Answers
Solution:
Given the absolute inequality below:
[tex]\lvert4x-6\rvert>10[/tex]From the absolute law,
[tex]\begin{gathered} \lvert u\rvert>a \\ implies\text{ } \\ u>a\text{ } \\ or \\ u<-a \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6>10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6>10+6 \\ \Rightarrow4x>16 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}>\frac{16}{4} \\ \Rightarrow x>4 \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6<-10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6<-10+6 \\ \Rightarrow4x<-4 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}<-\frac{4}{4} \\ \Rightarrow x<-1 \end{gathered}[/tex]Plotting the solution to the inequality, we have the line graph of the inequality to be
Hence, the correct option is D.
Related Questions
what is 2 to the 6 power
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Which point is part of the solution of the inequality y ≤ |x+2|-3A.(-1,-1)B.(1,0)C.(0,0)D.(0,1)
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We are going to test all options to see which is true and false.
The one that is true will be the point that is part of the solution.
[tex]\begin{gathered} A) \\ (-1,-1) \\ y\leq\lvert x+2\rvert-3 \\ -1\leq\lvert-1+2\rvert-3 \\ -1\leq\lvert1\rvert-3 \\ -1\leq1-3 \\ -1\leq-2 \\ \text{Not true, so the point (-1,-1) is not a part of the solution} \end{gathered}[/tex]We will move to the next option and test:
[tex]\begin{gathered} B) \\ (1,0) \\ y\leq\lvert x+2\rvert-3 \\ 0\leq\lvert1+2\rvert-3 \\ 0\leq\lvert3\rvert-3 \\ 0\leq3-3 \\ 0\leq0 \\ \text{The above solution is true, so it is a point that is part of the solution.} \\ \text{The correct answer is option B.} \end{gathered}[/tex]The price of Stock A at 9 A.M. was $12.42. Since then, the price has been increasing at the rate of $0.12 each hour. At noon the price of Stock B was $12.92. It begins to decrease at the rate of $0.09 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
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The hours when the prices of the two stocks be the same is 2.38 hours.
How to illustrate the information?From the information, the price of Stock A at 9 A.M. was $12.42 and the price has been increasing at the rate of $0.12 each hour. This will be the expressed as 12.42 + 0.12h.
At noon the price of Stock B was $12.92. It begins to decrease at the rate of $0.09 each hour. This will be:
= 12.92 - 0.09h
where h = number of hours
Equate both equations. This will be:
12.42 + 0.12h = 12.92 - 0.09h
Collect like terms
12.92 - 12.42 = 0.12h + 0.09h
0.21h = 0.50
h = 0.50 / 0.21
h = 2.38 hours.
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At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner radius is 7 yd and its outer radius is 9 yd.We are going to give a new layer of coating to the path. If one gallon of coating can cover 5v * d ^ 2 how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for pi.)
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Use the distance formula to calculate the length of the leg CD
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To calculate the distance between two points on the coordinate system you have to use the following formula:
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Where
d represents the distance between both points.
(x₁,y₁) are the coordinates of one of the points.
(x₂,y₂) are the coordinates of the second point.
To determine the length of CD, the first step is to determine the coordinates of both endpoints from the graph
C(2,-1)
D(-1,-2)
Replace the coordinates on the formula using C(2,-1) as (x₁,y₁) and D(-1,-2) as (x₂,y₂)
[tex]\begin{gathered} d_{CD}=\sqrt[]{(2-(-1))^2+((-1)-(-2))}^2 \\ d_{CD}=\sqrt[]{(2+1)^2+(-1+2)^2} \\ d_{CD}=\sqrt[]{3^2+1^2} \\ d_{CD}=\sqrt[]{9+1} \\ d_{CD}=\sqrt[]{10} \end{gathered}[/tex]The length of CD is √10 units ≈ 3.16 units
13. slove for x so the [tex]f(x) = 5[/tex]
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Solution
We have the following function given:
f(x) = -3x+5
And we need to do the following:
5= -3x+5
And if we subtract 5 in both sides we got:
0 =-3x
Dividing both sides by -3 we got:
[tex]\frac{0}{-3}=\frac{-3x}{-3}[/tex]And finally we got:
x= 0
Problem 17
17) f(-2)= 3
18) f(0)= 3
19) f(1)= 0
20) f(-1)= 5.2
The following circle passes through the origin. Find the equation.
