Number of Workers and Hours to Complete 1 mile of Highway (10, 50) 50 Number of Hours to Complete 1 mile of Highway 30 : (25, 20) 10 10 25 15 20 Number of Workers As the values of x increase, the values of y y :: increase :: decrease : remain the same
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In the graph you can see that all the points do not pass through a single line, however, you can obtain the slope of the line that passes through the points.
*If the slope is positive, the values of y increase as the values of x increase.
*If the slope is negative, the values of y decrease as the values of x increase.
The formula for the slope is
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} (x_{1,}y_1)=(10,50) \\ (x_{2,}y_2)=(25,20) \end{gathered}[/tex][tex]\begin{gathered} m=\frac{20-50}{25-10} \\ m=\frac{-30}{15} \\ m=-2 \end{gathered}[/tex]Therefore, since the slope of the line that passes through these points is negative then the correct answer is:
As the values of x increase, the values of y decrease.
Related Questions
Venus is approximately 1.082×107
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To express the number in standard notation we need to move the decimal point 9 times to the right, then:
[tex]1.082\times10^9=1,082,000,000[/tex]Therefore the answer is d
In the function y+ 3 = (2x) + 1, what effect does the number 2 have on the graph, as compared to the graph of 1=1? 2 A. It shrinks the graph horizontally to 1/2 the original width B. It shrinks the graph vertically to 1/2 the original height. O C. It stretches the graph horizontally by a factor of 2. D. It stretches the graph vertically by a factor of 2
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The given transformation f(2x) represents a horizontal compression by a scale factor of 1/2.
Therefore, the right answer is A.I need help with this practice problem It asks to answer (a) and (b) Please put these separately so I can see which is which
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We have a series:
[tex]\sum ^{\infty}_{n\mathop{=}1}a_n=\sum ^{\infty}_{n=1}(\frac{2n!}{2^{2n}})\text{.}[/tex](a) The value of r from the ratio test is:
[tex]\begin{gathered} r=\lim _{n\rightarrow\infty}|\frac{a_{n+1}}{a_n}| \\ =\lim _{n\rightarrow\infty}\frac{\frac{2(n+1)!}{2^{2(n+1)}}}{\frac{2n!}{2^{2n}}} \\ =\lim _{n\rightarrow\infty}\frac{2(n+1)!\cdot2^{2n}}{2n!\cdot2^{2(n+1)}^{}} \\ =\lim _{n\rightarrow\infty}\frac{2(n+1)\cdot n!\cdot2^{2n}}{2n!\cdot2^{2n}\cdot2^2} \\ =\lim _{n\rightarrow\infty}\frac{(n+1)}{2^2} \\ =\infty. \end{gathered}[/tex](b) Because r = ∞ > 1, we conclude that the series is divergent.
Answer
(a) r = ∞
(b) The series is divergent.
- Solve 2cos (3x) - 1 = 0 on the interval [0, 21).T 77 97 151 177 23T12' 12' 12' 12 12'12T7T4' 4No solutionT 137 251 111 231 35718' 18 18 '18 18 1899
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Let's solve the trig equation >>>
[tex]\begin{gathered} \sqrt[]{2}\cos (3x)-1=0 \\ \sqrt[]{2}\cos (3x)=1 \\ \cos (3x)=\frac{1}{\sqrt[]{2}} \\ 3x=\frac{\pi}{4},\frac{7\pi}{4} \\ x=\frac{\pi}{12},\frac{7\pi}{12} \end{gathered}[/tex]To get the other angles within 2π, we add 2π to these two angles. Thus,
[tex]undefined[/tex]18 8 12 8 4 13 what is the median & mean
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The Median is 10
The mean is 10.5
Explanation:To find the median, we need to arrange the data in an ascending or descending order.
In an ascending order, we have:
4, 8, 8, 12, 13, 18
The median is the middle number.
Since the number of data is even, the median is the mean of the two middle numbers.
The two middle numbers are: 8 and 12
The mean is (8 + 12)/2 = 20/2 = 10
The median is 10
The mean of the data is the sum of the data divided by the number of data.
