The equation of a straight line is
y = mx + c
4x + 20y = -180
make 20y the subject of the formula
20y = -180 - 4x
20y = -4x - 180
divide all through by 20
20y/20 = -4x/20 - 180/20
y = -1/5x - 9
The answer is y = -1/5x - 9 where your slope is -1/5 and intercept is -9
Consider the function y = f(x) shown at right, trace each interval where the function behavior is A. Increasing, using a GREEN pencil Identify the interval(s) ___B. Decreasing, using a RED pencil Identify the interval(s) ___ C. Constant, using a YELLOW pencil Identify the interval(s) ___ D. State the Domain of the function ___ E. State the Range of the function ___ F. What thoughts do you have about the intervals stated above? Did you use brackets (closed/included points) or parentheses (open/non-included points)? Why or why not?
You have a function f(x). To identify the increasing interval and decreasing interval of f(x), you consider that an increasing interval is determined by the values of x in which the value of f(x) increases. For the decreasing interval you focus on the values of x in which the values of f(x) decreases.
You can notice in the given graph:
The increasing interval is (-8 , -4) U (3 , 6)
The decreasing interval is (-4 , -2)
The constant interval is (-2 , 3)
The domain of the function is (-8 , 6)
The previous interval is given by the available values of x
The range of the function is (-4 , 8)
The previos interval is given by the values of f(x) for the values of x in the domain.
The following image is a sketch of the graph with the respective intervals.
The vertices of a figure are A(1, -1), B(5, -6), and C(1, - 6). Rotate the figure 90° counterclockwise about the origin. Find the coordinates of the image. Polygon
A'(1,1)
B' (6,5)
C' (6,1)
Explanation
Step 1
Let
A(1,-1)
B(5,-6)
C(1,-6)
Step 2
find the image (A'B'C')
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
Hence
[tex]\begin{gathered} A\mleft(1,-1\mright)\rightarrow A^{\prime}(1,1) \\ B(5,-6)\rightarrow B^{\prime}(6,5) \\ C(1,-6)\rightarrow C^{\prime}(6,1) \end{gathered}[/tex]so, the coordinates of the image are
A'(1,1)
B' (6,5)
C' (6,1)
I hope this helps you
Which two ratios are NOT equal? 1:6 and 3:18 OB. 2:14 and 3:42 OC. 12:6 and 2:1 OD 3:11 and 6:22
Let's check the ratios:
[tex]\begin{gathered} \frac{1}{6} \\ \text{and} \\ \frac{3}{18} \\ \end{gathered}[/tex]First one is already reduced. Let's reduce the 2nd fraction by dividing top and bottom by 3, so
[tex]\frac{3}{18}=\frac{1}{6}[/tex]So, they are equal.
Next ratio:
[tex]\begin{gathered} \frac{2}{14}\text{and}\frac{3}{42} \\ \end{gathered}[/tex]Let's divide both top and bottom by 2 (1st fraction) and top and bottom by (3) in 2nd fraction:
[tex]\begin{gathered} \frac{2}{14}=\frac{1}{7} \\ \text{and} \\ \frac{3}{42}=\frac{1}{14} \end{gathered}[/tex]They aren't equal. So, we have already found our answer.
OB. 2:14 and 3:42 --- is our answer.
Cassie’s latest financial goal is to eliminate her credit card debt
Based on Cassie's financial goal to eliminate her credit card debt, the graph that would best model her situation in terms of scale and label is B. X-axis scale, 0-12; label, Months y-axis scale, 0-8,000; label, Total Debt ($)
How to model a graph?When modeling a graph, the time period is often the independent variable. This means that the time period which are in months (months that Cassie makes monthly payments) need to be on the x-axis and will be labelled from 0 to 12 months for the months of the year.
The amount of credit card debt would then be on the y-axis. It is best to have a scale that is larger than the maximum debt Cassie has to that the data can be included properly. So a limit of 0 - 8,000 is best and would properly incorporate the $5,000 she already owes.
Full question is:
Cassie's latest financial goal is to eliminate her credit card debt. She has about $5,000 in credit card debt. She determines that she can afford to make
monthly payments of about $500. To track her progress, she plans to create a graph to model her situation. How should Cassie label and scale her
graph?