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Answer
(x - 2)² + (y - 2)² = 8
Step-by-step explanation
The equation of the circle centered at (h, k) with radius r is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]In this case, the center of the circle is the point (2, 2), then h = 2 and k = 2, that is,
[tex](x-2)^2+(y-2)^2=r^2[/tex]Given that the circle passes through the center, then the point (0, 0) satisfies the above equation. Substituting x = 0 and y = 0 into the equation and solving for r²:
[tex]\begin{gathered} (0-2)^2+(0-2)^2=r^2 \\ 4+4=r^2 \\ 8=r^2 \end{gathered}[/tex]Substituting r² = 8 into the equations, we get:
[tex](x-2)^2+(y-2)^2=8[/tex]Hi, i tried to solve this problem, but I can't manage to do it, can you help me ?
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Length of y is 25.2.
Given:
The angle is given as 35 degree and a side is 36.
The objective is to find the length of the side y.
In a right angled traingle, the side opposite to the given angle is called oppotise side, the other smaller side is called adjacent side and the longer side is called hypotenuse.
Here, opposite side is y and adjacent side is 36.
Then, the relationship between oppsote and adjacent can be calculated using the trigonometric ratio of tan theta.
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 35^0=\frac{y}{36} \\ y=36\cdot\tan 35^0 \\ y=36(0.7) \\ y=25.2 \end{gathered}[/tex]Hence, the length of y is 25.2.
2. Consider drawing a card at random from a standard deck of cards,Part A: Determine the probability that the card is a spade, given that it is black,Part B: Determine the probability that the card is red, given that it is a heart,Part C: Determine the probability that the card is an ace, given that it is black.Part D: Determine the probability that the card is a queen given that it is a face card,
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Consider drawing a card at random from a standard deck of cards,
Part A: Determine the probability that the card is a spade, given that it is black,
Part B: Determine the probability that the card is red, given that it is a heart,
Part C: Determine the probability that the card is an ace, given that it is black.
Part D: Determine the probability that the card is a queen given that it is a face card,
we have 52 cards
A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)
so
Part A: Determine the probability that the card is a spade, given that it is black,
If the card is black, that means the possible outcomes are 26 cards
so
P=13/26
P=0.5Part B: Determine the probability that the card is red, given that it is a heart,
if the card is a heart, that means, the possible outcomes are 13
so
P=13/13
P=1because all the cards that are heart are red
Part C: Determine the probability that the card is an ace, given that it is black.
if the card is black the possible outcomes are 26
therefore
P=2/26
P=1/13Part D: Determine the probability that the card is a queen given that it is a face card
Question 37?Find the indicated function and state its domain in interval notation?
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Given the functions:
[tex]\begin{gathered} f(x)=-\sqrt[]{x-3} \\ g(x)=3x \end{gathered}[/tex]You need to multiply them, in order to find:
[tex](f\cdot g)(x)[/tex]Then, you get:
[tex]\begin{gathered} (f\cdot g)(x)=(-\sqrt[]{x-3})(3x) \\ (f\cdot g)(x)=-3x\sqrt[]{x-3} \end{gathered}[/tex]In order to find the Domain, you need to remember that the Domain of a Radical Function are those input values (x-values) for which the Radicand is positive. Then, in this case, you need to set up that:
[tex]x-3\ge0[/tex]Now you have to solve for "x":
[tex]x\ge3[/tex]Therefore:
[tex]Domain\colon\lbrack3,\infty)[/tex]Hence, the answer is:
[tex]\begin{gathered} (f\cdot g)(x)=-3x\sqrt[]{x-3} \\ \\ Domain\colon\lbrack3,\infty) \end{gathered}[/tex]To achieve mastery of this lesson, make sure you develop responses to the following questions: How are exponential functions graphed? How do you compare exponential functions? How do you transform exponential functions? help
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For exponential functions, it is found that:
They are graphed looking at the asymptote, the intercept, the rate of change and the end behavior.They are compared by the rate of change.They are transformed with translations and stretching/compression.What is an exponential function?An exponential function is modeled according to the rule presented as follows:
[tex]y = ab^x + c[/tex]
In which the coefficients of the rule are given as follows:
a is the intercept of the function, the value of y when it crosses the y-axis.b is the rate of change of the function.c is the asymptote of the function.To graph the function, along with the coefficients of the function, the end behavior of the function is needed, as follows:
Limit of y when x goes to negative infinity: gives the behavior at the left end of the graph.Limit of y when x goes to positive infinity: gives the behavior at the right end of the graph.They are compared by their rate of changes, if they are increasing/decreasing, and which one increases faster.
