Graph the line. y = -x - 3

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer: D. 18

Step-by-step explanation:

      We will use the order of operations (sometimes known as PEMDAS).

Given:

  2(4 - 1)²

Subtraction:

  2(3)²

Square:

  2(9)

Multiply:

  18

             D. 18

The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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The distance between A and B based on the diagram is approximately 1,685.2 cm.

Hypotenuse = 1,920 cm

Adjacent = 920 cm

A and B = opposite

Hypotenuse² = adjacent² + opposite²

1920² = 920² + AB²

3,686,400 = 846,400 + AB²

3,686,400 - 846,400 = AB²

2,840,000 = AB²

find the square root of both sides

AB = √2,840,000

AB = 1685.229954635271

Approximately,

AB = 1,685.2 cm

Hence, distance between A and B is 1,685.2 cm.

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The value of dy/dt  at x= 1 if y = [tex]3x^2[/tex] - 3 and dx/dt = 3 is 18.

To find dy/dt at x = 1, we need to differentiate the given equation y = [tex]3x^2[/tex] - 3 with respect to t and then substitute x = 1 and dx/dt = 3.

Let's begin by differentiating y = [tex]3x^2[/tex]- 3 with respect to t using the chain rule. Since y is a function of x and x is a function of t, we have:

dy/dt = (dy/dx) * (dx/dt)

Given dx/dt = 3, we can rewrite the equation as:

dy/dt = [tex](dy/dx) * 3[/tex]

Now, let's find the derivative of y = [tex]3x^2 - 3[/tex] with respect to x:

dy/dx = d/dx[tex](3x^2 - 3)[/tex]

= 6x

Substituting this back into the equation for dy/dt, we get:

dy/dt = [tex](6x) * 3[/tex]

= 18x

Finally, we can evaluate dy/dt at x = 1:

dy/dt at x = 1 = 18(1)

= 18

Therefore, the value of dy/dt at x = 1 is 18.

It's important to note that the value of dx/dt = 3 was given, and we used it to find dy/dt using the chain rule and the derivative of the equation with respect to x.


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We can make the decision as per rational or irrational from the solution of the equations.

A. The solution is irrational

B. The solution is rational

C. The solution is rational

D. The solution is irrational

A rational solution refers to a solution that can be expressed as a ratio of two integers, where the denominator is not zero. It is a value that satisfies an equation or inequality and can be written in the form of a fraction.

For the equation[tex]5x^2 + 4x - 14 = 0[/tex], we obtain the solution as;

-2/5 ±1/5√74

For the equation we have that[tex]4x^2 + 8x - 5 =0[/tex]. The solution would be x = 1/2 or -5/2

For the third equation we have that [tex]x^2 + x - 42 = 0[/tex] The solution is x = 6 and -7

For the fourth equation; is 3x^2 + 4x - 2= 0. The solution of the equation is -2/3 ± 1/3√10

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Answer: x=15

Step-by-step explanation:

If JH is a midsegment, then J is the midpoint of LK and H is the midpoint of KM. This also means that triangles JKH and triangles LKM are similar. Since H is the midpoint of KM, assume KM = 2y (KH=y). 30/x=2/1. Thus x=15.

Answer:

x = 15

Step-by-step explanation:

The midsegment of a triangle is a line segment that connects the midpoints of two sides of a triangle.

Therefore, if JH is the midsegment of ΔKLM then JH is parallel to LM, and triangles KJH and KLM are similar: ΔKJH ~ ΔKLM.

In similar triangles, corresponding sides are always in the same ratio.

Since JH is the midsegment of ΔKLM, then KJ is half the length of KL, and KH is half the length of KM. This means that JH is half the length of LM.

Given the measure of LM is 30:

[tex]x=\overline{JH}=\dfrac{30}{2}=15[/tex]

Answer: (C) 1/3

Step-by-step explanation:

Look at the base lengths. For A'B'C', the length is 2. For ABC, it is 6. The ratio of the length of A'B'C' to the length of ABC is 1/3. Thus the answer is C.