A.X-axis scale, 0-8; label, Total Debt ($) y-axis scale, 0-5,000; label, MonthsB. X-axis scale, 0-12; label, Months y-axis scale, 0-8,000; label, Total Debt ($)C. X-axis scale, 0-8; label, Years y-axis scale, 0-5,000; label, Total Debt ($)D. x-axis scale, 0-12; label, Total Debt ($) y-axis scale, 0-8,000; label, YearsFind out more on models at https://brainly.com/question/22049822
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A circle has a radius of .10 in. Find
the increase in area when the radius is increased by 2 in. Use
3.14 for
The increase in area of the circle when the radius is increased by 2 is 13.8 in.
How to calculate area of circle?Area of a circle can be described as the region that is been taken by the circle.
The area of the circle can be expressed as A=πr^2
We were told that the radius of the circle is been given as 0.10 in.
Then we can calculate the are of the circle by input the given radius into the formula above as:
A=πr^2
r= radius of the circle
A= area of the circle
A=3.14 (0.10)^2 =0.0314 in.
Then we were told that the radius is increased by 2 in.
Then the area of the circle will now be A=3.14* (2.10)^2 =13.85 in.
Then the the increase in area can be calculated as : (13.85 in. - 0.0314 in.) = 13.8 in.
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which of the following lines are parallel, skew, intersection, or none of these.
Parallel lines are lines that have the same direction and there is always the same distance between them
Skew lines are lines that are not on the same plane (they are not coplanar) and also they do not intersect.
Intersecting lines are lines that cross at a point, they can be on the same plane or on different planes.
Let's analyze the parts of this problem.
DE and AB.
These two lines are shown in red and blue in the following diagram:
These are not parallel lines because one line is vertical and the other line is horizontal. They are also not intersecting lines because they do not cross at any point. Lines DE and AB are skew lines because they do not intersect and they are on different planes.
--> DE and AB --> skew
CB and
What is the median of the data set 4 7 9 10 5 12 6
The median is the value of the data set that separates the sample in halves.
To determine the median of a determined data set, you have to calculate its position.
The given sample has n=7 elements, to determine the position of the median given that the data set is odd, you have to use the following formula:
[tex]\text{PosMe}=\frac{1}{2}(n+1)[/tex]Replace it with n=7
[tex]\begin{gathered} PosMe=\frac{1}{2}(7+1) \\ \text{PosMe}=\frac{1}{2}\cdot8 \\ \text{PosMe}=4 \end{gathered}[/tex]This result indicates that the media is the fourth observation of the data set.
Next, you have to order the data set from least to greatest:
Original data set: 4, 7, 9, 10, 5, 12, 6
Ordered from least to greatest: 4, 5, 6, 7, 9, 10, 12
Once the data set is ordered, you have to count starting from the left until you reach the fourth observation:
O4, 5, 6, 7, 9, 10, 1
The fourth value of the data set is 7, which means that the median of the data set is 7.
Median=7
2
A store is having a " 15 % off sale on perfume . You have a coupon for 50 % off any perfume . What is the final price , in dollars , of a $ 30 bottle of perfume ? If necessary round your answer to the nearest cent .
ANSWER
$12.75
EXPLANATION
The store is selling the perfumes at 15% off the original price, so if a bottle of perfume costs $30, then they are selling it at,
[tex]30\cdot\frac{100-15}{100}=30\cdot\frac{85}{100}=30\cdot0.85=25.50[/tex]But you also have a coupon for 50% off, so you get to buy the perfume at half that price,
[tex]25.50\cdot\frac{50}{100}=25.50\cdot0.5=12.75[/tex]Hence, the final price of the perfume is $12.75.
use a power reducing formula to to simplify 20cos^4x
We can replace trigonometric terms in formulas with trigonometric terms of smaller powers using the trigonometric power reduction identities. This is significant for using calculus to integrate the powers of trigonometric expressions, among other applications.
Explain about the power reducing?2cos2 will be equal to 1 plus cos 2. We arrive at an equation for cos2 by dividing by 2. Because they enable us to reduce the power on one of the trig functions when the power is an even integer, these are commonly referred to as "power reduction formulae."
