Mr. Jackson had to attend a meeting in San Fransisco 300 miles from his home. He traveled the first 90 minutes at 64 miles per hour. The next hour he traveled 66 miles per hour. If he reached San Fransisco three hours later what was his average speed for the last three hours?
Let's call the average speed for the last three hours "S".
First, we need to find the total distance that Mr. Jackson traveled in the last three hours. He traveled 300 miles in total, and he covered 64 miles in the first 90 minutes, so he had 300 - 64 = 236 miles left to travel.
Next, we need to find the time he spent traveling in the last three hours. If he traveled for three hours, and the first hour he traveled at 66 miles per hour, then he covered 66 miles in the first hour. So, he had 236 - 66 = 170 miles left to travel in the last two hours.
Finally, we can use the formula for average speed: distance divided by time. The total distance he traveled in the last three hours was 170 miles, and the time he spent traveling was 2 hours, so his average speed for the last three hours was:
S = 170 miles / 2 hours = 85 miles per hour
So, Mr. Jackson's average speed for the last three hours was 85 miles per hour.
Answer:
68 mph
Step-by-step explanation:
Let's call the average speed for the last three hours "S".
The total distance traveled for the last three hours is 300 - 64 * 1.5 = 300 - 96 = 204 miles.
So, over the last three hours, Mr. Jackson covered a distance of 204 miles at a speed of S.
The time it took him to cover that distance is 3 hours.
We can use the formula distance = speed * time to find S:
204 = S * 3
Solving for S:
S = 68 mph
So the average speed for the last three hours was 68 mph.
please help me I'm frustrated at this problem i know nothing about percentaes and im in 10th grade cryin inside...
Step-by-step explanation:
To find a percentage, it's the portion divided by the total. 100% represents the total between the children or adults respectively in the maintee and evening.
So, to answer, let's find the total of children and adults.
34+27 = 61 is the total for children.
38+46 = 84 is the total for adults.
Now, to find each percentage, take one of the numbers (Children-Maintee, Children-Evening) and divide it by the total we found.
34/61 = 0.557 or 55.7%
27/61 = 0.442 or 44.2%
I'm leaving it in fractional form in case you need a specific decimal answer.
As for adults, it's the same procedure.
38/84 = 0.452 or 45.2%
46/84 = 0.548 or 54.8%
Question 10 / 1 pointWhich one of the following best defines the notion of "the P-value of a hypothesistest?"Question options:The probability of a type I error.The probability of a type II error.The probability of rejectingH0{"version":"1.1","math":"H_0"}, whether it's true or not.The probability of obtaining a test statistic at least as extreme as the one you calculated, assuming the nullhypothesis is true.
Option A: The probability of rejecting H_o, whether it's true or not, best describes the notion of the P-value of a hypothesis test.
The level of marginal significance within the hypothesis test that represents the probability of occurrence of a given event is referred to as its P-value. In order to provide the least significance at which the null hypothesis would be rejected, it is utilized as a choice for the rejection point. This signifies that the option A is correct.
The P-value is known as the probability value. It can be defined as the probability of getting a result that is either the same or more advanced than the actual observations. There is more support for the alternative hypothesis when the P-value is low.
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Correct way to ask the question is:
Which one of the following best defines the notion of the P-value of a hypothesis test?
The probability of rejecting H_o, whether it's true or not
The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.
The probability of the type I error
The probability of the type II error
A family purchased tickets to a museum and spent a total of $38.00. The family purchased 4 tickets. There was a $1.50 processing fee for each ticket. Write and solve an equation that can be used to find x, the cost of one ticket to the museum. Show your work or explain your answer.
Answer:
Equation: 4(x + 1.5) = 38
Ticket Cost: $8, or x = 8
Step-by-step explanation:
The processing fee for each ticket is $1.50, or 1.5. This applies to each ticket, meaning that the price of one ticket (or x) should be added to 1.5. x + 1.5 represents the sum of a ticket and the processing fee. Since there were 4 tickets purchased, x + 1.5 is multiplied 4 times. That results in 4(x + 1.5). Finally, the total amount of money spent was $38, so 4(x + 1.5) = 38.
4(x + 1.5) = 38
4x + 6 = 38
4x = 32
x = 8
Check:
4 * 8 = 32 (cost of 4 tickets)
4 * 1.5 = 6 (cost of 4 processing fees)
32 + 6 = 38 (4 tickets + 4 processing fees = total)
Which of the following are valid names for the given triangle? Check all that
apply.