Answer:

The product of each pair of complex conjugates is:

(3 + 8i)(3 – 8i) = (9 - 8^2) + i(9 + 8^2) = (-81) + i(99) = (-81) + i(11) = (-81) + 11i

And

(4 + 5i)(4 – 5i) = (16 - 25) + i(16 + 25) = (-9) + i(41) = (-9) + 41i

So, the products are:

(-81) + 11i

and

(-9) + 41i

Answer:

73

41

Step-by-step explanation:

The value of c in the domain of f(x) depends on the specific function f(x) and its domain.

In order to determine which value of c is in the domain of f(x), we need to know the function f(x) and its domain. A domain is the set of all possible input values of a function.

If a value of c is in the domain of f(x), then we can plug it into the function and get a valid output.

In general, a function f(x) can have a restricted domain due to certain conditions or limitations. For example, a square root function cannot have negative values under the radical because that would result in an imaginary number.

Thus, the domain of a square root function is restricted to non-negative values.

In order to find the domain of a function, we need to consider any restrictions on the input values. For example, if we have the function f(x) = 1/x, we cannot plug in x = 0 because that would result in division by zero, which is undefined.

Therefore, the domain of f(x) is all real numbers except 0. We can write this as D(f) = {x : x ≠ 0}.Once we know the domain of f(x), we can check which value of c is in the domain by seeing if it satisfies the condition.

For example, if the domain of f(x) is D(f) = {x : x > 2}, then c = 3 is in the domain because 3 is greater than 2. On the other hand, c = 1 is not in the domain because 1 is less than 2.

Therefore, the value of c in the domain of f(x) depends on the specific function f(x) and its domain.

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To calculate the monthly house payment for a $65,000 home loan with a 5.25% annual percentage rate (APR) over a 25-year term, we can use the formula for calculating the monthly payment on an amortizing loan. The formula is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Loan principal amount

r = Monthly interest rate (APR divided by 12 and expressed as a decimal)

n = Total number of monthly payments (number of years multiplied by 12)

Let's calculate the values and substitute them into the formula:

P = $65,000

r = 5.25% / 100 / 12 = 0.004375

n = 25 * 12 = 300

Now, let's plug these values into the formula:

M = 65000 * (0.004375 * (1 + 0.004375)^300) / ((1 + 0.004375)^300 - 1)

After evaluating this expression, the monthly house payment, rounded to the nearest cent, would be approximately $406.23.

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The truth values of the statements can be determined as follows:

Statement p: "A square has 4 sides."

This statement is true. A square is a polygon with four equal sides and four equal angles, so it has 4 sides.

Statement q: "A triangle has 5 sides."

This statement is false. A triangle is a polygon with three sides and three angles, not five. It is a fundamental geometric shape with specific characteristics, and one of those characteristics is having three sides.Therefore, the truth values of the statements are:

p is true.

q is false.

It's important to note that truth values are based on established definitions and properties of geometric shapes. The statement p aligns with the definition of a square, while the statement q contradicts the definition of a triangle.

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The points will  meet x when it is folded are C or E

A point is a location of an item by taking reference of the origin, in typical case we regard it at (0,0), At the origin value of both the coordinate position is considered to be Zero, In simple words point indicates how much it is above or below the coordinate axes.

The vertical distance from the x axis is referred to as the y coordinate, while the horizontal distance from the x axis is referred to as the x coordinate.

A green colored Net,

After folding x point will  meet the points = ?

When we start folding,

First step,

Side ABCD and DEFG will be folded,

C and E will meet with each other

Second Step,

Side ABCD and AGHI will be folded,

B and I will meet with each other

Third step,

Side DEFG and AGHI will be folded,

F and H will meet each other

Fourth step,

Upper portion AHI will cover the upper portion BCF of the box

X will at position of C or E

Hence, the X will meet

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The following question may be like this:

When this net is folded up, which two points meet X?

The expression which represents the quotient of the model is x² + 5x.

The correct answer choice is option B.

The quotient of a number is the number resulting from the division of one number by another.

There is one x²

There are 5 x

Hence, the quotient of the expression is x² + 5x

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To calculate the ratio as a decimal, we divide the number of owners by the total population for each city.

For Indianapolis: Ratio = 6,245 / 0.9 million = 0.006938

For New York: Ratio = 911,216 / 18.6 million = 0.049019

For Cairo: Ratio = 10,598 / 19.1 million = 0.000554

For Beijing: Ratio = 959,611 / 21.2 million = 0.045270

For Tokyo: Ratio = 1,700,510 / 26.5 million = 0.064234

To calculate the owners per 100, we multiply the ratio by 100.

