Answer:
Step-by-step explanation:
The area of a rectangle can be found by multiplying its length and breadth. In this case, the length is 11/5 cm and the breadth is 13/5 cm. Therefore, the area of the rectangle is (11/5 cm)*(13/5 cm) = 143/25 sq. cm = 5.72 sq. cm.
What does the statement T(60(>T(10)+T(30) mean
T(60) > T(10) + T(30) means that the number of tenants living on 60th floor is greater than the sum of tenants that are living in 10th and 30th floor.
What is meant by n, T(n) and tenant:
n = number of floor of the Princess Tower (Floor Number)
T(n) is a function of n (floor number) which tells how many tenants are beings living on the nth floor
Tenant means a person occupying a rented land or property (A resident for simple understanding)
Therefore:
T(60) means the number of tenants living on 60th floorT(10) means the number of tenants living on 10th floorT(30) means the number of tenants living on 30th floorThus using the above information, it should be clear that:The statement: T(60) > T(10) + T(30)
Means that: The number of tenants living on 60th floor is greater than the sum of tenants living on 10th and 30th floor.
Just for an example If we have T(60) = 30, T(10) = 10, T(30) = 5
Then T(60) > T(10) + T(30) means that 30 > 10 + 5 which becomes 30 > 15
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Solve the simultaneous equations by substitution 2 x − 3 y = 8
Answer:
To solve the simultaneous equations by substitution, we can first solve one equation for one of the variables, and then substitute that expression into the other equation. Here is one way to solve the given equation:
2x - 3y = 8
We can solve for x by adding 3y to both sides:
2x = 3y + 8
We can divide both sides by 2 to get x by itself:
x = (3y + 8)/2
Now we can substitute this expression for x into the other equation:
2((3y + 8)/2) - 3y = 8
Simplifying and solving for y:
3y + 8 - 3y = 8
8 = 8
So the solution for y is any value.
Now we can substitute the value of y into the equation x = (3y + 8)/2 and we'll get the value of x.
x = (3 * y + 8) / 2
For example if we substitute y = 2
x = (3 * 2 + 8) / 2 = 14/2 = 7
So the solution for the simultaneous equations is x = 7, y = 2
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What type of triangle is it if the lengths are 4 cm 5 cm and 6 cm?
A triangle with given lengths 4cm , 5cm , and 6cm is scalene and acute angled triangle.
As given in the question,
In the given triangle ,
Lengths of the sides of a triangle is given by :
4cm , 5cm , and 6cm.
All the sides are of different measure , it is a scalene triangle.
Apply cosine rule to find the measure of largest angle:
c = 6cm is the longest side opposite to largest angle.
c² = a² + b²- 2abcosα
⇒ 6² = 4² + 5² - 2(4)(5)cosα
⇒cosα = ( 16 + 25 - 36 ) / 40
⇒ cosα = 5/40
⇒ α = cos⁻¹( 1/8)
⇒ α = 82.8° < 90°
It is an acute angled triangle.
Therefore, for the given lengths of the triangle it is a scalene and acute angled triangle.
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Answer questions for points
It can be concluded that -
Version A of iced tea will be sweetest.Nick's claim is true.What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the questions as shown in the image.
[1] -
Greater is the value of amount of tablespoon of sugar per oz of tea, sweetest it will be.
For table {1}, we can write -
m₁ = (12/18) = 2/3
For table {2}, we can write -
m₂ = 6/16 = 3/8
m₁ = 2/3 = (2 x 8)/(3 x 8) = 16/24
m₂ = 3/8 = (3 x 3)/(8 x 3) = 9/24
m₁ > m₂
Version A of iced tea will be sweetest.
[2] -
Greater is the value of amount of strawberry puree per unit of the total amount of liquid, stronger will be the strawberry flavor.
For Nick -
m₁ = 8/12 = 80/120
For Sam -
m₂ = 12/20 = 72/120
m₁ > m₂
Hence, Nick's claim is true.
Therefore, it can be concluded that -
Version A of iced tea will be sweetest.Nick's claim is true.To solve more questions on expressions, visit the link below -
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A forest covers 51,000 acres. A survey finds that 0.4% of the forest is old-growth trees. How many acres of old-growth trees are there?
If a forest covers 51,000 acres. A survey finds that 0.4% of the forest is old-growth trees. The number of acres of old-growth trees that are there is: 204 acres.
