Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages?
Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Let
x ------> Ethan's age
y -----> Jess's age
we have that
y=3x-6 -------> equation A
xy=45 ------> equation B
substitute equation A in equation B
x(3x-6)=45
solve for x
3x^2-6x=45
3x^2-6x-45=0
Solve using the formula
so
a=3
b=-6
c=-45
substitute
[tex]x=\frac{-(-6)\pm\sqrt[]{-6^2-4(3)(-45)}}{2(3)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{576}}{6} \\ \\ x=\frac{6\pm24}{6} \end{gathered}[/tex]the solutions for x are
x=5 and x=-3 (is not a solution)
Find the value of y
y=3(5)-6
y=9
therefore
Ethan's age is 5 years
Jess's age is 9 years
Instructions: Find the value of the trigonometric ratio. Makesure to simplify the fraction if needed.
sin C = 3/5
Explanation:Given:
CB = 32
AC = 40
AB = 24
To find:
sin C
To determine sinC, we will apply the sine ratio:
[tex]\begin{gathered} sin\text{ C = }\frac{opposite}{hypotenuse} \\ \\ oppoite\text{ =side opposite the angle = AB = 24} \\ hyp\text{ = 40} \end{gathered}[/tex][tex]\begin{gathered} sin\text{ C}=\text{ }\frac{24}{40} \\ \\ sin\text{ C}=\text{ }\frac{3}{5} \end{gathered}[/tex]Antonio has a balance of $4273.56 on a credit card with an annual percentage rate of 21.1%. He decides to not make any additional purchases with his card until he has paid off the balance. a) Many credit cards require a minimum monthly payment of 2% of the balance. What is Antonio's minimum payment on the balance of $4273.56? b) Find the amount of interest charged this month
a) To calculate the minimum payment of the balance, you calculate the 2% of $4273.56. You proceed as follow:
(2/100)(4273.56) = 85.47
Hence, the mimum payment of the balance is $85.47
b) You calculate the amount of interest charged this month as follow:
convert the annual percentage rate to decimal form:
21.1/100 = 0.211
divide the previous result by 12 to get the monthly interest rate:
0.2111/12 = 0.0175
multiply the previoues result by the balance:
0.0175 x 4273.56 = 75.143 ≈ 75.14
convert the monthly rate to a percentage:
0.0175 x 100 = 1.75%
Hence, the amount of interest was $75.14, which corresponds to a 1.75%
Write the equation of the circle given the following graph.
Given:
Equation of a circle on a graph with center(3, -2).
To find:
Equation of a circle.
Explanation:
General eqution of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]Solution:
From the graph, we can see that center is (3, -2) and radius equal 3.
So, equation of a circle is
[tex](x-3)^2+(y+2)^2=3^2[/tex]Hence, this is the equation of a circle.
What are the lengths of segments PQ and QR? input the lengths. then click done.
The length of a room is twice as its breadth and breadth is 6 cm. If it's height is 4 cm, find the total surface area.
The breadth of the room = 6 cm
Since the length of the room is twice its breadth
Then
Length of the room = 2 times 6cm = 12cm
The height of the room = 4cm
Since the shape of the room is a cuboid
The surface area of a cuboid is given as
[tex]SA=2(lh+lw+hw)[/tex]Substitute l = 12, w = 6 and h = 4 into the formula
This gives
[tex]SA=2(12\times4+12\times6+4\times6)_{}[/tex]Simplify the expression
[tex]\begin{gathered} SA=2(48+72+24) \\ SA=2(144) \\ SA=288 \end{gathered}[/tex]Therefore, the total surface area of the room is
[tex]288cm^2[/tex]The population of a school of fish decreases at a rate of 18% per month. There are currently500 fish in the school. How many fish will there be in 3 months?
Population decreasing rate is
18% monthly
Actual population = 500
Then
In 1 month decreases (500/100)• 18 = 90
Population = 500-90= 410
No find (410/100)•18 = 73.8
410-73.8= 336.2
In 3 months
(336.2/100) •18 = 60.5
336.2 - 60.5 = 276 fishes
ANSWER IS 276 fishes remain
Good morning, thanks for helping meHi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.
