3. (1) The population of a city was 1,20,000 in the year 2078 and the population growth rate was 4.5% 20,000 people migrated here from other places in the year 2079
(a) Find the population reached in the year 2079.
(b) What will be the total population in the year 2081?​

The words for which the probability of selecting the letter A at random is 1/3 are:

a) CAB

b) ANT

c) ABOARD

Given data ,

Let the probability of selecting the letter A at random be P ( A ) = 1/3

Now , the number of letters in the words CAB are = 3

The number of A's in the word CAB = 1

So , the probability is P ( A ) = 1/3

Now , Now , the number of letters in the words ANT are = 3

The number of A's in the word ANT = 1

So , the probability is P ( A ) = 1/3

And , Now , the number of letters in the words ABROAD are = 6

The number of A's in the word ABROAD = 2

So , the probability is P ( A ) = 2/6 = 1/3

Hence , the probability is solved

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Answer:

Area = 40

Perimeter = 26

Step-by-step explanation:

length = 8

width = 5

Area = 8 x 5 = 40

Perimeter = 2(8 + 5) = 26

| P | Q | ~Q | ~Q → P | ~P | (~Q → P) ⋀ ~P |

|---|---|----|--------|----|----------------|

| T | T | F  | T      | F  | F              |

| T | F | T  | T      | F  | F              |

| F | T | F  | T      | T  | T              |

| F | F | T  | F      | T  | F              |

To construct a truth table for the logical statement (~Q → P) ⋀ ~P, we need to consider all possible truth values for the variables Q and P. The symbol "~" represents negation or "not" in logic, so ~Q denotes "not Q" and ~P denotes "not P".

In the above table, we first list all possible truth values for P and Q and then determine the truth values for ~Q, ~Q → P, and ~P based on these values. Finally, we evaluate the logical statement (~Q → P) ⋀ ~P based on the truth values for (~Q → P) and ~P to determine the overall truth value of the statement for each combination of P and Q.

The output of the above truth table shows that the statement (~Q → P) ⋀ ~P is true only in one case when P is false and Q is true. In all other cases, the statement is false. Therefore, we can infer that the statement is not always true and hence it is not a tautology. The statement is only true in one specific case where P is false and Q is true.

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Both the angles are supplementary angles hence the value of x is 8°.

To solve for the value of x in the given scenario, we can use the fact that the interior angles between two parallel lines are supplementary, meaning they add up to 180 degrees.

Given:

Angle 1: (8x + 1)

Angle 2: 115°

Since these two angles are supplementary, we can set up the equation:

(8x + 1) + 115 = 180

Now we can solve for x by simplifying and isolating the variable:

8x + 1 + 115 = 180

8x + 116 = 180

8x = 180 - 116

8x = 64

To isolate x, we divide both sides of the equation by 8:

8x/8 = 64/8

x = 8

Therefore, the value of x is 8.

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When a student is selected at random, the solution for the various possible outcome would be given below as follows:

p(pass or did not study)=0.409

p(pass or did study)=0.312

p(fail and pass)= 0.201

p(pass or fail)= 1

The formula that is used to calculate probability = possible outcome/sample space.

The total number of scores of the statistics students = 93

For p(pass or did not study):

possible outcome = 38

sample size = 93

probability = 38/93 = 0.409

For p(pass or did study):

possible outcome = 29

sample size = 93

probability = 29/93 = 0.312

For p(fail and pass):

p(fail) = 26/93

p(pass) = 67/93

probability = 26/93× 67/93

= 1742/8649

= 0.201

For p(pass or fail);

P(pass) = 67/93

P(fail) = 26/93

Probability of pass or fail = 67/93+26/93

= 93/93 = 1

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Answer:

None of the options provided (a, b, c, d) matches the correct probability. The correct probability is 1/18.

Step-by-step explanation:

a. The variables are x and y which represents 2 shots and 3 shots respectively.

b. The system of equations are;

x + y = 11

2x + 3y = 29

a. Let's define the variables to write the system of equations:

Let x be the number of two-point shots Noah made.

Let y be the number of three-point shots Noah made.

b. We can write a system of equations that model this problem.

Equation 1: x + y = 11

This equation represents the total number of shots Noah made, which is 11.

Equation 2: 2x + 3y = 29

This equation represents the total number of points Noah scored, which is 29. Since each two-point shot is worth 2 points and each three-point shot is worth 3 points, we can multiply the number of two-point shots (x) by 2 and the number of three-point shots (y) by 3 and sum them up to get the total score of 29.

The system of equations that can be used to determine the number of two-point shots Noah made and the number of three-point shots he made is:

x + y = 11

2x + 3y = 29

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In the year 2000, it was estimate that the population of the world was 6, 082, 966, 429 people.

Based on data provided by the table give, the global population in the year 2000 was estimated to be around 6, 082, 966, 429 individuals. This remarkable figure, serving as a testament to the expansive tapestry of humanity, reflects the vastness and intricacy of our interconnected world during that period.

