Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 JQK
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?

A company manufactures rubber balls, random variable X in words is diameter of the rubber ball, standard deviation is -1.5 and z-score of the x = 2 is 2.123.

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. Random variables are frequently identified by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.

In probability and statistics, random variables are used to measure outcomes of a random event, and hence, can take on various values. Real numbers are often used as random variables since they must be quantifiable.

1) X denotes the diameter of the rubber ball.

So the correct option was A. (option A)

Therefore,  the random variable X in words is diameter of the rubber ball.

2) For 1.5 Standard deviations left to the mean , Z score will be -1.5

option(A)

So, standard deviation to the left of the mean is -1.5.

3) [tex]Z=\frac{(x-\mu)}{\sigma}[/tex]

x=2

sigma = √2

Z = 2-(-1)/ √2

Z = 3/√2

Z = 2.123

Hence, the z-score of the x = 2 is 2.123.

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Complete question:

A company manufactures rubber balls. The mean diameter of a rubber ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X

diameter of a rubber ball

rubber balls

mean diameter of a rubber ball

12 cm

Question 2 What is the z-score of x=9, if it is 1.5 standard deviations to the left of the mean? Hint: the z-score of the mean is =0 −1.5 1.5 9 Question 3 Suppose X∼N(−1,2). What is the z-score of x=2 ? Hint: z=(x−μ)/σ 1.5 −1.5 0.2222

Therefore , the solution of the given problem of function comes out to be f(x) = sec(x) has a period of 2. 2 is the answer.

The midterm test questions will cover all of the topics, including actual as well as fictitious locations and arithmetic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox has a particular spot that might be used as a haven.

Here,

=> F(x) = sec(x) has a 2 phase.

Because the secant function is periodic, its values recur after a predetermined amount of time.

This interval's length is equal to the secant function's duration.

The formula for the secant function is

=> sec(x) = 1/cos.(x).

The cosine function repeats its values every 2 units of x, which is known as its period.

Consequently, the secant function has a period of 2 as well.

Therefore, f(x) = sec(x) has a period of 2. 2 is the answer.

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Answer:

g h hh h

Step-by-step explanation:

Answer: -3/2

Step-by-step explanation:

FIrst rearrange the equation in y = mx + b form.

4x - 6y = -24

-6y = -4x - 24

y = 2/3x + 4

If the line is perpendicular, the slope must be the negative reciprocal of the current line.

The negative reciprocal of 2/3 is -3/2.

When three dices are rolled.

Total number of outcomes =  = 216

Sum of 13 can be achieved in the following ways:

From the digits 6,4,3

So, there are 3! ways =  = 6

From the digits 6,2,5

So, there are 3! ways =  = 6

From the digits 5,4,4

So, there are  ways = 3

From the digits 6,6,1

So, there are  ways = 3

From the digits 3,5,5

So, there are  ways = 3

So, total numbers whose sum is 13=

So, Probability = .

Therefore, the probability of getting sum as 21 on rolling three dice =   .

Neither anushka nor lukas are correct as both of their calculations are wrong.

Basic arithmetic operations like addition, subtraction, multiplication, and division are used to isolate the variable on one side of a linear equation and solve it. The objective is to make the equation as simple as possible until the variable can be identified and its value calculated. In order to solve a linear equation, you must first combine like terms to simplify the expressions on both sides of the problem.

Then, you can use inverse operations to get rid of constants and coefficients. The value of the variable can be ascertained by solving for it once it has been isolated. By looking at the coefficients and constants of the equation, it can be established if the equation has no solution or infinite solutions. In various disciplines, such as science, engineering, and finance, linear equations are used to represent connections between variables.

2/5b + 1 = -11

2/5b = -12

b= -12 x 5/2

b = -30

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The answer of the given question based on the  transformation from its parent function the explanation part is given below and The equation of the function is y = -2(x+3)².

In mathematics,  function is  relation between  set of inputs and  set of possible outputs with  property that each input is related to exactly one output. It is  rule that assigns to each input value exactly one output value. Functions can be represented in various ways, like algebraic expressions, graphs, tables, and words. They are used to model relationships between variables, to describe how one quantity depends on another, and to make predictions about future values. Functions are  important concept in many fields of mathematics, as well as in science, engineering, economics, and other areas where quantitative analysis is used.

a. The graph appears to be a reflection of the parent function f(x) = x² over the x-axis followed by a vertical stretch by a factor of 2 and a horizontal shift to the left by 3 units.

b. The equation of the function is y = -2(x+3)².