6.
(a)
The slope for the side AB is:
[tex]\begin{gathered} A=(-5,-4)=(x1,y1) \\ B=(5,-2)=(x2,y2) \\ m_{AB}=\frac{y2-y1}{x2-x1}=\frac{-2-(-4)}{5-(-5)}=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]The slope for the side BC is:
[tex]\begin{gathered} B=(5,-2)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_{BC}=\frac{6-(-2)}{7-5}=\frac{8}{2}=4 \end{gathered}[/tex]The slope for the side DC is:
[tex]\begin{gathered} D=(-3,4)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_{DC}=\frac{y2-y1}{x2-x1}=\frac{6-4}{7-(-3)}=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]And the slope for AD is:
[tex]\begin{gathered} A=(-5,-4)=(x1,y1) \\ D=(-3,4)=(x2,y2) \\ m_{AD}=\frac{4-(-4)}{-3-(-5)}=\frac{8}{2}=4 \end{gathered}[/tex](b) According to the previous results:
[tex]\begin{gathered} m_{AB}=m_{DC} \\ so \\ m_{AB}\parallel m_{DC} \end{gathered}[/tex][tex]\begin{gathered} m_{BC}=m_{AD} \\ so\colon \\ m_{BC}\parallel m_{AD} \end{gathered}[/tex](c) Since it has two pairs of parallel sides, also, The opposite sides are of equal length, we can conclude that this figure is a parallelogram
Hello! I need some help with this homework question, please? The question is posted in the image below. Q15
ANSWER:
A.
[tex]x=-1,-3,11[/tex][tex]f(x)=(x+3)(x-11)(x+1)[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=x^3-7x^2-41x-33[/tex]To find the zeros of the function we must set the function equal to 0 in the following way:
[tex]x^3-7x^2-41x-33=0[/tex]We reorganize the equation in order to be able to factor and calculate the zeros of the function, like this:
[tex]\begin{gathered} x^3-7x^2-41x-33=0 \\ -7x^2=-8x^2+x^2 \\ -41x=-33x-8x \\ \text{ Therefore:} \\ x^3-8x^2+x^2-33x-8x-33=0 \\ x^3-8x^2-33x=-x^2+8x+33 \\ x(x^2-8x-33)=-(x^2-8x-33) \\ x^2-8x-33 \\ -8x=3x-11x \\ x^2+3x-11x-33 \\ x(x+3)-11(x+3) \\ (x+3)(x-11) \\ \text{ we replacing} \\ x(x+3)(x-11)=-1 \\ x(x+3)(x-11)+(x+3)(x-11)=0 \\ (x+3)(x-11)(x+1)=0 \\ x+3=0\rightarrow x=-3 \\ x-11=0\rightarrow x=11 \\ x+1=0\rightarrow x=-1 \end{gathered}[/tex]Therefore, the zeros are:
[tex]x=-1,-3,11[/tex]And in its factored form the expression would be:
[tex]f(x)=(x+3)(x-11)(x+1)[/tex]xin uses 20 yards of fencing to build the walls of a square Chicken Coop which equation and solution represents x, the length, in yards, of each wall of the square coop?A: [tex]x + 4 = 20 \\ x = 16[/tex]b:[tex]x + 4 = 20 \\ x = 24[/tex]c:[tex]4x = 20 \\ x = 80[/tex]d:[tex]4x = 20 \\ x = 5[/tex]
Since the coop is in square shape The fencing is in the shape of a square
So equation is 4x=20, x=5
In a certain country, the probability that a baby that is born is a boy is 0.52 and the probably that a baby that is born is a girl is 0.48. A family has two children. If X is the number of girls born to a family, find the probability that the family has 0, 1, or 2 girls.(a) Draw a tree diagram showing the possibilities for each outcome.(b) Create the binomial distribution table for p(X)
Given:
The probability that a baby that is born is a boy is 0.52.
