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The value of g(f(x)) is 9r² + 24.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are two functions.

f(r) = r² + 4

g(r) = 9r - 12

Composition of two functions f and g is the third function h such that f(g(x)) = h(x).

g(f(x)) = g(r² + 4)

         = 9 (r² + 4) - 12

         = 9r² + 36 - 12

         = 9r² + 24

Hence the new function which is the composition of the two given function is 9r² + 24.

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Answer:

78° + B = 180°

B = 102°

Step-by-step explanation:

"Supplementary" means angle A and B added together are 180°.

We know A is 78, but we don't know B

Write an equation:

A + B = 180°

Fill in what we know.

78° + B = 180° this is the equation the question is asking for.

To solve, subtract 78 from both sides of the equation.

B = 102°

The speed of the boat in still water is 20.625 km/hr. and the speed of the current is 66 km/hr.

The speed formula is speed = distance / time.

Consider x= speed of current and y = speed of still water

The speed of the boat in still water can be calculated by dividing the total distance traveled by the total time taken;

(165 km x 2 = 330 km)

(5 hours + 11 hours = 16 hours).

Therefore, the speed of the boat in still water

330 km/16 hours = 20.625 km/hr.

The speed of the current can be calculated by dividing the total distance traveled by the total time taken for the downstream trip ;

(165 km x 2 = 330 km)

(5 hours).

Therefore, the speed of the current = 330 km/5 hours = 66 km/hr.

Hence,

speed of still water = 20.625 km/hr.

speed of current = 66 km/hr

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A. Mean = 71

B. Median = 75

C. Mode = 0

D. Mean is used to represent data, because mean measures central tendency.

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.

We have the Data set: 35, 42, 43, 51, 55, 57, 62, 66, 68, 69, 74, 75, 76, 77, 78, 79 , 82, 84, 86, 88, 93, 94, 101

So, Mean = average

                = sum of all numbers / total number of values .

                 = 1635 / 23

                 = 71.08

                 = 71

and, Median = middle term = 12th term = 75

lastly, Mode = Most repeated term or term that has high frequency.

Here no terms are repeating so mode = 0

A comparison of the mean, median, and mode

Data are represented using the mean.

Because it averages all of the values in the data set, the mean is the most widely used measure of central tendency.

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Distance is increasing with a speed of 0.2 Miles/Min

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Time in Minutes      Distance in Miles

0                              0.0

2                              0.4

4                              0.8

6                              1.2

8                              1.6

Here, Myra’s distance is increasing as time increase with a constant Speed.

Now, In every 2 mins distance traveled = 0.4 Miles

Hence, In every 1 min Distance traveled = 0.4/2 = 0.2 Miles/Min

Thus, Distance is increasing with a speed of 0.2 Miles/Min.

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Down payment = $198, total monthly payment = $2088, installment price = $2286, finance charge = $1782

Down payment is the amount of money that a purchaser needs to pay at the early stage of purchasing an expensive goods.

Given, purchasing price = $1980, 18 monthly payments of $116 each.

down payment = 10%

amount of down payment = $1980 × 10/100

                                          = $198

Total amount of monthly payment = $116 × 18 = $2088

Total paid for the snow thrower on the installment plan = Down payment + all monthly payment = $198 + $2088

Total installment price = $2286

total finance charge = Stated purchased price - down payment

                                = $1980 - $198

                                 = $1782

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If Sal saves $55 per month, the expression for his total savings for x years is 55x.

Amount is a term used to describe the total sum of money, quantity, or value of something. It is usually used to refer to a specific figure or a set of figures, such as the amount of money in a bank account, the number of items in a store, or the total cost of a purchase. Amount can also be used to describe the amount of time, energy, or effort put into something.

a. The down payment is 10% of $1,980, which is $198.

b. The total amount of the monthly payments is 18 x $116, which is $2,088.

c. Jean paid a total of $1,980 + $198 = $2,178 for the snow thrower on the installment plan.

d. The total finance charge is $2,088 - $2,178 = $90.

If Sal saves $55 per month, the expression for his total savings for x years is 55x.

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Answer: The given expression is:

m² +........+ 1/m²

We can notice that the expression has an even number of terms, and the first and last term are perfect squares, which suggests that it might be possible to write the expression as the square of a binomial.

Let's try to write the expression in the form of (a + b)²:

(a + b)² = a² + 2ab + b²

If we set a = m and b = 1/m, we get:

(a + b)² = m² + 2(m)(1/m) + (1/m)² = m² + 2 + 1/m²

Comparing this with the given expression, we see that it is the same as the given expression with 2 added to it.

Therefore, to make the given expression a perfect square, we need to add 2 to it.

So, the term to be inserted is 2.

The expression m² +........+ 1/m² can be written as (m + 1/m)² - 2.

Step-by-step explanation:

Answer:

P+n<20

Step-by-step explanation:

The given situation can be expressed as an inequality as p + n ≤ 20.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

Ethan has p pennies and n nickels.

Number of pennies = p

Number of nickels = n

Total number of coins is no more than 20.

This means that the combined total of pennies and nickels does not exceed 20.

sum of p and n is less than or equal to 20.

p + n ≤ 20

Hence the required inequality expression is p + n ≤ 20.

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Answer:

50 children tickets; 60 adult tickets

Step-by-step explanation:

Let a = number of adult tickets.

Let c = number of children tickets.

a + c = 110

5a + 3c = 450

  -3a - 3c = -330

  5a + 3c = 450

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

   2a        = 120

a = 60

a + c = 110

c = 50

Answer: 50 children tickets; 60 adult tickets

Math 220 at UIUC is a calculus course offered at the University of Illinois at Urbana-Champaign.

It is designed to introduce students to the fundamental concepts of calculus, including limits, differentiation, and integration. The course also covers applications of these concepts to real-world problems, such as optimization and modeling.

Students are expected to have a strong foundation in algebra and trigonometry before taking Math 220. The course is typically taken by students in the College of Engineering and the College of Liberal Arts and Sciences.

The textbook for the course is the 8th edition of Calculus: Early Transcendentals by James Stewart. Additionally, Math 220 students must obtain access to the online homework system MyMathLabPlus and a copy of the textbook (hard copy or eBook).

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Flipping a coin 10 times and recording if it comes up heads is an example of binomial experiment. Option (c) is correct.

Further Explanation:

Given:

The options are follows,

(a). Flipping a coin until it comes up tails.

(b). flipping a coin until 8 heads are recorded

(c). flipping a coin 10 times and recording if it comes up heads

(d). flipping a coin by 10 different people and recording the age of each person

Explanation:

Conditions for binomial experiment are as follows,

(1). The experiment should be independent means that the probability of successive trial will not be affected by the previous trial.

(2). The experiment should have a finite number of trials.

(3). The probability of success will remain same for each trial.

(4). The experiment should have only two outcomes.

Flipping a coin has only two outcomes head or tail.

Flipping a coin 10 times and recording if it comes up heads is an example of binomial experiment. Option (c) is correct.

Option (a) is not a binomial experiment as the experiment is not for finite number of times.

Option (b) is not a binomial experiment as the experiment is not for finite number of times.

Option (c) is a binomial experiment.

Option (d) is not a binomial experiment as the experiment doesn’t have the same probability of occurrence.

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Answer details:

Grade: College

Subject: Statistics

Chapter: Binomial experiment

Keywords: binomial experiment, flipping a coin, tails, heads, recorded, 10 different people, probability, each person.

This experiment has a fixed number of trials (10), each trial has only two possible outcomes (heads or tails), the probability of success (heads) is the same for each trial (0.5), and there is no interdependence between the trials.

The following features of the binomial experiment apply:

These traits allow us to identify the following characteristics of the binomial experiment:

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In a parallelogram, the opposite angles have equal measures. Therefore, 2n + 32 = 4n - 2

32 = 2n - 2

34 = 2n

17 = n

Answer:

x-17/2

Step-by-step explanation:

here, we can set the number to x

the question is asking for 2(x-7)=3

let's solve this by distributing

2x-14=3

2x=17

x=17/2

Answer: 2 (x - 7) = 3

Use the distributive property: 2x - 14 = 3

2x - 14 = 3 + 14

2x = 17

2x/2 = 17/2

x = 8.5

The value of x is 2√13 units.

The correct option is D.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given:

A right-angled triangle.

The value of the base is 12 units.

And the length of the perpendicular is 8 units.

Therefore,

x = √{(8)² + (12)²}

x = √(64 + 144)

x = √208

x = 2√13

Therefore, x = 2√13.

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The a-value for the quadratic equation x² - 7x - 18.5 = 0 is 1.

The b-value for the quadratic equation x² - 7x - 18.5 = 0 is -7.

