The length of the garden which is in the shape of a rectangle with a perimeter of 18 meters and whose length is 3 meters more than twice the width, is 7 metres.
Let's name the width "w" and the length "l" of the rectangle.
We know from the problem description that the rectangle's perimeter is 18 metres, thus we can formulate an equation:
2l + 2w = 18
We also know that the length is 3 metres longer than the breadth, thus we can solve the following equation:
l = 2w + 3
We may plug the second equation into the first to remove the letter "l" and get an equation with only one variable:
2(2w + 3) + 2w = 18
When we simplify this equation, we get:
6w + 6 = 18
When we subtract 6 from both sides, we get:
6w = 12
When we divide both sides by 6, we get:
w = 2
We can use the second equation to get the length now that we know the width is 2 metres:
l = 2w + 3 = 2(2) + 3 = 7
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paul records data that indicate that the number of hot chocolates sold at a concession stand increases as temperature outside decreases. (for example, more hot chocolates are purchased during late fall than late spring) which statement is the most accurate depiction of this finding?
Paul records data that the number of hot chocolates sold increases as temperature outside decreases. The depiction of the finding is "There is a correlation between two variables". So, the correct option is A.
Specifically, the data suggest that there is a relationship between two variables - the number of hot chocolates sold and the temperature outside.
When the temperature outside decreases, more hot chocolates are sold, and when the temperature increases, fewer hot chocolates are sold. This indicates that there is a correlation between the two variables, as they appear to be related.
However, we cannot determine from this information alone whether the correlation is strong or weak, or whether it is positive or negative.
The strength of the correlation would depend on how much the sales of hot chocolate increase or decrease as the temperature changes, while the direction of the correlation (positive or negative) would depend on whether the increase or decrease in hot chocolate sales is associated with an increase or decrease in temperature, respectively.
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Complete question is:
Paul records data that indicate that the number of hot chocolates sold at a concession stand increases as temperature outside decreases. (for example, more hot chocolates are purchased during late fall than late spring) which statement is the most accurate depiction of this finding?
a) There is a correlation between two variables
b) There is a strong , positive correlation between two variables
c) There is a weak , positive correlation between two variables
d) There is a negative correlation between two variables
please answer parts a and b correctly and let it make sense. if it's correct ill give it all stars and brainxvlest and also I will cavxsh app u
just put ur tag below. thank u
Answer:
11 inches
Step-by-step explanation:
If its cubic inches, we just need to cube root it
Plug it into the calculator and you get a number that rounds up to 11
Reasoning is because it is cubic, so to find the distance which is a normal number, you need to cube root it
distinguish between the following terms: a.sensitivity and detection limit b.loq and limit of linearity c.quantitation by calibration curve and the method of standard addition. d.confidence interval and confidence limits
These terms describe various aspects of quantitative analysis and measurement in different scientific fields such as analytical chemistry, biology, and statistics.
A. Sensitivity - the ability of a measurement method or instrument to detect small changes in the quantity being measured.
B. Detection limit - the minimum amount of a substance that can be reliably detected by a measurement method or instrument.
C. LOQ (Limit of Quantitation) - the minimum concentration of a substance that can be accurately quantified by a measurement method or instrument.
D. Limit of Linearity - the range of concentrations of a substance over which the measurement method or instrument produces proportional results.
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Distinguish between the following terms:
A. sensitivity and detection limit
B. Log and limit of linearity
C. quantitation by calibration curve and the method of standard addition.
D. confidence interval and confidence limits
Which situation most accurately matches the graph?
The situation that matches the information in the graph is a boy rides a bicycle on flat ground and goes quickly down a large hill (option A).
What does the graph show?The graph shows how the movement of a body changes over time. In general, it can be observed the movement is first linear as in moving on a flat surface, then the body goes down, then it goes up, and finally, the movement is linear again.
Based on this, it can be concluded that the option that describes the graph is a boy rides a bicycle on a flat group, then he goes down a large hill and finally he drives on flat ground again (option A).
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5 3/5 + 1/2 = ? what is the answer
Answer:
61/10
Step-by-step explanation:
Convert the mixed number to an improper fraction
28 / 5 + 1 / 2
= 61/10
Answer:
Simplified form: 6 1/10
Improper form: 61/10
Step-by-step explanation:
5 3/5 + 1/2
= 28/5 + 1/2
Then, you multiply both fractions so that the denominator is the same number. In this case, multiply the fraction (numerator and denominator) on the left by 2 and on the right by 5.