An integral problem can be solved using a reduction formula by first breaking it down into simpler integral problems, which can then be broken down into simpler problems, and so on.
P = E/t is the equation, where P stands for power, E for energy, and t for time in seconds. According to this equation, power is defined as the amount of energy consumed per unit of time.
The Equivalent expression for Cos 4x= 8cos4(x) - 8 cos2(x) + 1.
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Compute the percent of profit or loss on shares of stock purchased at8.625 and sold at 10.75.
ANSWER:
24.63%
STEP-BY-STEP EXPLANATION:
The first thing is to mention that it is a profit because it was bought at a lower amount than it was sold, therefore
We take 100% as the lowest value, and thus we calculate the profit percentage
[tex]10.75\cdot\frac{100}{8.625}=124.63[/tex]Then the difference between both percentages is the profit percentage
[tex]124.63-100=24.63[/tex]Please show formula and explain work in 6th grade format
The surface area of a pyramid is given as:
[tex]SA=\frac{1}{2}pl+B[/tex]where p is the perimeter of the base, l is the slant height and B is the area of the base.
In this case the slant height is 4 in.
Now, since the base is a square which sides that has length 5 in. then the perimeter is:
[tex]p=4\cdot5=20[/tex]The area of the base is the length of the side squared, then we have:
[tex]B=5^2=25[/tex]Once we know the values we plug them in the formula, then we have:
[tex]\begin{gathered} SA=\frac{1}{2}(20)(4)+25 \\ SA=40+25 \\ SA=65 \end{gathered}[/tex]Therefore the surface area is 65 squared inches.
Write this ratio as a fraction in simplest form without any units.75 minutes to 1 hourYou can use the table below to help convert the units.1 minute = 60 seconds1 hour = 60 minutes-1 day = 24 hours1 week = 7 days0
To get an unitless ratio, both of our quantities have to be in the same units. Let's convert that hour into minutes:
[tex]1h\rightarrow60\min [/tex]Thereby, our ratio would be:
[tex]\frac{75\min }{60\min }\rightarrow\frac{5}{4}[/tex]A If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
we have
y=x+2
y=-2x+8
Solve the system of equations
equate both equations
x+2=-2x+8
x+2x=8-2
3x=6
x=2
Find the value of y
y=(2)+2
y=4
the solution is (2,4)
that means
(2,4) is a common point , that satisfy both equations
Solve for "x":3x - 5 < -14 or 2x - 1 > 7
We are given the following inequalities:
[tex]\begin{gathered} 3x-5<-14,(1)\text{ or} \\ 2x-1>7,(2) \end{gathered}[/tex]First, we will solve for inequality 1. To do that we will add 5 to both sides:
[tex]3x-5+5<-14+5[/tex]Solving the operations:
[tex]3x<-9[/tex]Now we divide both sides by 3:
[tex]\frac{3x}{3}<-\frac{9}{3}[/tex]Solving the operations:
[tex]x<-3[/tex]Now we solve for "x" in inequality (2). To do this we will add 1 to both sides:
[tex]2x-1+1>7+1[/tex]Solving the operations:
[tex]2x>8[/tex]Now we divide both sides by 2:
[tex]\frac{2x}{2}>\frac{8}{2}[/tex]Solving the operations:
[tex]x>4[/tex]Therefore, the solution to the system is:
[tex]x<-3\text{ or x > 4}[/tex]Which of the binomials below is a factor of this trinomial?x^2 - 13x + 42A. x + 84B. x - 7C. x^2 +12D. x + 7
Given the following trinomial:
[tex]x^2-13x+42[/tex]To factor the trinomial, we need two numbers the product of them = 42
And the sum of them = -13
Two of the numbers of factors of 42 = -6, and -7
So, the factor of the trinomial will be as follows:
[tex]x^2-13x+42=(x-6)(x-7)[/tex]So, the answer will be option B. x - 7
A machinist must follow part drawing with scale 1 to 16. Find the dimensions (in inches) of the finished stock shown in the figure. That is find the lengths A, B, C, and D.