The transformations are as follows:
Translation: a constant is added to either x or y(changing the asymptote if y), meaning that the function can be moved down, up, left or right.Stretching: a constant multiplies x or y, meaning that the graph can be either compressed or stretched vertically or horizontally.More can be learned about exponential functions at https://brainly.com/question/25537936
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Select the graph for the solution of the open sentence. Click until the correct graph appears. Ix| + 3 > 3
Answers
Given the sentence;
[tex]\mleft|x\mright|+3>3[/tex]Subtracting 3 from both sides;
[tex]\begin{gathered} \mleft|x\mright|+3>3 \\ |x|+3-3>3-3 \\ \mleft|x\mright|>0 \end{gathered}[/tex]Given the absolute value of x to be greater than zero, the range of value of x is;
[tex]\begin{gathered} x>0 \\ or \\ x<0 \end{gathered}[/tex]Therefore, the correct graph of the solution is;
The formula for the perimeter of a
rectangle is P = 2l + 2w. Solve the formula for
w.
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P = 2( l + w )
P/2 = 2( l + w ) /2
P/2 = l + w
answer: w = P/2 - 1
True or false the surface area of a sphere with a radius of 10 units is larger than the surface area of a cube with edge lengths of 10 units
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The surface area of a sphere is given by
[tex]S_s=4\pi r^2[/tex]in our case r=10 units ( the radius). By substituting this value into the last formula, we have
[tex]S_s=4(3.1416)(10^2)[/tex]which gives
[tex]S_s=1256.64u^2[/tex]On the other hand, the surface area of a cube is given by
[tex]S_c=6L^2[/tex]where L is the length of one side, that is, L=10. Then, we have
[tex]\begin{gathered} S_c=6\cdot(10^2) \\ S_c=6\cdot100=600u^2 \\ S_c=600u^2 \end{gathered}[/tex]By comparing both results, we can see that the surface area of our sphere is larger than the surface area of the given cube. So the answer is TRUE.
Solve the following system of equations graphically on the set of axes below. Plot two or more dotes on the graphy = 2x - 8 y = -x + 4
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Given:-
[tex]y=2x-8,y=-x+4[/tex]To find the graphical representation.
So the graph of y=2x-8 is,
Also the graph of y=-x+4 is,
Combining we get the graph
So the point is (4,0).
need help please 16x=-44-4y
-8x=28+4y
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Answer: (x,y)= (-2/5,-43/5)
Step-by-step explanation:
Please help me come you just tell me the answer I don’t really need you to explain
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Given:
[tex]\begin{gathered} \angle JKL=65 \\ \angle KJL=50 \end{gathered}[/tex]Sum of the angle of any triangle is 180
So:
[tex]\begin{gathered} \angle JKL+\angle KJL+\angle KLJ=180 \\ 65+50+\angle KLJ=180 \\ \angle KLJ=180-(65+50) \\ \angle KLJ=180-115 \\ \angle KLJ=65 \end{gathered}[/tex]Then two sides are also equal.
[tex]\begin{gathered} 3x-2=x+10 \\ 3x-x=10+2 \\ 2x=12 \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]So the value of x is 6.
Solve any quality express your answer in interval notation you decimal forms for numerical values
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Solution
[tex]\begin{gathered} 5z-11<-6.6+3z \\ Subtract\text{ 3z from both side} \\ 5z-3z-11<-6.6+3z-3z \\ 2z-11<-6.6 \\ Add\text{ 11 to both sides } \\ 2z-11+11<-6.6+11 \\ 2z<4.4 \\ \end{gathered}[/tex][tex]\begin{gathered} Divide\text{ both sides by 2} \\ \frac{2z}{2}<\frac{4.4}{2} \\ z<2.2 \\ z<2.2 \end{gathered}[/tex]In interval notation, we have
[tex]\left(-\infty \:,\:2.2\right)[/tex]The answer is
[tex]\left(-\infty \:,\:2.2\right)[/tex]Which statements describe one of the transformations performed on f(x) = x?to create g(x) - 3(x + 5)2 - 2? Choose all that apply.DA. A translation of 2 units to the leftI B. A vertical stretch with a scale factor of 3O C. A vertical stretch with a scale factor of3O D. A translation of 5 units to the left
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Solution:
The Function transformation of f(x) is:
[tex]g(x)=f(x+c)+d[/tex]If c > 0, then the graph shift left f(x+c).
