assume a child is under observation by a researcher. he is given 6 blocks uniquely labeled a, b, c, d, e, and f. the child is equally likely to choose any of the blocks. find the probability the child arranges the blocks in such a way that block f is in either the 1st position or the last position.

(i) P(A ∩ B) = 0.32.

(ii) P(A|B) = 0.64.

(iii) P(A ∪ B) = 0.98.

(i) Using the formula P(B|A) = P(A and B) / P(A), we can rearrange to get:

P(A and B) = P(B|A) * P(A) = 0.4 * 0.8 = 0.32

Therefore, P(A ∩ B) = 0.32.

(ii) Using Bayes' theorem, we can calculate P(A|B) as follows:

P(A|B) = P(B|A) * P(A) / P(B)

We are given P(B|A) = 0.4, P(A) = 0.8, and P(B) = 0.5, so:

P(A|B) = 0.4 * 0.8 / 0.5 = 0.64

Therefore, P(A|B) = 0.64.

(iii) Using the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B), we can plug in the values we have already calculated:

P(A ∪ B) = 0.8 + 0.5 - 0.32 = 0.98

Therefore, P(A ∪ B) = 0.98.

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If all sequences of six characters are equally likely, then the probability that the license plate will contain no duplicate letters or numbers is 0.59.

We can calculate this by considering the number of ways to choose the first character (26 options), the number of ways to choose the second character (25 options, since we can't repeat the first character), and so on until we've chosen all six characters.

The number of such sequences is 26 * 25 * 24 * 23 * 22 * 21 = 26!/(26-6)! = 26!/(20!) = 26 * 25 * 24 * 23 * 22 * 21/6! = 26 * 25 * 24 * 23 * 22 * 21/720 = 308,915,776.

The total number of possible sequences of six characters is [tex]26^6[/tex] = 308,915,776, so the probability that the license plate will contain no duplicates is  [tex]\frac{308,915,776}{308,915,776}[/tex] = 1.

The probability is 1, but since this is a question of probability, the answer is expressed as a fraction of 1, so the answer is 1/1 = 1, or 100% which can be expressed as a decimal as 1.

So the correct answer is d) 0.59.

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The composite function of f(x) and g(x) is given as follows:

f(g(x)) = x² - 6x - 2.

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

The functions for this problem are given as follows:

The composite function is the numeric value of f(x) at g(x) = x - 6, replacing each instance of x by x - 6, hence:

f(g(x)) = f(x - 6) = (x - 6)² + 6(x - 6) - 2

f(g(x)) = x² - 12x + 36 + 6x - 36 - 2

f(g(x)) = x² - 6x - 2.

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Answer:8 16 34

gdgdfgdf

Step-by-step explanation:

dgdfgdfgdfgdfgdfgdf

Answer:by adding 8

Step-by-step explanation:

i just took it

The expression of the polynomial is 0.1(x - 1)^2(x - 5)

From the question, we have the following parameters that can be used in our computation:

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x - 1)^2(x - 5)

The y-intercept is -0.5

So, we have

a * (0 - 1)^2(0 - 5) = -0.5

This gives

a =0.1

So, we have

P(x) = 0.1(x - 1)^2(x - 5)

Henc,e the expression is P(x) = 0.1(x - 1)^2(x - 5)

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The equation is x - 2.5 = 5.25.

The elevation of the plane before its descent is 7.75 miles.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

An airplane descends 2.5 miles to an elevation of 5.25 miles.

This means,

The plane was at x miles before it descents.

x - 2.5 = 5.25

Solve for x.

x = 5.25 + 2.5

x = 7.75

Thus,

The elevation of the plane before its descent is 7.75 miles.

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Answer:

x = [tex]\frac{15}{2}[/tex] or 7.5

Step-by-step explanation:

To find x, you cross multiply.

3x * 4 = 12x

9 * 10 = 90

12x = 90

x = [tex]\frac{90}{12} = \frac{15}{2}[/tex]

Answer:

Step-by-step explanation:

To solve for x in the equation:

3x/10 = 9/4

We can start by multiplying both sides by 10 to eliminate the fraction on the left side:

3x = 10 * (9/4)

Next, we can simplify the right side by multiplying 10 by 9/4:

3x = 22.5

Finally, we can isolate x by dividing both sides by 3:

x = 22.5 / 3

x = 7.5

Therefore, the solution to the equation 3x/10 = 9/4 is x = 7.5.

10 more than triple P can be expressed as 3p+10

10 more than triple P can be written as expression 3p+10

The expression 3p+10 is obtained by following the order of operations (PEMDAS) to evaluate the expression "10 more than triple P".

"Triple P" means 3 times P, which can be written as 3P.