Length of the dimensions of the finished stock shown are as follow:
A = 13/4 inches , B = 3/4 inches , C =5/2 inches , D = 3/16 inches.
As given in the question,
Mechanist must follow part drawing with scale 1 to 16.
Dimensions of the finished stock shown in the figure
A represents the length .
B represents the height
C represents the length
D represents the height
Length of A is
= 3 1/4 inches
= 13 /4 inches
Height of B is
=3/4 inches
Length of C is
= 2 1/2 inches
= 5/2 inches
Height of D is
= 3/16 inches
Therefore, length of the dimensions of the finished stock shown are as follow: A = 13/4 inches ,B = 3/4 inches ,C =5/2 inches , D = 3/16 inches.
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A square has side length (2x+3). The perimeter is 60cm. Find the length of one side in centimetres
As given by the question
There are given that the side length is (2x+3) and perimeter is 60 cm.
Now,
From the formula of perimeter:
[tex]\text{Perimeter =4}\times side[/tex]So,
[tex]\begin{gathered} \text{Perimeter =4}\times side \\ 60=4\times(2x+3) \\ 60=8x+12 \\ 8x=60-12 \\ 8x=48 \\ x=\frac{48}{8} \\ x=6 \end{gathered}[/tex]Then,
Put the value of x into the given side length (2x+3)
So,
[tex]\begin{gathered} 2x+3=2\times6+3 \\ =12+3 \\ =15 \end{gathered}[/tex]Hence, the one side of length is 15 cm.
Which ratio table shows equlvalent ratios? O First Quantity 63 Second Quantity 8 5 o First Quantity Second Quantity 15 4 22 First Quantity Second Quantity 6 3 First Quantity 2.1 Second Quantity 4 2
we are asked to determine which ratios are equivalent. For ratios to be equivalent the quotient of the ratios must be the same. For the ratios:
[tex]\frac{2}{4},\frac{1}{2}[/tex]If we take 2/4 and divide the numerator and denominator by 2 we get:
[tex]\frac{\frac{2}{2}}{\frac{4}{2}}=\frac{1}{2}[/tex]Since we got the same fraction that means that the ratios are equivalent.
A chemist needs to mix a 12% acid solution with a 20% acid solution to obtain 160 ounces of a 15% acid solution. How many ounces of each of the acid solutions must be used?
Answer:
100 ounces of 12% solution and 60 ounces of the 20% solution.
Step-by-step explanation:
Let x ounces be the amount of 12% solution, then there will be 160-x ounces of the 20% solution.
So, we have the equation:
0.12x + 0.20(160 - x) = 0.15* 160
0.12x - 0.20x + 32 = 24
-0.08x = -8
x = 100.
So, it is 100 ounces of 12% solution and 60 ounces of the 20% solution.
Which of the following represents the set of possible rational roots for thepolynomial shown below?2x3 + 5x2 - 8x - 20 = 0oa{=}, +2, +1, +2, +3, +3 + 1}O B. {+1, +2, +4, +5, +10, 20}O a {, +1, +2 +3 +4, + 3, +10, +20)02 (1.1,2,3,4,5,10,20)
We will have that the set of rational roots for the expression will be:
[tex]\mleft\lbrace\pm\frac{1}{2},\pm1,\pm2,\pm\frac{5}{2},\pm4,\pm5,\pm10,\pm20\mright\rbrace[/tex][Option C].
A tourist from the U.S. is vacationing in China. One day, he notices that has cost 6.84 yuan per liter. On the same day, 1 yuan is worth 0.14 dollars. How much does the gas cost in dollars per gallon? Fill in the two blanks on the left side of the equation using two of the ratios. THEN WRITE THE ANSWER ROUNDED TO THE NEAREST HUNDREDTH. Will send pic of question.
