If you were to simply guess the answer to both questions, you would have a 6.25% chance of getting both answers right according to probability
Assuming that each answer choice is equally likely to be correct, the probability of guessing the correct answer to one question is 1/4 or 0.25. Since there are two questions, the probability of guessing both correctly is the product of the probabilities of guessing each question correctly.
P(guessing both questions correctly) = P(guessing first question correctly) x P(guessing second question correctly)
P(guessing both questions correctly) = (1/4) x (1/4)
P(guessing both questions correctly) = 1/16 or 0.0625
Therefore, the probability of guessing both questions correctly is 1/16 or 0.0625.
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In triangle ABC, point D lies on side BC such that ΔABD and ΔACD have the same perimeter. Points E and F are constructed on sides CA and AB in a similar manner, respectively, each dividing ΔABC into two triangles of equal perimeter. If BD=5, DC=3, and the perimeter of ΔABC is 18, what is the ratio of the area of ΔDEF to the area of ΔABC?
Answer:
10
Step-by-step explanation:
What is the median of 1 3/4 and 1 2/3?
Answer:
Step-by-step explanation:
In numerical order:
[tex]1\frac{2}{3},1\frac{3}{4}[/tex]
Since there are only 2 scores the median(middle score) will be the same as the mean:
[tex](1\frac{2}{3}+ 1\frac{3}{4}) \div 2=(\frac{20}{12}+ \frac{21}{12}) \div 2=\frac{41}{12} \times \frac{1}{2} =\frac{41}{24}=1\frac{17}{24}[/tex]
A line is drawn on a coordinate grid by the equation y = 1. Which of the following lines would represent a row perpendicular to it?
Among the answer choices, the line that represents a row perpendicular to y = 1 is x = 4.
What is coordinate geometry?
Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric figures using coordinates.
The line y = 1 is a horizontal line that goes through all points on the y-axis with a y-coordinate of 1.
To find a line perpendicular to it, we need to find a line that has a slope that is the negative reciprocal of the slope of y = 1. The slope of y = 1 is 0, so the slope of the perpendicular line is undefined (since any number divided by 0 is undefined).
Therefore, the perpendicular line must be a vertical line, and its equation would be of the form x = c, where c is a constant.
Hence, among the answer choices, the line that represents a row perpendicular to y = 1 is x = 4.
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PLSS ANSWER QUICK
Based on the line of best fit, what is the expected distance Bobby has traveled after 8 hours?
A.475 miles
B. 300 miles
C. 400 miles
D. 500 miles
Answer: 475 is ur answer
Step-by-step explanation:
myas rectangular yard is 10 feet wide and 15 feet long. how many square feet of grass does she need to plant if she wants to cover the entire yard?
ANSWER FASTTTTT
To cover the entire yard, Mya needs to plant 150 square feet of grass.
Mya's rectangular yard is 10 feet wide and 15 feet long. To find the area of the yard, we need to multiply the width by the length:
Area of yard
= width x length
= 10 ft x 15 ft
= 150 square feet
Therefore, Mya needs to plant 150 square feet of grass to cover the entire yard
A rectangular yard is a type of outdoor space that is often used for gardening, outdoor activities, or as a place for relaxation. To calculate the area of a rectangular yard, you need to know its dimensions, which are typically expressed in feet or meters. The area of a rectangular yard can be found by multiplying its length by its width. The formula for the area of a rectangle is A = L x W, where A represents the area, L represents the length, and W represents the width. Once you have calculated the area of the yard, you can use this information to determine how much grass or other landscaping materials you need to cover the area.
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[tex]\sqrt{ 6^{2} +(x-2)^{2} }[/tex]
Answer:
[tex] \sqrt{36 + x {}^{2} } - (2) {}^{2} \\ 6 + x + - 2 \\ 6 - 2 + x \\ 4 + x \\ \: \:answer = 4 + x \\[/tex]
I need help with the last one which is prove AB and CD.
Answer:
because triangle ABD is congruent to triangle CBD
by CPCT
AB = CD
The vertices of a rectangle are plotted.
A graph with both the x and y axes starting at negative 7, with tick marks every one unit up to 7. The points negative 4 comma 2, 5 comma 2, 5 comma negative 3, and negative 4 comma negative 3 are each labeled.