The sum of data is:
4 + 8 + 8 + 12 + 13 + 18 = 63
The number of data is 6
Mean = 63/6 = 10.5
Which of the following equations represent relationships where y is a linear function of x? SELECT ALL THAT APPLY A)2x + 3y = 6B)Y = 5C)X = 1D)y = 10 - xE)y = x^2 + 5x + 6F)y = -x
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D) and F)
Explanation
Step 1
a linear function has 1 as the exponent of the variable, so we can discand option E)
Step 2
y is a function of x, it means that y depends on x ,
then, the equations that fit this
[tex]\begin{gathered} f(x)=y \\ y=f(x) \\ D)\text{ y=10-x} \\ F)y=-x \end{gathered}[/tex]D) and F), because B and C does not depend on x
I hope this helps you
Save Sub Hillery condujo 96 millas hoy. Bob llevó medio a todos los que Hillery. Cuántas millas conducen combinado? GO A) 120 B) 144 ) 192 D) 288 Expressions and Equat
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Hillery condujo 96 millas hoy.
También sabemos que Bob condujo la mitad de lo que condujo Hillery, es decir, 96/2 = 48
En total, los dos condujeron 96 + 48 = 144 millas
Respuesta:
B) 144
Which of the following equations describes the line shownbelow? Check all that apply.6((-6,2)(-1,-4)
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First, we have to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=-6 \\ x_2=-1 \\ y_1=2 \\ y_2=-4 \end{gathered}[/tex][tex]m=\frac{-4-2}{-1-(-6)}=\frac{-6}{-1+6}=\frac{-6}{5}=-\frac{6}{5}[/tex]This means A and B represent the line because they use the same slope and the same coordinates.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=-\frac{6}{5}(x+6) \\ y+4=-\frac{6}{5}(x+1) \end{gathered}[/tex]which funtion has the largest value for f(-3)?. f(x)=2-4x. f(x)=2x-5. f(x)=6-3^x. f(x)=2^×+10
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The notation f(-3) indicates that you have to calculate the value of the function f(x) for x=3.
To determine which value has the largest value for f(-3) you have to replace each function with x=3 and calculate the corresponding value of f(x)
1.
[tex]\begin{gathered} f(x)=2-4x \\ f(-3)=2-4(-3) \\ f(-3)=2-(-12) \\ f(-3)=2+12 \\ f(-3)=14 \end{gathered}[/tex]2.
[tex]\begin{gathered} f(x)=2x-5 \\ f(-3)=2\cdot(-3)-5 \\ f(-3)=-6-5 \\ f(-3)=-11 \end{gathered}[/tex]3.
[tex]\begin{gathered} f(x)=6-3^x \\ f(-3)=6-3^{-3} \\ f(-3)=\frac{161}{27} \\ f(-3)\approx5.92 \end{gathered}[/tex]4.
[tex]\begin{gathered} f(x)=2^x+10 \\ f(-3)=2^{-3}+10 \\ f(-3)=\frac{81}{8} \\ f(-3)\approx10.125 \end{gathered}[/tex]Now that we calculated f(-3) for each one of the functions, you can compare them.
The function that has the largest value of f(-3) is the first one: f(x)=2-4x
20 grams of table sugar has a density of 1.59 what is the volume of the sample
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Problem
20 grams of table sugar has a density of 1.59 what is the volume of the sample
Solution
For this case we can use the definition of density:
d= m/v
And if we solve for v we got:
v= m/d
And replacing we got:
v= 20/1.59= 12.58
find the measure of angle cdb. explain your reasoning including the postulate you used. find the measure of angle abd. find the measure of angle a.
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We get that the triangles ADB and CDB are congruent because of SSS(Side, Side, Side postulate) . So we get that the angles are also congruents
[tex]\begin{gathered} \angle ADB+\angle CDB=72^{\circ} \\ \end{gathered}[/tex]But ADB and CDB are the same so
[tex]\angle CDB=\frac{72}{2}=36^{\circ}[/tex][tex]\begin{gathered} \angle ABD=\angle CBD \\ 2\angle CBD=180 \\ \angle CBD=90^{\circ} \end{gathered}[/tex]The angle A is equal to
[tex]\angle A=180-90-36=54^{\circ}[/tex]I need help with my math
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Last season Mafalda had a 0.585 save percentage
This season Mafalda's save percentage is 0.738
Mafalda's save percentage improved by 0.738 - 0.585 = 0.153
Mathematical patterns: Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
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Solution
Step-by-step explanation:
We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.
Let the first five terms of a sequence be 5, 10, 20, 40 and 80
These terms are taken from a geometric sequence with first term
[tex]a_15,r=2[/tex]first term a = 5
common ratio r = 2
Therefore, we have
[tex]\begin{gathered} a_2=a_1\times r \\ a_3=a_2\times r \end{gathered}[/tex]Therefore, the recursive formula is
[tex]\begin{gathered} a_{n+1}=2a_n \\ a_1=5 \end{gathered}[/tex]And explicit formula is
[tex]a_n=a_1r^{n-1}[/tex]) What is the vertical asymptote for the rational function f(x)2x-523x + 6A) X = 2BB) x = }3.(x = -2D)x=-D56.