Solve:
[tex]\frac{6.84\text{ yuan}}{1\text{ L}}\times\frac{0.14\text{ dollars}}{1\text{ yuan}}\times\frac{3.79\text{ L}}{1\text{ gal}}=3.63\frac{dollars}{gal}[/tex]Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (-6, -6); y=-2x+4
Answer:
y = 2x + 6
Step-by-step explanation:
Parallel lines have the same slope, so the slope is 2.
y = mx + b
When need the slope which is given to be 2
We will use the point given (-6,-6) for an x and y on the line
m= 2
x -= -6
y = -6
y=mx+ b
-6 = 2(-6) + b Sole for b
-6 = -12 + b Add 12 to both sides
6 = b
y = 2x + 6
Write the expression as a product of two factors. 12s + 10 + 6y
to write the expression as a product between two factors you must identify the common factor between all the terms in tis case the common factow will be 2
[tex]12s+10+6y=2\cdot(6s+5+3y)[/tex]The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (-5.3, 1). The finishing point will be at(1, -5.3). Quadranto Quadrant P Quadrant Quadrants Part A: Use the grid to determine in which quadrants the starting point and the finishing point are located. Explain how you determined the locations. (6 points) Part B: A checkpoint will be at (5.3, 1). In at least two sentences, describe the difference between the coordinates of the starting point and the checkpoint, and explain how the points are d. (4 points)
The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (-5.3, 1). The finishing point will be at(1, -5.3). Quadranto Quadrant P Quadrant Quadrants Part A: Use the grid to determine in which quadrants the starting point and the finishing point are located. Explain how you determined the locations. (6 points) Part B: A checkpoint will be at (5.3, 1). In at least two sentences, describe the difference between the coordinates of the starting point and the checkpoint, and explain how the points are d. (4 points)
Part A
we have
starting point of the race is (-5.3, 1)
the x-coordinate is negative and the y coordinate is ;positive
that means-------> is located on quadrant Q
finishing point is (5,3, 1)
x-coordinate is postive and y coordinate is positive
that means -----> is located on Quadrant P
Answer:
Step-by-step explanation:
part A
find the slope and y intercept, then write out the linear equation (y=mx+b) below
Answer:
y = 2x + 3
Step-by-step explanation:
You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.
Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.
The slope is 2. Fill in 2 in place of m in
y = mx + b
y = 2x + b
Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.
y = 2x + 3
keisha is an avid reader. One day she read for 8 hours. She read a total of 600 pages during that time. How many pages did keisha read per minute?
To find the number of page she read per minute
First let's chenge the 8 hours to minute
8 hours = 8 x 60 = 480 min
Since she read 600 pages
Number of pages read per min = 600/ 480
=1.25 pages
Hi I have a meeting at my house in about
The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.
The function is given to be:
[tex]T(t)=Ate^{-kt}[/tex]where A and k are positive constants.
We can find the derivative of the function as follows:
[tex]T^{\prime}(t)=\frac{d}{dt}(Ate^{-kt})[/tex]Step 1: Pull out the constant factor
[tex]T^{\prime}(t)=A\cdot\frac{d}{dt}(te^{-kt})[/tex]Step 2: Apply the product rule
[tex]\frac{d(uv)}{dx}=u \frac{dv}{dx}+v \frac{du}{dx}[/tex]Let
[tex]\begin{gathered} u=t \\ v=e^{-kt} \\ \therefore \\ \frac{du}{dt}=1 \\ \frac{dv}{dt}=-ke^{-kt} \end{gathered}[/tex]Therefore, we have:
[tex]T^{\prime}(t)=A(t\cdot(-ke^{-kt})+e^{-kt}\cdot1)[/tex]Step 3: Simplify
[tex]T^{\prime}(t)=A(-kte^{-kt}+e^{-kt})[/tex]QUESTION A
At t = 0, the instantaneous rate of change is calculated to be:
