(a) To find the probability that a randomly selected adult who visited a therapist during the past year also used antidepressants, we use the formula:
P(A|B) = P(A and B) / P(B)
where A is the event that an adult used antidepressants, and B is the event that an adult visited a therapist. We are given:
P(A) = 0.43
P(B) = 0.27
P(A and B) = 0.20
Plugging these values into the formula, we get:
P(A|B) = 0.20 / 0.27 ≈ 0.74
Therefore, the probability that a randomly selected adult who visited a therapist during the past year also used antidepressants is approximately 0.74.
(b) To find the probability that an adult visited a therapist during the past year, given that he or she used antidepressants, we use Bayes' theorem:
P(B|A) = P(A|B) * P(B) / P(A)
where A and B are defined as before. We have already calculated P(A|B) and P(B), and we know:
P(A) = 0.43
Plugging these values into Bayes' theorem, we get:
P(B|A) = (0.74 * 0.27) / 0.43 ≈ 0.47
Therefore, the probability that an adult visited a therapist during the past year, given that he or she used antidepressants, is approximately 0.47.
The Pickle Family had 10 1/2 pounds of candy to fill 4 pinatas. Each pinata would have 6 kids sharing the candy that fell from it. How much candy would each child get?
Each child would get 7/8 of a pound of candy from each pinata.
To find out how much candy each child would get, we need to first determine the total amount of candy in all four pinatas, and then divide that amount by the total number of kids who will be sharing the candy.
To start, we can convert the 10 1/2 pounds of candy into a mixed fraction:
10 1/2 = 10 + 1/2 = 20/2 + 1/2 = 21/2
So the Pickle Family had 21/2 pounds of candy to fill the pinata.
To find out how much candy each piñata would have, we can divide the total amount of candy by the number of piñatas:
21/2 ÷ 4 = 21/2 × 1/4 = 21/8
So each pinata would have 21/8 pounds of candy.
Now we need to determine how much candy each child would get. Since each pinata will be shared among 6 kids, we can divide the amount of candy in each pinata by 6:
21/8 ÷ 6 = 21/8 × 1/6
= 7/8
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the radius of a sphere was measured and found to be 21 cm with a possible error in measurement of at most 0.03 cm. what is the maximum error in using this value of the radius to compute the volume of the sphere?
The maximum error in using the value of the radius to compute the volume of the sphere is approximately 554.86 cubic centimeters.
What is sphere ?
A sphere is a three-dimensional shape that is perfectly round, with all points on the surface at an equal distance from the center.
The formula for the volume of a sphere is given by V = (4/3)πr³, where r is the radius of the sphere.
The maximum error in the measurement of the radius is given as 0.03 cm. Therefore, the actual radius of the sphere can be anywhere between 20.97 cm (21 - 0.03) and 21.03 cm (21 + 0.03).
To find the maximum error in using this value of the radius to compute the volume of the sphere, we need to find the maximum possible difference in the volumes calculated using these two values.
So, we can calculate the volume of the sphere using the maximum and minimum values of the radius as follows:
V_max = (4/3)π(21.03)³
V_min = (4/3)π(20.97)³
Now, we can find the difference between these two values to get the maximum possible error:
Max error = V_max - V_min
Max error = (4/3)π(21.03)³ - (4/3)π(20.97)³
Max error ≈ 554.86 cubic centimeters
Therefore, the maximum error in using the value of the radius to compute the volume of the sphere is approximately 554.86 cubic centimeters.
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Linda's Dog Walking Service
Cost ($)
5 8 8 8 8
50
30
20
0
20 40 60 80 100 120
# of minutes
According to the graph the value of the Dog Walking Service would be $0.75 per minute.
How to know the value per minute of Linda's service?To know the value per minute of the Dog Walking Service offered by Linda we must carry out the following mathematical procedure:
Rule of three.If every 20 minutes is worth $15, how much is each minute worth?
To do this we must follow the following rule of three:
20 minutes = $151 minute = ?1 * 15 / 20 = $0.75Additionally, we must take into account that according to the graph, the value per minute decreases if we contract more hours of service. For example, with 40 minutes of service it would be worth 0.5 each minute.
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what is the 95 % conversion in decimal ?
The 95 % conversion in decimal is 0.95.
To convert a percentage to a decimal, you divide the percentage by 100.
Therefore, to convert 95% to a decimal, you divide 95 by 100:
95 ÷ 100 = 0.95
So, 95% as a decimal is 0.95.