Within the context of demographic analysis, the United Nations diligently compiled and analyzed extensive data to derive this population estimate for statistical reasons.

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The full question is:

In the year 2000 the world population was

Where the above is given, Area of Δ ACB ≈ 282.62

The area of a triangle is given as

Area = 1/2 Base x Height

In this case,

Base = AB

Height = CP

Thus, it is correct to state that Area of Δ ACB = 1/2AB * CP.

First we need to find the height and hypotenuse of the triangle.

that is CP and CB.

CB = a/Cos (63)

CB = 26.43227

CP = √(CB²-PB²)

CP = √(26.4322711750232² - 12²)

CP = 23.55133

Area of ΔPCB = (CP x PB)/2

(12 × 23.551326066062)/ 2

= 141.30796

Since ΔPCB = ΔPCA

and ΔACB = ΔPCB + ΔPCA

Thus,

Area of  ΔACB = 141.30796 + 141.30796 = 282.61592

≈ 282.62

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

2.5

Step-by-step explanation:

the length has increased by 7.5/3 = 2.5.

so the scale factor is 2.5

The perimeter of the dilated rectangle C'D'E'F' is 200 units.

To find the perimeter of the dilated rectangle C'D'E'F', we need to determine the new coordinates of its vertices after the dilation.

Given that the scale factor is 5 and the dilation is centered at (0, 0), each coordinate of the original rectangle CDEF will be multiplied by 5 to obtain the corresponding coordinate of the dilated rectangle C'D'E'F'.

The original coordinates of CDEF are:

C (-10, 10)

D (5, 10)

E (5, 5)

F (-10, 5)

To find the coordinates of the dilated rectangle C'D'E'F', we multiply each coordinate by 5:

C' = (-10 × 5, 10 × 5) = (-50, 50)

D' = (5 × 5, 10 × 5) = (25, 50)

E' = (5 × 5, 5 × 5) = (25, 25)

F' = (-10 × 5, 5 × 5) = (-50, 25)

Now, we can calculate the perimeter of the dilated rectangle C'D'E'F' by summing the lengths of its sides.

Length of side C'D':

√[(-50 - 25)² + (50 - 50)²] = √[(-75)² + 0²] = √[5625] = 75

Length of side D'E':

√[(25 - 25)² + (50 - 25)²] = √[0² + 625] = √[625] = 25

Length of side E'F':

√[(25 - (-50))² + (25 - 25)²] = √[75² + 0²] = √[5625] = 75

Length of side F'C':

√[(-50 - (-50))² + (25 - 50)²] = √[0² + 625] = √[625] = 25

Now, we add up the lengths of all four sides to find the perimeter:

Perimeter = C'D' + D'E' + E'F' + F'C'

= 75 + 25 + 75 + 25

= 200

Therefore, the perimeter of the dilated rectangle C'D'E'F' is 200 units.

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x ≤ 8 or x > 10 is the solution of the inequality 11 ≥ 2x - 5 or 2x - 5 > 15.

To solve the compound inequality 11 ≥ 2x - 5 or 2x - 5 > 15, we will solve each inequality separately and then combine the solutions.

Solve the first inequality: 11 ≥ 2x - 5

Add 5 to both sides to isolate 2x:

11 + 5 ≥ 2x

16 ≥ 2x

Divide both sides by 2:

8 ≥ x

So the solution to the first inequality is x ≤ 8.

Solve the second inequality: 2x - 5 > 15

Add 5 to both sides to isolate 2x:

2x > 15 + 5

2x > 20

Divide both sides by 2:

x > 10

So the solution to the second inequality is x > 10.

Combining the solutions, we have x ≤ 8 or x > 10.

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Answer:

Volume ≈ 153.93804 cm^3

Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.

Step-by-step explanation:

The average fourth grader is about three times as tall as the average newborn baby. If babies are on average 45 cm 7 mm when they are born,  137 cm 1 mm is the height of the average fourth grader.

Given information,

Baby height is typically 45 cm. 7 mm 45 cm Since there are 10 millimeters in a centimeter, 7 mm is equal to 45.7 cm.

Assume that a fourth-grader is x inches tall.

The average height of a newborn baby (x) = 3 times the height of a fourth-grader.

A fourth-grader's height (x) is equal to 3 x 45.7.

A fourth-grader's height is equal to (x)=137.

Fourth-grader height (x) = 137 cm 1 millimeter

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The curved surface area of the cylinder is 24 cm².

We have,

To find the curved surface area of a cylinder, we need to know its height (h) and the circumference of its base (C).

Given:

Circumference (C) = 4 cm

Height (h) = 6 cm

The formula to calculate the curved surface area of a cylinder is A =  Ch, where A is the curved surface area, C is the circumference, and h is the height.

Substituting the given values:

A = 4 cm x 6 cm

A = 24 cm²

Therefore,

The curved surface area of the cylinder is 24 cm².