For Indianapolis: Owners per 100 = 0.006938 * 100 = 0.7 (rounded to one decimal place)

For New York: Owners per 100 = 0.049019 * 100 = 4.9 (rounded to one decimal place)

For Cairo: Owners per 100 = 0.000554 * 100 = 0.1 (rounded to one decimal place)

For Beijing: Owners per 100 = 0.045270 * 100 = 4.5 (rounded to one decimal place)

For Tokyo: Owners per 100 = 0.064234 * 100 = 6.4 (rounded to one decimal place)

Therefore, the ratio as a decimal and the owners per 100 for each city are as follows:

Indianapolis: Ratio = 0.006938, Owners per 100 = 0.7

New York: Ratio = 0.049019, Owners per 100 = 4.9

Cairo: Ratio = 0.000554, Owners per 100 = 0.1

Beijing: Ratio = 0.045270, Owners per 100 = 4.5

Tokyo: Ratio = 0.064234, Owners per 100 = 6.4

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Answer:

7*pi

Step-by-step explanation:

If the diameter is 7, the radius is 7/2

Therefore, the circumference would be 2*pi*(7/2)=7*pi

About of Bhutan's population lives in Thimphu Dzongkhag. Chhukha Dzongkhag has about of 3 4 the population of Thimphu Dzongkhag. Approximately 3/7  fraction of Bhutan's population resides in Chhukha Dzongkhag.

Let's denote the population of Thimphu Dzongkhag as T and the population of Chhukha Dzongkhag as C. We are given that "about 3/4" of Thimphu Dzongkhag's population is the population of Chhukha Dzongkhag.

Mathematically, this can be represented as:

C = (3/4) * T

Now, we need to determine the fraction of Bhutan's population that lives in Chhukha Dzongkhag. To do this, we need to calculate the fraction C/(T+C).

Substituting the value of C from the equation above:

C/(T+C) = [(3/4) * T] / (T + [(3/4) * T])

Simplifying the expression:

C/(T+C) = (3/4) * T / (T + (3/4) * T)

        = (3/4) * T / (4/4 * T + 3/4 * T)

        = (3/4) * T / (7/4) * T

        = (3/4) / (7/4)

        = 3/7

Therefore, the fraction of Bhutan's population that lives in Chhukha Dzongkhag is 3/7.

This calculation is based on the given information that Chhukha Dzongkhag has about 3/4 the population of Thimphu Dzongkhag.

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When given that x + y = 4, the algebric expression 2(x + y) simplifies to 8.

To find the value of 2(x + y) when given that x + y = 4, we can substitute the value of x + y into the expression.

We are given x + y = 4.

To solve for 2(x + y), we multiply both sides of the equation x + y = 4 by 2:

2(x + y) = 2 * 4

This simplifies to:

2(x + y) = 8

Therefore, the value of 2(x + y) is 8.

To explain the reasoning behind this, let's break it down step by step:

1. We start with the equation x + y = 4.

2. To find 2(x + y), we distribute the 2 to both terms inside the parentheses: 2 * x + 2 * y.

3. This simplifies to 2x + 2y.

4. Since x + y = 4, we can substitute 4 for x + y in the expression 2x + 2y.

5. Therefore, 2(x + y) becomes 2 * 4, which equals 8.

In summary, when given that x + y = 4, the expression 2(x + y) simplifies to 8.

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(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.

Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.

Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.

(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).

Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.

(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.

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Nave Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 27.27%.

To calculate the manufacturing cycle efficiency (MCE) for Nave Corporation's elevators, we need to determine the ratio of value-added time to the total lead time.

Value-added time refers to the time spent on activities that directly contribute to the production or customization of the elevators, while lead time refers to the total time from order placement to installation.

Given the breakdown of time:

12 days for manufacturing and customization

5 days for waiting or non-value-added time

The value-added time is 12 days, and the total lead time is 44 days.

To calculate MCE, we divide the value-added time by the total lead time and multiply by 100 to express it as a percentage:

MCE = (Value-added time / Total lead time) x 100

MCE = (12 / 44) x 100

MCE = 27.27%

Therefore, Nave Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 27.27%.