Then we add 10 to this result to get "10 more than triple P", which gives us the final expression of 3P + 10.

Hence,  10 more than triple P can be expressed as 3p+10

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The width of this rectangular pool is equal to 71 meters.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

6532 = 92W

Width, W = 6532/92

Width, W = 71 meters.

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Step-by-step explanation:

man male Manjar bahan master milkman Monk Mr nephew papa poet

A variable is defined as the alphabetic character that expresses the unknown value or unknown number. It can be changed according to the operations performed.

In this experiment,

Each side of the shower is sprayed with lemonade juice to determine whether it has any changes in the cleanliness of the shower. So each side of the shower with lemon juice is an independent variable.

This dependent variable is a variable that can measure Lemonade a manipulated variable or independent variable has any effect on it, such as whether lemonade juice cleans the slime off of the side or not.

A control is something that remains unchanged to assess the condition or impact which has not changed or may be contrasted to it. In the this scenario, the water spray is under command.

The experiment concludes drinking lemonade seems to not influence the cleaning of slime inside the shower.

Thus, slime is constant.

Hence,

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The heights for the given radius and volume are 35.35 units, 8.83 units, 1.41 units and 141.40 units

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, a cone a volume of 37 units³, we need to find the heights for given radii,

We know that, the volume of a cone = π×radius²×height/3

Therefore,

1) If the cone's radius is 1, then its height =

37 = π×1×h/3

h = 37×3/3.14

h = 35.35 units

2) If the cone's radius is 2, then its height =

37 = π×4×h/3

h = 37×3/3.14×4

h = 8.83 units

3) If the cone's radius is 5, then its height =

37 = π×25×h/3

h = 37×3/3.14×25

h = 1.41 units

4) If the cone's radius is 1/2, then its height =  

37 = π×1×h/3×4

h = 141.40 units

Hence, the heights for the given radius and volume are 35.35 units, 8.83 units, 1.41 units and 141.40 units

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The number of minutes that the passenger can travel in the taxi would be = 6.67mins.

The amount of money paid for 1 minute = $3.00

The amount of money that a passenger has = $20

The number of minutes that the passenger can travel = ?

That is;

1 minute = $3.00

X minutes = $20

make X the subject of formula:

X mins = 20×1 /3

X mins = 6.67mins

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Answer:

Mean: 23

Median: 23.5

Range: 22

Step-by-step explanation:

How to find the mean: Add all the numbers then divide by the amount of numbers.

How to find the median: Find the middle of all the numbers, there are two middle numbers here so you have to add those two middle numbers and then divide by two to get your answer.

How to find range: Take your highest number and subtract by your lowest

Answer:

the semiannual interest payment is $153.77 and the total interest earned over the life of the bond is $9,226.20.

Step-by-step explanation:

To find the semiannual simple interest payment, we need to divide the annual interest rate by 2, since there are 2 semiannual periods in a year:

Semiannual interest rate = Annual interest rate / 2

= 6.268% / 2

= 3.134%

To find the semiannual interest payment, we multiply the face value of the bond by the semiannual interest rate:

Semiannual interest payment = Face value x Semiannual interest rate

= $4900 x 3.134%

= $153.77 (rounded to two decimal places)

To find the total interest earned over the life of the bond, we need to multiply the semiannual interest payment by the number of semiannual periods in the bond's life. Since the bond has a 30-year term and 2 semiannual periods in a year, the bond has a total of 60 semiannual periods:

Total interest earned = Semiannual interest payment x Number of semiannual periods

= $153.77 x 60

= $9,226.20 (rounded to two decimal places)

Therefore, the semiannual interest payment is $153.77 and the total interest earned over the life of the bond is $9,226.20.

The solution is, the product of these matrices, of

AB =  [tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\\\end{array}\right][/tex][2×3]

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns.

here, we have,

matrix A = [tex]\left[\begin{array}{ccc}-1&4\\0&5\\\end{array}\right][/tex][2×2]

matrix B = [tex]\left[\begin{array}{ccc}7&9&2\\2&0&-3\\\end{array}\right][/tex][2×3]

As, no. of column of A = no. of column of B

so, the product of AB = [tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\\\end{array}\right][/tex][2×3]

Hence, The solution is, the product of these matrices, of

AB =  [tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\\\end{array}\right][/tex][2×3]

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Answer:

C) [tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\\\end{array}\right][/tex] is the answer

Step-by-step explanation:

Rules of Multiplication of Matrices:-

Matrix multiplication

A= [tex]\left[\begin{array}{ccc}-1&4\\0&5\end{array}\right][/tex] 2x2   B=[tex]\left[\begin{array}{ccc}7&9&2\\2&0&-3\end{array}\right][/tex]2x3

