Devin invested money into a bank account. The table below is the value of Devin’s investment over time.
Answers
given
Table which shows the value of Devin's investment over time.
Find
a) type of equation
b) regression equation
c) y - intercept
d) strong correlation or not?
e) value of investment after 6 years?
Explanation
let X = year
Y = value
[tex]\begin{gathered} \sum_^X=72 \\ \\ \sum_^Y=242300 \\ \\ \sum_^X\cdot Y=3568900 \\ \sum_^X^2=1038 \\ \sum_^Y^2=12600850000 \end{gathered}[/tex]a) linear equation would best fit the data.
b) equation of regression line is y = ax + b
where
[tex]\begin{gathered} b=\frac{(n\sum_^XY-\sum_^X\sum_^Y)}{(n\sum_^X^2-(\sum_X)^2)} \\ \\ b=3800.575 \end{gathered}[/tex]and
[tex]\begin{gathered} a=\frac{(\sum_^Y-(b\sum_^X))}{n} \\ \\ a=-5223.563 \end{gathered}[/tex]so , equation of regression is
y = -5223.563 + 3800.575X
c) y- intercept is the value when x = 0
so , y - intercept is -5223.563
d) there is strong and positive correlation between variables.
because
[tex]r=\frac{(N\sum_^XY)-\sum_^X\sum_^Y}{\sqrt{N\sum_(X)^2-(\sum^X)^2-N\sum_(Y)^2-(\sum^Y)^2}}[/tex]r = 0.945
e) when X = 6
[tex]\begin{gathered} Y=-5223.563+3800.575\times6 \\ Y=17579.89\approx17580 \\ \end{gathered}[/tex]Final Answer
Hence , the above are the required answers
Related Questions
Using the net below, find the surface area of the pyramid. Blin 2 in Surface Area . - [?] in.2 Enter
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The Solution:
The correct answer is 16 square in.
Given the net in the picture on the Question section, we are asked to find the surface area of the pyramid that can form using the given net.
The pyramid (or the net) has a total of 5 surfaces, these are:
4 similar triangles, each with a base of 2 inches and a height of 3 inches; and a square of side 2 inches.
So,
The required surface area is the total area of all 5 surfaces.
By formula, the area of a triangle is
[tex]A=\frac{1}{2}bh[/tex]While the area of a square is
[tex]A=l\times l[/tex]So, the required area of the pyramid is
[tex]\text{Area}=4(\frac{1}{2}bh)+(l\times l)[/tex]In this case,
[tex]\begin{gathered} =\text{base}=2\text{ in.} \\ h=\text{height}=3\text{ in.} \\ l=\text{side}=2\text{ in.} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]\text{Area}=4(\frac{1}{2}\times2\times3)+(2\times2)=(4\times3)+4=12+4=16in.^2[/tex]Therefore, the correct answer is 16 square in.
Find the mean for the scores: 3,860; 5,300; 8,560; 4,400, 5,360..The mean for the scores is
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We have to find the mean of this list of scores.
We can calculate the mean as:
[tex]\begin{gathered} M=\dfrac{1}{n}\sum ^n_{i=1}\, x_i \\ M=\dfrac{1}{5}(3860+5300+8560+4400+5360) \\ M=\dfrac{27480}{5} \\ M=5496 \end{gathered}[/tex]Answer: The mean of this set of values is 5,496.
write the equation of the slope intercept form with the given point and slope or two points. (-7,13) slope = -2
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Slope-intercept form of a line:
y = mx+ b
where m is the slope and b is the y-intercept.
Replacing into the equation with m = -2 and point (-7, 13) we get:
13 = -2(-7)+ b
13 = 14+ b
13 - 14 = b
-1 = b
Then, the equation is:
y = -2x - 1
Find the standard form of the ellipse with the information below:Foci: (7, 10), (7,2)co vertices: (10,6), (4,6)
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The general form of the equation of an ellipse is given as:
Solve the system. 2x + y + 3z = 20 x + 2y - z = -11 3x 2z = -3 Enter your answer as an ordered triple
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The procedure 20 x + 2y - z = -11 3x 2z = -3 denotes an ordered triple with x = 1, z = 3, and y = 2.