How to find the number of acres?Using this formula to find the number of acres that are there.
Number of acres = Number of forest covers acres × Forest old growth tree percentage
Where:
Number of forest covers acres = 51,000 acres
Forest old growth tree percentage = 0.4% or 0.004
Let plug in the formula
Number of acres = 51,000 acres × 0.004
Number of acres = 204 acres
Therefore we can conclude that the number of acres is 204 acres.
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In a class of 100 students, 30 are computer science majors, 49 are mechaincal engineering majors, 13 are civil engineers and the rest are general engineering majors. Assume students only have one major.Suppose five students from the class are chosen at random what is the probability none are mechanical engineering majors?My info I know: The mechanical engineers account for 49% of the students, making 51% not mechanical engineers? Do I take five out of the 51, so 0.05 X 0.51?
The probability that none of the five students chosen at random are mechanical engineering majors is 0.0111 or about 1.11%.
The probability that none of the five students chosen at random are mechanical engineering majors is
=(51/100) * (50/99) * (48/98) * (47/97) * (46/96)
= 0.0111
This means that the probability is about 1.11%
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
The probability means that the chances of an event to occur or do not occur and it lies between the range of 0 and 1.
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Why are there two answers in absolute value?
The absolute value of a number is always positive, but the number itself can be positive or negative, and there are always two possible solutions for the absolute value equation, one positive and one negative, that are the same distance from 0.
An absolute value equation of the form |x| = k (where k is a constant) will have two solutions, one positive and one negative, that are the same distance from 0 on the number line.
For example, if the equation is |x| = 5, the two solutions of the equation are x = 5 and x = -5.
This is because the absolute value of a number represents the distance of that number from 0 on the number line, and this distance is the same regardless of whether the number is positive or negative. Therefore, for any non-negative value k, there are two numbers that are that distance away from 0, one positive and one negative.
For example, the distance of 5 from 0 is 5 units, and the distance of -5 from 0 is also 5 units. Therefore, |5| = |-5| = 5.
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What single factor made the Hindu arabic number system superior
Invention of 0
What are the two purposes of numerals or digits
Show the cardinal value (how many)
And show the place value (10s, 100s, 1000s)
Natural numbers in a counting process
Does not include 0
1-2-3-4-5-6-7-8-9-10-11- infinity
Principle of closure
Addition- if you add any two natural numbers, the result will always be a natural number. Called closed under addition
Multiplication- if you multiply any two naturals, you get naturals. Called closed under addition
Subtraction- you cannot achieve closure when subtracting larger number from smaller number (i.e. 6-7)
Division - when you divide two natural numbers, it is possible to get a fraction. Not closed by division.
Integers
Positive and negative numbers, start at 0 and expand infinitely at both ends.
Closed under addition, multiplication, subtraction. NOT DIVISION
Rational numbers
Numbers that can be expressed as fractions, that is the quotient of two integers
Irrational numbers
Non terminating, repeating decimals
Three axioms of equality
Reflexive- law of identity. Any number reflects itself or is equal to itself (i.e. A=A)
Symmetric- any equality is reversible (i.e. A=B, then B=A)
Transitive property - possible to identity two numbers as being equal to a third quantity (a=b and b=c then a=c)
Commutative property
When adding, it doesn't matter the order
a+b=b+a
Order in which things are multiplied does not affect product (a*b=b*a)
Associative property
Law states that the order in which Addends are grouped, the sum will be unaffected. (a+b)+c = a + (b+c)
(A*b)*c = a(b*c)
Distributive property
Multiplication can be distributed over addition.
a(b+c)= (a*b) + (a*c)
Unity element
Number 1 is the identity element of multiplication. Any number multiplied by one equals itself
Zero element
Identity element for addition
Will destroy number, anything multiplied by 0 =0
Dividing by 0 is error.
0 /# = 0
The Hindu-Arabic numeral system is superior to other numeral systems because of its invention of the number 0. This allows for the representation of the concept of nothingness or absence, which allows for the development of more advanced mathematical operations such as negative numbers and decimal fractions.
The two purposes of numerals or digits are to show the cardinal value (how many) and to show the place value (10s, 100s, 1000s). The cardinal value is the actual quantity of a number, while the place value is the position of a digit in a number, which determines its value in relation to other digits.