What is the perimeter of the rectangle?
10 units
18 units
28 units
45 units
Answer:
Answer is 28
Step-by-step explanation:
Length = 5
Width = 9
Perimeter = length*2 + width*2
Perimeter = 5*2 + 9*2
Perimeter = 10 + 18 = 28
Directions: Rewrite each expression using positive exponents.
1. X-5
2. 3m-2
3. -7a-4b3
4. 9x6y-3
Answer:
1) X0=1
2) 19m2
3) there is something missing i think
4) 6x3y
The area A of a rectangular swimming pool is given by the equation A=12w-w^2, where w is the width of one side. Write an expression for the other side of the pool.
Answer: y=mx+c
Step-by-step explanation:
what is the pattern of the sequence 10, 11, 21, 32?
Example:
Sequence- 2, 6, 18, 54
Pattern- x3
The pattern of the sequence is "add increasing multiples of 9 starting with 1."
To find the pattern in the sequence 10, 11, 21, 32, follow these steps:
1. Identify the differences between consecutive terms:
11 - 10 = 1
21 - 11 = 10
32 - 21 = 11
2. Notice that the differences are increasing by 9 (10 - 1 = 9 and 11 - 10 = 1).
3. Based on this observation, the pattern can be described as adding a value that increases by 9 each time:
10 + 1 = 11
11 + 10 = 21
21 + 11 = 32
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Solve the system of linear equations by elimination. -x+y=1 and 3x+y=7
We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.
3x + y = 7
-x + y = 1
Add the equations together:
2x + 2y = 8
Divide both sides by 2:
x + y = 4
Subtract the second equation from the first:
-x + y = 1
x - y = -3
Add the equations together:
2x = -2
Divide both sides by 2:
x = -1
Substitute -1 for x in the equation x + y = 4:
-1 + y = 4
Subtract -1 from both sides:
y = 5
The solution is x = -1 and y = 5.
We begin by solving the system of linear equations by elimination. We need to get the variables to one side of the equation and the constants to the other side. We start by adding the two equations together: 3x + y = 7 and -x + y = 1. This gives us 2x + 2y = 8, which we can then divide both sides by 2 to get x + y = 4. We then subtract the second equation from the first to get -x + y = 1 and x - y = -3. We then add these two equations together to get 2x = -2 and divide both sides by 2 to get x = -1. We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.
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What are the steps in the design process, and how are they organized in Architecture?
These steps in the design process are often iterative, meaning that architects may revisit earlier steps as they refine and develop the design. The overall goal of the design process in architecture is to create a functional, safe, and aesthetically pleasing building that meets the needs and goals of the client.
What are the steps in the design process?The following are the steps in the design process, organized in architecture:
Programming: In this first step, architects work with their clients to understand the project requirements, goals, and objectives. They may gather information about the site, zoning and building codes, budget, and other constraints.
Schematic Design: In this step, architects use the information from the programming phase to create rough sketches and drawings that show the basic layout and massing of the building. This phase is an opportunity to explore various design options and to get feedback from the client.
Design Development: In this step, the architects refine the design, incorporating structural and mechanical systems, and developing detailed drawings and specifications. This phase also includes working with consultants such as engineers and contractors.
Construction Documents: In this step, the architects prepare the final construction documents, which include detailed drawings and specifications that will be used by contractors to build the project.
Bidding and Negotiation: In this step, the architects help the client solicit bids from contractors and negotiate the terms of the construction contract.
Construction Administration: In this final step, the architects oversee the construction process, ensuring that the project is built according to the design documents and that any changes or issues are addressed.
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What additional information would be sufficient, along with the given, to conclude that lmno is a parallelogram? check all that apply. ml ∥ no ml ⊥ lo lo ≅ mn ml ≅ lo mn ⊥ no
To conclude that quadrilateral LMNO is a parallelogram, we need either ML ∥ NO, LO ≅ MN, or ML ⊥ LO.
Since LO ∥ MN, we know that ∠LON = ∠OMN and ∠NOM = ∠LMO. To conclude that LMNO is a parallelogram, we need to show that opposite sides are parallel and equal in length.