What is meant by mathematical equations?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. The true power of equations lies in their ability to precisely describe various aspects of the world. (This is why, when one can be found, a solution to an equation can be useful.)Therefore,
let x + 2y + 3z = 14...…(1)
3x + y + 2z = 11.....(2)
2x + 3y + z = 11.....(3)
multiplying (2) by 2 and subtracting (1) from it we get,
=5x + z = 8...…..(4)
again multiplying (2) by 3 and subtracting (3) from it we get,
= 7x + 5z = 22.....(5)
Now multiply (4) by 5 and subtract (5) from it we get 18x = 18
therefore x = 1
substituting the x in (4) we get the value of z as
= 5(1) + z = 8
∴ z = 8 - 5 = 3
and substitute x and z in (1) we get
1 + 2y + 3(3) = 14
2y = 14 - 1 - 9 = 4
∴ y=2
The complete question is:
The solutions of the equations x+2y+3z=14, 3x+y+2z = 11, 2x + 3y + z = 11
A [tex]$\quad \mathrm{x}=\mathrm{O}, \mathrm{y}=2, \mathrm{z}=4$[/tex]
B [tex]$\quad \mathrm{x}=1, \mathrm{y}=\mathrm{O}, \mathrm{z}=4$[/tex]
C [tex]$\mathrm{x}=\mathrm{O}, \mathrm{y}=1, \mathrm{z}=8$[/tex]
D [tex]$x=1, y=2, z=3$[/tex]
To learn more about mathematical equations, refer to:
https://brainly.com/question/22688504
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A suit was marked with a 10% discount.
If the discount is $10.00, what was the original price of the suit?
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Answer:
The suit originally cost $100.
Step-by-step explanation:
To find the original price of the suit, you can set up a ratio and solve for the missing variable. In this case, we can set up a ratio as such:
10%/100% = $10.00/x, where x is the original price, and $10.00 is 10% of the original. In fraction form, this looks like [tex]\frac{10}{100} =\frac{10}{x}[/tex]. Here, it is clear that for these two to be equal, x must be equal to 100.
How Much Paint Would Cover This Pyramid Without The Square Base ?
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To answer this question, we will assume that the pyramid's slant height is 10ft.
We have a square pyramid in which we have:
• The pyramid's base is a square with a side that measures 6ft.
,• The height of the pyramid is equal to 8ft.
,• The slant height is 10ft
Then we need to find the surface area of the pyramid without the square base, and we can see that:
1. We can see that the surface area of the pyramid without the square base is represented by four (4) triangles with equal base (6ft) and equal height (10ft). Then since the area of a triangle is given by:
[tex]A___{triangle}=\frac{bh}{2}[/tex]2. Therefore, we need to find the area of one of the triangles, and then multiply this result by 4 to find the asked area as follows:
[tex]A_{triangle}=\frac{6ft*10ft}{2}=\frac{60ft^2}{2}=30ft^2[/tex]3. Then the total area of the pyramid without the square base is:
[tex]\begin{gathered} A_{4triangles}=4(30ft^2)=120ft^2 \\ \\ A_{4triangles}=120ft^2 \end{gathered}[/tex]Therefore, in summary, the paint would cover 120ft² (square feet) without the square base.
two angles in a triangle measure (2.3×+25)° and (5.8×+11)°. what is the value of x if the angles are congruent to one another?
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If the angles are congruent to one another, we can conclude:
[tex]\begin{gathered} (2.3x+25)=(5.8x+11) \\ \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} 25-11=5.8x-2.3x \\ 14=3.5x \\ x=\frac{14}{3.5} \\ x=4 \end{gathered}[/tex]sina ½ sin ( a + b) + sin(a = b)] OA. cos a OB.. sina OC. sinb D. cos b
Answers
Answer:
A. cos a
Explanation:
The relevant trigonometric formula we have is
[tex]\sin a\cos a=\frac{1}{2}[\sin(a+b)+\sin(a-b)][/tex]Now comparing the above formula with the one given in the question tells us that the missing term in the equation is cos a.
Therefore, choice A is the right answer!
Parallel lines never meet and will never cross each other.
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True
Parallel lens are never meet and cross each other
17. To measure the amount of space in rectangular prism, we need three dimensional figures as unit of measure. Which is the formula for finding the volume?A. V= 1/3 x B x HB. V= S x S x SC. V= L x W x H18. A rectangular prism has length of 4 cm, width of 3 cm and height of 5 cm. Find the volume.A. 50 cu cmB. 55 cu. cmC. 60 cu. cmD. 45 cu. cm19. A wooden box has 20 cm on each edge. Find its volume.A. 875 cu. cmB. 8 000 cu. cmC. 8 875 cu. cm20. Juana’s sewing box is 3 dm long, 2dm wide, and 4 dm high. What is its volume?A. 12 cu. dmB. 24 cu. dmC. 33 cu. dmD. 34 cu. dm21. Five metal cubes with sides of 5 cm were melted and casted into a bigger cube. Find the volume of the new cube.A. 125 cu.cmB. 405 cu. cmC. 325 cu. cmD. 625 cu. cm
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(17) The First part of the question asked us to find the formula used in determining measure of the amount of space in a rectangular prism which is invariably the volume.