The natural numbers are the numbers used in a counting process and do not include 0. They include the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on to infinity. The principle of closure is the idea that certain operations, such as addition and multiplication, will always result in a natural number when performed on natural numbers. However, subtraction and division do not result in natural numbers in all cases.
Integers are positive and negative numbers that start at 0 and expand infinitely in both directions. They are closed under addition, multiplication, and subtraction. However, division is not closed under integers.
Rational numbers are numbers that can be expressed as the quotient of two integers. Irrational numbers are non-terminating, non-repeating decimals.
The three axioms of equality are the reflexive property (A = A), the symmetric property (if A = B, then B = A), and the transitive property (if A = B and B = C, then A = C).
The commutative property states that the order of the numbers does not affect the result in operations such as addition and multiplication. The associative property states that the grouping of numbers does not affect the result in operations such as addition and multiplication. The distributive property states that multiplication can be distributed over addition.
The unity element for multiplication is the number 1, which serves as the identity element for multiplication. The zero element for addition is 0, which serves as the identity element for addition. Dividing by 0 is an error and not allowed.
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An experienced bricklayer can work twice as fast as an apprentice bricklayer. after the bricklayers work together on a job for 4 hours, the experienced bricklayer quits. the apprentice requires 14 more hours to finish the job. how long would it take the experienced bricklayer, working alone, to do the job?
The total time taken by the experienced bricklayer to complete the job as per given condition is equal to 13 hours.
As given in the question,
Let the time taken by experienced bricklayer be 't' hours
Then time taken by apprentice bricklayer be '2t' hours
Time to complete 1 complete work is
Experienced bricklayer worked for 4 hours
Apprentice bricklayer worked for ( 4 + 14 ) = 18 hours
Required equation to complete 1 work is :
( 4/x) + ( 18 /2x) = 1
⇒( 8 + 18 )/ 2x = 1
⇒26/2 = x
⇒ x = 13 hours
Therefore, time taken by the experienced bricklayer to complete the job is equal to 13 hours.
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At nyu in 2013 the cost of the weekly meal options could be described as a function of the number of meals is the cost of the meal plan linear or non linear function
Correct option is A, the cost of the meal plan is non-linear.
How can a function's linearity or nonlinearity be determined?The simplest approach to tell if a function is linear is to look at its graph. A linear function produces a straight line on a graph. A nonlinear function is not straight and is curved in some way. A linear function results in a straight line on a graph. As a result, non-linear functions can be of any kind. Although determining a function's linearity from its input/output table or equation is the simplest method, it is also possible to do so.
Based on the given conditions, formulate:
The definition of linear function
8-10 meals = (135-123) = (10-8) =10/2=5
10-12 meals: (155-135) = (12-10)
=20/2
= 10
12-21 meals: (220-155) = (21-12)
= 65/9
=7 2/9
5 < 7 2/9 < 10
So the cost of the meal plan is non-linear.
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Complete question -
4 Which number is included in the set of integers that when added to –4 gives a sum of less than zero? Select all that apply. A 3 B 7 C 9 D –2 E 4 F 0
The number included in the set of integers that when added to -4 gives a sum less than zero are 0, -2 and 3
How to find the integers in a word expression?The question wants us to find the numbers included in the set of integers that when added to -4 gives a sum less than zero.
The options are 3, 7, 9, -2, 4 and 0.
Therefore,
let
the number added = x
Hence,
-4 + x < 0
Base on the options, the numbers that fits into the inequality are as follows:
The numbers are 0, -2 and 3.
Therefore,
-4 + 0 < 0
-4 + -2 < 0
-4 + 3 < 0
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How do you graph absolute value equations on a coordinate plane?
To graph an absolute value function, choose several values of x and find some ordered pairs. Plot the points on a coordinate plane and connect them.
Absolute value equations are the equations in which the absolute value operator is used.
To graph such an equation, we must first get rid of the absolute value equation by dividing the equation into different parts. Then graph the equations of these parts separately.
If the value of the expression or the number inside the operator is negative, then the result is the negative of the expression or the number.
Suppose we have an expression: |x+1|
If (x+1) is positive or equal to 0, then |x+1| =x+1
However, if (x+1) is negative, then |x+1| =-(x+1)=-x-1.
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Given the points (3, -9) and (-9, 5) find the slope
Answer:0.5
Step-by-step explanation:
50% of what number is 140?