The following statements would be sufficient to conclude that LMNO is a parallelogram:
ML ∥ NO: If ML is parallel to NO, then ∠LMO = ∠NOM, and since ∠NOM = ∠LMO, we have ∠LMO = ∠NOM = ∠NLO = ∠OML. Therefore, opposite angles are equal, and LMNO is a parallelogram.
LO ≅ MN: If LO is equal in length to MN, then we have LO = MN and ∠LON = ∠OMN. Therefore, triangle LON is congruent to triangle MON by the side-angle-side (SAS) congruence criterion. This implies that ∠LNO = ∠MNO and ∠LON = ∠MON. Since ∠LNO + ∠LON = 180° and ∠MNO + ∠MON = 180°, we have ∠LNO = ∠MON and ∠LON = ∠MNO. Therefore, opposite angles are equal, and LMNO is a parallelogram.
ML ⊥ LO: If ML is perpendicular to LO, then ∠LMO = 90° and ∠NOM = 90°. Therefore, opposite angles are equal, and LMNO is a parallelogram.
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The given question is incomplete, the complete question is:
In quadrilateral LMNO, LO ∥ MN. What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply. ML ∥ NO ML ⊥ LO LO ≅ MN ML ≅ LO MN ⊥ NO.
im training my robot to eat cuppy cupcakes every 7 days it eat 4 ill like to buy enough for the last 14 days
Rοunding up tο the nearest whοle cupcake, yοu shοuld buy 8 cupcakes tο ensure that yοur rοbοt has enοugh cupcakes tο last fοr the next 14 days.
What is equatiοn?An equatiοn is a mathematical statement that indicates that twο expressiοns are equal. It cοntains an equals sign (=) between twο expressiοns, with οne expressiοn οn each side οf the equals sign. Equatiοns can cοntain variables, cοnstants, cοefficients, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Here,
If yοur rοbοt eats 4 cupcakes every 7 days, it means it eats 4/7 = 0.57 cupcakes per day (rοunded tο twο decimal places).
Tο buy enοugh cupcakes fοr the last 14 days, yοu need tο multiply the number οf days by the daily cοnsumptiοn rate:
0.57 cupcakes per day x 14 days = 7.98 cupcakes
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Complete question:
If your robot eats 4 cupcakes every 7 days. So to buy enough cupcakes for the last 14 days, how much cupcake is consumed daily?
Ready
Chef Allen wants to know how much he will pay for different amounts of beans.
Plot two points that show the cost of
15 pounds and 20 pounds of beans,
Cost (dollars)
20
18
16
14
12
10
8
6
4
2
0
05
Cost of Beans
10 15 20 25 30 35 40 45 50
Beans (pounds)
The graph of the following function has been attached with the answer.
What Does Graphing Functions Mean?The procedure of graphing a function entails drawing the graph (curve) of the relevant function. While it is relatively straightforward to graph simple functions like linear, quadratic, cubic, etc., complex functions like rational, logarithmic, etc. call for knowledge and a comprehension of specific mathematical concepts.
In order to graph functions, one must first:
If possible, identifying the shape. A line would be the graph of a linear function of the type f(x) = axe + b, for instance; a parabola would be the graph of a quadratic function of the form f(x) = ax2 + bx + c.
Determining some of its points involves substituting some arbitrary values for x and then using the function to determine the corresponding values for y.
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By influencing some of its points' x values to random numbers, the function can be used to find the equivalent values for y.
What Does Graphing Functions Mean?Drawing the graph (curve) of the pertinent function is the first step in the process of graphing a function. While graphing basic functions like linear, quadratic, cubic, etc. is generally easy, complex functions like rational, logarithmic, etc. demand an understanding of and knowledge of particular mathematical concepts.
Prior to drawing a graph of a function, one must:
Identifying the form, if you can. For example, the graph of a linear function of the form f(x) = axe + b would be a line; the graph of a quadratic function of the form [tex]f(x)=ax^2+bx+c[/tex] would be a parabola.
By influencing some of its points' x values to random numbers, the function can be used to find the equivalent values for y.
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The graph is attached below,
would your confidence intervals of parts a and c be valid if the distribution of the original population were not normal?
The 95% confidence interval for μ is (80.52, 82.68).
To find the 95% confidence interval for the population mean (μ), we can use the following formula
CI = X ± z* (σ / √n)
where X is the sample mean, σ is the population standard deviation (unknown), n is the sample size, and z* is the critical value from the standard normal distribution corresponding to the desired confidence level (in this case, 95%).
The critical value z* can be found using a standard normal distribution table or calculator, or using a statistical software. For a 95% confidence level, the z* value is 1.96.
Plugging in the values given, we get
CI = 81.6 ± 1.96 × (5.4 / √100)
Simplifying this expression, we get
CI = 81.6 ± 1.08
= (80.52, 82.68)
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The given question is incomplete, the complete question is:
A random sample of 100 observations from a normally distributed population possesses a mean equal to 81.6 and a standard deviation equal to 5.4 . Find a 95% confidence interval for μ
A box contains 40 pens. 30 of the pens are blue and the rest are green. One pen is taken out at random and replaced by Live of the other colour. Another pen is taken out at random and replaced by Live of the other colour. A Linal pen is taken out at random. (a) Work out the probability that all three pens are green
Work out the probability that all three pens are green p = 10/40 * 4/44 * 8/48 = 3/352.
a) p = 10/40 * 4/44 * 8/48 = 3/352
b) p = 3/352 + 30/40 * 24/44* 28/48
=3/352+ 203/704
= 209/704
= 19/64
c) p= 1 - 19/64
= 64/64 - 19/64
= 45/64
Probability is just the way that possible something is to occur.
Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of events administered by probability is called insights.
The probability of an occasion must be somewhere in the range of 0 and 1 and can likewise be composed as a rate.
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report the level of significance. of ball bearings from this manufacturing process is 2.30 cm. based on the sample of 50 that you collected, is there evidence to suggest that the average diameter is greater than 2.30 cm? perform a hypothesis test for the population mean at alpha
Yes, there is evidence to suggest that the average diameter is greater than 2.30 cm.
To perform a hypothesis test for the population mean at alpha, use a two-tailed t-test. Assume the null hypothesis is that the average is equal to 2.30 cm and the alternative hypothesis is that the average is greater than 2.30 cm. Calculate the test statistic and then compare it to the critical value.
If the test statistic is greater than the critical value, then you can reject the null hypothesis and conclude that the average is greater than 2.30 cm.
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what is the value of
7p+ q/3
when p= 6 and q=12
a 14
b 36
c 42
d 46
7p + q /3
p = 6 and q = 12
7(6) + (12) / 3
42 + 12/ 3
54/3
18
18 is the correct answer, but isn't present as an option in the list.
Answer:D.46
Step-by-step explanation: because 7(6)+12/3
First 7(6)=42
Then 12/3=4
Finally 42+4=46
A student simplified the rational expression
using the steps shown.
Is the answer correct? Explain.
Step-by-step explanation & Answer
No, the answer is not correct
In the second step, the student did not use the quotient of powers property correctly. Instead, they should have subtracted inside the parentheses instead of dividing. This would have left them with [tex]x^{(\frac{4}{5} )}[/tex]. They should have then multiplied this power by [tex]^{\frac{1}{2} }[/tex] resulting in [tex]x^{(\frac{4}{10})}[/tex] which simplified is [tex]x^{(\frac{2}{5}) }[/tex] which is the correct answer.
That is just an example on how the answer is done.
if two different students are randomly selected (i.e., without replacement), find the probability that both the first and second student studied.
The probability that both the first and second student studied = p²
To find the probability that both the first and second students studied when two different students are randomly selected, we can use the multiplication rule of probability.
What is the multiplication rule of probability?The multiplication rule of probability states that if the probability of event A is p(A), and the probability of event B, given that event A has occurred, is p(B|A), then the probability of the joint occurrence of A and B is given by p(A and B) = p(A) × p(B|A).
So, if we let A be the event that the first student studied, and B be the event that the second student studied, then we need to find the probability of the joint occurrence of A and B.