The probability that a baby that is born is a girl is 0.48.
To find:
The probability that the family has 0, 1, or 2 girls.
Explanation:
Using the binomial distribution,
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]Here,
[tex]\begin{gathered} n=2 \\ P(Birth\text{ of girls\rparen=}p=0.48 \\ P(B\imaginaryI rth\text{ of boys\rparen=}1-p=0.52 \end{gathered}[/tex]The probability that the family gets 0 girl child is,
[tex]\begin{gathered} P(X=0)=^2C_0(0.48)^0(0.52)^2 \\ =0.2704 \end{gathered}[/tex]The probability that the family gets 1 girl child is,
[tex]\begin{gathered} P(X=1)=^2C_1(0.48)^1(0.52)^1 \\ =0.2496 \end{gathered}[/tex]The probability that the family gets 2 girl children is,
[tex]\begin{gathered} P(X=2)=^2C_2(0.48)^2(0.52)^0 \\ =0.2304 \end{gathered}[/tex]So, the probability that the family has 0, 1, or 2 girls is,
[tex]\begin{gathered} P(E)=0.2704+0.2496+0.2304 \\ =0.7504 \end{gathered}[/tex]a) The tree diagram is,
b) The binomial distribution table for p(X) is,
Bobby says the dilation can be represented by (1\3X, 1,\3Y)Betty says the dilation can be represented by (3X, 3Y)who is correct and why?
Bobby is right because the measurements were made smaller so the dilation factor must be a number less than 1, and 1/3 is less than 1
Base on table above is the scenario a proportional relationship
No
Explanations:A relationship is called a proportional relationship if it has two variables that are realated by the same ration. In this case there will be a proportionality constant.
In this table:
Let Height be represented as H
Let Time be represented as T
For the relationship to be a proportional relationship, it must obey the relation:
[tex]\begin{gathered} H\propto\text{ T} \\ H\text{ = kT} \\ \text{Where k is the proportionality constant} \end{gathered}[/tex]When T = 3, H = 15
Using H = kT
15 = 3k
k = 15 / 3
k = 5
When T = 6, H = 30
H = kT
30 = 6k
k = 30 / 6
k = 5
When T = 12, H = 45
H = kT
45 = 12k
k = 45 / 12
k = 3.75
Since the constant of proportionality is the the same for the three cases in the table, the scenario is not a proportional relationship
entionaction f(x) = 4.12x +12. If f(x) = -2(5)*, what is f(2)?A100B.20fC227-2050C. -20D. -50boioht of 144I
Problem
We have the following expression given:
f(x)= -2(5)^x
And we want to find f(2)
Solution
so we can do the following:
f(2)= -2 (5)^2 = -2*25 = -50
Use compatible numbers to determine if 455+ 229 is more than 650
Step 1
compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.
Step 2
Math problem
455 + 229
Compatible numbers
455 + 225 = 680
680 is close to 455+229 = 684
Step 3:
Hence
By compatible numbers, 455 + 229 is more than 650.
Instructions: Complete the following table, computing each students' mean, median, mode, and range: Math Test Scores ( picture attached ) What is the mean score for Test 2? What is the mode of Test 7? ________What is the median score of Test 4? ________What is the range of Test 6? ________
The completed worksheet is the following:
This worksheet involves three measures of central tendency: Mean, Median, Mode and Range
Mean: To get the mean of a dataset, add up all the data and divide by the number of datum (or inputs)
Median: To get the median of a dataset, sort the data in ascending order, and choose the central datum.
For example, if you have a dataset with 7 inputs, sort it in ascending order and select the 4th datum, as there would be 3 values above and 3 below (Hence it being the central datum).
Mode: The mode is the most repeated value of a dataset.
Range: The range is the difference between the biggest and smallest values of a dataset.
Andre is looking at apartments with 1 of his friends. They want the monthly rent to be no more than $1000. If the roommates split the rent evenly among the two of them, what is the maximum rent each will pay?