The valid names for the given triangle are options:
B. ΔMLZ
D. ΔLMZ
E. ΔZML
What is the triangle about?A triangle is a two-dimensional shape that is formed by three line segments that are connected end-to-end. It is a fundamental shape in geometry, and its properties and uses are numerous.
Therefore, The triangle in the picture has three vertices labeled L, M, and Z. To name the triangle, we use the labels of the vertices and write them in capital letters. It doesn't matter which vertex we start with, as long as we keep the letters in order as we go around the triangle. So, the names for the triangle in the image can be : ΔLMZ, ΔLZM, ΔMLZ, ΔMZL, ΔZLM, and ΔZML.
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to identify the point in a distribution at which 50% of scores fall above and 50% fall below a given score, which measure of central tendency would you report? group of answer choices mode mean median average
The median is the point in a distribution where 50% of the scores fall above and 50% fall below a certain score.
In a distribution, the median is the number that separates the top 50% of scores from the bottom 50% of scores. When the data is organised from lowest to highest, it is the midway value.
The mode is the most common value in a distribution, and it is not always the same as the median. The mean is the total of all scores divided by the number of scores, and it is impacted by outliers or extreme values in the data. Depending on the context, the term "average" can refer to either the mean or the median. When individuals say "average" without any qualification, they typically mean the mean.
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A pack of cinnamon-scented pencils sells for $6.00. What is the sales tax rate if the total cost of the pencils is $6.42?
Please show how you did it
Answer:
7% sales tax
Step-by-step explanation:
If the pencils cost $6, then the sales tax costs $6.42 - $6 = $0.42. To find the rate, we must divide $0.42 by $6. $0.42/$6 = 0.07. 0.07 is 7%.
Seth has a bank account which pays 1.01% interest, compounded quarterly. Seth withdraws $4,567 from the account every quarter for 35 years. Assuming that Seth does not make any deposits into this account and that the withdrawals occur at the end of every quarter, find the initial value of the account, rounded to the nearest cent.
The closest answer to initial value of the account is $538,021.66
It is given that the money Seth withdraws was compounded every quarter for 35 years. So, we get,
Amount withdrawn every quarter, P = $4567
Rate of interest, r = = 0.002525
Time period, n = 35 × 4 = 140
Now, as we know the formula for annuity as,
[tex]PV = PMT[(1 - (1 / ( 1 + r)^n)) / n][/tex]
where P = installments, PV = present value, r = rate of interest and n = time period.
This gives,[tex]PV = PMT[(1 - (1 / ( 1 + r)^n)) / n]= 4567[1 - (1 / 1.00253^40)) / 0.00253][/tex]
= 4567[(1 - 0.70254) / 0.00253]
= 4567[117.80636]
= $538,021.66
So, the closest answer to initial value of the account is $538,021.66
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The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.30 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
The total cost of the meal is $
Answer:
$82.21
Step-by-step explanation:
cost of meal: $78.30
15% discount: 15% of $78.30 = 0.15 × $78.30 = $11.75
tip: 20% of $78.30 = 0.20 × $78.30 = $15.66
total cost = $78.30 - $11.75 + 15.66 = $82.21
Answer: $82.21
Convert (-z-2)^2 into a quadratic trinomial and (-n+4)^2 and (-m-10)^2
(please help)
The quadratic trinomial of the given expressions are z² + 4 + 4z, 16 + n² - 8n, m² + 100 + 20m respectively.
What do you understand by Quadratic Trinomial?A trinomial is an algebraic expression that has three terms. An algebraic expression consists of variables and constants of one or more terms.
A polynomial is an algebraic expression that has one or more terms and is written as [tex]a_0x^n + a_1x^{ n - 1} + a_2x^{n-2} + ...+ a_n x^0[/tex] in the standard form. Where [tex]a_0, a_1, a_2, ....,a_n[/tex] are constants and n is a natural number.
A quadratic trinomial is a type of algebraic expression with variables and constants. It is expressed in the form ax² + bx + c, where x is the variable and a, b and c are non-zero real numbers. A quadratic trinomial also describes the discriminant D where it defines the quantity of an expression and it is written as D = b² - 4ac.
Given:
(-z - 2)²
⇒ [-(z + 2)]²
⇒ (z)² + (2)² + 2(z)(2)
⇒ z² + 4 + 4z
(4 - n)²
⇒ (4)² + (n)² - 2(4)(n)
⇒ 16 + n² - 8n
(-m - 10)²
[-(m + 10)]²
⇒ (m)² + (10)² + 2(m)(10)
⇒ m² + 100 + 20m
So, the expressions are converted into quadratic trinomial.
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Find the value of x and y
56% of is 3.92?