Answer:280
Step-by-step explanation:
You are using a 9-inch paint roller to paint a wall of your bedroom. The roller has a diameter of 158 inches and a nap thickness of 14 inch, as shown. The nap is the fuzzy material on the surface of the roller.
The area covered by the roller in one full revelation is 1674 square inches.
Step-by-step explanation:
Given that You are using a 9 inch paint roller to paint a wall of your bedroom. The roller has a dimension of 158 inches as diameter and a nap thickness of 14 inch, as shown,
The nap is the fuzzy materials on the surface roller. How much area does the roller cover in one full revelation
The parameters to be considered are:
Diameter = 158 inches
Thickness = 14 inches
After one revolution rolling, the dimensions of the length will be:
L = 14 + 158 + 14
L = 186 inches.
Let the width be equal to 9 inches
The area covered = L × W
Substitute L and W into the formula
Area = 186 × 9
Area = 1674 square inches.
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During the summer, 1.3% of the water in the kiddie pool evaporates every day. if the kiddie pool holds 8,000 gallons of water and is not refilled for 10 days, how many gallons of water will be in the pool?
7019 gallons of water will be in the pool.
Initial volume of water = 8000 gal
Daily reduction = 1.3%
Time = 10 days
Required equation:
=8000*(1- 0.013)^10
=8000*0.987^10
=7018.7781 ≈ 7019 rounded to the nearest gallon.
An expression that uses constant algebraic numbers, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
In contrast, since they are not derived from integer constants and algebraic operations, transcendental numbers like and e are not algebraic. The definition of e necessitates an infinite number of algebraic operations, while the construction of is typically done as a geometric relationship.
Any expression that can be converted into a rational fraction using the properties of the arithmetic operations is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).
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the sum of fifteen and three times a number is equal to 24. find the number
Answer:
The number is 6Step-by-step explanation:
The equation given:
[tex]15 + \left(3x\right) = 24[/tex]
Our goal is to find x. To find x, what I like to do is add the given values together, then subtract them by 24 to find x's value.
[tex]15 + 3 = 18\\24 - 18 = x\\x = 6[/tex]
Hope this helps!
Think About the Process At a supermarket, a 6-ounce bottle of brand A salad dressing costs $1.56. A 14-ounce bottle costs $3.36. A 20-ounce bottle costs $5.60. What unit prices do you need to know to find the best buy? What is the best buy?
a) The unit prices to determine the best buy are as follows:
6-ounce bottle = $0.2614-ounce bottle = $0.2420-ounce bottle = $0.28.b) The best buy is the 14-ounce bottle of salad dressing with a unit cost of $0.24 since they are all Grade A products.
What is the unit price?The unit price or cost is the cost for an item or a unit.
The unit price can be compared to the unit rate, which is the quotient of the total cost and the number of units.
6 ounces 14 ounces 20 ounces
Total costs $1.56 $3.36 $5.60
Unit cost $0.26 $0.24 $0.28
($1.56/6) ($3.36/14) ($5.60/20)
Thus, buying a 14-ounce bottle of salad dressing is more economical than others.
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Hello I need some help with math
Answer:
y = 136
x=15
Step-by-step explanation:
to work this question out you must know the angles on a straight line add up to 180 degrees. By doing that we can find the top angle inside of the triangle.
180 - 104 = 76
to find x we need to know that angles in a triangle add up to 180 degrees.
180 = (3x-1) + 4x + 76
To solve for x, we can first simplify the equation.
180 = (3x-1) + 4x + 76
This can be re-arranged as:
(3x-1) + 4x = 104
and then combined as:
7x = 105
Finally, we can solve for x by dividing both sides by 7:
x = 105/7
x = 15
So the value of x that satisfies the equation is 15
to find y we need to know that angles on a line equal 180
180 = (3(15)-1) + y
180 = 44 + y
To find the value of y, we can subtract 44 from both sides
y = 180-44
y = 136
Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation. What is the scale factor of the dilation?
The scale factor of the dilation is the ratio of the lengths of the corresponding sides of the two triangles. Since triangle ABC and triangle A'B'C' both have side lengths of AB, BC, and CA, the scale factor is 1.