A percentage is a fraction expressed as a fraction of 100 in mathematics. It is frequently used to express percentages, rates, or frequencies in terms of 100. For example, if 95 out of 100 people agree on something, we can express this as a 95% probability.
To convert a percentage to a decimal, simply divide it by 100. The outcome is a number between 0 and 1, with 1 representing the entire (or 100%). In the case of 95%, dividing by 100 yields 0.95 as the decimal equivalent.
Simply multiply a decimal by 100 to convert it to a percentage. To convert 0.95 to a percentage, multiply it by 100 to get:
0.95 x 100 = 95%
As a result, percentages and decimals are two different ways of representing the same value. While percentages are frequently used to express proportions or rates, decimals are frequently used in mathematical computations or scientific notation.
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An angle measures 120.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
the angle measures 59.9°, and its supplementary angle measures 180° - 59.9° = 120.1°.
Step-by-step explanation:
Let x be the measure of the angle we are trying to find.
By definition of supplementary angles, we know that the angle's supplementary angle measures 180° - x.
We are also given that the angle measures 120.2° less than its supplementary angle. This can be written as:
x = (180° - x) - 120.2°
Simplifying the equation, we get:
x = 59.9°
Therefore, the angle measures 59.9°, and its supplementary angle measures 180° - 59.9° = 120.1°.
Are the two triangles similar?
Yes or no?
How do you know?
Step-by-step explanation:
yes, they are, because both triangles have the same 3 angles :
the right angle = 90°
65°
25°
now, the side lengths can be different, but because of the same angles, the ratio between the corresponding side lengths will be the same for all sides (e.g. if one pair of sides has the scaling factor of 3 from the smaller to the larger triangle, then the other pairs will also have the same scaling factor 3).
that is the difference between equivalent and similar : for "equivalent" also the side lengths must be the same.
for "similar" only the angles need to be the same.
pls help with this homework question
Answer:
h = 12 feet
Step-by-step explanation:
using the right triangle shown in the diagram.
the base of the triangle is half the measure of the base of the square side.
then base of triangle = [tex]\frac{1}{2}[/tex] × 32 = 16 feet and hypotenuse = 20 feet
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
h² + 16² = 20²
h² + 256 = 400 ( subtract 256 from both sides )
h² = 144 ( take square root of both sides )
h = [tex]\sqrt{144}[/tex] = 12
the height h of the pyramid is 12 feet
What is 729 cube rooted?
The value of 729 cube root is 9.
The cube root function is important in various mathematical applications, including calculus, geometry, and physics.
The cube root of 729 is the number that when multiplied by itself three times, results in 729. This number is often represented as the symbol ³√729.
In other words, if we cube the cube root of 729, we get back the original number 729. The cube root of 729 is 9, since 9 x 9 x 9 = 729.
In mathematical terms, the cube root of 729 can be expressed as: ³√729 = 9.
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To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted
the number of trees with diameters exceeding 12 inches in each square. The data are listed here.
O
Relative Frequency
Relative Frequency
7
9
2
11
9
7
X+S
9
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
8
x + 2s
9
x + 3s
H
Need Help?
7 4 8 10
1
6
5
10
8
748
10 8
USE SALT
5. 526
8
4
9
8
7
(a) Construct a relative frequency histogram to describe the data.
Frequency of lumber
5
Interval
Read It
3. 382 to 11. 961
6
06 9
11 10 11 8 8 10 8 8 12
1. 237 to 14. 106
7
7
11
8 8 10
9
9560
Frequency of lumber
L
77
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
7 8
to 9. 816
7 7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
7 7
10 10 7 4 8 7
(c) Calculates for the data. (Round your answer to three decimal places. )
S = 2. 145
✔timber trees
(b) Calculate the sample mean x as an estimate of μ, the mean number of trees for all 50-by-50-foot squares in the tract.
(Round your answer to three decimal places. )
X = 7. 671
timber trees
Construct the intervals x ±s, x ± 2s, and X + 3s. Calculate the percentage of squares falling into each of the three intervals,
and compare with the corresponding percentages given by the Empirical Rule and Tchebysheff's Theorem. (Round your
interval values to three decimal places. Round actual percentages to two decimal places. )
Actual Percentage
Relative Frequency
X %
Relative Frequency
X %
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
X %
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
Frequency of lumber
7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
Frequency of lumber
at least 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
Tchebysheff
at least 75%
at least 89%
%
95
Empirical
≈ 68%
≈ 99. 7%
%
The amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted the number of trees with diameters exceeding 12 inches in each square is 16.67
In order to estimate the amount of lumber in a tract of timber, an owner will use a technique called sample size estimation.