AB will be of 2x3 order

AB11= -1x7+4x2=1

AB12= -1x9+4x0=-9

AB13= -1x2+3x(-3)= -14

AB21= 0x7+5x2=10

AB22= 0x9+5x0=0

AB23= 0x2+5x(-3)=-15

AB=[tex]\left[\begin{array}{ccc}1&-9&-14\\10&0&-15\end{array}\right][/tex]

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The value of n in the expression is 16

From the question, we have the following parameters that can be used in our computation:

y^2 + 8y + n

Take the coefficient of y

So, we have

k = 8

Divide by 2

k/2 = 4

Square both sides

(k/2)^2 = 16

This means that

n = 16

Hence, the value of n is 16

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Answer:

13,262

Step-by-step explanation:

f(x) = 100000[tex](1-.02)^{x}[/tex]

f( x) = 100000([tex](.098)^{100}[/tex]

f(x) = 13,262  Rounded to the nearest person

Answer:

Step-by-step explanation:

The percentage of people living in cities more than doubled in 100 years.

The units digit of any integer that is the sum of two fourth powers must be 0, 1, 2, 5, 6, or 7.

Let n be an integer that can be written as a sum of two fourth powers. Then, n = a4 + b4, for some integers a and b. We can write n as n = 10k + c, where k is an integer and c is the units digit of n.

We want to show that the units digit of n must be either 0, 1, 2, 5, 6, or 7. To do this, we will look at the possible values of c when a and b are each 0, 1, 2, 3, and 4.

When a = 0 and b = 0, c = 0. When a = 0 and b = 1, c = 1. When a = 0 and b = 2, c = 4. When a = 0 and b = 3, c = 9. When a = 0 and b = 4, c = 6.

When a = 1 and b = 0, c = 1. When a = 1 and b = 1, c = 0. When a = 1 and b = 2, c = 7. When a = 1 and b = 3, c = 6. When a = 1 and b = 4, c = 5.

When a = 2 and b = 0, c = 4. When a = 2 and b = 1, c = 7. When a = 2 and b = 2, c = 0. When a = 2 and b = 3, c = 3. When a = 2 and b = 4, c = 2.

When a = 3 and b = 0, c = 9. When a = 3 and b = 1, c = 6. When a = 3 and b = 2, c = 3. When a = 3 and b = 3, c = 0. When a = 3 and b = 4, c = 7.

When a = 4 and b = 0, c = 6. When a = 4 and b = 1, c = 5. When a = 4 and b = 2, c = 2. When a = 4 and b = 3, c = 7. When a = 4 and b = 4, c = 0.

Thus, when a and b are each 0, 1, 2, 3, and 4, c can only be 0, 1, 2, 5, 6, or 7. Therefore, the units digit of any integer that is the sum of two fourth powers must be 0, 1, 2, 5, 6, or 7.

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The statement is true. Solving a linear system is the same as finding the solution set of the system. The solution set of a linear system can also expressed using a parametric description.

A linear system can be solved by locating a parametric description of the solution set. The set of all vectors that fulfil a linear system is known as the solution set, and we can parametrically define this set by expressing the solutions in terms of one or more parameters.

We can determine the pivot variables and the free variables once the system is in row-echelon form. The remaining equations determine the values of the pivot variables, which are the leading coefficients in the equations.

In conclusion, since both entail discovering the values of the variables that satisfy the system, finding a parametric description of the solution set of a linear system is comparable to solving the system.

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Answer:

False,

Step-by-step explanation:

There is not enough information given.

The given statement - "All the races are 175 miles long" is true.

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is to find whether all races are more than 175 miles or not.

All the races are 175 miles long. The given statement is true.

Therefore, the given statement - "All the races are 175 miles long" is true.

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The solution is, the volume: V = 41.65

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

You need to use this formula to calculate the volume of the square pyramid:

V = s^2*h/3

Where "s" is the lenght of any side of the square base and "h" is the height of the pyramid.

Find the height with the Pythagorean Theorem:

a^2 +b^2 = c^2

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle. Let be "c" the height of the pyramid.

You can identify in the figure that:

a=12

b =10

so, c = 15.62 = h

Then, you can find the height:

h = 15.62

Then, knowing that:

s= 2

You can calculate the volume:

V = 41.65

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Assuming the wealthy, generous and whimsical friend chooses the k recipients uniformly at random, there are nCk ways to select the k people from the n who show up at the party.

The number of ways that you and your best friend can both receive iPhones is equal to the number of ways to select k-2 people from the remaining n-2 people, multiplied by 2 (since you can be selected first or second among the k recipients).