The three dimensions needed to determine the Volume of a rectangular prism are:
Length
width
Height.
To get the volume, we mutiply the three together.
So:
Volume = Length * Width * Height.
V = L * W * H
Therefore, the correct option is C, which is V = L x W x H.
(18) Givne the following dimensios of a rectangular prism as:
Length = 4 cm
Width = 3 cm
Height = 5 cm
We are to find the volume
Recall, the formula for finding volume of the rectangular prism is:
V = L x W x H
V = 4 x 3 x 5
V = 60 cm³
Therefore, the volume of the rectangular prism = 60 cm³
So, the correct option is C, which is 60 cm³.
Find θ for 0 < θ< 2 pisin θ =0.3148
Answers
The given trigonometric expression is:
sin θ =0.3148
To find the value of θ, we need to find the arc sin of 0.3148
[tex]\begin{gathered} θ=\sin^{-1}0.3148 \\ θ=18.35^0,161.65^0\text{ } \end{gathered}[/tex])) How many terms are in this expression? 7c+ 3d Submit
Answers
The number of terms is the expression is equal to 2.
7c
3d
In algebra, terms are the values on which the mathematical operations take place in an expression.
A term can be a constant or a variable or both in an expression.
In the expression, 7ca + 3d, 7c and 3d are terms.
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Consider the following function.f(x) = 6x^2 − 4xFind the limit.
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Given:-
[tex]f(x)=6x^2-4x[/tex]To find:-
[tex]\lim _{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}_{}[/tex]So now we substitute the known values we get,
[tex]\frac{f(x+\Delta x)-f(x)}{\Delta x}_{}=\frac{6(x+\Delta x)^2-6x^2+4x}{\Delta x}[/tex]So by furthur simplification. we get,
[tex]\frac{6(x+\Delta x)^2-6x^2+4x}{\Delta x}=\frac{6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x}{\Delta x}[/tex]So we get is,
[tex]\frac{6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x}{\Delta x}=\frac{12x\Delta x+(\Delta x)^2^{}+4x}{\Delta x}[/tex]So by furthur simplification we get,
[tex]undefined[/tex]Determine the domain and range of the quadratic function. (Enter your answer using interval notation.)f(x) = 2x2 − 4x + 2domain range
Answers
we have the equation
[tex]f\mleft(x\mright)=2x^2−4x+2[/tex]The domain of any quadratic equation is all real numbers
so
The domain is the interval (-infinite, infinite)To find out the range, we need the vertex
Convert the given equation into vertex form
[tex]\begin{gathered} f\mleft(x\mright)=2x^2−4x+2 \\ f(x)=2(x^2-2x)+2 \end{gathered}[/tex]Complete the square
[tex]\begin{gathered} f(x)=2(x^2-2x+1-1)+2 \\ f(x)=2(x^2-2x+1)+2-2 \\ f(x)=2(x^2-2x+1) \\ f(x)=2(x-1)^2 \end{gathered}[/tex]The vertex is the point (1,0)
The vertical parabola opens upward (the leading coefficient is positive)
The vertex is a minimum
therefore
The range is the interval [0, infinite)All real numbers greater than or equal to zero
Need help with #81, specifically don’t understand how to determine the domain
Answers
ANSWERS
a) Domain: x ∈ (-∞, -1) ∪ (-1, ∞)
b) Domain: x ∈ (-∞, 0) ∪ (0, ∞)
EXPLANATION
These compositions are:
a)
[tex]f\circ g=f(g(x))=\frac{2}{g(x)}=\frac{2}{x+1}[/tex]And
b)
[tex]g\circ f=g(f(x))=f(x)+1=\frac{2}{x}+1[/tex]To find the domain in each function we have to find the values that x cannot take. If there aren't any, then the domain is all real values.
For composition a) note that x is in the denominator as (x+1). As we know, for real numbers the denominator can't be 0, so that's our restriction:
[tex]x+1\ne0[/tex]Solving for x:
[tex]x\ne-1[/tex]The domain for f º g is all real values except x = -1
For composition b) we have x in the denominator too, but it is alone. Therefore, as said before, x cannot be 0.
Which point is located at (0, -7)? O 4 8
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The point with the coordinates x=0 and y=-7 is point E
write an equation for the line that has a slope of 1/2 and passes through the point (2,4)!!
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Answer:
x-2y=-6.