= 56/10 + 5/10
This way, you can add the numbers because they have the same denominator.
=61/10
Travel agents were designing a marketing program to promote tourism in Canada. To determine the target audience for their program, the travel agents surveyed people across two different age groups about whether they have been to Canada in the past six months. The table below shows the results of the survey.
Answer: 63%
Step-by-step explanation:
22 divided by 35 times 100
A picture 6 1/2 feet long is to be centered on a wall that is 21 feet long. How much space is there from edge of the wall to the picture
On solving the provided question, we can say that by fractions, the space from the edge of the wall to the picture = 17/4*1/2 = 17/8
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
Simply subtract the length of the image from the length of the wall to get the total area below and above the picture from the edge of the wall. So.
[tex]14\frac{1}{2} - 10\frac{1}{4}[/tex]
29/2 - 41/2
17/2
the space from the edge of the wall to the picture = 17/4*1/2 = 17/8
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suppose lacrosse balls come in 3 colours: red, yellow, and blue. how many different combinations of colours are possible in a 6-pack of lacrosse balls?
There are 20 different combinations of colors possible in a 6-pack of lacrosse balls.
What is the combination?
A combination is a choice of items from a group of different items where the order of the choices is irrelevant. Either the process of combining or the condition of combining. a combination of several things a mixture of thoughts. something created through fusion: A chord is made up of several notes.
Here, we have
Given: lacrosse balls come in 3 colors: red, yellow, and blue.
We have to find the different combinations of colors that are possible in a 6-pack of lacrosse balls.
We apply here combination formula and we get
= ⁶C₃
= (6×5×4×3!)/(3!×3×2×1)
= 20
Hence, there are 20 different combinations of colors possible in a 6-pack of lacrosse balls.
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Question 1 of 5
Drag each value to the correct location on the circle. Not all values will be used.
Circle F has radius of 4 inches with a central angle of 120°. Determine the measure of the central angle in radians, the arc length of RS
, and the area of sector RFS.
The area of sector RFS is approximately 8π square inches, and the measure of the central angle in radians is approximately 2π/3 radians.
What is the central angle?
A central angle is an angle with endpoints and located on a circle's circumference and a vertex located at the circle's center. A central angle in a circle determines an arc.
To determine the measure of the central angle in radians, we can use the formula:
radians = degrees * (π / 180)
So, for the central angle of 120°:
radians = 120 * (π / 180) = 2 * π / 3
The measure of the central angle in radians is approximately 2 * π / 3 radians.
To find the arc length of RS, we can use the formula:
arc length = (central angle / 360) * circumference
The circumference of the circle is given by 2 * π * r, where r is the radius:
circumference = 2 * π * 4 = 8 * π
So the arc length is:
arc length = (120 / 360) * (8 * π) = 4 * π / 3
The arc length of RS is approximately 4 * π / 3 inches.
To find the area of sector RFS, we can use the formula:
area = (central angle / 360) * π * r²
So the area of sector RFS is:
area = (120 / 360) * π * (4)² = 8 * π
Therefore, The area of sector RFS is approximately 8π square inches, and the measure of the central angle in radians is approximately 2π/3 radians.
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Answer:
Arch length = 8pi/3
Area of sector = 16pi/3
Central angle in radians = 2pi/3
Step-by-step explanation: see picture-
.
What is the coefficient in this expression?
-17+(-b)+(-25)
Answer:
In the expression -17 + (-b) + (-25), the coefficient is a number that multiplies a variable. In this case, the coefficients are -17, -1 (which multiplies the variable "b"), and -25.
Step-by-step explanation:
Let ∠1 , ∠2 , ∠3 , and ∠4 have the following relationships. ∠1 and ∠2 are vertical angles. ∠3 and ∠4 are right vertical angles. ∠3 is adjacent to both ∠1 and ∠2 . What is the sum of the measure of ∠4 and the measure of ∠1 minus the measure of ∠2 ?
Answer:
Since ∠1 and ∠2 are vertical angles, they have equal measure. And since ∠3 and ∠4 are right vertical angles, they have measure 90° each.