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The length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

Since the area of the soap carvings is 300 square inches, we want the top of the bookcase to have the same area. Let's assume the length of the top of the bookcase is "l" and the width is "b". Then we have:

Area of top of bookcase = lb

We want this area to be equal to 300 square inches. Therefore, we can write:

lb = 300

We are solving for "b", so we can rearrange this equation to solve for "b":

b = 300/l

Since we don't know the value of "l", we can't solve for "b" exactly. However, we can approximate it by assuming a value for "l". Let's say we assume that "l" is 20 inches. Then we can calculate "b" as follows:

b = 300/20 = 15

So if the length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

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The required simplified forms are 3x - 1, 6x , 2x² - 10x , a + 2b , 15x - 8 , x² + 2x + 6 , x² - y² , 6x² - 22x.

the definition of an equation is a mathematical statement that demonstrates that two mathematical expressions are equal. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' symbol.

Simplified forms of the equation are

[tex]$c: 3(x-2)+5=3x-6+5=3x-1$[/tex]

[tex]$f: 2x(3-x)+x^2=6x-x^2+x^2=6x$[/tex]

[tex]$i: 7x^2-5x(x+2)=7x^2-5x^2-10x=2x^2-10x$[/tex]

[tex]$c: 2a-(a-2b)=2a-a+2b=a+2b$[/tex]

f: [tex]$3x-4(2-3x)=3x-8+12x=15x-8$[/tex]

[tex]$x(x+4)-2(x-3)=x^2+4x-2x+6=x^2+2x+6$[/tex]

[tex]$x(x+y)-y(x+y)=(x-y)(x+y)=x^2-y^2$[/tex]

[tex]$o: 4x(x-3)-2x(5-x)=4x^2-12x-10x+2x^2=6x^2-22x$[/tex]

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Therefore, the monthly payment for a student loan of $15,000 at a fixed APR of 12% for 20 years is $144.36.

Interest is the cost of borrowing money or the return on investing money. When you borrow money, you usually have to pay back more than you borrowed, and the additional amount you pay is the interest. The interest rate is expressed as a percentage of the borrowed amount, and it can vary depending on factors such as the borrower's credit score, the term of the loan, and the lender's policies.

Given by the question.

Assuming the loan has a fixed interest rate of 12% per annum, the amount of interest charged each year will be:

12% of $15,000 = $1,800

The total interest charged over 20 years will be:

$1,800 x 20 = $36,000

The total amount to be repaid (principal + interest) will be:

$15,000 + $36,000 = $51,000

If the loan is being repaid in equal monthly installments over the 20-year term, the monthly payment can be calculated using the following formula:

M = P * (r[tex](1+r)^{n}[/tex]) / ([tex](1+r)^{n}[/tex]- 1)

Where:

M = Monthly payment

P = Principal amount (in this case, $15,000)

r = Monthly interest rate (12% per annum / 12 months = 1% per month)

n = Total number of payments (20 years x 12 months per year = 240)

Plugging in the values:

M = $15,000 * (0.01[tex](1+0.01)^{240}[/tex]) / ([tex](1+0.01)^{240}[/tex] - 1)

M = $144.36

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Answer:

Step-by-step explanation:

i think it B

Answer:

B is correct

Step-by-step explanation:

If it is spun twice then the probability of it landing on 2 and then an odd number is:

Pr(2,1) or Pr(2,3) or Pr(2,5) or Pr(2,7)

1/49 * 4

4/49

Answer:

Step-by-step explanation:

its 60

The required answers are 80.8, 79,and g(42) > f(42).

Part A:

To determine the test average for the math class after completing test 2, we need to evaluate the function f(x) at x=2. That is,

[tex]$$f(2) = 0.9(2) + 79 = 80.8$$[/tex]

Therefore, the test average for the math class after completing test 2 is 80.8.

Part B:

To determine the test average for the science class after completing test 2, we need to find the equation of the linear function g(x) that passes through the given points (1,78) and (2,79). The slope of the line passing through these points is

[tex]$m=\frac{y_2-y_1}{x_2-x_1}=\frac{79-78}{2-1}=1$$[/tex]

We can use the point-slope form of a line to find the equation of the line passing through the point (1,78) with slope m=1. That is,

[tex]$$y-78 = 1(x-1)$$[/tex]

Simplifying, we get

y = x + 77

Therefore, the test average for the science class after completing test 2 is

g(2) = 2 + 77 = 79

Part C:

To determine which class had a higher average after completing test 42, we need to evaluate f(42) and g(42) and compare the results. We have

[tex]$$f(42) = 0.9(42) + 79 = 117.8$$[/tex]

To find (42), we need to extend the linear function g(x) beyond the given data points by assuming that the function is linear and continues with the same slope m=1. That is,

g(x) = x + 77

for all [tex]$x\geq 1$[/tex]. Therefore,

[tex]$$g(42) = 42 + 77 = 119$$[/tex]

Since g(42) > f(42), we conclude that the science class had a higher average after completing test 42.