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Answer:
C. x=-2
Explanation:
Given the rational function:
[tex]f(x)=\frac{2x-5}{3x+6}[/tex]To find the vertical asymptote of f(x), set the denominator of f(x) equal to 0 and solve for x:
• Denominator of f(x) =3x+6
Solve for x:
[tex]\begin{gathered} 3x+6=0 \\ 3x=-6 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}=-\frac{6}{3} \\ x=-2 \end{gathered}[/tex]The vertical asymptote of f(x) is x=-2.
Option C is correct.
gotta double check a Answer
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Solution
For this case we have the following relationship given:
R90° ccw r y=x
And for this case we can conclude that the best answer is:
90 degree counterclockwise rotation about the origin
Mr Sanders wants to display his American flag in a triangular case as shown below what is the area of this triangular case
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Solution
For this case we have a triangle with the following dimensions:
b= 14 2/5 = 72/5 = 14.4 in represent the base
h= 8.5 in represent rhe height
And the area is given by:
[tex]A=\frac{b\cdot h}{2}=\frac{14.4\cdot8.5}{2}=61.2in^2[/tex]Then the final answer is 61.2 in^2
About 51% of U.S. college students are below 25 years old. About 24% of U.S. college students are above 34 years old. What is the probability that a U.S. college student chosen at random is below 25 or above 34 years?0.760.740.751.75
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Answer
0.75
Explanation
The probability that a U.S college student chosen at random is below 25 years is:
[tex]\begin{gathered} =51\text{ \%} \\ =\frac{51}{100}=0.51 \end{gathered}[/tex]The probability that a U.S college student chosen at random is above 34 years is
Now, by addition law of probability, the probability that a U.S college student chosen at random is below 25 or above 34 years would be
[tex]\begin{gathered} 0.51+0.24 \\ =0.75 \end{gathered}[/tex]if you draw one card at random what is the probability that card is a 7 out of diamonds
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Assuming that all the cards have the same probability of being randomly drawn, we conclude that the probability is:
P = 1/52 = 0.019
How to get the probability?We assume all the cards have the same probability of being randomly drawn.
Then the probability of drawing the card 7 of diamonds will be equal to the quotient between the number of 7 of diamonds in the deck (there is only one) and the total number of cards in the deck (52).
P = 1/52 = 0.019
The probability is 0.019
Learn more about probability:
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what is 15 what is 15 - 3/10
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15 - 3/10 = ?
convert 3/10 to decimal:
So, 3/10 = 0.3
So,
15 - 3/10 = 15 - 0.3 = 15.0 - 0.3 = 14.7
In the accompanying diagram of right trianglesABD and DBC, AB = 5, AD = 4, and CD=1. Findthe length of BC, to the nearest tenth.B54DYour answerI
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Consider the triangle ABD.
Determine the length of side BD by using pythagoras theorem.
[tex]\begin{gathered} (BD)^2=(AB)^2-(AD)^2 \\ BD=\sqrt[]{(5)^2-(4)^2} \\ =\sqrt[]{9} \\ =3 \end{gathered}[/tex]Consdier the triangle BDC.
Determine the length of side BC using pythagoras theorem.
[tex]\begin{gathered} (BC)^2=(BD)^2-(CD)^2 \\ BC=\sqrt[]{(3)^2-(1)^2} \\ =\sqrt[]{9-1} \\ =\sqrt[]{8} \\ =2.828 \\ \approx2.8 \end{gathered}[/tex]Thus length of sdie BC is 2.8.
determine the range of each function y=3-√3x-2
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Given
[tex]y=3-\sqrt[]{3x-2}[/tex]We can analyse the range in parts, first, let's see the range of the square root function:
[tex]y=\sqrt[]{3x-2}[/tex]A square root is always a positive number, because the square root of a negative number is not defined, so, the range of a square root is all positive numbers, including 0, here, it doesn't matter the function inside the square root, we just have to guarantee it's positive. So the range of the square root is
[tex]R=\mleft\lbrace y\ge0\mright\rbrace[/tex]The graph is
As we can see, the range is all positive numbers, but if we put the minus sign, the range changes to all negative numbers, it's what happens here, because we have
[tex]y=3-\sqrt[]{3x-2}[/tex]As we can see, the minus sign follows the square root, then the graph changes to
Now we are almost done. Now we just have to analyse how the constant +3 changes the range:
[tex]y=3-\sqrt[]{3x-2}[/tex]Every time we sum a constant to a function we are moving the function up or down, if we do a sum, it's moving upwards, if it's subtraction, it's going downwards. Here, we have a sum, then we must move the graph 3 units up, then the final graph will be
Then, the range will change to all numbers below or equal 3.