0 4
O 5
O 6
O 7
The number of which 3.92 is 56 percent, is 7.
What is percent?A percentage of an object is how many parts of it there are out of 100 equal parts. For example, if you split a shape into 100 parts, 20 of the parts make 20%.
Given that, 3.92 is what number's 56%,
Let the number be x,
Therefore, by the definition of percentage,
56% of x = 3.92
56/100 × x = 3.92
x = 3.92 × 100/56
x = 392/56
x = 7
Hence, the number of which 3.92 is 56 percent, is 7.
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let f be the continuous function defined on [-4,3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) =
Answer: no exact answer
Step-by-step explanation:
Ethan is planning for his retirement. He has narrowed it down to two investment options. The first is an IRA where monthly payments are made, in the amount of $416.66, for 30 years. The second is a Roth IRA where annual payments are made, in the amount of $5000, for 30 years. If both compound interest at a rate of 2.5%, determine which account will yield the largest future value for Ethan, and how much greater that value will be than that of the other account. Round your final answer to the nearest cent.
To compare the two investment options, we must compute the future value (FV) of each account after 30 years of compounding at a 2.5% rate.As an outcome, the IRA will have a future value that is $107,116.33 greater than the Roth IRA.
How to find IRA?We have monthly payments of $416.66 for 30 years, or 360 months, on the IRA. Using the following formula to calculate the future value of an annuity:
[tex]FV = PMT * [(1 + r)^n - 1] / r[/tex]
We can calculate the future value of the IRA using the following formula: where PMT is the monthly payment, r is the monthly interest rate (2.5% / 12), and n is the number of payments (360):
[tex]FV IRA = 416.66 * [(1 + 0.025/12)^360 - 1] / (0.025/12) = $358,888.91[/tex]
We have annual payments of $5000 for 30 years on the Roth IRA. Using the following formula to calculate the future value of a lump sum:
[tex]PV * (1 + r)n = FV[/tex]
where PV is the present value (the lump sum), r is the annual interest rate (2.5%), and n is the number of years (30), we can calculate the Roth IRA's future value:
5000 * (1 + 0.025)30 = $251,772.58 FV Roth
As a result, the IRA will outperform the Roth IRA in terms of future value by:
$358,888.91 - $251,772.58 = $107,116.33 FV IRA - FV Roth
As a result, the IRA will have a future value that is $107,116.33 greater than the Roth IRA.
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There are 10 girls and 30 boys ina class find the ratio of
a. No of girls to no of boys
The ratio of girls to boys in the class is 1:3, meaning that for every one girl there are three boys.
There are 10 girls and 30 boys in the class.
The ratio of girls to boys can be expressed as a fraction: 10/30.
To make the fraction easier to understand, we can simplify it to its lowest form: 1/3.
The ratio of girls to boys in the class is therefore 1:3, meaning that for every one girl there are three boys.
The ratio of girls to boys in a class can be determined by dividing the number of girls by the number of boys. In this case, there are 10 girls and 30 boys, so the ratio is 10/30. This fraction can be simplified to its lowest form, 1/3. This means that for every one girl there are three boys in the class. Knowing the ratio of girls to boys can be helpful in a variety of situations, such as organizing activities or determining the number of supplies needed. This ratio can also be expressed as a percentage, with 10% of the class being girls and 30% being boys. Knowing the ratio of girls to boys can also be a useful tool in understanding the demographics of the class.
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please answer asap i need helpp
Answer:
110°
Step-by-step explanation:
]%}}%¶¢{^[€{¢¶¢¶€¶
Answer: 110˚
Step-by-step explanation:
Complementary angles have a sum of 90˚
With this knowledge, we can say <B = 90 - <A = 90 - 20 = 70˚
Supplementary angles have a sum of 180˚
With this knowledge we can say <C = 180 - <B = 180 - 70 = 110˚
∴ Measure of angle C = 110˚
please help! I'm struggling a lot with this domain and range.
=====================================================
Explanation:
The domain is the set of allowed x inputs.
In this case, we can plug in anything but x = 2 because of the vertical asymptote here.
This means the domain is the interval notation [tex](-\infty,2) \cup (2,\infty)[/tex] that notation basically says "start with the entire real number line. Then poke a hole, or remove, 2 from the number line".
------------
The range is the set of possible y outputs. In this case, the domain and range lead to the same interval notation since we're kicking out "2" each time. This time we focus on the horizontal asymptote. The curve gets closer and closer to these dashed lines but never actually reaches them.
Since [tex](-\infty,2) \cup (2,\infty)[/tex] is one of the possible ways to represent the range, one of the answers is choice A.