Since ∠3 is adjacent to both ∠1 and ∠2, we can say that:
∠1 + ∠3 = 180°
∠2 + ∠3 = 180°
Adding these two equations together:
∠1 + ∠2 + 2∠3 = 360°
Substituting the values we have:
∠1 + ∠2 + 2(90°) = 360°
∠1 + ∠2 + 180° = 360°
Solving for ∠1 + ∠2:
∠1 + ∠2 = 180° - 180° = 0°
Finally, the sum of the measure of ∠4 and the measure of ∠1 minus the measure of ∠2 is:
∠4 + (∠1 - ∠2) = 90° + (∠1 - 0°) = 90° + ∠1
So the answer is 90° + ∠1.
Louise is planning to renovate her house. She intends to spend no more than $30 000. She has
$20 000 to invest in an account that pay 4.28% compounded monthly. How long will it take
Louise to meet her goal? Show your work. Round your answer to the nearest tenth of a year.
Answer:
Step-by-step explanation:
To determine how long it will take for Louise to reach her goal of $30,000, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A is the amount of money Louise will have after "t" years,
P is the initial investment of $20,000,
r is the annual interest rate of 4.28%,
n is the number of times the interest is compounded per year (12 times per year), and
t is the number of years.
We can rearrange this formula to solve for t:
t = (log(A/P)) / (log(1 + r/n))
Plugging in the values:
t = (log(30000/20000)) / (log(1 + (0.0428/12)))
t = 5.97 years
Rounding to the nearest tenth of a year, Louise will need to wait 6.0 years in order to reach her goal of $30,000.
sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to:
Sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to underestimate the true population variance and standard deviation.
The reason for this is that the sample variance and standard deviation are based on a sample of the population, not the entire population. The sample may not accurately represent the entire population, and thus the sample variance and standard deviation may not accurately reflect the true population variance and standard deviation. To correct for this bias, a correction factor is usually added to the sample variance calculation. For example, when estimating the population variance from a sample of size n, the sample variance is divided by (n-1) instead of n. This correction factor helps to provide a more accurate estimate of the population variance. Similarly, the sample standard deviation is calculated as the square root of the sample variance, and the correction factor is also applied to the sample standard deviation calculation. This corrected sample standard deviation is known as the unbiased sample standard deviation.
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Complete Question
sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to: What?
please help me with my homework!!
10. The value of a book is $58 and decreases at a rate of 10% per year; 8 years.
Answer:
$24.96
Step-by-step explanation:
The question was incomplete. If you are asking how much is the book worth after 8 years, here's how to do it
Original cost = $58
Since the rate of decrease = 10%, the cost of the book after 1 year is 90% of the original price
90% = 90/100 = 0.9
Therefore after 1 year, the book cost is 58(0.9)
After another year(effectively 2 years) the above cost will drop by another 10% to 90% of the first year value: 58(0.9)(0.9) = 58(0.9)²
So the value of the book after a period of n years is modeled by the function
V = 58 (0.9)ⁿ
After 8 years the value is
58 (0.9)⁸ = 58 x 0.43046721
V = $24.96 rounded to the nearest cent
A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34. 5-foot shadow. How tall is the building (Round your answer to the nearest tenth. )
A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34. 5-foot shadow then the building is approximately 95.2 feet tall.
What is similar triangles ?
Similar triangles are useful in geometry and other fields because they allow us to solve problems involving unknown distances or heights. We can use the known lengths and angles of one triangle to find the lengths and angles of the other triangle, as long as we know that the two triangles are similar. This can be done using the properties of proportional relationships and the rules of similar figures.
Let's use similar triangles to solve this problem. The height of the building and the height of the flagpole are proportional to the lengths of their shadows. We can set up the following equation:
height of building / length of building's shadow = height of flagpole / length of flagpole's shadow
Let x be the height of the building. Then we have:
x / 103 = 32 / 34.5
Simplifying this equation, we get:
x = 103 * (32 / 34.5) ≈ 95.23
Therefore, the building is approximately 95.2 feet tall.
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Vocabulary Explain how to isolate the variable in the eqaution -2/3n = 7 + 15
The variable n in the original equation -2/3n = 7 + 15 is equal to -12.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable maybe pointed search is the energy.
