Evaluate 2(4 -1)2.
A. 30
B. 60
C. 36
D. 18​

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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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

Answer:

The 3.907 is approximate.

====================================

Explanation:

x = number of hours that elapse

y = f(x) = number of tokens

If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907

At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.

The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907

------------

Plug in x = 0 to find y = 84. This is the largest value in the range.

The smallest value is y = 0.

The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84

Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.

The x value can be fractional because 3.907 hours for instance is valid.

------------

Extra info:

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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Answer:

Diameter=20 cm, Area=100[tex]\pi[/tex]

Step-by-step explanation:

To find the diamter of a circle (given the radius), you multiply the radius by 2.  10cm*2=20 cm.  The area of a circle is the radius squared times pi.  10^2 times pi is equal to 100[tex]\pi[/tex].

x = 8.33 and the solution to the equation 12x = 100 is x = 8.33 (rounded to the nearest hundredth).

To solve the equation 12x = 100, we need to isolate the variable x. We can do this by dividing both sides of the equation by 12.

12x = 100

Dividing both sides by 12:

(12x)/12 = 100/12

Simplifying:

x = 100/12

Now, let's calculate the value of x.

x = 8.33 (rounded to the nearest hundredth)

Therefore, the solution to the equation 12x = 100 is x = 8.33 (rounded to the nearest hundredth).

Here's the step-by-step solution:

12x = 100 (given equation)

Divide both sides by 12: (12x)/12 = 100/12

Simplify: x = 8.33

Please note that the answer is rounded to the nearest hundredth as requested.

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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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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?

Answer: 50$

Step-by-step explanation:

To calculate the amount the college student can spend on fast food in December, we need to find the total amount he can spend in 5 months, given that he wants to spend an average of $50 per month.

Let's start by finding the total amount he can spend in 5 months:

Total amount = 5 x $50 = $250

Now, we can subtract the amount he spent in the other 4 months from the total amount to find out how much he can spend in December:

The amount he can spend in December = Total amount - Amount spent in 4 months

Amount spent in 4 months = $35 + $90 + $15 + $60 = $200

Amount he can spend in December = $250 - $200 = $50

Therefore, the college student can spend $50 on fast food in December to meet his goal of spending an average of $50 per month on fast food for the remaining 5 months of the year.

If the bottle is completely full at 11:40 a.m., the statements that help explain this result include:

Exponential growth involves a pattern or process that increases the initial quantity or value over time at a constant rate.

In an exponential growth situation, the rate or speed of growth remains proportional to the initial population.

The reasons for choosing Options A, B, and D follow:

Option A: at 11:35 a.m., the bottle was 1/2 full.  If at 11:40 a.m. it is completely full, it implies that it takes 5 minutes to become full (11:40 a.m. - 11:35 a.m.)

Option B: At 11:30 a.m., the bottle was 1/4 full and 10 minutes later, 11:40 a.m. it was full, meaning that it doubled its volume after 10 minutes.

Option D: Exponential growth involves a constant rate of growth and can be expressed as a(1+r)ˣ, where a is the initial value or quantity, r is the growth rate, 1+r is the growth factor,, and x is the exponent in time.

Thus, in this situation, the correct options are A, B, and D.

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A) The bottle was 1/2 full at 11:35 a.m. and doubled again after 5 minutes means that at 11:40 a.m. the bottle is completely full.

B) The bottle was 1/4 full at 11:30 a.m. and doubled twice after 10 minutes means that at 11:40 a.m. the bottle is completely full.

C) The bottle was 1/2 full at 11:35 a.m. and more bacteria were added to fill the bottle means that the bottle is completely full but with bacteria present in it.

D) Exponential growth involves a constant multiplicative rate of change means that bottle level rises with a constant multiplicative rate of change.

E) Exponential growth involves a constant additive rate of change means that bottle level rises with a constant additive rate of change.

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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Answer:

The Answer Will Be 16

Step-by-step explanation:

Beacuse , To Find Number of subsets we can use 2n Where 2 is number can't be changed but n is cardinal number so it's 16

type the whole number 16

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 area of the trapezium with bases 20cm and 10cm and a height of 16cm is 240 square centimeters.

A trapezium is simply a two-dimensional quadrilateral that has one pair of parallel sides.

The area of a trapezium is expressed as:

Area = 1/2 × ( a + b ) × h

Where a and b are the base measure and h is the height.

From the diagram:

Base a = 20 cm

Base b = 10 cm

Height h 16 cm

Area = ?

Plug the values into the above formula and solve for the area:

Area = 1/2 × ( a + b ) × h

Area = 1/2 × ( 20 + 10 ) × 16

Area = 1/2 × ( 30 ) × 16

Area = 15 × 16

Area = 240 cm²

Therefore, the area of the trapezium is 240 square centimeters.

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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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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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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.

To create a box from a flat piece of metal, you typically cut equal-sized squares from each corner, then fold up the sides. This effectively reduces the size of the base of the final box by twice the length of the side of the squares.

The original size of the piece of tin is 40 cm x 70 cm. Let's represent the length of the side of the squares cut from the corners as x (in cm). After the squares are removed, the size of the base of the box will be (40 - 2x) cm by (70 - 2x) cm.

The problem states that the base area of the box is 1984 cm^2. Thus, we can set up the following equation:

(40 - 2x) * (70 - 2x) = 1984.

Expanding this equation gives:

2800 - 140x - 80x + 4x^2 = 1984,

4x^2 - 220x + 2800 = 1984,

4x^2 - 220x + 816 = 0.

Dividing through by 4 gives:

x^2 - 55x + 204 = 0.

This quadratic equation can be solved using the quadratic formula, x = [ -b ± sqrt(b^2 - 4ac) ] / 2a. Here, a = 1, b = -55, and c = 204.

The discriminant, b^2 - 4ac = (-55)^2 - 4*1*204 = 3025 - 816 = 2209.

The square root of 2209 is 47.

Therefore, the solutions for x are:

x = [55 ± 47] / 2

x = 51, 4.

Since the length of the sides of the squares (x) must be less than half the length of the shorter side of the original tin piece (which is 40 cm / 2 = 20 cm), the valid solution is x = 4 cm. Thus, each square cut from the corners is 4 cm on a side.

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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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:

Answer:

(A) AA similarity

Step-by-step explanation:

In ΔABC,

∠A + ∠B + ∠C = 180

∠A + 27 + 90 = 180

∠A = 180 - 90 - 27

∠A = 63

Comparing ΔABC and ΔMNP,

∠A = ∠M = 63

∠C = ∠P = 90

Therfore, by AA property, the two triangles are similar

Answer: y = (-28)x + 14

Step-by-step explanation:

The equation for the line tangent at point (a, b) can be found using the formula y = mx + c, where m is the slope of the line and c is the y-intercept. At point (6, 14), we need to find the value of m.

We start by finding the derivative of the original function g(x). Its derivative is given by:

dg(x)/dx=7/(x^2-3x+1)

Then, substitute x = 6 into the derivative expression to obtain:

dg(6)/dx = d/dx [7 * ln|x-3| ] evaluated at x = 6 = 7/3

Next, evaluate the original function g(x) at x = 6 to get g(6) = 7 * ln |6 - 3| / (6 - 3) = 7 * ln 3.

Since we know the coordinates of the point of tangency (6, 14), we can substitute them into the general form of the linear equation y = mx + c:

14 = 7 * 6 + c

14 = 42 + c

c = -28

The final equation of the line tangent at point (6, 14) is therefore:

y = (-28)x + 14

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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(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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The measure of line segment x in the game board is approximately 13.6.

The secant-tangent power theorem states that "if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

It is expressed as:

( tangent segment )² = External part of the secant segment × Secant segment.

From the given figure:

Let;

Tangent segment = 12

Secant segment = 7 + x

External part of the secant segment = 7

Plug these values into the above formula and solve for x.

( tangent segment )² = External part of the secant segment × Secant segment.

12² = 7( 7 + x)

144 = 49 + 7x

7x = 144 - 49

7x = 95

x = 95/7

x = 13.6

Therefore, the value of x is approximately 13.6.

Option C) 13.6 is the correct answer.

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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

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]

(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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The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that [tex]c^2 = a^2 + b^2[/tex] - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get [tex]c^2 = 43^2 + 67^2[/tex] - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get [tex]c^2[/tex] ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have [tex]c^2[/tex] ≈ 6338 - 5156.898.

7. Calculating [tex]c^2[/tex], we find [tex]c^2[/tex] ≈ 1181.102.

8. Finally, taking the square root of [tex]c^2[/tex], we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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