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Answer: D. As x → -∞, y → -∞.

Step-by-step explanation:

The graph shows the function approaching negative infinity on the x-axis (left side).  When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.

The correct option is -C: No, 6 is the geometric mean of 4 and 9, however if the altitude is 6, then the hypotenuse is the geometric mean of the two segments.

An average technique multiplies several values and determines the number's root is known as the geometric mean. You locate the nth root for their product for a collection of n numbers. This descriptive statistic can be used to sum up your data.

Mean Geometric The square root of the product of two numbers is the geometric mean amongst them. The geometric mean of two positive numbers an as well as b is the positive number x as in percentage Cross multiplication results in x² = ab,.

For the given question.

geometric mean of a and b :

From the drawn diagram.

a = 4

b = 9

x = √ab

x = √9*4

x = 6

geometric mean: 6

Applying the altitude rule:

h² = x.y

6² = 9*4

36 = 36

Thus, the geometric mean calculated by friend is correct but the marking on the diagram is wrong.

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Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.

The above statement is True.

In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.

A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.

Sometimes the term linear function has the same meaning as linear map, but not in analysis.

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Answer:

Step-by-step explanation:

[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]

But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.

The area to the right of x is 0.877.

In a normal distribution, the entire area under the curve is identical to 1. The area to the left of a specific value of x represents the possibility of observing a value largely lesser than or same tox.

However, we're capable to discover the area to the right of x with the aid of abating the left area from 1, If the place to the left of x is given.

In this case, the area to the left of x is 0.123. thus, the place to the right of x is

1-0.123 = 0.877

Thus, the area is 0.877 to the right of x.

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Parallelogram (Opposite sides have the same length). Parallelogram (Area is one-half the base times the height). Parallelogram (Opposite sides are parallel). Parallelogram (Angles can be right angles)

According to the parallelogram law, the sum of the squares of a parallelogram's four sides is equal to the sum of the squares of its two diagonals. It is essential for the parallelogram to have equal opposite sides in Euclidean geometry.

A parallelogram is a particular sort of polygon. It is a quadrilateral in which the opposite side pairs are parallel to one another. There are six crucial parallelogram characteristics to be aware of: Congruent sides are those when AB = DC.

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Answer:

159 proper subsets.

Step-by-step explanation:

Given a set {2, 4, 6, 8...100}, how many proper subsets are there?

First, find how many subsets there are in 2 - 10:

That's 16.

Then because there are 10 10s in 100, multiply by 10:

16 x 10 = 160

Finally, because it says proper subsets, subtract by 1:

160 - 1 = 159 proper subsets.

Therefore, there are 159 proper subsets in {2, 4, 6, 8...100}

Step-by-step explanation:

We have:

x = a sin 2t

Differentiating with respect to t, we get:

dx/dt = 2a cos 2t

Next, we have:

y = a(cos 2t + log tan t)

Differentiating with respect to t, we get:

dy/dt = -2a sin 2t + (1/tan t)(1/ln 10)

Using the identity:

sin^2 t + cos^2 t = 1

We have:

sin 2t = 2sin t cos t

And:

cos 2t = cos^2 t - sin^2 t

cos 2t = 2cos^2 t - 1

Using these identities, we can rewrite dx/dt and dy/dt in terms of x and y:

dx/dt = 2a sqrt(1 - x^2/a^2)

dy/dt = -2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t)

Therefore, we have:

dx/dy = dx/dt ÷ dy/dt

Substituting the expressions for dx/dt and dy/dt, we get:

dx/dy = (2a sqrt(1 - x^2/a^2)) / (-2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t))

Simplifying, we get:

dx/dy = (-2 sqrt(1 - x^2/a^2)) / (2 sqrt(1 - x^2/a^2) - (1/ln 10)(y - a cos 2t))

If λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

[tex]v^T A^T = \lambda v^T[/tex]

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

[tex]\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right][/tex]

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

[tex]v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T[/tex]

Now, for transpose of A:

[tex]A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right][/tex]

The eigen vectors are:

[tex]u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T[/tex]

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.