We have the next inequality
[tex]2x\le1000[/tex]where x is the rent of each person
[tex]\begin{gathered} x\le\frac{1000}{2} \\ x\le500 \end{gathered}[/tex]The maximum rent each will pay is $500
Help!
find all zeros of p(x). include any multiplicities greater than one.
The most appropriate choice for polynomial will be given by
1) Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]
where [tex]i = \sqrt{-1}[/tex]
2) Zeroes of P(x) = 3, 2i, -2i
3) Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]
4) Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]
What is a polynomial?
An algebraic expression of the form [tex]a_0 + a_1x +a_2x^2 + a_nx^n[/tex] is called a polynomial of degree n.
[tex]1) P(x ) = 3x^3 -10x^2 + 10x -4\\P(2) = 3(2)^3 - 10(2)^2 +10(2) - 4\\[/tex]
[tex]= 24 -40 + 20 -16\\= 0[/tex]
(x - 2) is a factor of P(x)
[tex]P(x) = 3x^2(x - 2) -4x(x - 2) +2(x-2)\\[/tex]
= [tex](x - 2)(3x^2 - 4x + 2)[/tex]
[tex]=(x-2)(x -a)(x - b)[/tex]
where,
[tex]a = \frac{-(-4)+\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\a =\frac{ 4 + \sqrt{-8}}{6}\\a = \frac{4 + 2\sqrt{2} i}{6}\\a = \frac{2(2 + \sqrt{2}i)}{6}\\a = \frac{2 + \sqrt{2}i}{3}[/tex]
[tex]b = \frac{-(-4)-\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\b =\frac{ 4 -\sqrt{-8}}{6}\\b = \frac{4 - 2\sqrt{2} i}{6}\\b = \frac{2(2 - \sqrt{2}i)}{6}\\b = \frac{2 - \sqrt{2}i}{3}[/tex]
Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]
where [tex]i = \sqrt{-1}[/tex]
[tex]2) P(x) = x^3 - 3x^2+4x-12\\P(3) = (3)^3 - 3(3)^2 +4(3) -12\\ P(3) = 0[/tex]
(x - 3) is a factor of P(x)
[tex]x^2(x - 3) + 4(x - 3)\\(x - 3)(x^2 + 4)\\(x - 3)(x -a)(x-b)\\[/tex]
where,
[tex]a = \sqrt{-4}\\a = 2i[/tex]
[tex]b = -\sqrt{-4}\\a = -2i[/tex]
Zeroes of P(x) = 3, 2i, -2i
[tex]3) 2x^3 - 3x^2 +8x-12= 0\\[/tex]
x = 2 satisfies the equation
[tex]2x^2(x -\frac{3}{2}) + 8(x-\frac{3}{2})=0\\(2x^2+8)(x - \frac{3}{2}) = 0\\[/tex]
[tex]2x^2 + 8 = 0[/tex] or [tex]x - \frac{3}{2} = 0[/tex]
[tex]x^2 = -\frac{8}{2}[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x^2 = -4[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x = \sqrt{-4}[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x = 2i[/tex] or [tex]x = -2i[/tex] or [tex]x = \frac{3}{2}[/tex]
Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]
4)
[tex]x^4 - 5x^3 +3x^2 +x = 0\\x(x^3 -5x^2 + 3x +1) = 0\\[/tex]
[tex]x = 0[/tex] or [tex]x^3 -5x^2+3x +1 = 0[/tex]
For [tex]x^3 -5x^2+3x +1 = 0[/tex]
x = 1 satisfies the equation
[tex]x^2(x -1) -4x(x-1)-1(x-1) = 0\\(x - 1)(x^2 - 4x -1) = 0\\[/tex]
[tex]x -1 = 0[/tex] or [tex]x^2 - 4x -1 = 0[/tex]
Roots are x = 1 or x = a or x = b
where,
[tex]a = \frac{-(-4) + \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\a = \frac{4+\sqrt{20}}{2}\\a = \frac{4 + 2\sqrt{5}}{2}\\a = \frac{2(2 + \sqrt{5})}{2}\\a = 2 + \sqrt{5}[/tex]
[tex]b = \frac{-(-4) - \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\b = \frac{4-\sqrt{20}}{2}\\b = \frac{4 - 2\sqrt{5}}{2}\\b = \frac{2(2 - \sqrt{5})}{2}\\b = 2 - \sqrt{5}[/tex]
Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]
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f(x) = x ^ 3 + 3x ^ 2 + 4x + 5 and g(x) = 5 , then g(f(x)) =
we have the functions
[tex]\begin{gathered} f\mleft(x\mright)=x^3+3x^2+4x+5 \\ g(x)=5 \end{gathered}[/tex]so
g(f(x))=5HELP ASAP
QUESTION IS ATTACHED!
Answer:
(2,8) and (-6,0)Step-by-step explanation:
(3,9)
(-5*3) +( 3*9) > 12
-15 + 27 > 12
12 > 12
not true
(-5,5)
(-5*5) + (3*5) > 12
-25 + 15 > 12
-10 > 12
not true
(3,-6)
(-5*3) + (3*-6) > 12
-15 + -18 > 12
-33 > 12
not true
(-2,-5)
(-5*-2) + (3*-5) > 12
10 + -15 > 12
5 > 12
not true
(2,8)
(-5*2) + (3*8) > 12
-10 + 24 > 12
14 > 12
true(-6,0)
(-5*-6) + (3*0) > 12
30 + 0 > 12
30 > 12
trueis 6x0=O and example of distributive property?
we have that
Distributive property is the product of a factor and a sum (or difference) equals the sum (or difference) of the product
In this exanple
6x*0=0
Is not the product of a factor and a sum or difference
An animal shelter spends $1.50 per day to care for each cat and $6.50 per day to carefor each dog. Gavin noticed that the shelter spent $97.00 caring for cats and dogs onMonday. Gavin found a record showing that there were a total of 18 cats and dogs onMonday. How many cats were at the shelter on Monday?
4 cats and 14 dogs.
Explanation:
Data :
Amount of cats : c = ?
Cost per cats : $1.50
Amount of dogs : d = ?
Cost per dogs : $6.50
Total spent for dogs and cats : $97.00
Total number of dogs and cats : 18
Formulas:
1.50c + 6.50d = 97.00
c + d = 18
Solution:
c + d = 18 => c = 18 - d
1.50(18 -d) + 6.50d = 97.00
27 - 1.50d + 6.50d = 97.00
27 - 1.50d + 6.50d - 27 = 97 -
Given that 4 is a zero of the polynomial function f(x), find the remaining zeros.f(x) = x³ - 6x² + 25x - 68List the remaining zeros (other than 4).4(Simplify your answer. Type an exact answer, using radicals and i as needed. Use a cc
ANSWER
[tex]\begin{gathered} x=1+4i \\ x=1-4i \end{gathered}[/tex]EXPLANATION
Given:
[tex]\begin{gathered} f(x)=x^3-6x^2+25x-68 \\ \end{gathered}[/tex]Also,
One of the zeros: x = 4
Desired Outcome:
List the remaining zeros using radicals and i.
Simplify the polynomial using x - 4 = 0
Determine the remaining polynomials by simplifying x^2 - 2x + 17 = 0 using the quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where:
a = 1,
b = -2
c = 17
Substitute the values
[tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(17)}}{2(1)} \\ x=\frac{2\pm\sqrt{4-68}}{2} \\ x=\frac{2\pm\sqrt{-64}}{2} \\ x=\frac{2\pm\sqrt{64\times-1}}{2} \\ x=\frac{2\pm(\sqrt{64}\times\sqrt{-1})}{2} \\ x=\frac{2\pm8\sqrt{-1}}{2} \\ x=1\pm4\sqrt{-1} \\ \text{ Recall: }\sqrt{-1}\text{ = }i \\ x=1\pm4i \\ x=1+4i\text{ }or \\ x=1-4i \end{gathered}[/tex]
state income tax? Jim Koslo earns $156,200 annually as a plant manager. He is married and supports 3 children. The state tax rate in his state is 3.55% of taxable income. What amount is withheld yearly for state income tax?