By using this data, the owner can then calculate an estimate of the total amount of lumber present in the tract of timber.
In this case, the sample size is 70, the square size is 2500 square feet, and the diameter of the trees is 12 inches. Therefore, the formula becomes:
=> Total Trees = (Number of Trees in Sample / 70) x (2500 / 12).
If we plug in the number of trees counted in each square, we can find the total estimated number of trees in the tract of timber.
If the owner counted 7 trees in the first square, the formula would be
=> (7 / 70) x (2500 / 12) = 16.67.
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Complete Question:
To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here.
7 9 8 10 3 7 7 9 9 11 7 9 5 5 10 10 9 8 2 8 5
etermine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Weight of subject (kg) Choose the correct answer below. O A. The ordinal level of measurement is most appropriate because the data can be ordered, but differences (obtained by subtraction) cannot be found or are meaningless. OB. The nominal level of measurement is most appropriate because the data cannot be ordered. OC. The ratio level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is a natural zero starting point. OD. The interval level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, but there is no natural zero starting point.
The correct option is (A) The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.
The ordinal level of measurement is most commonly used when dealing with data that can be ordered, but the differences b/w the data points are not significant or cannot be determined. This type of data is commonly used when looking for ranking or grading data.
For example In customer satisfaction surveys, or when categories are assigned values, like when a student's performance in a class is assigned a letter grade. With the ordinal data, the values are ordered in a meaningful way, but the differences between the values are not necessarily significant.
For example, if you assign a letter grade to a student's performance, difference between an A and a B is not importantly difference among C and D. This type of data is useful for finding a quick and easy way to compare data points, but this gives no information about the actual differences between the data points.
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Look at the data under PURCHASE BEHAVIOR. How often do consumers in this segment purchase a backpack? Purchase behavior last quarter - 23% : a. Once every 6 years b. Once every 3 years c. Once every year d. Once every 2 years e. Once every 5 yrs
By looking at the data under PURCHASE BEHAVIOR, we can see that the consumers in this segment purchase a backpack at a range of purchase every five years. The Option E is correct.
What determines a Consumer purchase interval?We have several factors that can determine a consumer's purchase interval, including:
Product usage: How frequently a product is used or consumed can influence the consumer's purchase interval. If a product is used frequently, the consumer may need to purchase it more often.Product durability: The durability of a product can impact the purchase interval. If a product is durable and lasts a long time, the consumer may not need to purchase it as frequently.Price: The price of a product can also determine the purchase interval. If a product is expensive, the consumer may wait longer before making another purchase.Consumer behavior: Consumer behavior, such as brand loyalty or habit, can also influence the purchase interval. Consumers who are loyal to a particular brand may purchase that brand more frequently, while others may be more open to trying different brands and products etc.Read more about Consumer
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Answer:
Step-by-step explanation:
answer is c. once every year
A 19 ft rope is tied from the top of a tent pole to a stake 11 ft away. To the nearest degree, what is the angle of elevation from the stake up to the tent pole?
The angle of elevation from the stake up to the tent pole is, 54.55°.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, A 19 ft rope is tied from the top of a tent pole, It is the hypotenuse length.
Also, The state is 11 feet away and it is the adjacent length.
We know, cos = adjacent/hypotenuse.
cos = 11/19.
Ф = cos⁻¹(0.58).
Ф = 54.55°.
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Mr. shaw graphs the function f(x) = –5x 2 for his class. the line contains the point (-2, 12). what is the point-slope form of the equation of the line he graphed? y – 12 = –5(x 2) y – 12 = 2(x 2) y 12 = 2(x – 2) y 12 = –5(x – 2)
Answer:
y - 12 = -5(x + 2)
Step-by-step explanation:
the area of a rectangle is 42 square inches and one side is 12 inches long. Find the peremiter of the rectangle. Show your work
Answer:
The area is one side times the other side
Make the other side x.
12x=42
x=42/12=3.5
The perimeter is 2x+2y where x and y are sides of the rectangle.
P= 2(3.5)+2(12)=7+24=31 inches
Hope this helps.
Answer: 3.5
Step-by-step explanation:
42/12 = 3.5
what is 21% of .31 with work shown
Answer:
0.0651
Step-by-step explanation:
To find 21% of 0.31, we can use the following formula:
21% × 0.31
We can convert the percentage to a decimal by dividing by 100:
0.21 × 0.31
Multiplying these two numbers, we get:
0.0651
Therefore, 21% of 0.31 is 0.0651.
Mathematics word problem. Working out would be really helpful. 20 points
Answer:
d = 86e = 94Step-by-step explanation:
You want the measures of angles d° and e° in the given figure.
AssumptionsUsually, geometry problems tell you not to assume anything that isn't marked or stated regarding the figure. In order to answer this question, we need to assume ...
∆ACD is isosceles∆ABE ~ ∆ACDIsosceles triangleThe base angles in an isosceles triangle are congruent. That means each of them is the complement of half the vertex angle.
∠D = 90° -1/2∠A = 90° -8°/2 = 86°
The segments CD and BE are parallel, so angle E is the supplement of angle D:
∠E = 180° -86° = 94°
The angle measures are d° = 86° and e° = 94°.
__
Additional comment
This is not a "word problem." All of the relations necessary for answering the question are shown in the diagram, not stated in words. (The question is necessarily written in words—for any problem.)
If b is a base angle and v is the vertex angle of an isosceles triangle, then the sum of angles is ...
b + b + v = 180°
2b = 180° -v . . . . . . subtract v
b = 90° -v/2 . . . . . . divide by 2
Effectively, the altitude of an isosceles triangle bisects the vertex angle and creates two congruent right triangles. The acute angles in that triangle are the original base angle and half the vertex angle. They are complementary.
What is the conversion of 720 minutes to hours?
The conversion of 720 minutes to hours is equal to 12 hours.
The units involved in this conversion are minutes and hours.The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. An hour (symbol: h; also abbreviated hr.) is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions.The conversion factor from minutes to hours is 0.0166667, which means that 1 minutes is equal to 0.0166667 hours:1 min = 0.0166667 hr, There are 60 minutes in one hour. To convert 720 minutes to hours, you can divide 720 by 60:
720 minutes ÷ 60 minutes/hour = 12 hours
So, 720 minutes is equal to 12 hours.
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y=80(1.3)^x growth or decay
The +equation represents exponential growth
What is the exponential functions?
An exponential function is a mathematical function that has the form f(x) = a*b^x, where a and b are constants, and x is the independent variable.
The equation y = 80(1.3)^x represents exponential growth.
In this equation, "y" represents the value of the function at a given time or input, "x" represents the time or input, and "1.3" is the growth factor, which is greater than 1.
As "x" increases, the value of the function "y" grows at an increasing rate. This is because the growth factor is greater than 1, which means that each input value results in a larger output value than the previous one.
Hence, this equation represents exponential growth.
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when multiplying matrices, multiply the elements in each of the first matrix times the corresponding elements in each. is it true?
False, every component of the matrix is multiplied by the same amount when you multiply a matrix by a number. A new matrix is created by this operation; it is known as a scalar multiple.
A rectangular matrix is a grouping of numbers in rows and columns. A matrix element/entry is the term used to describe each number in the matrix. The combination of a real number and a matrix is referred to as scalar multiplication.
Each entry/element of the matrix is multiplied by the specified scalar in scalar multiplication. Comparatively, matrix multiplication describes the result of two matrices. This operation is totally different. We can't just multiply the corresponding entries in two matrices to multiply them.
The first matrix must have exactly as many columns as the second matrix has rows in order to perform matrix multiplication. The resulting matrix has the same number of columns and rows as the second matrix, and its number of columns matches the number of rows in the first matrix.
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Enter a range of values for x. + 42° 3x+15 3x+15° 23 21 [ ? ]
The value of x is given as follows:
x = 9.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Similar triangles have congruent angle measures, and the angles of 3x + 15º and 42º are congruent, hence the value of x is obtained as follows:
3x + 15 = 42
3x = 27
x = 9.
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how many different triangles can be constructed with angles that measure 120, 40, and 60
Answer:
It would be zero
Step-by-step explanation:
Find the rate of change between:
(-2/3,-4)
(-3,4)
Would appreciate some help I don’t understand this at all.
Answer:
The rate of change between (-2/3, -4) and (-3, 4) is:
(change in y) / (change in x) = (4 - (-4)) / (-3 - (-2/3))
= 8 / (-2/3)
= -12
Therefore, the rate of change is -12.
