Wayne is hanging a string of lights 89 feet long around the three sides of his rectangular patio, which is adjacent to his house. The length of his patio, the side along the house, is 5 feet longer than twice its width. Find the length and width of the patio.
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SOLUTION:
Case: Rectangles
Method:
The sum is:
w + w + 2w + 5 = 89
4w + 5 = 89
4w = 89 - 5
4w = 84
w = 84/ 4
w= 21 feet
The length, l
l = 2w + 5
l = 2( 21) + 5
l = 42 + 5
l = 47 feet
Final answer:
length of the patio, l = 47 feet
width of the patio, w= 21 feet
Related Questions
The elimination method is used in place over substitution when one equation is not easily solved for ______________ variable.A) a standardB) a dependentC) an independentD) a single
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Given:
There are given the statement about the elimination method and substitution method.
Explanation:
According to the concept:
One equation cannot be easily solved for a single variable.
Final answer:
Hence, the correct option is D.
Question 13 (3 points)
Intel's microprocessors have a 1.8% chance of malfunctioning. Determine the
probability that a random selected microprocessor from Intel will not malfunction.
Write the answer as a decimal.
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EXPLANATION
The probability that Event A happening is the following:
[tex]P(A)[/tex]
The probability of Event A not happening is the following:
[tex]100-P(A)[/tex]Therefore, we have:
[tex]P(Malfunctioning)+P(Non\text{ Malfunctioning\rparen=100\%}[/tex]Plugging in the terms into the expression:
1.8 + P(Not malfunctioning) = 100%
Subtracting -1.8 to both sides:
[tex]P(Not\text{ malfunctioning\rparen=100-1.8}[/tex]Subtracting numbers:
[tex]P(Not\text{ malfunctioning\rparen=98.2}[/tex]In conclusion, the probability of not malfunctioning is 0.982
The line 3x + 4y - 7 = 0 is parallel to the line k . x + 12y + 3 = 0. What is the value of k?
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The function is solved below
What is a function?
The function is instantly given a name, such as a, in functional notation, and its description is supplied by what it does to the input x, using a formula in terms of x. Instead of sine, put sine x. (x). Leonhard Euler invented functional notation in 1734. Some commonly used functions are represented with a symbol made up of many letters (usually two or three, generally an abbreviation of their name). In this scenario, a roman font is typically used, such as "sine" for the sine function, rather than an italic font for single-letter symbols. A function is also known as a map or a mapping, however some writers distinguish between "map" and "function."
The function can be written as
3x+4y-7 = 0
or, y = (-3/4)x + 7/4
so, slope = -3/4
and other function is
kx+12y+3 = 0
or, y = (-k/12)x - 1/4
so, slope = -x/12
Given the lines are parallel, so slopes are equal
i.e., -3/4 = -k/12
or, k = (3/4)12 = 9
Hence, the value of k is 9.
To know more about a function, click on the link
https://brainly.com/question/10439235
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The Hornet's soccer team scored 5 goals in their last match.The other team, the Panthers, won by 3 goals. Which integerrepresents the number of goals that the Panthers won by?
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The match was Hornet's vs Panthers
Hornets's scored 5 goals
Panthers won by 3 goals, this means that the panters scored 3 more goals than the Hornets.
That would be +3 goals.
Convert 253 inches to yards using dimensional analysis.
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As given by the question
There are given that the 253 inches
Now,
To convert the inches to yards, multiply the value in inches by the conversion factor 0.0277777787.
So,
[tex]253\times0.0277777787=7.0277778.[/tex]Hence, the value of the given inches is 7.0278 yards.
While reviewing the previous day’s arrest report, a police sergeant that seven suspects were arrested, all of whom had either one or two previous arrests. Including yesterday arrests, there were 16 total among them. How many suspects had had less than two prior arrests?
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ANSWER :
EXPLANATION :
160 is what percent of the sum of 100 and 120 and 160
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42.105%
1) Let's first add thosse numbers up: 100 +120+160 =380
2) Now we can write out the following ratio, to find out what percentage is equivalent to 160 out of that 380:
[tex]\begin{gathered} 160----x \\ 380----100 \\ \frac{160}{380}=\frac{x}{100} \\ 380x=16000 \\ \frac{380x}{380}=\frac{16000}{380} \\ x=42.105\% \end{gathered}[/tex]Note that we had to cross multiply that.