We can assume that the probability that any student studied is equal to some value p, and the probability that any student didn't study is equal to q = 1 - p. Since there are only two possibilities for each student (studied or not studied), then p + q = 1. So, we can use the complement rule of probability to write:
p(A) = probability that the first student studied = p, and
p(not A) = probability that the first student didn't study = q = 1 - p,
p(B|A) = probability that the second student studied, given that the first student studied = p, and
p(B|not A) = probability that the second student studied, given that the first student didn't study = p.To find the probability that both the first and second student studied, we need to find the probability of the joint occurrence of A and B. Using the multiplication rule, we get:
p(A and B) = p(A) × p(B|A) = p × p = p².
Which is the probability that both the first and second students studied.
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Find the area of the regular trapezoid below
Answer:
54inch^2
Step-by-step explanation:
3×6=18
18÷2=9
6×6=36
36+9+9= 54
answer: 54inch^2
For each of the shapes below, state whether it is a regular polygon, an irregular
polygon or neither.
A
D
B
E
C
Each of the shapes below, The polygons are identified as:
A- Irregular polygon
B- Neither
C- Regular polygon
D- Regular polygon
E- Regular polygon
What is polygon?A polygon is a two-dimensional geometric shape that is defined as a closed figure with three or more straight sides and angles. Polygons can be convex or concave, depending on whether all of their interior angles are less than or greater than 180 degrees, respectively. Some common examples of polygons include triangles (3 sides), squares (4 sides), pentagons (5 sides), hexagons (6 sides), and octagons (8 sides). Polygons are frequently used in geometry, as they can be used to calculate areas, perimeters, and other properties of shapes.
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if (2x10^n)+(4.02x10^5), what is n?
The vaIue οf n = 5 .
What is an equatiοn?A mathematicaI statement knοwn as an equatiοn cοnsists οf twο aIgebraic expressiοns separated by equaI signs (=) οn either side.
It demοnstrates the equaIity οf the reIatiοnship between the printed statements οn the Ieft and right.
Left side equaIs right side in aII fοrmuIas.
Tο find the vaIues οf unknοwabIe variabIes, which stand in fοr unknοwabIe quantities, yοu can sοIve equatiοns.
A statement is nοt an equatiοn if it Iacks the equaIs sign.
When twο expressiοns have the same vaIue, a mathematicaI statement knοwn as an equatiοn wiII incIude the symbοI "equaI tο" between them.
Accοrding tο οur questiοn-
[tex]2 \times 10^{(n+5)} + 4.02 \times 10^5 = 2 x 10^{(n+5)} + 4.02 \times 10^n[/tex]
Subtracting [tex]2 \times 10^{(n+5)[/tex] frοm bοth sides:
[tex]4.02 \times 10^5 = 4.02 \times 10^n[/tex]
Dividing bοth sides by 4.02:
[tex]10^5 = 10^n[/tex]
Therefοre, n = 5.
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COMPLETE QUESTION-
if [tex](2\times10^n)+(4.02\times10^5)[/tex], what is n?
1. FINANCIAL LITERACY Mika invests $1400 in an account with a 2% annual simple
interest rate, making no other deposits or withdrawals. What will his account
balance be after 6 months? 2 years?
2. FINANCIAL LITERACY Ardella invests $3100 in an account with a 3.2% annual
interest rate compounded monthly, making no other deposits or withdrawals.
What will Ardella's account balance be after 1 year? 3 years?
3. FINANCIAL LITERACY Marquis borrows $900 with a 3.8% annual interest rate
compounded continuously. If he does not make any payments, how much will
Marquis owe after 2 months? 18 months?
Example 4
4. FINANCIAL LITERACY Trina wants to invest $5000 at a bank offering three
different accounts. Account A earns 2.2% annual simple interest, Account B earns
2.2% interest compounded annually, and Account C earns 2.2% interest
compounded continuously. If no other deposits or withdrawals are made,
compare the balances of the accounts after each period of time.
a. 6 months
b. 1 year
c. 3 years
After answering the presented question, we can conclude that Account B: $5463.84 ($5000 multiplied by 1.0223) $5474.60 in Account C ($5000 x e(0.022 x 3))
what is interest ?In mathematics, interest is the amount of money earned or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest every year for three years, for a total of $15.