[tex]\begin{gathered} t=0 \\ \therefore \\ T^{\prime}(0)=A(-k(0)e^{-k(0)}+e^{-k(0)}) \\ T^{\prime}(0)=A(0+e^0) \\ Recall \\ e^0=1 \\ \therefore \\ T^{\prime}(0)=A \end{gathered}[/tex]The rate of change is:
[tex]rate\text{ }of\text{ }change=A[/tex]QUESTION B
At t = 30, the instantaneous rate of change is calculated to be:
[tex]\begin{gathered} t=30 \\ \therefore \\ T(30)=A(-k(30)e^{-k(30)}+e^{-k(30)}) \\ T(30)=A(-30ke^{-30k}+e^{-30k}) \\ Collecting\text{ }common\text{ }factors \\ T(30)=Ae^{-30k}(-30k+1) \end{gathered}[/tex]The rate of change is:
[tex]rate\text{ }of\text{ }change=Ae^{-30k}(-30k+1)[/tex]QUESTION C
When the rate of change is equal to 0, we have:
[tex]0=A(-kte^{-kt}+e^{-kt})[/tex]We can make t the subject of the formula using the following steps:
Step 1: Apply the Zero Factor principle
[tex]\begin{gathered} If \\ ab=0 \\ a=0,b=0 \\ \therefore \\ -kte^{-kt}+e^{-kt}=0 \end{gathered}[/tex]Step 2: Collect common terms
[tex]e^{-kt}(-kt+1)=0[/tex]Step 3: Apply the Zero Factor Principle:
[tex]\begin{gathered} e^{-kt}=0 \\ \ln e^{-kt}=\ln0 \\ -kt=\infty \\ t=\infty \end{gathered}[/tex]or
[tex]\begin{gathered} -kt+1=0 \\ -kt=-1 \\ t=\frac{-1}{-k} \\ t=\frac{1}{k} \end{gathered}[/tex]The time will be:
[tex]t=\frac{1}{k}[/tex]how does the common ratio and ratio of the perimeters of FDE to CAB compare
Answer
The common ratio and the ratio of the perimeters of the two triangles are exactly the same (2/3).
Explanation
The common ratio is obtained by expressing corresponding sides as a fraction of each other.
The common ratio for this triangles = (8/12) = (6/9) = (12/18) = (2/3)
Perimeter is expressed as the sum of all the exterior dimensions of a figure.
For the first figure, Perimeter = 8 + 6 + 12 = 26 inches
For the second figure, Perimeter = 12 + 9 + 18 = 39 inches
Ratio of perimeters = (26/39) = (2/3)
Hope this Helps!!!
The Editor-in-Chief of the student newspaper was doing a final review of the articles submitted for the upcoming edition. Of the 12 total articles submitted, 5 were editorials. If he liked all the articles equally, and randomly selected 5 articles to go on the front cover, what is the probability that exactly 3 of the chosen articles are editorials? Write your answer as a decimal rounded to four decimal places.
This is a problem of binomial probability. We have two possible outcomes:
• the article selected is an editorial,
,• the article selected is not an editorial.
The probability of success (select an article that is an editorial) is:
[tex]p=\frac{5}{12}[/tex]Because we have 12 total articles submitted, and 5 of them were editorials.
To calculate the probability that selecting 5 random articles, getting as a result that exactly 3 of the chosen articles are editorials, we use the binomial probability formula:
[tex]P(n,x)=C(n,x)\cdot p^x\cdot(1-p)^{n-x}[/tex]Where:
• n = the number of trials = the number of articles selected randomly = 5,
,• x = the number of success = the number of editorials that we expect = 3,
,• p = the probability of getting an editorial = 5/12,
,• C(n,x) = n! / (x! (n-x)!).
Replacing the data in the formula above, we get:
[tex]P(n=5,x=3)=\frac{5!}{3!\cdot(5-3)!}\cdot(\frac{5}{12})^3\cdot(1-\frac{5}{12})^{5-3}\cong0.24615=0.2462[/tex]Answer
Rounded to four decimal places, the probability that exactly 3 of the chosen articles are editorials is 0.2462.
jonathans science class places weights on a scale during an experiment. each weight weighs 0.2 kilograms. if the class puts 16 weights on the scale at the same time, what will the scale read?
Given the scale reading:
Each weight weighs 0.2 kilograms
If the class put 16 weights on the scale
Then the scale reading will be
[tex]\begin{gathered} 1\text{ weight -}\longrightarrow\text{ 0.2 kg} \\ 16\text{ weight -}\longrightarrow\text{ x} \\ x=16\times0.2 \\ x=3.2\operatorname{kg} \end{gathered}[/tex]Hence the scale reading will be 3.2kg