The c-value for the quadratic equation x² - 7x - 18.5 = 0 is -18.5.

The a-value for the quadratic equation 2x² + 15x + 12 = 0 is 2.

The b-value for the quadratic equation 2x² + 15x + 12 = 0 is 15.

The c-value for the quadratic equation 2x² + 15x + 12 = 0 is 12.

In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

For the quadratic equation x² - 7x - 18.5 = 0, we have:

[tex]x = \frac{-(-7)\; \pm \;\sqrt{(-7)^2 - 4(1)(-18.5)}}{2(1)}[/tex]

For the quadratic equation 2x² + 15x + 12 = 0, we have:

[tex]x = \frac{-(5)\; \pm \;\sqrt{(5)^2 - 4(2)(12)}}{2(2)}[/tex]

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The equation of the line is y = -4x - 15.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line y = m(1)x + c is perpendicular to y = x/4 - 2.

This means,

y = (1/4)x - 2 is in the form of y = m(2)x + c

So,

m(1) x m(2) = -1

m(1) = -1 / (1/4)

m(1) = -4

Now,

The line intersects (4, -1).

So,

y = -4x + c

-1 = -4(4) + c

-1 = -16 + c

c = - + 16

c = -15

Thus,

The equation of the line perpendicular to y = x/4 - 2 is y = -4x - 15.

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The measure of angles from the given figure A, B, C, D, E, F, G and H are 61°, 130°, 58°, 50°,  84°, 85°, 146° and 145° respectively.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

1) By using the angle sum property of triangle

∠A+58°+61°=180°

∠A+119°=180°

∠A=61°

2) ∠B+50°=180° (Adjacent angles)

∠B=130°

3) ∠A=∠C (Angles of same segment)

∠C=58°

4) ∠D=50° (Vertically opposite angles)

5) 111°+90°+75°+∠E=360° (Sum of interior angles of quadrilateral)

∠E= 84°

6) 111°+84°+130°+130°+x=540° (Sum of interior angles of pentagon)

∠F=x=85°

∠F= 85°

7) 70°+50°+y=180° (angle sum property of triangle)

y=60°

70°+84°+60°+∠G=360° (Sum of interior angles of quadrilateral)

∠G=146°

8) ∠G+∠A+58°+130°+∠H=540°

146°+61°+58°+130°+∠H=540°

∠H=145°

Hence, ∠A=61°, ∠B=130°, ∠C=58°, ∠D=50°, ∠E= 84°, ∠F= 85°, ∠G=146° and  ∠H=145°.

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Answer:

Step-by-step explanation:

A: 61°

B:130°

C: 58°

D: 50°

E: 84°

F: 85°

G:146°

H: 145°

The population after 5 years will be approximately 8.45 billion.

The exponential equation to model the world population (in billions) after t years is P(t) = 8(1.011)^t, where P(t) is the population in billions and t is the number of years after 2022.

To write this equation, we need to use the information provided in the question. The initial population in 2022 is 8 billion, so this is our starting value. The growth rate is 1.1% per year, which can be written as 1.011 in decimal form.

We can use the formula for exponential growth, P(t) = P0(1 + r)^t, where P0 is the initial population, r is the growth rate, and t is the number of years.

Substituting the values for P0 and r into the equation, we get:

P(t) = 8(1.011)^t

This equation can be used to find the population after t years.

For example, to find the population after 5 years, we can substitute t = 5 into the equation and get:

P(5) = 8(1.011)^5 ≈ 8.45 billion

Therefore, the population after 5 years will be approximately 8.45 billion.

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The expression m - (8 - 3m) is equivalent to the expression 4m - 8.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ m - (8 - 3m)

Simplify the expression, then we have

⇒ m - (8 - 3m)

⇒ m - 8 + 3m

⇒ 4m - 8

The expression m - (8 - 3m) is equivalent to the expression 4m - 8.

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The result of the operation is 14x - y = 19

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

6x − y = 7

2x + y = 5

The operation is given as

Using the above as a guide, we have the following:

12x − 2y = 14

+ 2x + y = 5

Evalaute the sum

14x - y = 19

Hence, the solution is 14x - y = 19

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Answer:

27) #3 --> 12x - 24 = 60

29) 2x^2 + x - 15

Step-by-step explanation:

27) If x represents the number of boxes, and there are 12 cookies in each box, multiplying 12 by x results in the total number of cookies Kendal bought. However, she kept 2 boxes for herself, which is the same as 2(12) = 24 cookies. Kendal ended up with 60 cookies at the party, so subtracting 24 cookies from the total number of cookies (12x) equals 60 cookies.