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The value οf the given angle x = 39.8 degree

Trigοnοmetry uses six fundamental trigοnοmetric οperatiοns. Trigοnοmetric ratiοs describe these οperatiοns. The sine functiοn, cοsine functiοn, secant functiοn, cο-secant functiοn, tangent functiοn, and cο-tangent functiοn are the six fundamental trigοnοmetric functiοns.

The ratiο οf sides οf a right-angled triangle is the basis fοr trigοnοmetric functiοns and identities. Using trigοnοmetric fοrmulas, the sine, cοsine, tangent, secant, and cοtangent values are calculated fοr the perpendicular side, hypοtenuse, and base οf a right triangle.

In the figure tanx = p/h

[tex]x = tan^{-1(15/18)}[/tex]

x = 39.8

Hence the value οf the given angle x = 39.8 degree

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Answer:

They are similar

Step-by-step explanation:

It's because 27/18 = 12/8

27/18 = 1.5

12/8 = 1.5

When rounded to two decimal places, the radius of the can is approximately 1.6 inches.

Surface fοrmed by a straight line mοving parallel tο a fixed straight line and intersecting a fixed planar clοsed curve. a sοlid οr surface defined by a cylinder and twο parallel planes that cut all οf its elements. See Vοlume Fοrmulas Table, particularly fοr the right circular cylinder.

The volume of a cylinder can be calculated using the following formula:

V = πr²h

where

V denotes volume,

r denotes radius, and

h denotes height.

The cylindrical aluminium can has a height of 7 inches and a volume of 56 cubic inches. We can calculate the radius using the volume of a cylinder formula:

V = πr²h

56 = πr²(7)

56 = (22/7)r²(7)

56 = 22r²

56/22 = r²

2.54 = r²

r = [tex]\sqrt{2.54}[/tex]

r ≈ 1.6

As a result, when rounded to two decimal places, the radius of the can is approximately 1.6 inches.

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The answer of the given question is (a) TR = p(40 - (4/3)p), or TR = 40p - (4/3)p² , (b)  TC = 9q + (3/10)q² + 30 , (c) π = 40p - (4/3)p² - 9q - (3/10)q² - 30 , (d) TR ≈ 342.67 , (e) the profit when 20 units are produced is approximately RM188.27 , (f)  the profit when 7 units are produced is approximately -RM24.44, indicating a loss , (g) the output required to obtain a profit of RM100 is approximately 8.78 units.

An equation is  mathematical statement that asserts yhe equality of two expressions. It typically consists of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division, among others. Equations are often used to solve problems, to model real-world phenomena, and to describe mathematical relationships.

(a) The total revenue is given by TR = p x q. Substituting the demand equation q = 40 - (4/3)p, we get TR = p(40 - (4/3)p), or TR = 40p - (4/3)p².

(b) The total cost is given by TC = q x AC. Substituting the given average cost function, we get TC = 9q + (3/10)q² + 30.

(c) The profit is given by π = TR - TC. Substituting the expressions we found in parts (a) and (b), we get π = 40p - (4/3)p² - 9q - (3/10)q² - 30.

(d) At the break even point, the firm earns zero profit, so we set π = 0 and solve for q. Substituting the expression we found in part (a) for p, we get:

0 = 40p - (4/3)p² - 9q - (3/10)q² - 30

0 = 40(40/3 - (3/4)q) - (4/3)(40/3 - (3/4)q)² - 9q - (3/10)q² - 30

0 = 533.33 - 51.25q - 0.22q^2

Solving for q using the quadratic formula, we get:

q = (51.25 ± sqrt(51.25² - 4(-0.22)(533.33))) / 2(-0.22)

q ≈ 22.75 or q ≈ 206.58

We reject the solution q ≈ 206.58 because it is outside the relevant range of output, which is between 0 and 40. Therefore, the total output at the break even point is approximately 22.75 units. To find the total revenue at the break even point, we substitute q = 22.75 into the demand equation from part (a) and get:

p = (40/3) - (3/4)q

p ≈ 15.08

TR = p x q

TR ≈ 342.67

(e) To find the profit when 20 units are produced, we substitute q = 20 into the expression for profit we found in part (c) and get:

π = 40p - (4/3)p² - 9q - (3/10)q² - 30

π ≈ 188.27

Therefore, the profit when 20 units are produced is approximately RM188.27.

(f) To find the profit when 7 units are produced, we substitute q = 7 into the expression for profit we found in part (c) and get:

π = 40p - (4/3)p² - 9q - (3/10)q² - 30

π ≈ -24.44

Therefore, the profit when 7 units are produced is approximately -RM24.44, indicating a loss.