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The volume of the trapezoidal prism is 420 cm³

Volume is the amount of space that is occupied by a three dimensional shape or object.

The volume of a trapezoidal prism is the product of the base area and its height.

For the trapezoidal prism:

Area of base = (1/2)(15 + 5) * 7 = 70 cm²

Volume of Prism = Area of base * height = 70 cm² * 6 cm = 420 cm³

The volume of the figure is 420 cm³

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The values from figure is,

x = 2

NS = 3.5

We have to given that,

In the figure below, S is the center of the circle.

And, Suppose that JK = 16, MP = 8, LP = 2x + 4, and SP = 3.5.

Now, We know that,

By figure,

MP = LP

Substitute the given values,

8 = 2x + 4

8 - 4 = 2x

4 = 2x

x = 4/2

x = 2

Hence, We get;

LM = MP + LP

LM = 8 + (2x + 4)

LM = 8 + 2 x 2 + 4

LM = 8 + 4 + 4

LM = 16

Since, We have JK = 16

Hence, We get;

NS = SP

This gives,

NS = 3.5

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Answer:

LXXXIX

Step-by-step explanation:

ochenta y nueve es 89.

89 en numero romano es LXXXIX.

The quadratic function has the following domain: 0 ≤ t ≤ 8.

Herein we find a quadratic equation that models the height of the rocket in time. The domain is the set of all values of t such that all values of h exist.

Mathematically speaking, the domain of quadratic equations is the set of all real numbers, but physically speaking, this domain is formed by the set of all non-negative numbers such that h ≥ 0. The domain is found by algebra properties:

h = - 16 · t² + 128 · t

h = - 16 · t · (t - 8)

Then, the domain of the quadratic function is: 0 ≤ t ≤ 8.

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Answer:

solution:  (0,3)

Step-by-step explanation:

You can find the solution when the two lines intersect.

Rhombus and equilateral triangle will fit in regular circle and rectangle will fit in quadrilateral circle.

A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.

Here, rhombus and equilateral triangle are regular, and rectangle and triangle are not regular.

Therefore, rhombus and equilateral triangle will fit in regular circle and rectangle will fit in quadrilateral circle.

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Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

41.

Out of the 18 parts, we shade 5 parts

Out of the 27 parts, we shade 4 parts

42.

There are 60 pieces.

43.

The fractional part for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

We have,

41.

a.

1/3 x 5/6

= 5/18

This means,

Out of the 18 parts, we shade 5 parts

b.

2/9 x 2/3

= 4/27

This means,

Out of the 27 parts, we shade 4 parts

42.

String = 15 feet

Length of each piece = 1/4 feet

Now,

The number of 1/4 feet pieces.

= 15/(1/4)

= 15 x 4

= 60 pieces

43.

Original pizza = 1

Half pizza = 1/2

Number of people = 3

Now,

The fractional part for each person.

= 1/2 ÷ 3

= 1/6

44.

a.

7/6 x 9

= 7/2 x 3

= 21/2

= 10(1/2)

b.

1/7 ÷ 3

= 1/(7 x 3)

= 1/21

c.

4/5 x 3(2/3)

= 4/5 x 11/3

= 44/15

= 2(14/15)

d.

2 ÷ 1/9

= 2 x 9/1

= 18

Thus,

41.

Out of the 18 parts, we shade 5 parts

Out of the 27 parts, we shade 4 parts

42.

There are 60 pieces.

43.

The fractional part for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

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The length of side b in triangle ABC is 18.7 units.

In Mathematics and Geometry, the law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation (ratio):

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

In this context, the value of b can be determined as follows;

sin112/37 = sin28/b

b = 37sin28/sin112

b = 17.3705/0.9272

b = 18.7 units.

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Beth and Kelly were on vacation for 6 days. both spent same amount of money for dog sitting while on vacation.

Let's assume the number of days Beth and Kelly were on vacation is represented by 'd.'

For Beth:

Total cost for dog sitting = (Cost per day * Number of days) + Cleaning and food fee

24.50d + 90.50

For Kelly:

Total cost for dog sitting = (Cost per day * Number of days) + Cleaning fee

32d + 45.50

Since both Beth and Kelly spent the same amount, we can set their total costs equal to each other and solve for 'd':

24.50d + 90.50 = 32d + 45.50

Rearranging the equation:

24.50d - 32d = 45.50 - 90.50

-7.50d = -45

Dividing both sides by -7.50:

d = -45 / -7.50

d = 6

Therefore, both Beth and Kelly were on vacation for 6 days.

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Answer:

Not a right triangle

Step-by-step explanation:

[tex]10^2+15^2\stackrel{?}{=}18^2\\100+225\stackrel{?}{=}324\\325\neq324[/tex]

As the sides of the triangle do not follow the Pythagorean Theorem, then the triangle is not a right triangle.

Answer: z=3

Step-by-step explanation: