Use the parabola tool to graph the quadratic function y=-x^2 – 2x + 8Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
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We have that the parabola is the blue one, and the vertex is (1, 7).
Related Questions
What is the length of AB BC And AC in inches
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Since ∠A and ∠C are congruent, it follows that the sides opposite to these angles are also congruent.
[tex]\begin{gathered} \overline{AB}=\overline{BC} \\ \\ \text{Substitute the following sides using their given} \\ 5x-3=3x+7 \\ 5x-3=3x+7 \\ 5x-3x=7+3 \\ 2x=10 \\ \frac{\cancel{2}x}{\cancel{2}}=\frac{10}{2} \\ x=5 \end{gathered}[/tex]Now that we know the value of x, substitute this to AB and we get
[tex]\begin{gathered} \overline{AB}=5x-3 \\ \overline{AB}=5(2)-3 \\ \overline{AB}=10-3 \\ \overline{AB}=7\text{ inches} \end{gathered}[/tex]Therefore, the length of AB is 7 inches.
[tex]\begin{gathered} \overline{AC}=6x-3 \\ \overline{AC}=6(2)-3 \\ \overline{AC}=12-3 \\ \overline{AC}=9\text{ inches.} \\ \\ \overline{BC}=3x+7 \\ \overline{BC}=3(2)+7 \\ \overline{BC}=6+7 \\ \overline{BC}=13\text{ inches} \end{gathered}[/tex]Kim says that 32.697 rounded to the nearest hundredths place is 32.7 Do you agree? Why or why not?
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When you round to the nearest hundreths, you are approximating the second number after the decimal point. Then, a number wich has been rounded to its nearest hundreth is a number with two decimal numbers. Moreover, if the number right of the hundreth is 5 or greater, the hundreths increase one unit, otherwise, remain the same.
Then, 32.697 rounded to its nearest hundreth is 32.70, which is the same as 32.7
Hence, Kim is correct
The number of accidents in a week is ___________?a continuous random variable.a discrete random variable.neither continuous nor discrete variable.continuous and discrete variables.
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a discrete random variable.
Discrete variables are countable in a finite amount of time
Continuous variables would take forever to count. Hopefully we do not have that many accidents. Continuous variables would be like time.
Discrete things are things we can count and thats it, like the amount of change in your pocket, or the number of tic tacs in the container.
A cash register contains $20 bills and $100 bills with a total value of $1460. If there are 21 bills total, then how many of
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The register contains 8 number of $20 bills and 13 number of $100 bills.
What is termed as the linear equation in two variables?A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers as well as the coefficients of x and y, i.e. a and b, are not equal to zero.Let 'x' be the of $20 bills.
Let 'y' be of $100 bills.
Total bill = 21
x+y = 21
y = -x+21 ......eq1
Now,
Total price = $1460.
20x + 100y = 1460
Put value of y from eq 1.
20x + 100(-x+21) = 1460
20x-100x+2100=1460
-80x=-640
x=8 (Number of $20 bill)
And,
-8+21=13
y=13 (Number of $100 bills)
Thus, the register contains 8 number of $20 bills and 13 number of $100 bills.
To know more about linear equation, here
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The complete question is-
A cash register contains $20 bills and $100 bills with a total value of $1460. If there are 21 bills total, then how many of each does the register contain?
In the diagram below , ^PQR = ^STR . Complete the statement PW = _
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Given:
[tex]\Delta PQR\cong\Delta STR[/tex]From the figure shown,
It is clear by the similarity of triangles,
[tex]\frac{PQ}{TS}\cong\frac{QR}{TR}\cong\frac{PR}{RS}[/tex]Therefore, Line PQ is congruent to line TS
Hence,
[tex]PQ\cong TS[/tex]Thus, option C is correct.
- Abby just sculpted a flat, solid bronze triangle for her art class. (What? There are no wrong answers in art.) If triangle's base is 4 feet long and she used 14 square feet of bronze, how tall is the sculpture?
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Area of a triangle: 1/2 x base length x height
We have:
area : 14 ft2
Length: 4 ft
Replacing:
14 = 1/2 (4) h
Solve for h (heigth)
14 = 2 h
14/2 = h
h= 7 ft
#22Graph the function and tell wether or not it has a point of discontinuity at x = 0. If there is a discontinuity, tell wether it is removable or non removable.
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Answer:
Removable discontinuity at x=0.
Step-by-step explanation:
By looking at the denominator of h(x), there will be a discontinuity.
Since the denominator cannot be zero, x has to be different from 0. Therefore, there is a discontinuity at x=0.
Now, to determine what type of discontinuity, check if there is a common factor in the numerator and denominator of the function. If there is an existent common factor, there is a removable discontinuity or a hole.
[tex]\begin{gathered} h(x)=\frac{x^3+x}{x} \\ h(x)=\frac{x(x^2+1)}{x}=x^2+1 \end{gathered}[/tex]There is a removable discontinuity, or a hole, at x=0.
The model for radioactive decay Is y = yor". A radioactive substance has a half-life of 60 years. Ir 100 grams are present today, in how many years will 68 es artis bepresent? While solving this problem, round the value of k to seven decimal places. Round your answer to two decimal places.KeypadAnswerHow to enter your answer opens in new windowadhat
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We are given that the radioactive decay of a substance is given by the following equation:
[tex]y=y_0e^{kt}[/tex]We need to determine the value of "k". To do that we will use the fact that the half-life of the quantity is 60 years. The half-life is the time for the quantity to be half the initial value, therefore, we have:
[tex]\frac{y_0}{2}=y_0e^{k(60)}[/tex]We can cancel out the initial quantity:
[tex]\frac{1}{2}=e^{k(60)}[/tex]Now, we take the natural logarithm to both sides:
[tex]ln(\frac{1}{2})=ln(e^{k(60)})[/tex]Now, we use the following property of logarithms:
[tex]ln(x^y)=ylnx[/tex]Applying the property we get:
[tex]ln(\frac{1}{2})=k(60)lne[/tex]We also have:
[tex]lne=1[/tex]Substituting we get:
[tex]ln(\frac{1}{2})=k(60)[/tex]Now, we divide both sides by 60:
[tex]\frac{1}{60}ln(\frac{1}{2})=k[/tex]Now, we solve the operations:
[tex]-0.011552=k[/tex]Now, we substitute the value of "k":
[tex]y=y_0e^{-0.011552t}[/tex]We are given that 100 grams is present today. If today is the value when time "t" is zero then 100 grams is the initial quantity, therefore, we substitute:
[tex]y=100e^{-0.011552t}[/tex]Now, we are asked to determine the time when "y = 68g":
[tex]68=100e^{-0.011552t}[/tex]Now, we solve for "t". First, we divide both sides by 100:
[tex]\frac{68}{100}=e^{-0.011552t}[/tex]Now, we take the natural logarithm:
[tex]ln(\frac{68}{100})=lne^{-0.011552t}[/tex]Now, we apply the property of logarithms:
[tex]ln(\frac{68}{100})=-0.011552tln(e)[/tex]Applying "ln (e) = 1";
[tex]ln(\frac{68}{100})=-0.011552t[/tex]Now, we divide both sides by -0.011552:
[tex]-\frac{1}{0.011552}ln(\frac{68}{100})=t[/tex]Solving the operation:
[tex]33.38=t[/tex]Therefore, the time required is 33.38 years.
What is the sequence of -4,-2,0,2
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Given:
The sequence is ,
[tex]-4,-2,0,2,\ldots\text{..}[/tex][tex]\begin{gathered} \text{First term of the sequence is,} \\ a_0=-4 \\ \text{Common difference is,} \\ d=2 \\ \text{The sequence is,} \\ a_n=a_0_{}+(n-1)d \\ a_n=-4+(n-1)2 \\ a_n=-4+2n-2 \\ a_n=2n-6 \end{gathered}[/tex]Answer:
[tex]a_n=2n-6[/tex]Clara asked some students in two different grades which superpower they would choose: the ability to stop and start time or the ability to fly. She put the results in the following two-way frequency table. Time Fly Total Freshmen 45 20 65 Sophomores 30 51 81 Total 75 71 146 What percent of the sophomores surveyed chose the ability to fly?
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Given:
Clara asked some students in two different grades which superpower they would choose: the ability to stop and start time or the ability to fly.
And given that a table :
Time Fly Total
Freshmen 45 20 65
Sophomores 30 51 81
Total 75 71 146
Required:
To find the percent of the sophomores surveyed chose the ability to fly.
Explanation:
The total number of students = 146
The number of sophomores who choose ability to fly = 51.
Now the percent of the sophomores surveyed chose the ability to fly is,
[tex]\begin{gathered} =\frac{51}{146}\times100 \\ \\ =34.93\times100 \\ \\ =35\% \end{gathered}[/tex]Final Answer:
35% of the sophomores surveyed chose the ability to fly.
the question:6x - 15 ≥ 33
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To determine the possible values of x you have to isolate the x-term in one side of the inequality and the numbers on the other side.
The first step is to pass "-15" to the right side of the expression by applying the opposite operation to both sides of it, i.e. you have to add 15
[tex]\begin{gathered} 6x-15+15\ge33+15 \\ 6x\ge48 \end{gathered}[/tex]Then you have to divide both sides by 6 to determine the value of x:
[tex]\begin{gathered} \frac{6x}{6}\ge\frac{48}{6} \\ x\ge8 \end{gathered}[/tex]A rectangular prism can be unfolded into the net shown below. Findthe total surface area of the rectangular prism.<4.8 in9.4 in7.6 in
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For this question, we need to use the formula for getting the surface area of a rectagular prism which is:
A = 2 (wl + hl + hw)
A = Area
w = width
l = length
h = height
According to the given,
w = 7.6
l = 9.4
h = 4.8
Now, using the formula stated above,
A = 2 (wl + hl + hw)
A = 2 [(7.6)(9.4) + (4.8)(9.4) + (4.8)(7.6)]
A = 306.08
The answer would be 306.08 cube inches.
In the following equation, what is f(5) or f (-2)?
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Given:
The function is
[tex]f(x)=x^2+3x-10[/tex]Required:
What is f(5) and f(-2)?
Explanation:
We have
[tex]f(x)=x^2+3x-10[/tex]Now,
[tex]\begin{gathered} f(5)=5^2+3(5)-10 \\ f(5)=25+15-10 \\ f(5)=30 \end{gathered}[/tex]and
[tex]\begin{gathered} f(-2)=(-2^)^2+3(-2)-10 \\ f(-2)=4-6-10 \\ f(-2)=-12 \end{gathered}[/tex]Answer:
So, f(5) = 30 and f(-2) = -12.
Simplify the following expression. Assume x>0 and write your answer without radicals.(169x)1/2⋅(4x−6/7)
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Answer
The answer is
[tex]52x^{-\frac{5}{14}}[/tex]
SOLUTION
Problem Statement
We are given the following expression to evaluate:
[tex](169x)^{\frac{1}{2}}\text{.}(4x^{-\frac{6}{7}})[/tex]Method
- To solve this question, we need to know some laws of indices. These laws are given below:
[tex]\begin{gathered} \text{ Law 1:} \\ a^b\times a^c=a^{b+c} \\ \\ \text{Law 2:} \\ (ab)^c=a^c\times b^c \end{gathered}[/tex]Implementation
Let us apply the law above to solve the question as follows:
[tex]\begin{gathered} (169x)^{\frac{1}{2}}\text{.}4x^{-\frac{6}{7}}) \\ By\text{ Law 2, we have:} \\ =169^{\frac{1}{2}}\times x^{\frac{1}{2}}\times4\times x^{-\frac{6}{7}} \\ \\ But\text{ }169^{\frac{1}{2}}=\sqrt[]{169}=13 \\ 169^{\frac{1}{2}}\times x^{\frac{1}{2}}\times4\times x^{-\frac{6}{7}}=13\times x^{\frac{1}{2}}\times4\times x^{-\frac{6}{7}} \\ \\ Collect\text{ like terms} \\ 13\times4\times x^{\frac{1}{2}}\times x^{-\frac{6}{7}}=52\times x^{\frac{1}{2}}\times x^{-\frac{6}{7}} \\ \\ By\text{ Law 1, we have:} \\ x^{\frac{1}{2}}\times x^{-\frac{6}{7}}=x^{\frac{1}{2}-\frac{6}{7}}=x^{-\frac{5}{14}} \\ \\ \therefore52\times x^{\frac{1}{2}}\times x^{-\frac{6}{7}}=52\times x^{-\frac{5}{14}} \end{gathered}[/tex]Final Answer
The answer is
[tex]52x^{-\frac{5}{14}}[/tex]
If f (sc) = 3x and g(x) = 2x – 1, find-() (a(2)
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We have two functions:
[tex]\begin{gathered} f(x)=3x \\ g(x)=2x-1 \end{gathered}[/tex]We have to find the expression for (g/f)(x). This is equivalent to write:
[tex](\frac{g}{f})(x)=\frac{g(x)}{f(x)}=\frac{2x-1}{3x}[/tex]Answer: (g/f)(x) = (2x-1) / 3x [Fourth option]
Find the real-number root.sqrt -1.21Options:-0.6051.1-1.1or no real number root
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Given:
[tex]\sqrt{-1.21}[/tex]You need to remember this property for Radicals:
[tex]\sqrt[n]{b^n}=b[/tex]You know that:
[tex]121=11\cdot11=11^2[/tex]Therefore, you can conclude that:
[tex]1.21=1.1^2[/tex]Hence, you can rewrite the expression as follows:
[tex]=\sqrt[]{-(1.1)^2}[/tex]By definition:
[tex]\sqrt[]{-1}=i[/tex]Then, you can rewrite it as:
[tex]=1.1i[/tex]Therefore, it is an Imaginary Root.
Hence, the answer is: Last option.
3. In a Complete Sentence, How much does it cost to send a letter thatweighs 2.5 ounces? *
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SOLUTION
The weight of the letter in consideration here is 2.5 ounces, and looking at the function P(w) given, it falls in the range of
[tex]2The corresponding cost for mailing letters that fall between that range is $2.29So if we are to put our answer in a complete sentence, it will go thus:
aPlease draw the combined vector (resultant) of the two vectors a + b by eithertriangle or parallelogram methods.
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The resultant of two vectors is one vector that acts as the two vectors combine. Given vectors a and b, the resultant is:
Above is a typical resolution of the resultant using the parallelogram method.
what value of x is the expression 6x + 4
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x in the expression
[tex]6x+4[/tex]Is what we call a variable quantity, or unknown. That means that x can hold any value. If it was a linear equation in one variable we'd be able to find out it's exact value.
Triangle area = 16 ft²B = 4ftH = ?
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The area of a triangle is given by the following formula:
[tex]A=\frac{bh}{2}[/tex]Since we are given the area and we need to find the height, we need to solve for "h". To do that we will first multiply by 2 on both sides:
[tex]2A=bh[/tex]Now we divide both sides by "b":
[tex]\frac{2A}{b}=h[/tex]Now we replace the known values:
[tex]\frac{2(16)}{4}=h[/tex]Solving the operations_
[tex]8=h[/tex]Therefore, the height is 8 ft
I need to verify if I did my sign chart right! For preclac
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Factoring the polynomial, we have:
[tex]\frac{x^2-4x}{x^2+5x+6}=\frac{x(x-4)}{(x+2)(x+3)}[/tex]The sign chart would be:
The graph would be:
The coordinates of triangle CDE are as follows:The triangle is dilated by a scale factor of 3.1. What are the new coordinates of triangle C'D'E'?2. Is this an enlargement, congruency, or a reduction? Explain.C (3,5)D (7,5)E (5,2)
Answers
ANSWER
1. C'(9, 15), D'(21, 15), E'(15, 6)
2. Enlargement
EXPLANATION
Assuming the center of dilation is the origin, the rule to find the image of each point on the figure after dilation by a scale factor of 3 is,
[tex](x,y)\rightarrow(3x,3y)[/tex]So, the vertices of the triangle have the images,
[tex]\begin{gathered} C(3,5)\rightarrow C^{\prime}(9,15) \\ D(7,5)\rightarrow D^{\prime}(21,15) \\ E(5,2)\rightarrow E^{\prime}(15,6) \end{gathered}[/tex]The triangle obtained is larger than the triangle CDE. This is because the scale factor is a value greater than 1, so it produces a larger image.
If the scale factor is between 0 and 1, it produces a smaller image and, if it is equal to 1, the image produced is congruent to the pre-image.
Hence, the coordinates of triangle C'D'E' are C'(9, 15), D'(21, 15), E'(15, 6), and the dilation is an enlargement.
mandi is paid $100 a week plus $10 for each new cell phone plan she sells. she may switch to a new company that pays $80 a week but $15 for each plan she sells. how many memberships per week does mandi need to sell for the new company to be a better deal for her? justify the response with mathematical reasoning and/or calculations.
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Answer:
Mandi needs to sell more than 4 memberships per week for the new company to be a better deal.
Explanation:
Given that Mandi is paid $100 a week plus $10 for each new cell phone plan she sells, let x be the number of new cell phone plan she sells, then
100 + 10x
is the expression for her earning.
She may switch to a new company that pays $80 a week but $15 for each plans she sells, her earnings is written as
80 + 15x
If the new company must be a better deal, then her earnings, then her earnings in the new company must be greater than her earnings in the old one.
80 + 15x > 100 + 10x
Solving the inequality above, we have the number of memberships per week she requires for the deal.
Subtract 10x from both sides of the inequality
80 + 15x - 10x > 100 + 10x - 10x
80 + 5x > 100
Subtract 80 from both sides
80 + 5x - 80 > 100 - 80
5x > 20
Divide both sides by 5
5x/5 > 20/5
x > 4
The number of memberships Mandi needs is greater than 4.
a.) HOW DO YOU COMPUTE SIMPLE INTEREST?
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Simple Interest can be computed by using the below formula;
[tex]I=P\ast r\ast t[/tex]Where I = Simple interest earned after a specified number of years
P = the principal( the initial money invested)
r = annual rate of interest
t = time(in years)
Let's pick an example, let's assume someone decided to invest $200 for 4 years with an interest rate of 3%;
From the above example, our P = $200, r = 3% = 0.03 and t = 4, so our simple interest will then be;
[tex]\begin{gathered} I=200\ast0.03\ast4 \\ =24 \end{gathered}[/tex]Therefore, the simple interest will be $24.
6 meters to centimeters
Answers
1 meter = 100 centimeters
So, we have to multiply the number of meters by 100
6 x100 = 600 centimeters
In 2003, a town’s population was 1431. By 2007 the population had grown to 2134. Assume the population is changing linearly. Answer the questions below and to earn full credit show all work/calculations/thinking.How much did the population grow between the year 2003 and 2007?How long did it take the population to grow from 1431 people to 2134 people?What is the average population growth per year?What was the population in the year 2000?Find an equation for the population, P, of the town t years after 2000.Using your equation, predict the population of the town in 2014.
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We know that the population in 2003 and 2007 is:
2003: 1431
2007: 2134
1. To know how much the population grow from 2003 to 2007, we need to subtract the population in 2003 from the population of 2007:
Growth = 2134 - 1431 = 703
2. It took (2007 - 2003) = 4 years for the population to grow from 1431 to 2134.
3. The average population growth per year can be calculated as:
Average = Growth / (# of years) = 703/4 = 175.75
4. Since it is a linear model, the growth rate is constant for all years. 3 years passed from 2000 to 2003, and the average growth per year is 175.75, so the population in the year 2000 is:
Population_2000 = Population_2003 - 3*Average
Population_2000 = 1431 - 3*175.75 = 903.75
To the nearest whole number, the population in the year 2000 was 904.
5. The linear model is:
[tex]P(t)=m\cdot t+b[/tex]Where P is the population of the town t years after 2000, m is the average growth per year and b is the population in the year 2000. Using our results:
[tex]P(t)=175.75\cdot t+904[/tex]6. For the year 2014 the value of t is 14. Then, using our linear model, the population is:
[tex]P(14)=175.75\cdot14+904=3364.5\approx3365[/tex]The population of the town in 2014 will be 3365.
Question 2. An absolute value equation can be rewritten as two equations that do not have absolute value symbols. Rewrite |x-31 = 7 as two equations.
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The given equation is
[tex]|x-3|=7[/tex]An absolute value equation can be rewritten as two equations because the binomial inside the bars can be positive or negative. Therefore, the two equations are
[tex]\begin{gathered} x-3=7 \\ x-3=-7 \end{gathered}[/tex]the table below shows percentages of votes each Sport received in a recent survey of students favorite sports. Which of the following sets of data could be the actual results of the survey? I will send image.
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Given:
Percentage of vote for Lacrosse is, 40%
Percentage of vote for Basketball is, 40%
Percentage of vote for Hockey is, 20%
The objective is to find the actual results of the survey.
In option (a), (b) and (d), Lacrosse and Basket ball has different amount of votes.
But in given data, both Lacrosse and Basketball has same percentage of votes.
Thus, option (c) will have same amount of 12 vote for Lacrosse and Basket ball.
Then, hockey will receive 6 votes.
Hence, option (C) is the correct answer.
Provide three examples of the rectangular coordinate system, which is the basis for most consumer graphs.
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Step 1
The rectangular coordinate system consists of two real number lines that intersect at a right angle. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis. These two number lines define a flat surface called a plane, and each point on this plane is associated with an ordered pair of real numbers (x, y). The first number is called the x-coordinate, and the second number is called the y-coordinate.
Step 2
Three examples of the rectangular coordinate system, which is the basis for most consumer graphs are;
[tex]\begin{gathered} 1)\text{lines} \\ 2)Trigonometric\text{ or sin}usoidal\text{ }functions \\ 3)\text{ Exponential functions} \end{gathered}[/tex]Hi can you help me to find the Mean, Medium, Mode, and Range please !
Answers
The given data set is:
[tex]12,12,18,19,19,21,23,23,23,23,32,32,41,50,50,50,82,82[/tex]a) The Mean:
[tex]\bar{x}=\frac{sum\text{ of observations}}{\text{number of observations}}[/tex]Thus,
[tex]\bar{x}=\frac{12+12+18+19+19+21+23+23+23+23+32+32+41+50+50+50+82+82}{18}[/tex][tex]\begin{gathered} \bar{x=\frac{612}{18}} \\ \operatorname{mean}=34 \end{gathered}[/tex]b) The median;
The median is the middle number or the average of the numbers if there are two(2) middle numbers.
However, the observations have to be arranged in ascending order.
In this case, the observations are already arranged from the lowest to the highest.
Thus, we have:
[tex]\begin{gathered} \text{middle numbers are 23 and 23} \\ \text{Median}=\frac{23+23}{2} \\ \text{Median}=\frac{46}{2}=23 \end{gathered}[/tex]c) The Mode;
The mode is the most occuring observation.
Thus, the Mode is 4
d) The Range:
[tex]\begin{gathered} \text{Range}=\text{highest number -lowest number} \\ \text{Range}=82-12=70 \end{gathered}[/tex]