3) Hence, the answer is 160 is approximately 42.105% of 380
Good morning, I need help on this questions. Thanks :)
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The observed values are given in the table shown in the question. The line of best fit is given to be:
[tex]y=-1.1x+90.31[/tex]where x is the average monthly temperature and y is the heating cost.
A residual is a difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line). The formula will be:
[tex]Residual=Observed\text{ }y\text{ }value-Predicted\text{ }y\text{ }value[/tex]QUESTION A
The average monthly temperature is 24.9:
[tex]x=24.9[/tex]Observed cost:
[tex]y=51.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(24.9)+90.31=-27.39+90.31 \\ y=62.92 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=51.00-62.92 \\ R=-11.92 \end{gathered}[/tex]QUESTION B
The average monthly temperature is 35.9:
[tex]x=35.9[/tex]Observed cost:
[tex]y=67.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(35.9)+90.31=-39.49+90.31 \\ y=50.82 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=67.00-50.82 \\ R=16.18 \end{gathered}[/tex]Answer: Hl
Step-by-step explanation:
Solve the system withelimination.1-2x + y = 813x + y = -2([?],[?]
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Now we substitute the value of x into the first equation to get the value of y
[tex]\begin{gathered} -2\cdot-2+y=8 \\ 4+y=8 \\ y=8-4=4 \end{gathered}[/tex]Finally the solution is (-2,4)
3x+5=8(x-2)+1
Solve the following equation for x
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Answer: x=4
Step-by-step explanation:
1. 3x+5 = 8x-16+1
2. 3x+5 = 8x-15
3. 3x+20 = 8x
4. 20 = 5x
5. x = 4
I have to find cars a speed in miles per hour
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The graph in the picture shows the relationship between the distance traveled (y-axis) and the time (x-axis) that car A traveled.
The slope of the line represents the speed at which the car traveled. To determine the said speed you have to calculate the slope of the line.
-The first step is to determine two points of the line:
(x₁,y₁) → (2,80)
(x₂,y₂) → (0,30)
-The second step is to calculate the slope using the following formula:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]Where
(x₁,y₁) represent the coordinates of one point of the line
(x₂,y₂) represents the coordinates of a second point of the line
Replace the formula with the coordinates of the points and calculate the slope:
[tex]\begin{gathered} m=\frac{(80-30)mi}{(2-0)hr} \\ m=\frac{50mi}{2hr} \\ m=25\frac{mi}{hr} \end{gathered}[/tex]The slope of the line, which represents the speed of the car, is 25 miles per hour
Which factoring do we use and why and how to know the difference between factoring simple trinomial and perfect square
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By definition, a perfect square trinomial is a trinomial that can be written as the square of a binomial. It is in the form:
[tex]a^2+2ab+b^2=(a+b)(a+b)[/tex]The simple trinomial is in the form:
[tex]ax^2+bx+c[/tex]Not all the simple trinomials can be written as the square of a binomial, then we need to check if the trinomial follows the structure of the perfect square trinomial. If it doesn't, then the factors won't be the same, and this is the main difference.
a. The given trinomial is:
[tex]x^2+5x+6[/tex]If it is a perfect square trinomial then:
[tex]\begin{gathered} a^2=x^2 \\ a=x \\ b^2=6 \\ b=\sqrt[]{6} \\ 2ab=5x \\ 2\cdot x\cdot\sqrt[]{6}\ne5x \\ \text{Then it is not a perfect square trinomial} \\ x^2+5x+6=(x+3)(x+2)\text{ It is a simple trinomial} \end{gathered}[/tex]b. The given trinomial is:
[tex]x^2+6x+9[/tex]Let's check if it is a perfect square trinomial:
[tex]\begin{gathered} a^2=x^2\to a=x \\ b^2=9\to b=\sqrt[]{9}=3 \\ 2ab=2\cdot x\cdot3=6x \\ \text{This is a perfect square trinomial, then } \\ x^2+6x+9=(x+3)(x+3)=(x+3)^2 \end{gathered}[/tex]A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6.ValueFrequency152332435463788397108113Give your answer as a single number. For example if you found the number of values was 14, you would enter 14.
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The number of values less than or equal to 6 is 5 + 3 +2 +3 +4 +3 = 20
use your theorem from 2-37 about the angles in a triangle to find in the diagram below. show all work.