Explanation:
Given a line with a slope of 1/2 that passes through the point (2,4):
[tex]\begin{gathered} m=\frac{1}{2} \\ (x_1,y_1)=(2,4) \end{gathered}[/tex]Substitute these into the point-slope form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]This gives:
[tex]\begin{gathered} y-4=\frac{1}{2}(x-2) \\ y-4=\frac{1}{2}x-\frac{1}{2}(2) \\ y-4=\frac{1}{2}x-1 \end{gathered}[/tex]We can simplify further:
[tex]\begin{gathered} y=\frac{1}{2}x-1+4 \\ y=\frac{1}{2}x+3 \\ \implies y=\frac{x+6}{2} \\ 2y=x+6 \\ x-2y=-6 \end{gathered}[/tex]The equation of the line is x-2y=-6.
Joe has brownies the length of each brownies is 7 cm and the width is 5 cm is its total area of the pan is 560 cm how many brownies did Joe have
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Start by calculating the area of a single brownie using
[tex]A=L\cdot W[/tex][tex]\begin{gathered} A=7\operatorname{cm}\cdot5\operatorname{cm} \\ A=35\operatorname{cm} \end{gathered}[/tex]To find the amount of brownies Joe can make in his pan, divide the area of the pan into the single brownie area
[tex]\frac{560}{35}=16[/tex]Joe had 16 brownies.
what's 3/4 put of 12?
Answers
Maria had 12 pieces of fruit. Three-fourths were apples.
We want to find how many fruits were apples,
That would be;
[tex]\begin{gathered} \frac{3}{4}\times12=\frac{36}{4} \\ =9 \end{gathered}[/tex]Therefore, 9 of the fruits were apples.
Which equation describes a line of symmetry for square ABCD? x = 0 y = x x = -2 y = -2
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The equation of the line is DB from y = mx + b
From the graph y = 0 when x =0
this means y = x
The graph cuts through the origin, Meaning the y -intercept = 0
answer is: y = x
8. Pentagon MNOPQ with M(-4,1),N(-2,3). O(0, 3), P(4, 3), and Q(2,-7): rotate 90° counterclockwise, then dilate by a factor of 2/3 120 What are the two arrow rules to show this composition? 12 b. Is the dilation an enlargement or reduction? How do you know? 710 с. What are the vertices of the image after the transformation?
Answers
Given data:
The given coordinates of the pentagon are M(-4,1),N(-2,3). O(0, 3), P(4, 3), and Q(2,-7).
The coordinatte after 90 degrees counterclockwise rotation is,
[tex]\begin{gathered} M(-4,1)\rightarrow M^{\prime}(-1,\text{ -4)} \\ N(-2,\text{ 3)}\rightarrow N^{\prime}(-3,\text{ -2)} \\ O(0,\text{ 3)}\rightarrow O^{\prime}(-3,\text{ 0)} \\ P(4,\text{ 3)}\rightarrow P^{\prime}(-3,\text{ 4)} \\ Q(2,\text{ -7)}\rightarrow Q^{\prime}(7,\text{ 2)} \end{gathered}[/tex]The final coordinates after 2/3 dilation factor is,
[tex]\begin{gathered} M^{\doubleprime}\rightarrow\frac{2}{3}(-1,\text{ -4)} \\ \rightarrow(-\frac{2}{3},\text{ - }\frac{8}{3}) \\ N^{\prime\prime}\rightarrow\frac{2}{3}(-3,\text{ -2)} \\ \rightarrow(-2,\text{ -}\frac{4}{3}) \\ O^{\doubleprime}\rightarrow\frac{2}{3}(-3,\text{ 0)} \\ \rightarrow(-2,\text{ 0)} \\ P^{\doubleprime}\rightarrow\frac{2}{3}(-3,\text{ 4)} \\ \rightarrow(-2,\frac{8}{3})^{} \\ Q^{\doubleprime}\rightarrow\frac{2}{3}(7,\text{ 2)} \\ \rightarrow(\frac{14}{3},\text{ }\frac{4}{3}) \end{gathered}[/tex]Thus, the final coordinates after transformation are M''(-2/3, -8/3), N''(-2, -4/3). O''(-2, 0), P''(-2, 8/3), and Q''(14/3, 4/3).
3(x-y) when x=4 and y=1
Answers
You deposit $4000 in an account earning 8% interest compounded monthly. How much will you have in the account in 15 years?
Answers
Given:
a.) You deposit $4000 in an account earning 8% interest compounded monthly.
Question: How much will you have in the account in 15 years?