Answer:
44,000
Let me know if its wrong
What tip will Brady get if a customer adds a 15% tip to his $18.52 meal cost?
Brandy will get a tip of $2.778
Here, we want to get the amount of tip Brandy will get
In the question, the tip is 15% of $18.52
That will mathematically be;
[tex]\begin{gathered} \frac{15}{100}\text{ }\times\text{ \$18.52} \\ \\ =\text{ }\frac{277.8}{100}\text{ = \$2.778} \end{gathered}[/tex]Simplify by combining like terms,8t3 + 8y + 7t3 + 6y + 9t2
The simplification of the expression will be; 15t³ + 9t² + 14y
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions. To derive equivalent expressions of some expressions, we can either make them look more complex or simple.
Given that the expression as 8t³ + 8y + 7t³ + 6y + 9t²
Now combining like terms;
8t³ + 7t³ + 9t² + 8y + 6y
Simplify;
15t³ + 9t² + 14y
It cannot be solved further because of unlike terms in the expression.
Therefore, the simplification of the expression will be; 15t³ + 9t² + 14y
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Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.
A quadratic function describes the relationship between the number of products x and the overall profits for a company.
The roots of the quadratic function are given as x = 0 and x = 28. We also know the graph's vertex is located at (14, -40).
The quadratic equation can be written in terms of its roots x1 and x2 as:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]Substituting the given values:
[tex]\begin{gathered} f(x)=a(x-0)(x-28) \\ \\ f(x)=ax(x-28) \end{gathered}[/tex]We can find the value of a by plugging in the coordinates of the vertex:
[tex]f(14)=a\cdot14(14-28)=-40[/tex]Solving for a:
[tex]a=\frac{-40}{-196}=\frac{10}{49}[/tex]Substituting into the equation:
[tex]f(x)=\frac{10}{49}x(x-28)[/tex]The graph of the function is given below:
The company actually loses money on their first few products, but once they hit 28 items, they break even again.
The worst-case scenario is that they produce 14 items, as they will have a profit of -40 dollars. The first root tells us the profit will be 0 when 0 products are sold.
In 2005 there were 744 radio stations, by 2015 that number had increased by 13.8%. How many radio stations in 2015?
Answer: We have to find the radio stations in 2015, which is 13.8% more than the radio stations in 2005 which were 744:
[tex]\begin{gathered} x=\text{ Radio stations in 2015} \\ \\ x=(1.138)\times(744) \\ \\ x=846.672 \\ \\ x\approx847 \end{gathered}[/tex]64 is 2/3percent of what number
We have to find the number x for which 64 is the 2/3.
Find the degree measure of the central angle for sector C. (image attached)
We will determine the angle as follows:
We know that the whole circle contains 360°, so we determine the angle of 0.35 as follows:
[tex]C=\frac{0.35\ast360}{1}\Rightarrow C=126[/tex]So, the measure of the central angle for sector C is 126°.
Given the following five-number summary, find the IQR.
2.9, 5.7, 10.0, 13.2, 21.1.
The IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
In the given question, a five number summary is given as follows
2.9, 5.7, 10.0, 13.2, 21.1
We need to find the IQR
So, first we'll find the median of the given series
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
So, the given series is already in ascending order. And the middle value is 10.0. So the median is 10.0
Now to find the IQR the given formula will be used,
IQR = Q3 - Q1
Where Q3 is the last term in lower series and Q1 is the last term in upper series
Lower series - 2.9, 5.7
Upper series - 3.2, 21.1
Q3 = 5.7 , Q1 = 21.1
IQR = Q3 - Q1 = 21.1 - 5.7 = 15.4 ( IQR is always positive)
Hence, the IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
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