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We have that, for any triangle, the sum of all its angles equals 180. In this case, we have the following:
[tex]96+2x+(x+12)=180[/tex]Now we solve for x to get the following:
[tex]\begin{gathered} 96+2x+x+12=180 \\ \Rightarrow2x+x=180-96-12 \\ \Rightarrow3x=72 \\ \Rightarrow x=\frac{72}{3}=24 \\ x=24 \end{gathered}[/tex]We have that x = 24, now to find the angles, we substitute this value on each expression:
[tex]\begin{gathered} 2x \\ x=24 \\ \Rightarrow2(24)=48 \\ x+12 \\ \Rightarrow24+12=36 \end{gathered}[/tex]therefore, the remaining angles are 48° and 36°
Could you tell me the process of solving the problem?
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Given:
[tex]Ln8=\frac{2\pi m\xi}{\sqrt{1-\xi^2}}[/tex]m=250
Required:
Find the value of
[tex]\xi[/tex]Explanation:
The value of ln8 is:
[tex]ln8=2.079[/tex][tex]\begin{gathered} 2.079=\frac{2\times3.14\times\xi}{\sqrt{1-\xi^2}} \\ 2.079(\sqrt{1-\xi^2})=6.28\xi^ \end{gathered}[/tex]Take the square on both sides.
[tex]\begin{gathered} 4.322(1-\xi^2)=39.44\xi^2 \\ \frac{1-\xi^2}{\xi^2}=\frac{39.4384}{4.322} \\ \frac{1}{\xi^2}-1=9.125 \\ \frac{1}{\xi^2}=9.125+1 \\ \frac{1}{\xi^2}=10.125 \end{gathered}[/tex]O EQUATIONS AND INEQUALITIESSolving a word problem with three unknowns using a linear...
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Given:
The sum of three numbers is 81, The third number is 2 times the second, The first number us 9 moe than the second.
Required:
We need to find all the numbers
Explanation:
Assume that a, b and c are the first, second and third numbers respectively.
By given ststement
[tex]\begin{gathered} a+b+c=81\text{ .....\lparen i\rparen} \\ c=2b\text{ .....\lparen ii\rparen} \\ a=b+9\text{ .....\lparen iii\rparen} \end{gathered}[/tex]substitute c and a in equation (i)
[tex]\begin{gathered} b+9+b+2b=81 \\ 4b=72 \\ b=18 \end{gathered}[/tex]now put value of b in equation (ii) and (iii)
[tex]c=2*18=36[/tex]and
[tex]a=18+9=27[/tex]FInal answer:
first number a = 27
second number b = 18
third number c = 36
8 O 6 4. N Which function is graphed? 2. 4 6 8 -8 -6 -4 -2 0 -2 -6 O A. Y- (x² + 4, x=2 1-x+4,452 (x² + 4, x2 OD. V- x + 4, x32 1-x+4,4
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The given curve is parabola and its last point is on the x axis at x = 2
So, the equation of curve is :
[tex]x^2+4,x<2[/tex]In the equation of line,
The line start from x = 2 so, x ≥ 2
So, Equation of line is : -x + 4, x ≥ 2
Answer : B)
[tex]y=\begin{cases}x^2+4,x<2 \\ \square \\ -x+4,\text{ x}\ge2\end{cases}[/tex]Given that DE is the midsegment of the scalene AABC, answer theprompts to the right.
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Answers:
Part A.
C. AD = AE
Part B.
BC = 26
Explanation:
Part A.
If DE is a midsegment of triangle ABC, D is a point that divides AB into two equal segments, so option A. 1/2 AB = AD is true.
Additionally, if DE is a midsegment of triangle ABC, its length is equal to half the length of the side that the segment doesn't cross. So:
[tex]\begin{gathered} DE=\frac{1}{2}BC \\ 2DE=2\times\frac{1}{2}BC \\ 2DE=BC \end{gathered}[/tex]Therefore, option B is also true.
Triangle ABC is scalene, it means that all their sides have different length, it means that AD is not equal to AE and option C is not true.
Finally, segments AE and EC form AB, so:
AC = AE + EC
AC - AE = AE + EC - AE
AC - AE = EC
So, option D is also true.
Therefore, the answer for part A is C. AD = AE
Part B.