29) (3 + x)(2x - 5)

3 * 2x = 6x

3(-5) = -15

x * 2x = 2x^2

x(-5) = -5x

6x - 15 + 2x^2 - 5x =

2x^2 + x - 15

The future value in 13 years when compounded continuously is; $18183.25

Continuous compounding is defined as the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.

The formula for continuous compounding is;

V = Pe^(rt)

where;

V is the value of the account in t years

P is the principal initially invested

e is the base of a natural logarithm.

r is the rate of interest

We are given;

P = $6770

r = 7.6% = 0.076

t = 13

Thus;

V = 6770 * e^(0.076 * 13)

V = $18183.25

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If a shopkeeper gives you a 15% discount on shirt of having total price 50, the price you will give after the 15% discount is 42.5 dollars.

If the original price of the shirt is 50 dollars, and the shopkeeper gives a discount of 15%, then the discount amount is calculated by:

Discount = Original price x Discount rate

Discount = 50 x 0.15

Discount = 7.5 dollars

The discounted price is calculated by subtracting the discount from the original price:

Discounted price = Original price - Discount

Discounted price = 50 - 7.5

Discounted price = 42.5 dollars

The discount rate of 15% means that you will save 15% of the original price, which is 7.5 dollars in this case. The discounted price is the price after subtracting the discount amount from the original price.

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Answer:

Below

Step-by-step explanation:

So you need to find a denominator that both will divide 'evenly' into...

  12 would work.....4 will divide into it 'evenly' = 3

 You do to need to do anything to the '5/12 ' ....

So change 3/4 to 12ths by multiplying by ' 1 ' in the for 3/3

     3/4  * 3/3 =  (3* 3 ) / ( 3*4 ) = 9 / 12     Done.

Answer: 39

Step-by-step explanation: 20 + 12+7

In discrete mathematics, a truth table is a table that lists all possible combinations of truth values for a given set of logical variables and shows the resulting truth values of a compound proposition.

In discrete mathematics, a truth table is a table that lists all possible combinations of truth values (usually either true or false) for a given set of logical variables and shows the resulting truth values of a compound proposition (a logical expression formed by combining the variables using logical operators such as AND, OR, and NOT). Each row of the truth table represents one possible combination of truth values, and the columns represent the variables and the various intermediate steps of the logical calculation. Truth tables are often used to determine the truth values of complex propositions and to test the validity of logical arguments.

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Answer:

Step-by-step explanation:

1.95 times 13= 25.35

The inequality B -2 ≥ -1 gives the value for B ≥ 1.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

B - 2 is greater than equal to -1

Writing the mathematical inequality is

B -2 ≥ -1

B ≥ -1 + 2

B ≥ 1

So, the value of B should be greater than 1.

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For the given algebraic expression, the value of p is 0.2 .

A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=x+9. Where:

m= the slope.

b= the constant term that represents the y-intercept

For the given example: m=1 and b=9.

The exercise presents the following algebraic expression:

14=p*70 and it asks you the value of p. Thus, you should divide the number 14 by 70. See below.

14=p*70

p=14/70

p=2/10

p=0.2

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Volume of cone =  100.48 cubic units.     and  The Volume of cylinder= 301.44 cubic units.

One of the fundamental three-dimensional forms in geometry is the cylinder, which has two distant, parallel circular bases. At a certain distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The distance between the two circular bases is used to define the cylinder's height. An LPG gas cylinder is one of the genuine examples of a cylinder. The cylinder is a three-dimensional object with two essential properties: surface area and volume. The whole surface area of the cylinder is composed of the combined curved surface area of the cylinder plus the areas of the two circular bases.

A cone has a radius of 4 units and a height of 6 units.

Volume of cone =  [tex]V=\frac{1}{3}\pi r^2h[/tex]

Where, r=4 and h=6

Volume of cone =  [tex]V=\frac{1}{3}\pi 4^2\times 6[/tex]

Volume of cone =  100.48 cubic units.                

If a cylinder has the same radius and the same height as the cone.

Volume of cylinder [tex]V=\pi r^2h[/tex]

Where, r=4 and h=6

[tex]V=\pi \times 4^2\times 6[/tex]

Volume of cylinder= 301.44 cubic units.

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