If c<0, then the graph shift right f(x-c)
If d > 0, then the graph shift up f(x) +d
If d < 0, then the graph shift down f(x) -d
When the given equation is:
[tex]f(x)=x^2[/tex]The transformation equation is given:
[tex]g(x)=3(x+5)^2-2[/tex]Then, the graph shifts down 2 units and shifts left 5 units.
Also, the vertical stretch with a scale factor 3.
Therefore, the correct options are B and D.
Use the rectangle at the right to answer the following questions. a. Find the area of the entire rectangle. Show your work. b. Calculate the perimeter of the figure. Show your work.
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Length of the entire rectangle = 12 + 5 = 17
Width of the entire rectangle = 6+4 = 10
Part a
Area of rectangle = Length x width
Area of the entire rectangle = 17 x 10 = 170 square units
Part b
Perimeter of rectangle = 2( length + width )
Perimeter of the entire rectangle = 2(17 + 10 )
=2 (27) = 54
Perimeter of the entire rectangle = 54 units
Length of the entire rectangle = 12 + 5 = 17
Width of the entire rectangle = 6+4 = 10
Part a
Area of rectangle = Length x width
Area of the entire rectangle = 17 x 10 = 170 square units
Part b
Perimeter of rectangle = 2( length + width )
Perimeter of the entire rectangle = 2(17 + 10 )
=2 (27) = 54
Perimeter of the entire rectangle = 54 units
what is the equation of the line passing through (-4,0) and (01)
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Hannah is saving money to buy some lirns. She invests $290 in a savings account that earns 7.6% interest, compounded annually. How much money will she have in her account after 2 years? Answer in dollars and round to the nearest cent.
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Principal amount, P= $290.
Rate, r = 0.076
Time, t = 2
Therefore, the total amount in her account after 2 years is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Hence,
[tex]\begin{gathered} A=290(1+0.076)^2 \\ =335.755 \end{gathered}[/tex]Therefore, the amount is 335.80 dollars.
That is, 335 dollars and 80 cents.
1. Abby baked 2-dozen brownies. She took 1 dozen to her scout meeting. Her family ate 8, and she put the rest in a container in the refrigerator. How can Abby find the number of brownies left in the refrigerator?
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In order to determine the amount of brownies left in the refrigerator, subtract 8 from 12.
How many brownies are left in the refrigerator?If Abby bakes 2 -dozen brownies, she baked 24 brownies. There are 12 pieces in 1 dozen, thus if she bakes two dozens, she baked 24 brownies ( 12 x 2).
The amount of brownies left after she takes one dozen to school = amount baked - amount taken for the meeting
24 - 12 = 12
Amount left in the refrigerator : amount left after she took a dozen for the meeting - amount eaten by her family
12 - 8 = 4
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the math club has 18 members and 50% are sixth graders.The science club has 25 members and 40% are sixth graders. The principal wants to know which club has more sixth graders.
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The science club had more sixth graders.
How to calculate the value?The math club has 18 members and 50% are sixth graders. The number of sixth graders will be:
= Percentage × Number of members
= 50% × 18
= 0.5 × 18
= 9
The science club has 25 members and 40% are sixth graders. The number of sixth graders will be:
= Percentage × Number of members
= 40% × 25
= 0.4 × 25
= 10
Since 10 is more than 5, the science class has higher number.
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Find the distance d(P1, P2) between the given points P1 and P2: P1 =(0,0) P2 = (2,3)d(P1,P2) = (Simplify your answer using radical as needed)
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Recall that given points (a,b) and (c,d) the distance between them would be
[tex]d=\sqrt[2]{(c\text{ -a\rparen}^2+(d\text{ -b\rparen}^2}[/tex]In our case we are given a=0,b=0,c=2,d=3. So the distance would be
[tex]d=\sqrt[2]{(2\text{ -0\rparen}^2+(3\text{ -0\rparen}^2}=\sqrt[2]{2^2+3^2}=\sqrt[2]{4+9}=\sqrt[2]{13}[/tex]so the distance between them is the square root of 13.