Therefore, the probability that you and your best friend both receive iPhones is: 2 * (n-2Ck-2) / nCk

Simplifying this expression using combinatorial identities, we get: 2 * (n-2Ck-2) / nCk = 2 * [(n-2)! / (k-2)! (n-k)!] / [n! / k! (n-k)!] = 2 * k(k-1) / n(n-1)

Thus, the probability that you and your best friend both receive iPhones is k(k-1) / n(n-1).

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Answer:

Step-by-step explanation:

950 times 30 hours = 28,500

28500 + 75= 28,575

75 is 3% of 2500 the total amount of sales he made

He earned 28,500 in his 30 hour week.

a.There are 2,268,760 different samples possible, b.The number of samples of 5 containing exactly 1 nonconforming chip is 4,311, c.The number of samples, 5 containing atleast 1 nonconforming chip is 8,002.

a. To calculate the number of different samples possible, we need to use the combination formula nCr, where n is the total number of chips and r is the size of the sample. In this case, n = 140 and r = 5. So the number of different samples possible is 140C5 = 2,268,760.

b. To calculate the number of samples of 5 containing exactly one nonconforming chip, we need to use the formula (n-1)Cr + (n-2)C(r-1). In this case, n = 10 and r = 5. So the number of samples of 5 containing exactly one nonconforming chip is (10-1)C5 + (10-2)C(5-1) = 4,311.

c. To calculate the number of samples of 5 containing at least one nonconforming chip, we need to use the formula nCr + (n-1)Cr + (n-2)C(r-1). In this case, n = 10 and r = 5. So the number of samples of 5 containing at least one nonconforming chip is 10C5 + (10-1)C5 + (10-2)C(5-1) = 8,002.

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6/11 is the probability that I cat an English muffin for breakfast.

Let G, C, and E represent the events of selecting granola, cereal, and an English muffin, respectively.

Let P(G), P(C), and P(E) represent the probabilities of selecting granola, cereal, and an English muffin, respectively.

We are given that:

P(E) = 2P(G) (the English muffin is selected twice as often as the granola)

P(E) = 3P(C) (the English muffin is selected three times as often as the cereal)

We can use these relationships to solve for P(G), P(C), and P(E):

P(G) = P(E)/2

P(C) = P(E)/3

P(G) + P(C) + P(E) = 1

Substituting the first two equations into the third equation and solving for P(E), we get:

P(E)/2 + P(E)/3 + P(E) = 1

11P(E)/6 = 1

P(E) = 6/11

Therefore, the probability that an English muffin is selected for breakfast is 6/11.

Hence, option (B) is the correct choice.

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In sections 4-6 of Treasure Island, C. describes how Dr. Livesey and Mr. Trelawney respond to the chart. People are disappointed and overwhelmed with skepticism about its authenticity.

Throughout Treasure Island, Dr. Livesey, a physician and judge, acts as the narrative's only sane figure. He is bold and straightforward enough already to start standing up to his pals and also the most infamous thieves.

here, we have,

What else does Dr. Livesey look like in Treasure Island?

Dr. Livesey describes oneself via deeds rather than being characterized by Stevenson. He possesses the traits that outweigh the cleverness and cruelty of his fearsome foe Silver: intelligence, bravery, and coolness.

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Answer:

To evaluate the functions for x = 0, we first need to substitute x with 0 in both functions. Therefore, for f(x), we get f(0) = 3(0)² = 0, and for g(x), we get g(0) = 1.5(2)^0 = 1.5.

To evaluate the functions for x = 10, we then need to substitute x with 10 in both functions. Therefore, for f(x), we get f(10) = 3(10)² = 300, and for g(x), we get g(10) = 1.5(2)^10 = 241.5. Therefore, the answers are f(0) = 0 and g(0) = 1.5, f(10)=300 and g(10)=241.5.

Answer:

Step-by-step explanation:

To evaluate the functions for x = 0 and x = 10, we simply substitute the values of x into the corresponding functions.

f(x) = 3x²

f(0) = 3(0)² = 0

f(10) = 3(10)² = 300

g(x) = 1.5(2)^x

g(0) = 1.5(2)^0 = 1.5(1) = 1.5

g(10) = 1.5(2)^10 ≈ 153.6

Therefore, the values of the functions at x = 0 and x = 10 are:

f(0) = 0 and g(0) = 1.5

f(10) = 300 and g(10) ≈ 153.6

The equation can you use to find c, the cost of an entrance ticket is x=13.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

Given that;

Total cost of 4 friends= $76

The cost of entrance ticket= $6

Now,

Based on the given conditions, formulate:

4 x (x+6)=76

Reduce the greatest common factor on both sides of the equation

x+6=19

Rearrange unknown terms to the left side of the equation:

x=19-6

Calculate the sum or difference:

x=13

Therefore, the equation will be x=13

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