In order to isolate the variable in the equation -2/3n = 7 + 15, the first step is to subtract 7 from each side of the equation. This results in -2/3n = 8. Next, multiply each side of the equation by 3 to cancel out the 3 in the denominator. This leaves -2n = 24. Finally, divide each side of the equation by -2 to isolate the variable n. This results in the equation n = -12. Therefore, the variable n in the original equation -2/3n = 7 + 15 is equal to -12.
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Help me with this math homework pls!
Rewrite every expression underneath, while replacing every sign "x" implied.
23 + 8b = .......
㎡ - 5g = .......
⅛ q + 7a/3 = .....
12k (g+h) =......
(2x + 3)(2 - 5x) = ......
The following expressions rewritten below;
23 + 8bm² - 5g(3q + 56a) / 2412kg + 12kh -10x² -11x + 6How to write algebraic expressions?23 + 8b
No common terms or factors
= 23 + 8b
㎡ - 5g
No common terms or factors
= m² - 5g
1/8 q + 7a/3
= (3q + 56a) / 24
12k (g+h)
= 12kg + 12kh
(2x + 3)(2 - 5x)
= 4x - 10x² + 6 - 15x
combine like terms
= -10x² -11x + 6
Therefore, algebraic expressions are solved by multiplying and combining like terms.
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Two more than 3 times a number is 20. Find the number.
Answer: the number is 6
Step-by-step explanation: First, set up an equation. Two more means +2, 3 times a number means 3x. So your equation would be 3x+2=20. Then solve the equation for x.
Answer:
x = 6
Step-by-step explanation:
Let the number be 'x'
Then, the equation becomes,
2 + 3x = 20
3x = 20 - 2
3x = 18
x = 18/3
x = 6
Hope it helped :)
What is (1/243) ^-x/3 = 4
Using the log, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].
What is a logarithm?The power to which a number must be increased in order to obtain another number is known as a logarithm.
For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.
So, solve using a log as follows: (1/243) ^-x/3 = 4
[tex]\begin{aligned}& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4\end{aligned}[/tex]
[tex]\begin{aligned}& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4\end{aligned}[/tex]
[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=12\end{aligned}[/tex]
[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=12 \\& -x=\log _{\frac{1}{243}}(12) \\& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& -x=\log _{\frac{1}{243}}(12)\end{aligned}[/tex]
Therefore, using the log, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].
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Gordon currently brings in an annual salary of $92,338 and anticipates a raise of 5% every
year. What will his salary be in 3 years?
If necessary, round your answer to the nearest cent.
Answer:
Gordon will have $106892.8 in three years
Step-by-step explanation:
92338 (0.05 + 1)³=
92338(1.05)³=
92338 x 1.16 =
106892.8
Given AB
and DC, complete the flowchart proof below. Note that the last statement reason have both been filled in for you.
The completed flowchart proof is that ΔΑΒΕ = ΔCDE
What is Geometry?Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and dimensions of objects in space. It is concerned with the properties of points, lines, curves, surfaces, and solids, as well as the relationships between them.
How to prove this:
<ABD = <BDC
(alternate angles)
<BAC = <ACD
(alternate angles)
Hence, BE = ED (given)
So, ΔΑΒΕ = ΔCDE
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What is the sum of 9.72 × 108 and 1.93 × 107?
Answer:
The solution is 9,913 × 10⁸
Step-by-step explanation:
9,72 × 10⁸ and 1,93 × 10⁷
9,72 × 10⁸ + 1,93 × 10⁷
Factor the shape
= 10⁷ (9,72 × 10 + 1,93)
= 10⁷ (97,2 + 1,93)
= 10⁷ × 99,13
= 9,913 × 10⁸
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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Two sides of a triangle are
shown. Find the range of
values of the third side.