We know that 2DE = BC, so replacing the expression for each segment, we get:
[tex]\begin{gathered} 2DE=BC \\ 2(2x+1)=5x-4 \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} 2(2x)+2(1)=5x-4 \\ 4x+2=5x-4 \\ 4x+2-4x=5x-4-4x \\ 2=x-4 \\ 2+4=x-4+4 \\ x=6 \end{gathered}[/tex]Now, with the value of x, we get that BC is equal to:
BC = 5x - 4
BC = 5(6) - 4
BC = 30 - 4
BC = 26
So, the answer for part B is 26.
Determine weather it is a function, and state it’s domain and range.
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Find the inverse of:
[tex]f(x)=(3x-24)^2[/tex]The variable x can take any real value and the function f(x) exists. This means
the domain of f(x) is (-∞, +∞).
Now find the inverse function.
[tex]\begin{gathered} y=(3x-24)^2 \\ \pm\sqrt[]{y}=3x-24 \\ \pm\sqrt[]{y}+24=3x \\ x=\frac{\pm\sqrt[]{y}+24}{3} \\ x=\pm\frac{1}{3}\sqrt[]{y}+8 \end{gathered}[/tex]Swapping letters, we get the inverse function:
[tex]y=\pm\frac{1}{3}\sqrt[]{x}+8[/tex]For each value of x, we get two values of y, thus this is not a function.
The domain of the inverse is restricted to values of x that make the square root exist, thus the domain is x ≥ 0, or [0, +∞)
The range of the inverse is the domain of the original function, that is, (-∞, +∞)
Function: No
Domain: [0, +∞)
Range: (-∞, +∞)
The choice to select is shown below.
Michael wants to save $55,000.00 for a down payment on a home. How much will he need to invest in anaccount with 8.5% APR, compounding daily, in order to reach his goal in 3 years?
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Step 1. The information that we have is:
The final amount that Michael wants to save is:
[tex]A=55,000[/tex]We will call that amount A.
The annual percentage rate of the investment, which we will label as r, is:
[tex]r=8.5[/tex]We will need this annual percentage rate represented as a decimal number, therefore, we divide it by 100:
[tex]\begin{gathered} r=8.5/100 \\ r=0.085 \end{gathered}[/tex]The time of the investment, t, is 3 years:
[tex]t=3[/tex]And it is compounded daily, let n be the number of times of compounding in a year:
[tex]n=365[/tex]Step 2. We need to find the initial amount of the investment, which will be called P or principal.
The formula we will use to find it is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Step 3. Substituting the known values:
[tex]55,000=P(1+\frac{0.085}{365})^{(365)(3)}[/tex]From this equation, we need to solve the operations and solve for P, the principal amount of the investment.
Step 4. Simplifying the equation:
[tex]55,000=P(1+0.0002328767)^{1095}[/tex]Continue simplifying:
[tex]\begin{gathered} 55,000=P(1.0002328767)^{1,095} \\ 55,000=P(1.2904233) \end{gathered}[/tex]Then, we solve for P:
[tex]\begin{gathered} \frac{55,000}{1.2904233}=P \\ 42,621.6726=P \end{gathered}[/tex]Rounding to the nearest cent (2 decimal places) The amount that he needs to invest is $42,621.67
Answer: $42,621.67
What are the coordinates of the four vertices and the two foci?
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I need help with this question... it's about special triangles and I need to find y and z.. it should also not be a decimal.