Step-by-step explanation:
=]
What is the conversion of 6,25% as a fraction?
After converting 6.25% into fraction we get 16/256 or 1/16.
The percentage means divied by hundred.
A fraction consists of two parts one is the numerator and other is denominator.
Where the number which is written in upper most part of the line is called numerator, and the number bottom most part of the line is called denominator.
To convert a percentage into a fraction divide the percentage by 100,
And simplify the resulting fraction.
So,
To convert 6.25% to a fraction,
We divide 6.25 by 100:
6.25% ÷ 100 = 0.0625
Divide by 0.0625
0.0625 ÷ 0.0625 = 1
1 ÷ 0.0625 = 16
Therefore, After simplification 6.25% is equal to 16/256 or 1/16.
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Find the equation of a line perpendicular to y=−4x+4 that contains the point (5,−1).
The equation of the line perpendicular to y = -4x + 4 that contains the point (5, -1) is y = 1/4x - 9/4.
The given equation is y = -4x + 4, which is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the given line, we can compare it to the slope-intercept form and see that the slope is -4.
Since we want to find the equation of a line that is perpendicular to the given line, we know that its slope will be the negative reciprocal of -4.
The negative reciprocal of -4 is 1/4, so the slope of the perpendicular line is 1/4.
Now we have the slope of the line and a point that it passes through, so we can use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope we just found.
Plugging in the values, we get:
y - (-1) = 1/4(x - 5)
Simplifying this equation, we get:
y + 1 = 1/4x - 5/4
Subtracting 1 from both sides, we get the final equation:
y = 1/4x - 9/4
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How to convert convert meters to miles?
To convert any number of meters to miles, you simply need to multiply the number of meters by this conversion factor 0.000621371192
The conversion factor from meter to miles is 0.000621371192
1 meter = 0.000621371192 miles
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
So, to convert meter to miles you can multiply the number of kilometers by 0.000621371192
The distance in miles = conversion factor × The distance in meters
Therefore, the steps to convert meter to miles has been explained
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A file that is 228 megabytes is being downloaded. If the download is 15.4% complete, how many megabytes have been downloaded?
Answer:
35.112
Step-by-step explanation:
15.4% = 0.154. 228*0.154=35.112.
6 × 20.16 this is very hard fo rmy lil brothr
Answer:
Step-by-step explanation:
120.96
Write the standard form of the equation of each line.
1) y=3x+1
2) y=-9/5x+3
helppppp plsssss
Answer:
Step-by-step explanation:
(1)To write this in standard form, we want the x and y terms on the same side of the equation and the constant on the other side. To do this, we can subtract 3x from both sides:
-3x + y = 1
So the standard form of the equation is:
-3x + y = 1
(2)y = -9/5x + 3
To write this in standard form, we want to eliminate the fraction by multiplying both sides by the denominator (5):
5y = -9x + 15
Next, we can move the x term to the left side by adding 9x to both sides:
9x + 5y = 15
So the standard form of the equation is:
9x + 5y = 15
I need help with the blank boxes please :]
Answer:
1) What are your options?
2) 847,200
3) 6.7 × 10^5
Step-by-step explanation: You always move the decimal until you get to the first digit after zeroes and then x 10 and the power is how many times it took to place the decimal in front of the number.
what are significant digits in a quantity?
Significant digits, also known as significant figures, refer to the digits in a quantity that are considered to be reliable and meaningful based on the precision of the measurement.
The significant digits in a given quantity include all the digits that are known with certainty, as well as one uncertain digit that is estimated based on the measurement's precision.
For example, if the length of a table is 1.23 metres, the digits "1," "2," and "3" are all significant, whereas the digit "0" is not significant because it is just a placeholder.
The number of significant digits in a number is determined by the measurement instrument or method used.
For example, if you use a centimeter-marked ruler to measure the length of a table, you can estimate the length to the nearest millimetre, implying that the last digit is uncertain and estimated. Because you have three certain digits and one estimated digit, the number of significant digits in this case is three.
When performing mathematical operations on numbers with varying numbers of significant digits, the result should be rounded to the same number of significant digits as the least precise measurement. This is necessary to maintain the calculation's accuracy and precision.
Understanding significant digits is essential for precise scientific measurements and calculations. It can aid in the prevention of errors and the production of reliable and meaningful results.
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