1. Calculate the length of the sides of triangle ABC:
AB = length of side AB of triangle ABC
BC = length of side BC of triangle ABC
CA = length of side CA of triangle ABC
2. Calculate the length of the sides of triangle A'B'C':
A'B' = length of side A'B' of triangle A'B'C'
B'C' = length of side B'C' of triangle A'B'C'
C'A' = length of side C'A' of triangle A'B'C'
3. Calculate the scale factor of the dilation:
Scale factor = (AB/A'B') x (BC/B'C') x (CA/C'A')
= (length of side AB of triangle ABC / length of side A'B' of triangle A'B'C')
x (length of side BC of triangle ABC / length of side B'C' of triangle A'B'C')
x (length of side CA of triangle ABC / length of side C'A' of triangle A'B'C')
= 1 x 1 x 1
= 1
Therefore, the scale factor of the dilation is 1.
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if xy + 8ey = 8e, find the value of y'' at the point where x = 0.
The value of y'' at the point where x = 0 is 8.
A derivative is a mathematical concept that measures how much a function changes as its input (or independent variable) changes. It is often represented by the symbol "dy/dx" or "f'(x)", and is used to calculate the slope of a function at a particular point.
To find the value of y'' at the point where x = 0, we first take the derivative of the equation with respect to x. This gives us y' + 8exy' = 0. Then, we take the derivative of this equation with respect to x again, which gives us y'' + 8exy'' + 8ey' = 0. Substituting x = 0 into this equation gives us y'' + 0 + 8e(0) = 0, which simplifies to y'' = 8.
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determine whether the series is convergent or divergent. 1 + 1 2 2 + 1 3 3 + 1 4 4 + 1 5 5 ⋯
We can see from the provided data that it is obviously divergent.
What in mathematics is convergent and divergent?Convergent sequence occurs when, as n approaches infinity, you arrive at a final as well as constant term through a number of terms. Divergent sequences are those in which individual terms never stabilize; instead, they constantly grow or decrease as n approaches infinity, approaching either infinity or -infinity.
Is divergence equivalent to infinity?A series diverges when it moves up, down, to infinity or minus infinity without settling on a value.
The series' parts are becoming larger and larger while being interrupted by some constant "1" (however they are useless in this situation since the series is divergent because there are always two numbers that follow an intercepting "1" that are greater by 1 than the two that came before it).
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Find the area of the figure.
Answer:
36.3 units²
Step-by-step explanation:
Area of a trapezoid = A = ((a+b)/2)h = [tex]\frac{a+b}{2}[/tex]h
a = 4
b = 1.5+7=8.5
solve for h using pythagorean theorem:
1.5² + h² = 6²
h² = 36 - 2.25 = 33.75
h = [tex]\sqrt{33.75}[/tex] = 5.81
A = [tex]\frac{4+8.5}{2}[/tex](5.81) = 36.3125
Give each trig ratio as a fraction in simplest form.
Answer:
[tex]df = \sqrt{ {29}^{2} - {20}^{2} } = 21 \\ \sin(d) = \frac{20}{29} \\ \cos(d) = \frac{21}{29} \\ \tan(d) = \frac{20}{21} \\ \sin(e) = \frac{21}{29} \\ \cos(e) = \frac{20}{29} \\ \tan(e) = \frac{21}{20} [/tex]
Answer:
Step-by-step explanation:
First, use the pythagorean theorem to complete the vales of each sides of the triangle. Then, use the respective trigonometric formulas and inverse the answer to compute the degree of every corners.
34 entre 250.6 con operacion
De acuerdo con la información del enunciado, el resultado de esta operación matemática (división) es 0,13
¿Cómo solucionar la división?Para solucionar la división, debemos realizar el siguiente procedimiento:Identificar las partes de la división (dividendo y divisor), en este caso como el divisor es más grande, debemos añadir un cero y una coma en el cociente para añadir un cero en el dividendo.Una vez hemos agregado un cero al dividendo, debemos identificar un número que al multiplicarlo con el divisor no de menor o igual al dividendo, en este caso sería 1, porque 250.6 * 1 = 250.6Entonces debemos hallar la diferencia entre 250.6 y 340, este procedimiento se hace con una resta y daría 89,4.Una vez hallamos este número, debemos identificar otro número para el cociente que multiplicado por 250,6 no de inferior o igual a 894, en este caso sería 3, 3 * 250,6 = 751.8En este paso debemos realizar otra resta para identificar la diferencia entre estos dos número. 894 - 751,8 = 142,2Esta división da como resultado un número decimal de varios valores por lo que podemos repetir este procedimiento tantas veces sea necesario dependiendo de la exactitud de nuestras necesidades.