We will be using the following formula:
[tex]\text{ A = P(}1\text{ + }\frac{r}{n})^{nt}[/tex]Where,
A=final amount
P=initial principal balance = $ 4,000
r=interest rate = 8% = 8/100 = 0.08
n=number of times interest applied per time period = monthly = 12
t=number of time periods elapsed = 15 years
We get,
[tex]\text{ A = P(}1\text{ + }\frac{r}{n})^{nt}[/tex][tex]\text{ A = (4,000)(}1\text{ + }\frac{0.08}{12})^{(12)(15)}[/tex][tex]\text{ = (4,000)(1 + }0.00667)^{180}=(4,000)(1.00667)^{180}[/tex][tex]\text{ = (4,000)(3.30889307445)}[/tex][tex]\text{ A = 13,235.57229780234 }\approx\text{ \$13,235.57}[/tex]Therefore, in 15 years, you will have $13,235.57 in your account.
In the diagram below, AD bisects ZC AB, mZADB = 95º and mZCAD = 34°. Find mZB.
Answers
please send me the picture of your question
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Please let me know if you have any question anytime or if you don’t see the answering tab
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle ADB we have that
mwe have that
m because AD bisects angle CAB
so
msubstitute
34+95+m
mmPlease, Do you understand all the steps so far?Does the explanation satisfy your question and do you understand the answer?
If you don’t need further explanation on this question, we can end the session. A pleasure to attend you, Remember that after our session, the answer is saved in your profile. Thanks and have a great day! Good Bye.
Can you please help me out with a question
Answers
37.5%
1) Examining the Spinner we can see that the total possibilities are:
90+45+90+135 = 360
2) Since the question is P(green or red) we can write out:
[tex]\begin{gathered} P(g\text{ or r) = }\frac{90}{360}+\frac{45}{360}=\frac{135}{360}=0.375 \\ P(g\text{ or r) = P(g) +P(r) } \end{gathered}[/tex]Note that the event of picking red or picking green can't exist simultaneously so they are mutually exclusive.
The result in percentage will be obtained by multiplying it by 100
3) Hence, the answer is 37.5%
Need to know the answers or how to do them.#1 please
Answers
Looking at angle G, it inscribes the arc FH, which is a diameter of the circle.
Since an inscribed angle measures half the inscribed arc (and arc FH measures 180°), angle G measures 90°.
Now, let's calculate angle F:
[tex]\begin{gathered} F+G+H=180\\ \\ F+90+48=180\\ \\ F+138=180\\ \\ F=180-138\\ \\ F=42° \end{gathered}[/tex]Arc GH is inscribed by the angle F, so we have:
[tex]\begin{gathered} F=\frac{1}{2}GH\\ \\ 42=\frac{1}{2}GH\\ \\ GH=2\cdot42\\ \\ GH=84° \end{gathered}[/tex]So the indicated arc measures 84°.
3) P(A) = 0.65 P(B) = 0.35 P(A and B) = A.0.2275B.0.2c.0.06d.0.315
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For the given probabilities:
[tex]\begin{gathered} p(AandB)=^{}0.65\cdot0.35 \\ p(AandB)=0.2275 \end{gathered}[/tex]Write the nth rule for each geometric sequence.4) -3, 1, -1/3, 1/9...
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In a geometric sequence each term is found by multiplying the previous term by a constant.
To find the nth term in a geometric sequence we use:
[tex]a_n=ar^{n-1}[/tex]where a is the first term and r is the common ratio.
To find the common ratio we can divide the second term by the first:
[tex]\frac{1}{-3}=-\frac{1}{3}[/tex]and the third one by the second:
[tex]\frac{-\frac{1}{3}}{1}=-\frac{1}{3}[/tex]we notice that this in fact is the common ratio. Now we plug it in the formula above, therefore the geometric sequence is:
[tex]a_n=-3(-\frac{1}{3})^{n-1}[/tex]A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. write an equation that represents the situation. Use x to represent the number of roast beef sandwiches. then determine how many sandwiches tje customer buys. Amount Used for payment =$50Change Received = $16.25The Customer buys. sandwiches ?
Answers
Let x be the number of sandwiches.
Since each sandwich has a cost of $6.75, then for x sandwiches the cost would be:
[tex]\text{6}.75x[/tex]The change received is the difference between the amount used for payment and the cost of the sandwiches.
The difference between the amount used for payment and the cost of the sandwiches can be represented algebraically as:
[tex]50-6.75x[/tex]This number must be equal to the change received. Then:
[tex]50-6.75x=16.25[/tex]Solve for x. To do so, substract 50 from both sides:
[tex]\begin{gathered} \Rightarrow-6.75x=16.25-50 \\ \Rightarrow-6.75x=-33.75 \end{gathered}[/tex]Next, divide both sides by -6.75:
[tex]\begin{gathered} x=\frac{-33.75}{-6.75} \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, the customer buys 5 sandwiches.