The interval notation [tex](-\infty,2) \cup (2,\infty)[/tex] is too vague because it's not clear if we're talking about the domain or range. The notation [tex]\left\{\text{y}|\text{y} \in \text{R}, \ \text{y} \ne 2\right\}[/tex] is more specific. It says "y is a real number such that it cannot equal 2". In other words "y can be anything but 2". This tells us that choice D is another answer.
So either y < 2 or y > 2 which represents us being below the horizontal asymptote or above it respectively.
The third and final answer is choice E.
A builder is constructing an office building with n floors that will have an antenna 13.5 feet tall on its roof. Each floor of the building will be 6.8 feet high. Which function can be used to find the total height, h, of the building in feet, including the antenna?
The function that can be used to find the total height, h, of the building in feet, including the antenna is h = 6.8n + 13.5.
How to use function to find the total height?A builder is constructing an office building with n floors that will have an antenna 13.5 feet tall on its roof. Each floor of the building will be 6.8 feet high.
Therefore, the function that can be used to find the total height of the building in feet including the antenna can be calculated as follows:
Therefore,
n = numbers of floors in the building.
h = total height of the building
Hence, the function is as follows
h = 6.8n + 13.5
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6. when constructing confidence interval for a parameter, we generally set the confidence level 1 - alpha close to 1 (usually between 0.90 and 0.99) because it is the probability that the interval includes the actual value of the population parameter. true or false
Since the chance that the interval contains the actual value of the population parameter is what we put the confidence level 1 - alpha near to 1 when creating confidence intervals for parameters. false
Parameters are a value or set of values that can be used to define or characterize a certain system, model, or process. It is a variable that can be changed to affect how the system or process to which it is connected functions. In mathematics, a parameter is a variable that is used to describe the overall properties of a function or equation. In computer programming, it refers to a value or variable that is passed to a function or procedure. The function or method can then use these parameters to perform a specific operation or calculation.A parameter in statistics is a number that characterizes a population or a sample of data. They help to specify the characteristics.
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Hunter designs two flags for his adventure club.
What is the length of the base,x, of the larger flag?
Enter your answer as a decimal.
See the attachment for the problem to be answered.
The length of the base, x, of the larger flag is 6.25 ft.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
The two flags are similar using the AA criteria.
Thus, the ratio of the segments of the two triangle are equal.
4/5 = 5/x
4x = 25
x = 25/4
x = 6.25 ft
Hence, the length of the base, x, of the larger flag is 6.25 ft.
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3
Type the correct answer in each box. Use numerals instead of words.
Consider this expression.
The equivalent expression to -4x² + 2x - 5(1 + x) is given as follows:
-4x² - 3x - 5.
How to obtain the equivalent expression?The expression for this problem is defined as follows:
-4x² + 2x - 5(1 + x)
To obtain the equivalent expression, we apply the distributive property to -5(1 + x) as follows:
-5(1 + x) = -5 - 5x.
Then the expression is given as follows:
-4x² + 2x - 5 - 5x.
Combining the like terms, we have that the expression is given as follows:
-4x² - 3x - 5.
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Which rate is greater
1,080 labels on 90 sheets 2,250 labels on 150 sheets
Answer: There would be a higher rate on the 2250 labels on 150 sheets.
Step-by-step explanation:
1080/90 = 12
2250/150 = 15
There would be a higher rate on the 2250 labels on 150 sheets.
Select a two-digit number whose 1st digit it 0,1,2,3, or 4, and whose 2nd digit is 5,6,7,8, or 9.
In 25 ways we can select 2-digit number from the given digits.
What is the Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Given that, a two-digit number whose 1st digit it 0,1,2,3, or 4, and whose 2nd digit is 5,6,7,8, or 9.
Number of ways selecting 1st digit is
P(5, 1) = 5!/(5-1)!
= 5
Number of ways selecting 2nd digit is
P(5, 1) = 5!/(5-1)!
= 5
Now, 5×5=25
Therefore, in 25 ways we can select 2-digit number.
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60°
V
U
S
A
120°
T
?
Solve for X
The measure of x in the figure is 180 degrees
How to determine the measure of xFrom the question, we have the following parameters that can be used in our computation:
The circle and the intersecting chords
The value of x represented by ? is then calculated as
120 = 1/2(x + 60)
Cross multiply the equation
This gives
x + 60 = 240
Subtract 60 from both sides
x = 180
Hence, the measure of x is 180 degrees
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please help me i dont understand
Answer:
x=15°
∡Q= 75°
Step-by-step explanation:
supplementary angles means the sum of the angles =180°
so, 5x+105°=180°
5x=75°
x=15°
∡Q= 75°
three coplanar circles intersect as shown. what is the maximum number of points on the circles that a line passing through all three circles can touch?
