Composition of functions worksheet

using f(x) = 8x squared and g(x) (2x+8), find:

Probability of people less than 19 year old = 0.5343

Probability of people greater than 10 year old = 0.8116

What is probability?

Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.

People under age 10 = 253

People between the age of 10-18 = 466

People between the age of 19-30 = 174

People above the age of 30 = 450

Total no. of people = 1343

a) people less than 19 years old = 253+466 = 719

probability of people<19 year old = P(age<19) = 719/1343 = 0.5354

b) people of age greater than 10 = 466+174+450 = 1090

probability of people >10 year old = P(age>10) = 1090/1343 = 0.8116

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Answer:

The answer is A

Step-by-step explanation: I'm so smart

The football field is longer than soccer field.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

We have a soccer field that is 105 meters long and a football field is 120 yards long.

In one yard, we have -

1 yard = 0.9144 meters

Then, in 120 yards, we will have -

120 x 0.9144 = 109.728 meters

Now, 109.728 meters > 105 meters.

Therefore, the football field is longer than soccer field.

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The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.

To find equivalent expression we can simplify the expression.

Therefore,

(6x² - 9x) - (2x -3)

open the brackets

6x² - 9x - 2x + 3

combine like terms

Therefore,

(6x² - 9x) - (2x -3) = 6x² - 11x + 3

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1) 16.7% probability of rolling 10+.

2) 50% probability an odd number is rolled.

3) 7 is the most likely total result.

These are all the possible outcomes:

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes

1) what is the probability of rolling 10+?

There are 6 possible outcomes in which 10+ is rolled:

(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).

So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.

2) what is the probability of rolling an odd number?

There are 18 possible outcomes in which an odd number is rolled.

So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.

3) what is the total that is most likely to result?

There are 6 outcomes in which 7 is rolled.

So 7 is the most likely total result.

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Answer:

one number is 8 and other is 4

Step-by-step explanation:

So we can say x+y=12.

And 3x+5y=44

For x+y=12, we can subtract x to get: y=12-x

Plug that in to get 3x+5(12-x)=44

3x+60-5x=44

Subtract 44: -2x+16=0

2x=16

x=8

12-8=4.

Answer:

8.m = ∞

9.[tex]m=\frac{20c-39}{54}[/tex]

Step-by-step explanation:

8.The equation is a vertical line, so the slope is ∞

so the answer for 8. is m = ∞

9.Switch sides:

2.7m + 1.95 = c

Multiply both sides by 100:

2.7m · 100 + 1.95 · 100 = c · 100

Refine:

270m + 195 = c · 100

Move 195 to the right side so it would be: 270m = c · 100 - 195

And now Divide both sides by 270

[tex]\frac{270m}{270}[/tex] = [tex]\frac{c*100}{270}[/tex] - [tex]\frac{195}{270}[/tex]

And now all that's left is to Simplify it

so the answer for answer 9. is [tex]m=\frac{20c-39}{54}[/tex]

The correct option which represents  sum expressed in sigma notation is A.

What is sigma notation?

A series is represented in an exceedingly compact type, referred to as summation or sigma notation. The greek capital letter, ∑ , is employed to represent the total.

The series 4+8+12+16+20+24 is expressed as ∑n= 4n . The expression is browse because the total of 4n as n goes from one to six . The variable n is termed the index of summation.

The geometric series.

Main body:

∑ 125 (1/5)ⁿ⁻¹ ; where, n = 1 to 4.

Now, Calculate the partial sum of the geometric series as;

The geometric series = ∑ 125 (1/5)ⁿ⁻¹

Substitute n = 1, 2, 3, 4, we get;

= 125 (1/5)¹⁻¹ + 125 (1/5)²⁻¹ + 125 (1/5)³⁻¹ + 125 (1/5)⁴⁻¹

= 125 (1/5)⁰ + 125 (1/5)¹ + 125 (1/5)² + 125 (1/5)³

= 125 + 25 + 125/25 + 125/125

= 125 + 25 + 5 + 1

Thus, The partial sum of the geometric series is;

⇒ 125 + 25 + 5 + 1

Option A is true.

The correct question is in the figure.

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Answer:

Website A is cheaper by 29 cents

Step-by-step explanation:

A

49.95 + 4.39 = 54.34

B

47.68 + 6.95 = 54.63

54.63 - 54.34 = 0.29

Answer:

the difference is 0.29 cents

website A is cheaper

Step-by-step explanation:

(47.68 + 6.95) - (49.95 + 4.39)

54.63 - 54.34 = 0.29

We can write the given statement as inequality as -

-(x/9) < 12

Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.

Reversal property : If (a > b) then (b < a) and  if (a < b) then (b > a).

Law of Trichotomy : The "Law of Trichotomy" says that - only one of the following is true : (a < b) or (a = b) or (a > b).

The general equation of a straight line is y = mx + c

Other possible equations of lines are -

We have the following statement -

"the quotient of a number and three minus twelve is less than 12".

We can write the inequality as -

-(x/9) < 12

Therefore, we can write the given statement as inequality as -

-(x/9) < 12

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The number of stores in each level of the shopping mall are 56 stores.

An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let x represent the number of stores on each level.

A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:

(4 × x) = 226

4x = 226

Divide

x = 226 / 4

x = 56.5

There are about 56 stores per level.

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The number of calories in one cup is 132 calories and the number of calories in 4 cups is 528 calories.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a box of cereal states that there are 99 calories in a ​3/4 cup serving.

The number of calories per cup is calculated as,

3 / 4 cup = 99 calories'

1 cup = 99 x (4 / 3 )

1 cup = 132 calories

The number of calories for 4 cups of cereal,

1 cup = 132 calories

4 cup = 132 x 4 calories

4 cup = 528 calories

Therefore, the number of calories in one cup is 132 calories and the number of calories in 4 cups is 528 calories.

Therefore, the number of calories in one cup is 132 calories and the number of calories in 4 cups is 528 calories.

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The graph y = - 0.5x + 12 has a slope of - 0.5 and decreases in nature.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, harper created a graph of a line by y = - 0.5x + 12.

∴ The graph will have a slope of - 0.5 which is decreasing in nature.

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The blanks are filled as below

Collinear points are those that are situated along a single straight line.

Collinear points are those that are on a line either close to or far from another point, it can be more than two points.

While coplanar points imply lying on the same plane

In the diagram,

E, F, and G are collinear points

D, B, E, F, and G are coplanar points

A, B, and C are another collinear points

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Answer: $21.33

Step-by-step explanation: 50 - 28.67 = 21.33

The sample space S for the net amount you win (after deducting the cost of pay) is S = {-$2, $1, $4, $7}.

What is cost?

A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to obtain it.

Let, a game consists of drawing three cards at random from a deck of playing cards.

You win $3 for each red card that is drawn.

It costs $2 to play.

After deducting the cost of pay the amount will start from -$2.

For first red card drawn you win $3.

So, the amount becomes, -$2 + $3 = $1.

For second red card drawn you again win $3.

So, the next amount becomes $1 + $3 = $4.

For third red card drawn the amount becomes,

$4 + $3 = $7.

Hence, the sample space S for the net amount you win is

S = {-$2, $1, $4, $7}.

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Answer:

200*1-0.95-0.95+0.9025

200*1-1.9+0.9025

200*0.0025

0.5