Therefore, the final answer is
[tex]R=\mleft\lbrace y\le3\mright\rbrace[/tex]R = {y ≤ 3}
The graph of the exponential function f(x)=3^x+3 is given with three points. Determine the following for the graph of f^-1(x).1. Graph f^-1(x)2. Find the domain of f^-1(x)3. Find the range of f^-1(x)4. Does f^-1(x) increase or decrease on its domain?5. The equation of the vertical asymptote for f^-1(x) is?
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Let's begin by listing out the given information:
[tex]\begin{gathered} f\mleft(x\mright)=3^x+3\Rightarrow y=3^x+3 \\ Switch\text{ }the\text{ }variables\text{ x \& y in the equation, we have:} \\ x=3^y+3\Rightarrow x-3=3^y \\ x-3=3^y\Rightarrow3^y=x-3 \\ \text{Take the }ln\text{ }o\text{f both }sides\text{, we have:} \\ y=\frac{\ln{\left(x - 3 \right)}}{\ln{\left(3 \right)}} \\ y=f^{-1}\mleft(x\mright) \\ f^{-1}\mleft(x\mright)=\frac{\ln{(x-3)}}{\ln{(3)}} \\ \end{gathered}[/tex]2.
The domain of a function is the set of input or argument values for which the function is real and defined. This is given by:
[tex]\begin{gathered} x-3;x>3 \\ \therefore x>3 \end{gathered}[/tex]3.
The range of a function is the set of output values for which the function is defined. This is given by:
[tex]\begin{gathered} 3^x+3\colon-\infty\: 4.The range of f(x) is the domain of f^-1(x) since they are inverse of one another.
[tex]\begin{gathered} f\mleft(x\mright)=3^x+3 \\ x=0 \\ f(0)=3^0+3=1+3=4 \\ x=1 \\ f(1)=3^1+3=3+3=6 \\ x=2 \\ f(2)=3^2+3=9+3=12 \\ \end{gathered}[/tex]Therefore, the domain of f^-1(x) increases
5.
The asymptote of a curve is a line such that the distance between the curve and the line approaches zero
[tex]\begin{gathered} \: \frac{\ln\left(x-3\right)}{\ln\left(3\right)}\colon\quad \mathrm{Vertical}\colon\: x=3 \\ \therefore x=3 \end{gathered}[/tex]What is the value of x that satisfies the equation í (& - 2(1 - 2) = $ (+2)
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Let's start clearing the value of x
[tex]\begin{gathered} 2(\frac{x}{2}-2)=3\cdot\frac{4}{3}(\frac{x}{3}+2) \\ 2(\frac{x}{2}-2)=4(\frac{x}{3}+2) \end{gathered}[/tex]Now we are going to multiply to open the parenthesis
[tex]\begin{gathered} 2\cdot\frac{x}{2}-2\cdot2=4\cdot\frac{x}{3}+4\cdot2 \\ x-4=\frac{4x}{3}+8 \\ \frac{4x}{3}-x=-4-8 \\ \frac{x}{3}=-12 \\ x=-12\cdot3 \\ x=-36 \end{gathered}[/tex]How does the graph of g(x)= 2^x+3differ from the graph of f(x) = 2^xАIt is moved up 3 unitsBIt is moved down 3 unitsCIt is moved right 3 units+DIt is moved left 3 units
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What is the solution of the inequality shownbelow?w +4 _<-1The less than is underlined and it’s throwing me off
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We will solve as follows:
[tex]w+4\le-1\Rightarrow w\le-5[/tex]what is y? i understood every question before this one, i think i maybe typing the answer wrong can you clarify what y is
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Answer:
[tex]y\text{ = 7}\sqrt{6}[/tex]Explanation:
Here, we want to get the value of y
What we have in the triangle is an isosceles right triangle (two of the internal angles are 45 degrees each)
Thus, we have the base equal to the height
To get the hypotenuse length, we use Pythagoras' theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides
Thus, we have it that:
[tex]\begin{gathered} \text{ y}^2\text{ = \lparen7}\sqrt{3\text{ }})\placeholder{⬚}^2\text{ + \lparen7}\sqrt{3}\text{ \rparen}^2\text{ } \\ y^2\text{ =147+ 147} \\ y^2\text{ = 294} \\ y\text{ = }\sqrt{294} \\ y\text{ = 7}\sqrt{6} \end{gathered}[/tex]Determine the x intercepts of the polynomial function: f(x)=x^4-x^2 Recall that the x intercept is a point (x,0) where our value for y is always zero. List the intercepts (x,0) from smallest to largest and separate them with a comma between each point.Answer:
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To find such x intercepts, we make our y-value 0 and solve for x as following:
[tex]\begin{gathered} f(x)=x^4-x^2 \\ \rightarrow x^4-x^2=0 \\ \rightarrow(x^2)(x^2-1)=0 \\ \rightarrow(x^2)(x+1)(x-1)=0 \\ \\ x^2=0\rightarrow x_1=0 \\ \\ x+1=0\rightarrow x_2=-1 \\ \\ x-1=0\rightarrow x_3=1 \end{gathered}[/tex]This way, we can conclude that the x intercepts are:
-1,0,1
Which inequality does NOT represent thecorrect position of two numbers on a numberline? A 41/2 > 25/4B -41/2 > -25/5C -6 < -5D -1/2 < 1/2
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4 1/2 > 25/4 (option A)
Explanation:To determine the inequality not in the correct positin, we will change the fractions to decimals. That way it is easy to compare:
[tex]\begin{gathered} a)\text{ 4}\frac{1}{2}\text{ > }\frac{25}{4} \\ \text{4}\frac{1}{2}\text{ > 6}\frac{1}{4} \\ 4.5\text{ > 6.25} \\ 4.5\text{ is less than 6.25 not greater than as s}en\text{ in the question} \\ \text{Hence, this is the incorrect one} \end{gathered}[/tex][tex]\begin{gathered} b)-4\frac{1}{2}\text{ > }\frac{-25}{5} \\ -4.5\text{ > -5} \\ \text{For negative numbers, the smaller numbers are greater than the bigger numbers} \\ \text{This is correct} \end{gathered}[/tex][tex]\begin{gathered} -6\text{ < -5} \\ \text{For negative numbers, the smaller numbers are greater than the bigger numbers} \\ \text{this is correct} \end{gathered}[/tex][tex]\begin{gathered} d)\text{ }\frac{-1}{2}\text{ < }\frac{1}{2} \\ -0.5\text{ < 0.5} \\ \text{Negative numbers are less than positive numbers} \\ \text{This is correct} \end{gathered}[/tex]What is the volume of this rectangular Pyramid picture to follow
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SOLUTION:
Case: Rectangular pyramid
Method:
The base has a dimension 5mm by 5mm
The height is 3mm
The Volume, therefore:
[tex]\begin{gathered} V=\frac{1}{3}\times l\times w\times h \\ V=\frac{1}{3}\times5\times5\times3 \\ V=\frac{75}{3} \\ V=25mm^3 \end{gathered}[/tex]Final answer:
The volume, V= 25 cubic millimeters
HomeHumber of newspapers070009PaulGaryValentinaOlivia904What is the mean of this data setWhat is the median of this data setiWhat is the mode of this datasetit more than one mode enter them in order from least to greatest, separated bycommes, and no spaces. If there is no mode, put NAWhat is the range of this dataset
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Answer:
[tex]undefined[/tex]Explanation:
Given the data on the table, let us arrange from least to the greatest.
[tex]84,86,89,97,98,98[/tex]The mean is the sum of all the data divided by the number of data;
[tex]\begin{gathered} \operatorname{mean}=\frac{84+86+89+97+98+98}{6} \\ \operatorname{mean}=\frac{552}{6} \\ \operatorname{mean}=92 \end{gathered}[/tex]The median is the middle number (the average of the middle numbers);
[tex]\begin{gathered} \operatorname{median}=\frac{89+97}{2} \\ \operatorname{median}=\frac{186}{2} \\ \text{median}=93 \end{gathered}[/tex]The mode is the highest occurring number;
[tex]\text{mode}=98[/tex]The range is the difference between the greatest and the least number.
[tex]\begin{gathered} \text{greatest number = 98} \\ \text{least number = 84} \\ \text{Range = 98 - 84} \\ \text{Range =14} \end{gathered}[/tex]