The maximum number of points on the circles that a line passing through all three circles can touch is 36.
Two circles may cross in two points, one point, or no points on a aeroplane, digression circles are coplanar circles that cross at a single point.Concentric circles are coplanar circles that share a common centre.
You can select any two circles in (₂³) ways and each pair will intersect at 2 points. Therefore total 3*2=6 points.
Similarly, 4 lines will intersect at (₂⁴)=6
points.
Now each line will intersect at 2 points with a circle. And since we can select a circle in (³₁) ways and a line in (₁⁴) ways, therefore total (₁³)∗(₁⁴)∗2=24 points they will intersect.
Therefore, total number of intersection points = 6 + 6 + 24 = 36 points.
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A water tower is 16 meters tall. Close by, there is a crane that is 24 meters tall. If the water tower's shadow is 30 meters long, how long is the crane's shadow?
Answer:
Tje answer is 36
Step-by-step explanation:
16-30=14
24+14=-36
Can someone explain this
There are quadratic equations as many as lead coefficients are. The functions that represent each parabola are:
Case A: y = (1 / 3) · (x + 4) · (x - 2)
Case B: y = (x + 4) · (x - 2)
Case C: y = 2 · (x + 4) · (x - 2)
Case D: y = - (1 / 3) · (x + 4) · (x - 2)
Case E: y = - 2 · (x + 4) · (x - 2)
How to determine a group of quadratic equations
In this problem we find five case of quadratic equations whose roots are x = - 4 and x = 2, but whose vertices are different. Quadratic equations can be described as a factor product of the form:
y = a · (x + 4) · (x - 2)
Where a is the lead coefficient.
The following parameters are for each parabola:
Case A: (x, y) = (- 1, - 3)
Case B: (x, y) = (- 1, - 9)
Case C: (x, y) = (- 1, - 18)
Case D: (x, y) = (- 1, 3)
Case E: (x, y) = (- 1, 18)
Now we determine the lead coefficient for each case:
Case A
- 3 = a · (- 1 + 4) · (- 1 - 2)
- 3 = - 9 · a
a = 1 / 3
Case B
- 9 = a · (- 1 + 4) · (- 1 - 2)
- 9 = - 9 · a
a = 1
Case C
- 18 = a · (- 1 + 4) · (- 1 - 2)
- 18 = - 9 · a
a = 2
Case D
3 = a · (- 1 + 4) · (- 1 - 2)
3 = - 9 · a
a = - 1 / 3
Case E
18 = a · (- 1 + 4) · (- 1 - 2)
18 = - 9 · a
a = - 2
All differences between all quadratic equations are due to different lead coefficients.
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Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement.a) 14.8mb) $10.25c) 0.05 Ld) 1.000 g/mLe) 6200cmf) 403 kg
Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e) 6200cm = 6200x cm. f) 403 kg = 40x kg.
a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.
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you have 10 stacks of 10 coins. all coins weigh 1 gram, except for in one of the stacks which consists of coins that weigh 2 grams (so 90 coins weigh 1 gram and 10 coins weigh 2 grams). you have an electronic scale ( not a balance). how many times do you have to use the scale to figure out the heavier stack?
The scale to figure out the heavier stack 2 gram higher.
To determine the heavier stack of coins, you will need to use the electronic scale. However, since you cannot weigh all the coins at once, you will have to use the concept of unitary method.
Based on this, you can calculate the total weight of the coins on the scale. Since each coin weighs 1 gram, the total weight of the coins should be equal to the sum of the natural numbers from 1 to 10, which is 55.
Next, you need to compare the weight of the coins on the scale to the expected weight of 55 grams. If the weight on the scale is less than 55 grams, then the stack of coins that you did not weigh is the heavier stack.
However, if the weight on the scale is more than 55 grams, you need to use the concept of unitary method again. Suppose the weight on the scale is 56 grams. This means that the heavier stack has one coin that weighs 2 grams, and the other stack has 10 coins that weigh 1 gram.
To determine which stack is heavier, you can subtract the expected weight of 55 grams from the weight on the scale (56 grams). The difference is 1 gram.
Now you need to divide the difference by 2 (since one coin weighs 2 grams). This gives you 0.5. This means that the heavier stack has 0.5 coins that weigh 2 grams.
Since you cannot have half a coin, this means that the stack with one coin that weighs 2 grams is the heavier stack.
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