Mika's account balance after 6 months would be $1413.33 ($1400 + $14.67 interest generated). His account balance after two years would be $1456 ($1400 + $56 interest earned).
Marquis would repay $907.02 after two months ($900 x e(0.038/12 x 2)). He would owe $1,033.72 after 18 months ($900 x e(0.038 x 1.5)).
a. 6 months later:
Account A: $5050 ($5000 + $55 earned in interest)
Account B: $5061 ($5000 multiplied by 1.0220.5).
$5061.68 in Account C ($5000 x e(0.022 x 0.5))
c. One year later:
Account A: $5100 ($5000 + $110 earned in interest)
Account B: $5112.20 ($5000 multiplied by 1.022).
$5113.85 in Account C ($5000 x e(0.022 x 1))
c. After three years:
Account A: $5330 ($5000 + $330 generated interest)
Account B: $5463.84 ($5000 multiplied by 1.0223)
$5474.60 in Account C ($5000 x e(0.022 x 3))
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can someone please help
Answer:
The circle x^2+y^2-2x-8y+17=0 has translated 5 units to the leftand 2units down.
Step-by-step explanation:
If we translate this circle to the left 5 units, and 2 units down,
we will subtract 5 from the center x coordinate and 2 for the center y coordinate
The center is (1,-4)
So the new center prime is (-4,-6)
Since a translation keep angles and measures,
Our radius will remain untouched so our new equation is
[tex](x + 4) {}^{2} + (y + 6) {}^{2} = 16[/tex]
During a sale, the price of all computers in a store is being reduced by 25%. Albert is interested in a computer with an original cost of $650. Two weeks later, the sale price of this computer is reduced by an additional 5%. Albert thinks he can now get the computer for 30% off the original price. Find the sale price after the double reduction, and then the sale price after a single reduction of 30%. Is the double reduction (25% off and then 5% off) the same as or different than the single reduction (30% off)?
The sale price of the computer after a single reduction of 30% is $455.
The double reduction (25% off and then 5% off) and the single reduction of 30% are different.
The sale price after the double reduction is $463.13, while the sale price after a single reduction of 30% is $455.
What is a percentage?
The percentage is a way of expressing a fraction or proportion out of 100. It is commonly used in many different areas such as finance, math, science, and everyday life.
First, we need to find the sale price of the computer after the double reduction.
When the price of all computers in the store is reduced by 25%, the sale price of the computer that originally cost $650 becomes:
Sale price after first reduction ,
=> 650 - 25% 0f 650
=> 650 - [tex]\frac{25}{100}\times[/tex]650 = $ 487.5
Then, when the sale price is reduced by an additional 5%, the sale price of the computer becomes:
Sale price after double reduction
=> 487.5 - 5% of 487.5
=> 487.5 - [tex]\frac{5}{100}\times[/tex]487.5 = $463.13
Therefore, the sale price of the computer after the double reduction is $463.13.
Next, we need to find the sale price of the computer after a single reduction of 30%.
When the original cost of the computer is reduced by 30%, the sale price becomes:
Sale price after single reduction ,
=> 650- 30% of 650
=> 650 - [tex]\frac{30}{100}\times[/tex] = $455
Therefore, the sale price of the computer after a single reduction of 30% is $455.
The double reduction (25% off and then 5% off) and the single reduction of 30% are different.
The sale price after the double reduction is $463.13, while the sale price after a single reduction of 30% is $455.
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HELPPPPPPPPPPPO!!!!!!!!!
Answer:
C
Step-by-step explanation:
Lauri spent 5% of x hours at her part-time job. What is x if 5% of x is about 10 hours? Explain how you estimated and which property of equality you used to find x.
To estimate x, we can use the fact that 5% is approximately equal to 1/20. Therefore, if 5% of x is about 10 hours, then we can estimate that 1/20 of x is also about 10 hours.
Multiplying both sides of the equation 1/20 x = 10 by 20, we get x = 200.
To check our answer, we can verify that 5% of 200 hours is indeed about 10 hours.
We used the multiplication property of equality to solve for x, which states that we can multiply both sides of an equation by the same non-zero number without changing the solution. In this case, we multiplied both sides by 20.