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To find z, consider the right-angled triangle at the botton in the diagram showm
[tex]\begin{gathered} \sin 45\text{ = }\frac{z}{20} \\ z\text{ = 20 }\sin 45 \\ z\text{ = }20\text{ }\times\frac{1}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ z\text{ = }\frac{20\sqrt[]{2}}{2} \\ z\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]Let the common base of both triangles be m
[tex]\begin{gathered} \cos 45\text{ = }\frac{m}{20} \\ m\text{ = 20 }\cos 45 \\ m\text{ = }\frac{20}{\sqrt[]{2}} \\ m\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ m\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]To find y:
[tex]\begin{gathered} \tan 30\text{ = }\frac{y}{m} \\ \tan 30\text{ = }\frac{y}{10\sqrt[]{2}} \\ \frac{1}{\sqrt[]{3}}=\text{ }\frac{y}{10\sqrt[]{2}} \\ y\text{ = }\frac{10\sqrt[]{2}}{\sqrt[]{3}} \\ y\text{ = }\frac{10\sqrt[]{6}}{3} \end{gathered}[/tex]To find x:
[tex]\begin{gathered} \sin 30=\frac{y}{x} \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\div x \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\times\frac{1}{x} \\ x\text{ = }\frac{20\sqrt[]{6}}{3} \end{gathered}[/tex]Find the horizontal and vertical components for a vector round to the nearest tenth
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SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The horizontal component of a vector having:
[tex]\text{ a magnitude of v and a direction of }\theta\text{ = v cos }\theta[/tex]The vertical component of a vector having:
[tex]a\text{ magnitude of v and direction of }\theta\text{ = v sin}\theta[/tex]
Then, with the information above, the horizontal component of a vector having a magnitude of 15 and a direction of 210 degrees:
[tex]\begin{gathered} \text{Horizontal component = 15 x cos 210}^{\text{ 0}}=\text{ 15 x -0.8860 = -12.99}\approx\text{ -13.0 } \\ \text{Taking the absolute value, we have } \\ \text{Horizontal component = 13.0 units ( to the nearest tenth)} \end{gathered}[/tex]The vertical component of a vector having a magnitude of 15 and a direction of 210 degrees:
[tex]\begin{gathered} vertical\text{ component = 15 x sin 210}^{\text{ 0}}=\text{ 15 x -0.5 = -7.5 } \\ \text{Taking the absolute value, we have } \\ Vertical\text{component = 7.5 units ( to the nearest tenth)} \\ \\ \text{Hence the horizontal and vertical component of the vector =} \\ (\text{ 13. 0 , 7. 5 ) ( to the nearest tenth)} \end{gathered}[/tex]Solve the inequality 8y- 5 < 3
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Solve the inequality as you do with equations.
[tex]\begin{gathered} 8y-5<3 \\ 8y<3+5 \\ y<\frac{8}{8} \\ y<1 \end{gathered}[/tex]y is less than 1.
The graph of the solution is:
Solve the following system algebraically. y= x2 - 9x + 18 y = x - 3
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we have
y=x^2-9x+18 -----> equation A
y=x-3 ------> equation B
Solve the system of equations
substitute equation B in equation A
x^2-9x+18=x-3
x^2-9x+18-x+3=0
x^2-10x+21=0
Solve the quadratic equation using the formula
[tex]x=\frac{-b\pm\sqrt[\square]{b^2-4ac}}{2a}[/tex]we have
a=1
b=-10
c=21
substitute the given values
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[\square]{(-10)^2-4(1)(21)}}{2(1)} \\ \\ x=\frac{10\pm\sqrt[\square]{100-84}}{2} \\ \\ x=\frac{10\pm\sqrt[\square]{16}}{2} \\ \\ x=\frac{10\pm4}{2} \\ \\ x=7 \\ x=3 \end{gathered}[/tex]Find the value of y for x=7
y=x-3
y=7-3=4
the first solution is (7,4)
Find the value of y for x=3
y=3-3=0
the second solution is (3,0)
therefore
the answer is the first optionA line passes through the point (-6,1) and has a slope of -5/2
Write an equation in slope - intercept form for this line .
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Answer: [tex]y=-\frac{5}{2}x+16[/tex]
Step-by-step explanation:
The equation in point-slope form is [tex]y-1=-\frac{5}{2}(x+6)[/tex]. To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]y-1=-\frac{5}{2}(x-6)\\\\y-1=-\frac{5}{2}x+15\\\\y=-\frac{5}{2}x+16[/tex]
given the residual plot below, which of the following statements is correct?
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Let me explain this question with the following picture:
We can recognize a linear structure when all the points have a pattern that seems like a straight line as you can see above for example.
In the graph of your question, we can see that the points don't have a definited pattern and that's clearly not seemed like a straight line.
Therefore, the answer is option B:
There is not a pattern, so the data is not linear.
need help with math
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For each of the following scenarios state the domain (starting set) show and state the mapping, and decide if it is a function. Be sure to label your set and indicate the direction of the relation.
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Domain: Number of pages
Range:Number of books
Mapping: Number of pages to the number of books.
Explaination: The number of pages is the independent variable and the number of books is the dependent variable.
The given mapping is a function as total number of pages can not have more than two output (number of books).
This relation map is the musician to the instrument they play. is this relation a function?