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Step-by-step explanation:

The circumference of a circle can be found using the formula:

C = πd

where C represents the circumference and d represents the diameter of the circle.

Given that the diameter of the circle is 4 feet, we can substitute this value into the formula:

C = π * 4

Therefore, the circumference of the circle is 4π feet.

The missing term in the polynomial X^3 - 95 is 0x^2.

Option A (Both 0x^2 and 0x) is the correct answer choice, as 0x represents the missing term with a degree of x (linear term) as well.

In the polynomial expression X^3 - 95, we can observe that there is a missing term with an x^2 degree.

To identify the missing term, we need to consider the standard form of a polynomial expression, which is written in descending order of exponents. In this case, the highest exponent present is x^3, followed by a constant term (-95).

To fill in the missing term, we look for the term with an x^2 degree. Since it is not present in the given expression, we can conclude that the missing term is 0x^2.

Therefore, the missing term in the polynomial X^3 - 95 is 0x^2.

Option A (Both 0x^2 and 0x) is the correct answer choice, as 0x represents the missing term with a degree of x (linear term) as well.

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The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

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Answer:

-5/6

-2/3

Step-by-step explanation:

it's easiest to write the line in the following form:

y=mx+b

where m is the slope

and b is the y intercept

In other words, we want to get y by itself

5x+6y= -4

6y= -4-5x

y=(-4-5x)/6

y=(-5/6)x-4/6

Thus, -5/6 is the slope

and -4/6= -2/3 is the y intercept

The transformation T maps the unit square to a figure with an area of 24 and a vertex at (5,3) which gives: T(x, y) = (6x + 5, 8y + 3).

To find a transformation T that maps the unit square to a figure with an area of 24 and a vertex at (5,3), we can use a combination of scaling and translation.

Let's denote the unit square as S, and the transformed figure as F.

To obtain a rectangle with an area of 48 and a vertex at (5,3), we can scale the unit square by multiplying the x-coordinates by 6 and the y-coordinates by 8, and then translate the scaled rectangle by adding (5,3) to the coordinates of each point.

Therefore, the transformation T can be expressed as:

T(x, y) = (6x + 5, 8y + 3)

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The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:

Point 1: (1, 0)

Point 2: (3, 6)

Step 1: Calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates:

m = (6 - 0) / (3 - 1)

m = 6 / 2

m = 3

Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).

Using Point 1 (1, 0):

0 = 3(1) + b

0 = 3 + b

b = -3

Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):

y = 3x - 3

Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.

Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.

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1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.

3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.

4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.

5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.

6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.

The manufacturing cycle efficiency (MCE) of Navems for its elevators is 38.6%

The correct answer choice is option A.

Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time.

Value-added production time;

Inspection time = 12 days

Process time = 5 days

Total = 17 days

Total cycle time:

Wait time = 12 days

Inspection time = 12 days

Process time = 5 days

Move time = 6 days

Queue time = 9 days

= 44 days

Hence,

Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time × 100

= 17 days / 44 days × 100

= 38.63636363636363

Approximately,

38.6%

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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(a)The experimental probability of rolling an odd number is 3/5.

(b) The theoretical probability of rolling an odd number is 1/2.

(c)The true statement is:

With a small number of rolls, it is not surprising when the experimental probability is much greater than the theoretical probability.

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments.

Theoretical probability is the theory behind probability. To find the probability of an event, an experiment is not required. Instead, we should know about the situation to find the probability of an event occurring.

We have:

Kala rolled a number cube 20 times.

(a) From Kala's results, odd number (1, 3 and 5) appearance is:

4 + 4 + 4 = 12

Thus, the experimental probability of rolling an odd number will be:

12/20 = 3/5

(b) If the cube is fair, we have the numbers have equal chance of appearance.

Theoretically, an odd numbers (1, 3 and 5) will have the probability of 3 out of 6 as illustrated with the numbers below:

1, 2, 3, 4, 5, 6

The theoretical probability of rolling an odd number will be:

3/6 = 1/2

(c)The true statement is:

With a small number of rolls, it is not surprising when the experimental probability is much greater than the theoretical probability.

Because when conducting a small number of rolls with a fair cube, the experimental probability may not necessarily align closely with the theoretical probability.

This difference is expected due to the limited sample size. As the number of rolls increases, the experimental probability tends to converge towards the theoretical probability.

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