Is Ari’s answer to the question, correct? If not, where did Ari make a mistake? If his answer is incorrect, explain what the correct answer is and why it is correct.
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None of Ari's answer to the question is correct. The right application of the laws of exponents to get the correct answer is explained below.
What are the Laws of Exponents?Some of the laws of exponents can be summarized as follows.
The product law of exponents: This states that we are to add the exponents together if we are multiplying two numbers that have the same base. For example, [tex]x^m \times x^n = x^{m + n}[/tex].The division law of exponents: this states that when dividing two numbers that have the same base, we are to find the difference of their exponents. For example, [tex]\frac{x^m}{x^n} = x^{m - n}[/tex].The negative law of exponents: This state that, [tex]x^{-m} = \frac{1}{x^m}[/tex].Based on the above laws of exponents, none of Ari's answer is correct. Below are the correct way to solve the questions:
1. [tex]4^2 \times 4^5 = 4^{2 + 5} = 4^7[/tex]
2. [tex](2^{-5})^3 = 2^{-3 \times 5} = 2^{-15} = \frac{1}{2^{15}}[/tex]
3. [tex]\frac{(\frac{1}{4})^4 \times (\frac{1}{4})^5 }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^{4 + 5} }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^9 }{(\frac{1}{4})^3} = (\frac{1}{4})^{9 - 3}} = (\frac{1}{4})^6[/tex]
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match the function rule with the graph of the function (number 24)
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It is given that the function is:
[tex]y=\frac{3}{4}\times4^x[/tex]Therefore y=0 then the value of x will be:
[tex]\begin{gathered} 0=4^x \\ x=-\infty \end{gathered}[/tex]Now at x=0, y will be:
[tex]y=\frac{3}{4}[/tex]at x=1, y will be:
[tex]y=\frac{3}{4}\times4=3[/tex]These 3 points that is (-inf,0),(0,3/4),(1,3) are on graph D.
Hence option D is coreect.
LaVelle is making a pitcher of caffe mocha. For each ounce of chocolate syrup, she uses 5 ounces of coffee. She wants to make 48 ounces of caffe mocha.
Let c represent the number of ounces of coffee, and let s represent the number of ounces of chocolate syrup used. Which of the following systems of equations models this situation?
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The systems of equations which correctly models the situation as described is;
s = 5c ands + c = 48Which systems of equations correctly models the situation as described in the task content?It follows from the task content that the system of equations which models the production process of caffe mocha be determined.
As given in the task content;
Let c represent the number of ounces of coffee.Let s represent the number of ounces of chocolate syrup.Hence, since For each ounce of chocolate syrup, she uses 5 ounces of coffee, the situation can be represented algebraically as;
s = 5c.Also, since she wants to make 48 ounces of caffe mocha; we have;
s + c = 48.Therefore, the required system of equations is;
s = 5c ands + c = 48.Read more on system of equations;
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Marco states that 7.696696669...... is a rational numberbecause it is a repeating decimal. Is he correct? Justifyyour answer.Yes he is correct because it keeps going and going and it will go on forever and ever so that is my guess
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The answer is NO, Marco is wrong.
The number 7.696696669.... has not a repeating decimal there is no a number that is repeating, like 0.6969696969... in the last number the 69 is repeating, in the Marco's number the decimal number change every time.
Finding the mode and range of a data set Each day, Kaitlin records the number of news articles she reads. Here are her results for the last eight days. 7, 3, 8, 5, 7,7,7,8 Find the mode and the range for the data. Mode: Range: X 5 ?
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Explanation:
The set of values are given below as
[tex]7,3,8,5,7,7,7,8[/tex]Mode:
This the data that occurs highest or the dat that has the highest frequency
Range:
The is the difference between the lowest val and the highest value
[tex]Range=highest-lowest[/tex]Hence,
The final answers are
[tex]\begin{gathered} mode=7(it\text{ occurs 4 times\rparen} \\ range=8-3=5 \end{gathered}[/tex]Hence,
The final answer is
[tex]\begin{gathered} mode=7 \\ Range=5 \end{gathered}[/tex]