10, 5
< X
Answer:
5 < x < 15
Step-by-step explanation:
The triangle inequality theorem states that the sum of the measures of any two sides of a triangle must be greater than the measure of the third side
In the given triangle we are provided measures of two of the sides as 10 and 5
Let the measure of the third side be x
So the three sides are 10, 5 and x
Then by the inequality theorem
10 + 5 > x
==> 15 > x or
x < 15 This is an upper bound for x
when we switch sides in an inequality > changes to < and < changes to >
We also have
x + 5 > 10 ==> x > 10 - 5 ==> x > 5
and
x + 10 > 5 ==> x > -5
Since x > 5 is more restrictive than x > -5, we conclude that x > 5 or 5 < x is the lower bound on x
Combining all inequalities we get
5 < x < 15
Note
We could also state the lower and upper bound limits as
difference of two sides < x < sum of two sides
10 - 5 < x < 10 + 5
or
5 < x < 15
While this may seem easier to compute than the explanation given above, the derivation is left out and may confuse some students
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle
and two congruent triangles. As a result, the altitude cuts the base into two equal
segments. The length of the altitude is 11 inches, and the length of the base is 6
inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.
In a group of 62 people 27 like cold tea while 42 like hot tea how many people like neither of the two
Answer:7
Step-by-step explanation:
let P(a)=27, like cold tea,
P(b)=42, like hot tea,
P(a∪b)=62,
using formula,
P(a∩b)=P(a)+P(b)-P(a∪b)
=27+42-62
=7
1/2 of 2/3 = 1/2 of ____ third(s) = ____ third(s)
The product of 1/2 and 2/3 is equivalent to one third
Taking the product of fractions
Fractions are expressions written as a ratio of two integers. For instance a/b is a fraction
Given the expression below
1/2 of 2/3
This can also be written as;
1/2 of 2/3 = 1/2 of two thirds
Simplify
1/2 * 2/3 = 2/6
1/2 of 2/3 = 1/3
Hence the resulting value of the expression is one third
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mr. tabor believes that less than 75% of the students at his school completed their math homework last night. the math teachers inspect the homework assignments from a random sample of 50 students at the school. what are the appropriate hypotheses for performing this significance test?
The null hypothesis statement is that the population is equal to the value mentioned in the claim:
[tex]H_{0} =P=75%=0.75[/tex]=[tex]\frac{75}{100}[/tex]=[tex]0.75[/tex].
[tex]H_{0} =P < 0.75[/tex]
The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis.
[tex]H_0} =P < 0.75[/tex]
A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.
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For a classical infinite square-well potential of width a. How does the classical result compare with the quantu
For small particles such as atoms and subatomic particles, quantum mechanics produces more accurate results than classical mechanics. As the particle size decreases, the differences between classical and quantum mechanical results become more pronounced.
The particle in an infinite square well potential is treated as a point particle with well-defined position and momentum in classical mechanics. The classical solution to the infinite square well problem involves a particle bouncing back and forth between the well's walls, its energy being provided by the kinetic energy associated with its motion inside the well.
In quantum mechanics, on the other hand, the particle in an infinite square well potential is treated as a wave function that solves the Schrödinger equation. The probability distribution of the particle's position and momentum inside the well is described by the wave function. The allowed energy levels of the particle are quantized and can be calculated using the problem's boundary conditions.
The following formula gives the classical result for a particle's energy in an infinite square well potential:
[tex]n2*h2/(8ma2) = E n[/tex]
where n is an integer, h is Planck's constant, and m is the particle's mass. According to this formula, energy levels are continuous and can take any value.
The quantum mechanical result for a particle's energy in an infinite square well potential, on the other hand, is given by the formula:
[tex]E n = (n2 * pi2 * h2) / (2ma2).[/tex]
n must be a positive integer. According to this formula, energy levels are quantized and can only take on discrete values.
As a result, the classical result for the energy of a particle in an infinite square well potential differs greatly from the quantum mechanical result. The classical result predicts continuous energy levels, whereas the quantum mechanical result predicts quantized energy levels.
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Ken bought a bike that was priced at $450. He was offered a 25% discount what was the discount on the bike
If discount offered is 25% then the discount on the bike is $112.50 by multiply the rate by the original price.
What is discount price?
Discount pricing is a type of promotional pricing strategy where the original price for a product or service is reduced with the aim of increasing traffic, moving inventory, and driving sales.
According to the question:
Ken bought a bike that was priced at $450
Discount percentage offered to him is 25%
To find the discount price, first the rate is usually given as a percent.
To find the discount, multiply the rate by the original price.
Discount = [tex]450 \times \frac{25}{100}[/tex]
Therefore the discount on the bike is $112.50
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