(g) To find the output required to obtain a profit of RM100, we set the profit equation equal to 100 and solve for q:

Profit = TR - TC

100 = pq - ACq

100 = (40-(4/3)p)*q - (9+(3/10)q+30/q)*q

100 = (40-(4/3)p - 9q - 3q²/10)

Multiplying by 10 and rearranging terms, we get a quadratic equation in q:

3q² + 91q - 310 = 0

Solving for q using the quadratic formula, we get:

q = (-91 ± sqrt(91² - 43(-310)))/(2*3)

q ≈ 8.78 or q ≈ -29.44

Since the quantity produced cannot be negative, the output required to obtain a profit of RM100 is approximately 8.78 units.

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Hence the conversion of given numbers according to given demand is

a) N=217 in binary = 11011001

b) N=99 in hexadecimal = 63

c) N= 344 in hexadecimal = 158

d) N= 136 in base 7 = 253.

e) N= 542 in base 5 = 4132.

f) N= 727 in base 8= 1327

g) N= 171 in hexa =1011

h) N=91 in base 3=10101.

i) N= 840 in base 9 =  1133

a) A good method to convert a decimal number to binary is dividing it by 2 and using the remainder of the division as the converted number, starting by the most significant bit (the right one). We can't divide anymore. So we have:

217÷2 = 108 + 1

108÷2 = 54 + 0

54÷2 = 27 + 0

27÷2 = 13 + 1

13÷2 = 6 + 1

6÷2 = 3 + 0

3÷2 = 2 +1

2÷2 = 1

The binary equivalent to 217 is 11011001

b) To convert a number from decimal to hex we can divide the number by 16, taking out the decimal part and multiplying it by 16 using that as our most significant number while using the result of the original division to continue our conversion. So we have:

99÷16 = 6.1875

The decimal part is 0.1875, we multiply it by 16 and obtain 3 as our most significant number. Since we can't divide 6 by 16 we have that as our least significant number then the hexadecimal equivalent is 63.

c) We follow the same steps as in item b:

344÷16 = 21.5

The most significant number is 0.5*16 = 8

21÷16 = 1.3125

The next number is 0.3125*16 = 5

Since we can't divide it anymore we have our result which is 158 in hex.

d) To convert from decimal to base 7 we'll use the same method as to hex, but this time dividing and multiplying by 7.

136÷7 = 19.428571

The most significant number is 0.428571 * 7 = 3

19÷7 = 2.71428571

The next number is 0.71428571*7 = 5

Since we can't divide it anymore we have our result which is 253.

e) To convert from decimal to a base 5 we'll use the same method as before but dividing and multiplying by 5.

542÷5 = 108.4

The most significant number is 0.4*5 = 2

108÷5 = 21.6

The next number is 0.6*5 = 3

21÷5 = 4.2

The next number is 0.2*5 = 1

Since we can't divide it anymore we have our result which is 4132.

f) To convert from decimal to a base 8 we'll use the same method as before but dividing and multiplying by 8.

727÷8 = 90.875

The most significant number is 0.875*8 = 7

90÷8 = 11.25

The next number is 0.25*8 = 2

11÷8 = 1.375

The next number is 0.375*8 = 3

Since we can't divide anymore we have our result which is 1327

g) Following the same steps as before:

171÷16 = 10.6875

The most significant number is 0.6875*16 = 11

Since we can't divide anymore we have our result which is 1011

h) Following the same steps as before:

91÷3 = 30.333333333

The most significant number is 0.333333*3 = 1

30÷3 = 10

The next number is 0

10÷3 = 3.3333333333

The next number is 0.333333*3 = 1

3÷3 = 1

Since we have the final value remainder as 0 the least significant number is 1

Since we can't divide anymore we have our result which is 10101.

i) Following the same steps as before:

840÷9 = 93.333333

The most significant number is 0.33333*9 = 3

93÷9 =  10.3333333

The next number is 0.333333*9 = 3

10÷9 = 1.11111111

The next number is 0.11111111*9 = 1

Since we can't divide anymore we have our result which is 1133

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

we have 2 possible cases for the coin and 6 possible cases for the die.

so, we have 2×6 = 12 combined possible cases :

heads, 1

heads, 2

heads, 3

heads, 4

heads, 5

heads, 6

tails, 1

tails, 2

tails, 3

tails, 4

tails, 5

tails, 6

out of these 12 cases, which ones (how many) are desired ?

all first 6 plus (tails, 3) = 7 cases

so, the correct probability is

7/12

formally that is calculated :

1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12

the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.