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You want to be able to withdraw $50000 from your account each year for 30 year after you retire. You expect to retire in 15 year. If your account earn 4% interet, how much will you need to depoit each year until retirement to achieve your retirement goal?
You need to deposit $55,555 each year until your retirement to achieve your retirement goal.
To find the amount you need to deposit each year, you need to calculate the present value of your future withdrawals, considering the time value of money and taking into account the interest rate.
One way to do this is to use the formula for present value:
PV = FV/(1 + r)^t
where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years until the future value.
In this case, FV is $50000 per year for 30 years, so the total future value is $50000 × 30 = $1,500,000. And t is 15 years, so the present value is:
PV = $1,500,000/(1 + 0.04)^15 = $1,500,000/1.8 = $833,333
So, you need to deposit $833,333/15 = $55,555 each year until you retire to achieve your goal.
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question at a gas station, 84% of customers buy gasoline. only 5% of customers buy gasoline and a beverage.what is the probability that a customer who buys gasoline also buys a beverage? round your answer to the nearest tenth.
On solving the provided question, we can say that The probability of a person purchasing both a beverage and gasoline is 0.060, or 6%.
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
At a gas station, 84% of customers buy gasoline
[tex]P (A) = 0.84[/tex]
5% of customers buy gasoline and a beverage
[tex]P (B) = = 0.05[/tex]
conditional probability = P (A and B) = P(A) × P(B/A)
[tex]P(B/A) = P (A and B) / P(A)\\P ( B/A ) = 0.0595 = 0.060 or 6%\\[/tex]
The likelihood of a person purchasing both a beverage and gasoline is 0.060, or 6%.
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Which linear graph represents a proportional relationship?
a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 5
a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1
a graph of a line that passes through the points 0 comma 4 and 1 comma 4
a graph of a line that passes through the points 0 comma 1 and negative 1 comma negative 3
The graph of the proportional relation is the one in the second option.
"a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1"
Which linear graph represents a proportional relationship?A general linear equation can be written as:
y = a*x +b
Where a is the slope and b is the y-intercept.
Particularly, if the y-intercept is 0, then we have:
y = a*x
We have a proportional relationship.
Notice that when x = 0 we have:
y = a*0
y = 0
So the proportional relationships always pass through the point (0, 0).
Then the correct option is the second one:
"a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1"
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Is Ishmael or Ian correct?
Answer:
Ian is correct
Step-by-step explanation:
The range of a function is the set of all possible values that the function can take. In other words, it is the values of y lying between minimum and maximum
From the graph we can see that the minimum value of y = 0
Maximum value of y = 30
So the range is 0 ≤ y ≤ 30
So Ian is correct
(Note that y ≤ 30 can include negative values which is not possible in this case)
After surveying 995 adults, 81.5% of whom were over 30, the National Sleep Foundation reported that 36.8% of all the adults snored. Thirty-two percent of the respondents were snorers over the age of 30.What percent of respondents were under 30 and did not snore? Hint: Draw a Venn diagram to represent the region of interest.
A. 73.91% of respondents were under the age of 30 and did not snore.
B. Data show that snoring is not age-independent as most snorers are over 30 years of age.
A. The first step is to convert all percentage population groups into numbers. This helps make things clearer.
Total number of adults surveyed = 995 adults
Number of adults over the age of 30 = 81.5% of 995
= 81.5/100 × 995
= 810.925
≈ 811(part of the population can be counted).
Number of adults under 30 = 995 - 811 = 184 adults.
Number of all adults who snore = 36.8% of 995
= 36.8/100 × 995 ≈ 366 adults who snore
Of the total 995, 32% of the snorers were over 30 was.
Number of snorers over 30 × 995 ≈ 318 adults
Snorers under 30 = 366 - 318 = 48 adults
Number of under 30s recorded 30 - under 30 snorers
= 184 - 48 = 136
Converting this to percentage: 136/184× 100 = 73.91%
so 73
B. From the data, snoring is not independent of age as most of the people that snored were above 30 years. Snoring is related to the age. This is because that the most of the younger adults did not snore, while more of the older adults snored.
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