by-step explanation:

To find the lengths of JK and KL, we need to first find the value of x. We know that the length of the entire line is 120. That means we need to add the lengths of JK and JL and set it equal to 120.

4x+6+7x+15 = 120

Combine like terms.

11x+21 =120

Subtract 21 from each side.

11x= 99

Divide both sides by 11.

x=9

Now that we know the value of x, we simply plug it into the equations to find out the lengths of each line segment.

JK = 4x+6

4(9)+6 (x is plugged in)

36+6 = 42

JK=42

Now lets do KL.

7x+15

7(9)+15

63+15 = 78

KL = 78  

The values of JK = 42 and KL= 78.

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment JL , where the length of line segment JL refers to the distance between its endpoints, J and L.

Given that JL = 120,

And JK = 4x + 6 and  KL= 7x + 15

J_________K______________L

⇒ JL = JK + KL

⇒ 120 = 4x + 6 + 7x + 15

⇒ 120 = 11x + 21

⇒ 11x = 99

⇒ x = 9

Substitute the values of x = 9 in the JK = 4x + 6 and  KL= 7x + 15,

JK = 4(9) + 6 = 42

KL= 7(9) + 15 = 78

Hence, the values of JK = 42 and KL= 78 .

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Answer:

A

Step-by-step explanation:

its the most logical one to me

Answer:

A

Step-by-step explanation: