[10 Points] In the standard numbering (shortlex ordering) of strings over the alphabet {a,b,c} what number corresponds to string cbbca cba cbc ?

The probability of F′∪A 0.9829

The probability can be defined as the likelihood that an event is going to happen.

We are to find the probability F′∪A.

What is F'

This is gotten as 1 - probability of F

F' = 1 - 0.2058

F' = 0.7942

Then we are to get the probability of event A from the question

P(A) = 0.1887

Hence the probability of F′∪A.

= P(A) + P(F`)

= 0.1887 + 0.7942

= 0.9829

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x is a component of the real number system 11 < 3x-2 ≤ 19, although as a compound inequality, it also belongs to 13/3 and 7.

A interaction between two terms or concepts that is neither equal in mathematics is referred to as an inequality. Consequently, inequity results from imbalance. In algebra, an inequality establishes the connection between two non-equal numbers. Egality and inequalities are not the same. Use the not comparable symbol most usually when two components are really not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two aspects until only the variables are left, many straightforward inequalities can be solved. But, a variety of factors support inequality: Both sides' 0 are split or added. Exchange the left and the right.

given

11 < 3x-2 ≤ 19

11< 3x-2

3x-2 ≤ 19

11+ 2 < (3x-2)+ 2

(3x-2)+ 2 ≤ 19 + 2

x belongs to 13/3 and 7

x is a component of the real number system 11 < 3x-2 ≤ 19, although as a compound inequality, it also belongs to 13/3 and 7.

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Problem 1

L = length

W = width

P = perimeter of the rectangle

P = 2L+2W

P = 20

2L+2W = 20

L+W = 10 after dividing everything by 2.

L = 10-W

area = length*width

A = L*W

A = (10-W)*W

A = -W^2 + 10W

Let x replace W for a temporary basis.

If we graphed y = -x^2+10x, then we'd see the highest point occurs at (5, 25). This means a width of 5 meters leads to the largest area of 25 square meters.

The length would be L = 10-W = 10-5 = 5 meters as well.

It turns out that a 5 meter by 5 meter square is the best choice when trying to max out this rectangle's area.

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

Problem 2

The results we got from the previous section was that a 5 by 5 square will max out the area.

If we allowed non-whole numbers into the mix, then it wouldn't change the previous answer. The best choice is still that 5 by 5 square.

The answer only would change if the result of the previous section was some non-integer value.

Answer: 485 is the answer.

Step-by-step explanation:

The required demand function and revenue per ticket are p(x) = -0.4 * (x - 21000) + $9 and  $9.

a) To find the demand function p(x), we can use the two data points: (21000, $9) and (26000, $7). To find the slope of the demand function, we can use the formula:

slope = (change in price) / (change in attendance)

Plugging in the two data points, we get:

slope = ($9 - $7) / (26000 - 21000) = -$2 / 5000 = -0.4

To find the y-intercept, we can use either data point and the slope we just found. Let's use the first data point:

p(x) = slope * (x - 21000) + $9

Now we have our demand function:

p(x) = -0.4 * (x - 21000) + $9

b) To maximize revenue, we need to find the price that will result in the maximum number of tickets sold. This is equal to the price that corresponds to the peak of the demand function, or the maximum value of x for which p(x) is decreasing. To find this, we can take the derivative of the demand function and set it equal to zero:

dp/dx = -0.4 = 0

x = 21000

So the maximum revenue is obtained by selling 21000 tickets at the price of $9 each, for a total revenue of $189,000. To maximize revenue, the ticket price should be set at $9.

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According to the question we have ,The area covered by the spotlight is 153.86 square feet. The correct option is c.

The diameter of a circle cuts through center whereas the radius extends from the center to the edges of the circle. A circle's diameter effectively splits the shape in half. The radius of a circle is the distance from the middle to any point on the edge. The diameter the radius are inversely proportional, or 2r=d2 r=d. A line connecting two points on either a circle is referred to as a chord.

We have the formula of Area of a circle: A = π[tex]r^2.[/tex]

According to the question we have ,there is a spotlight above the center of the ground that surrounds a 7-foot-radius lit area.

A = π[tex]r^2[/tex]. = π * [tex]7^2[/tex]

= 3.14 * 49 = 153.86 square feet.

So, the area covered by the spotlight is 153.86 square feet.

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The next shape in the pattern has four intersecting lines.

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

From the given pattern, we can see the number of lines are increasing.

In the next pattern there will 4 lines.

Therefore, the next shape in the pattern has four intersecting lines.

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The fifth term of the geometric progression is given as 1280

The formula for calculating the nth term of a geometric progression is expressed as:

Tn = ar^n-1

Given the following

First term = a = 5

Third term = ar^2 = 80

Determine the common ratio

5(r^2) = 80
r^2 = 16

r = 4

For the 5th term

T5 = ar^4

T5 = 5(4)^4
T5 = 1280

Hence the fifth term of the expression is 1280

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Complete question

The first and third term of a Gip are 5 and 80 respectively. What is the fifth term​

The surface area of the [tex]132cm^2.[/tex]

The surface area of a triangular prism is also referred to as its total surface area. The total surface area of a triangular prism is the sum of the areas of all the faces of the prism. A triangular prism has three rectangular faces and two triangular faces. The rectangular faces are said to be the lateral faces, while the triangular faces are called bases. If the bases of a triangular prism are placed horizontally, they are referred to as the top and the bottom (faces) of the prism, respectively.

Surface area of given triangular shaped prism

= 2 ×area of right angle triangle + area of3 rectangles

= 2(1/2 ab)+(ah+bh+ch)

=(3 cmx4 cm) +(3cm×10 cm +4cm×10cm+5cm×10cm)

=[tex]12 cm^2 +30cm^2+40cm^2+50cm^2=132cm^2[/tex]

Volume of prism = Area of base × height

=> V=( 1/2 ab) × height= 1/2 × 3 cm×4cm× 10 cm =[tex]60 cm^3[/tex]

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-22 < 7x is the inequality that is equivalent to the given inequality.

What is inequality?

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a < b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

Here, we have

Given: -4(x + 7) < 3(x - 2)

To find out which inequality is equivalent, you solve for x.

-4(x+7) < 3(x-2): distribute variables

-4x-28 < 3x-6: Add 6 to both sided

-4x-22 < 3x: add 4x to both sides

-22 < 7x

Hence,  -22 < 7x is the inequality that is equivalent to the given inequality.

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The coordinates of the position at which Pablo should stand are given as follows:

(6, 7.5).

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

Hence the x-coordinate of the position at which Pablo should stand is given as follows:

x = (2 + 10)/2

x = 6.

The y-coordinate of the position at which Pablo should stand is given as follows:

y = (3 + 12)/2

y = 7.5.

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The logical equivalence for the given statement is (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r).

Logical equivalence is the condition of equality that exists between two statements or sentences in propositional logic or Boolean algebra.

Given that, p → q ≡ ~p∨q and p ↔ q ≡ (~p∨q)∧(~q∨ p)

a) (p → r) ↔ (q → r)

Now, (p → r)≡ ~p∨r

(q → r)= ~q∨r

So, (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r)

Therefore, the logical equivalence for the given statement is (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r).

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The required final balance on interest rate of 6%per annul is  $354.

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

Simple interest is calculated as:

I = P * r * t

where I is the interest, P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the number of years.

So, in this case:

I = 300 * 0.06 * 3

I = 300 * 0.06 * 3 = 54

The final balance would be the sum of the initial investment and the interest earned:

Final balance = P + I

Final balance = 300 + 54

Final balance = 300 + 54 = 354

Rounded to the nearest cent, the final balance is $354.

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The outcomes for the event of rolling a number greater than 5 is 1.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, a number cube with faces labeled from 1 to 6 will be rolled once.

Now, sample space is {1, 2, 3, 4, 5, 6}

Total number of outcomes =6

Number of favourable outcomes =1

Here, the probability is 1/6

Therefore, the outcomes for the event of rolling a number greater than 5 is 1.

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It cannot be proven that the front faces are congruent triangles.

No, I cannot prove that the front faces of the two pyramids of Giza are congruent triangles. The exact dimensions and shapes of the pyramids have been lost to history, and the information we have today is based on estimates and interpretations of archaeological evidence.

The exact shape of the pyramids is still the subject of some debate among experts, and there is no consensus on whether the front faces are congruent triangles.

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Answer:

(4.44 + 0.55n) / n = p

(4.44 + 0.55 * 6) / 6 = p

(4.44 + 3.3) / 6 = p

(7.74) / 6 = p

1.29 = p

or

4.44 / 6 + 0.55 = p

Step-by-step explanation:

n = number of bottles

p = 1.29

The side length of a square with area of 7 units squared is given as follows:

2.65 units.

The area of a square of side length s is given by the side length squared, according to the equation given as follows:

A = s².

In this problem, we have that the output is of 7, that is, the area of the square is of seven, hence the side length of the square is given as follows:

s² = 7

s = sqrt(7)

s = 2.65 units.

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The values of the composite functions are g(f(0))= -3 and f(f(2)) = 5

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

f(x)= 2x-1 g(x)=3x and h(x)=x^2+1

To calculate g(f(0)), we have

f(0)= 2(0)-1 = -1

This means that

g(f(0)) = g(-1)

So, we have

g(f(0)) = 3(-1) = 3

For f(f(2)), we have

f(2)= 2(2)-1 = 3

So, we have

f(f(2)) = 2(3) - 1 = 5

Hence, the composite functions are g(f(0))= -3 and f(f(2)) = 5

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Answer:

4 feet and 4 inches of fringe

Step-by-step explanation:

The length and width of a square are equal to each other

Let x = length of a side of a square

Area of a square = Length × Width

                            = (x inches) × (x inches)

                            = [tex]x^{2}[/tex] [tex]in^{2}[/tex]

The area of the square placemat = 169 [tex]in^{2}[/tex]

∴                                            [tex]x^{2} in^{2}[/tex]  = 169 [tex]in^{2}[/tex]

Taking the square root on both sides of the equation to get rid of the square:

                                             x inches = [tex]\sqrt{169}[/tex] inches

                                            x inches = [tex]\sqrt{169}[/tex] inches

   ([tex]\sqrt{169} =[/tex] ± 13. However, the negative value will be rejected since the length of a side CANNOT be negative)    

        So, x = 13 inches

This means the perimeter of the square = (13 + 13 + 13 + 13) inches

                                                                   = 52 inches

∴ 52 inches of fringe will be needed by Sally

Unit conversion:

                                                   I foot = 12 inches

                                      ∴          y feet = 52 inches

     Cross-multiplication is applied:

                       (y feet)(12 inches) = (52 inches)(1 foot)

Isolating y and making it the subject of the formula:

                                   y feet = [tex]\frac{(52 inches)(1 foot)}{12 inches}[/tex]

Inches in the numerator and denominator will cancel each other out completely:

                                  y feet = [tex]\frac{52}{12}[/tex] feet

Applying long division:

The highest quotient to be multiplied by 12 to give a number, which is closest to 52 but still less than 52. 12×4 = 48. Therefore, the quotient is 4 and the remainder is 4.

∴ 52 inches = 4 feet and 4 inches

The probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country is 2 x 10⁻⁶³

Probability is a mathematical concept that describes the likelihood of a specific event occurring within a set of possible outcomes

Let's start by defining some terms. The force of mortality, also known as the death rate, is the number of deaths per unit time per unit of population.

The probability of survival is the chance that an individual will live past a certain age. In our case, we want to know the probability of surviving from age 30 to age 40 while living in country A.

To calculate the probability of survival, we will use the formula:

[tex]P(x) = e^{-qx}[/tex]

Where P(x) is the probability of survival at age x and qx is the force of mortality at age x.

First, we will calculate the force of mortality for the first five years after arrival in country A using the equation given in the question:

90x+1 = (6 - 1)9x+1

For x = 30, we have:

90(30) + 1 = (6 - 1)9(30) + 1

2701 = 5 * 891 + 1

2701 = 4445 + 1

2700 = 4445

So, q30 = 4445/30 = 148.5

Next, we will use this value to calculate the probability of survival for the first five years in country A:

[tex]P30 = e^{-q3} = e^{-148.5} = 1.2 \times 10^{-64}[/tex]

Since the force of mortality for those who have lived in country A for at least five years is 50% greater than the US Life Tables, 2002, Females, we can calculate the force of mortality for the next 10 years as follows:

qx = 1.5 x qx from US Life Tables

Using the values from Table 3.11, we have:

q31 = 1.5 x 98,424 = 147,636

q32 = 1.5 x 98,362 = 147,543

q33 = 1.5 x 98,296 = 147,444

q34 = 1.5 x 98,225 = 147,338

q35 = 1.5 x 98,148 = 147,222

q40 = 1.5 x 97,500 = 146,250

Finally, we can use these values to calculate the probability of survival from age 31 to age 40:

[tex]P31 = e^{-q31} = e^{-147,636} = 1.3 \times 10^{-65}\\ \\P32 = e^{-q32} = e^{-147,543} = 1.4 \times 10^{-66}\\\\P33 = e^{-q33} = e^{-147,444} = 1.5 \times 10^{-67}\\\\P34 = e^{-q34} = e^{-147,338} = 1.6 \times 10^{-68}\\\\P35 = e^{-q35} = e^{-147,222} = 1.7 \times 10^{-69}\\\\P40 = e^{-q40} = e^{-146,250} = 2.0 \times 10^{-63)}\\\\[/tex]

Complete Question:

When posted overseas to country A at age x, the employees of a large company are subject to a force of mortality such that, at exact duration t years after arrival overseas (t = 0,1,2,3,4), 90x+1 = (6 - 1)9x+1 where qx+t is on the basis of US Life Tables, 2002, Females. For those who have lived in country A for at least five years the force of mortality at each age is 50% greater than that of US Life Tables, 2002, Females, at the same age. Some lx values for this table are shown in Table 3.11.

An extract from the United States Life Tables, 2002,

Females. Age,

x 30 31 32 33 34 35 40

1x 98,424 98,362 98,296 98,225 98,148 98,064  97,500

Calculate the probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country.

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A polynomial of degree n can pass through n + 1 points. So, if we have n + 1 points, we can construct a unique polynomial that passes through all those points.

A nonzero polynomial passing through a specific point (x, y) means that the value of the polynomial at that x-coordinate must be equal to the y-coordinate of the point. So, if the point (2, 0) is one of the points that the polynomial passes through, then we have:

[tex]p(2) = 0[/tex]

We can construct a polynomial with this information. For example, one possible polynomial is:

[tex]p(x) = (x - 2)^2[/tex]

This polynomial satisfies the equation p(2) = 0 since:

[tex]p(2) = (2 - 2)^2 = 0^2 = 0[/tex]

Therefore, the polynomial [tex]p(x) = (x - 2)^2[/tex] is a nonzero polynomial that passes through the point (2, 0) and satisfies the equation p(x). Note that there could be other polynomials that also satisfy the given conditions.

In general, a polynomial of degree n can pass through n + 1 points. So, if we have n + 1 points, we can construct a unique polynomial that passes through all those points.

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The complete question is :

Find A Nonzero Polynomial P([tex]x[/tex]) Passing Through The Point (2,0) And Satisfying The Equation P([tex]x[/tex]) = P'([tex]x^2[/tex])?

Answer: To find the value of w, we need to set the expressions equal to each other:

(4w-8) = (3w+6)

Subtracting 3w from both sides:

w - 8 = 6

Adding 8 to both sides:

w = 14

So the value of w is 14.

Step-by-step explanation:

Answer:

$44

Step-by-step explanation:

Given,

Gas charges = $31 + $16 + $41

Total = $88

Half of the payment means dividing the final amount in two half.

= 88/2

= 44

Thus, your friend owes you $44 dollars for gas.

Answer: We can use the Pythagorean theorem to find the length of the hypotenuse (c) of the triangle:

c = √(a^2 + b^2) = √(75.4^2 + 41.7^2) = √(5702.76 + 1738.69) = √(7441.45)

c ≈ 86.38 yd

Next, we can use the inverse cosine function (arccos) to find angle A:

A = arccos(a/c) = arccos(75.4/86.38)

A ≈ 30.49°

Finally, we can use the complementary angle formula to find angle B:

B = 90° - A

B ≈ 59.51°

So, the length of the hypotenuse is approximately 86.38 yards, angle A is approximately 30.49 degrees, and angle B is approximately 59.51 degrees.

Step-by-step explanation:

The given triangle CDE is not Rectangular.

What are types of triangles ?

Acute triangle . . . all three angles are less than 90°

Right triangle . . . one angle is 90°

Obtuse triangle . . . one angle is greater than 90°

Equilateral triangle . . . all three sides are the same length

Isosceles triangle . . . two sides are the same length

Scalene triangle . . . all three sides are different lengths

Given:

CD = 36cm ; CE = 42cm and DE = 55

Hence , the given triangle CDE is not Rectangular.

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The number of non-real solutions is 2.

What is a quadratic equation?

The quadratic equation a equation in one variables whose power is 2. The solution of the quadratic equation can be found by equation the equation to 0 and then factoring it.

We are given a equation -3n^2-2n-6=0

To find the non-zero solution we first find the solution of the equation

we get

3n^2+2n+6 =0

We use the formula method to find the roots of the equation

[tex]n= \frac{-b}{2a}[/tex]±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

Substituting the values in the equation we get

n = -0.33333333333333 + 1.3743685418726i  and

n = -0.33333333333333 - 1.3743685418726i

Both the roots has i in them. it means both the roots are imaginary

Hence the number of complex roots are 2

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Inferential statistics is discussed below.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.

Given is inferential statistics.

Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.

Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.

Therefore, Inferential statistics is discussed above.

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Answer: (21, 3)

Step-by-step explanation:

Answer:

Step-by-step explanation:The equation for the nth term of an arithmetic sequence is given by:

an = a1 + (n-1)d

Where:

a1 is the first term of the sequence

d is the common difference

n is the number of the term we want to find

Using the given information, we have:

a1 = -9 and d = 2

Plugging these values into the formula, we get:

an = -9 + (n-1)2

To find the 12th term of the sequence:

n = 12

an = -9 + (12-1)2

an = -9 + 11 * 2

an = -9 + 22

an = 13

So the 12th term of the sequence is 13.