Consider a particle in a rigid box of length L. For each of the states n = 1, n = 2 and n = 3:
a. Sketch graphs of ǀ (x) ǀ2. Label the points x = 0 and x = L.
b. Where, in terms of L, are the positions at which the particle is most likely to be found?
c. Where, in terms of L, are the positions at which the particle is least likely to be found?
d. Determine, by examining your ǀ (x) ǀ2 graphs, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than 1 3. Explain your reasoning.
e. Calculate the probability that the particle will be found in the left one-third of the box.
Answers
For states, n = 1, 2, and 3 the probability of finding the particle at left 1/3rd of the box is P₁ = (3/4) * (2/L)² P₂ = (1/4) * (2/L)² and P₃ = (1/3) * (2/L)² respectively
a.
The wave function for the particle in a rigid box of length L for the state
n = 1, is given by:
|ψ₁(x)|² = (2/L)² * sin²(πx/L)
the wave function for the state n = 2, is given by:
|ψ₂(x)|² = (2/L)² * sin²(2πx/L)
And the wave function for the state n = 3, is given by:
|ψ₃(x)|² = (2/L)² * sin²(3πx/L)
The graphs of |ψ₁(x)|², |ψ₂(x)|², and |ψ₃(x)|² is attached.
b.
The points of maximum probability density, which occur at x = 0 and x = L for all three states are the positions at which the particle is most likely to be found.
c.
The points of minimum probability density, occur at x = L/2 for the state
n = 1, and at x = L/4 and x = 3L/4 for the state n = 2. For the state n = 3, the points of minimum probability density occur at x = L/3, x = 2L/3, and
x = L are the positions at which the particle is least likely to be found.
d.
Since the probability density is highest at x = 0, which is in the left one-third of the box for the state n = 1 the probability of finding the particle in the left one-third of the box is greater than 1/3.
Since the probability density is highest at x = 0 and x = L, which are both outside the left one-third of the box for the state n = 2, the probability of finding the particle in the left one-third of the box is less than 1/3.
Since the probability density is highest at x = 0, which is in the left one-third of the box for the state n = 3, the probability of finding the particle in the left one-third of the box is equal to 1/3.
e.
We need to integrate the probability density over the region of interest to calculate the probability that the particle will be found in the left one-third of the box for each of the states n = 1, n = 2, and n = 3.
the probability for the state n = 1, is given by:
P₁ = ∫ |ψ₁(x)|² dx = (2/L)² * ∫ sin²(πx/L) dx
The probability for the state n = 2, is given by:
P₂ = ∫ |ψ_2(x)|² dx = (2/L)² * ∫ sin²(2πx/L) dx
The probability for the state n = 3, is given by:
P₃ = ∫ |ψ₃(x)|² dx = (2/L)² * ∫sin²(3πx/L) dx
Here all integrals have limits 0 and L/3
Solving these integrals gives:
P₁ = (3/4) * (2/L)²
P₂ = (1/4) * (2/L)²
P₃ = (1/3) * (2/L)²
Thus, the probabilities that the particle will be found in the left one-third of the box are:
P₁ = (3/4) * (2/L)²
P₂ = (1/4) * (2/L)²
P₃ = (1/3) * (2/L)²
for the states n = 1, n = 2, and n = 3, respectively.
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Related Questions
line m and point p are graphed on the coordinate grid below. which equation represents a line that passes through point p and is parallel to line m?
Answers
The equation of the graphed on the coordinate grid parallel to line M y = x and passing through the point P(4, -7) is equal to y = x - 11.
As given in the question,
Equation of the line M is given by :
y = x
Slope of the line M by comparing it with standard equation of the line with slope m is given by :
y = mx + c
Equation of the line M is y = x
Here m = 1
Slope of the required line is m₁ = 1 as it is parallel to line M
Equation of the required line which passes through ( x₁ , y₁) = ( 4, -7) with slope m₁ = 1 is given by:
y - y₁ = m₁( x - x₁)
⇒ y + 7 = 1( x - 4)
⇒ y= x - 4 -7
⇒ y= x - 11
Therefore, the equation of the required line which is parallel to line M and passing through point P is equal to y = x - 11.
Line M is graphed on the coordinate grid. y = x. Which equation can be used to represent a line parallel to M passing through the point P(4, -7)?
A. x = 4 B. x = -7 C. y = -7 D. y = 4
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The number t is rational and positive. Which statement about ग/t is true?
Answers
The number π/t is an irrational and positive number.
What are rational and irrational numbers?The rational numbers are composed by the set of all numbers that can be represented by fractions, such as whole numbers, terminating decimals, or repeating decimals.
The irrational numbers, conversely, are composed by the set of numbers that cannot be represented by fractions, such as non-exact roots and non-terminating decimals.
The number π is defined as follows:
π = 3.1415...
Which is a non-terminating decimal, hence it is an irrational number.
When an irrational number is divided by a rational number, as is the case in this problem, the result is irrational.
π is a positive number, just like t, hence the quotient is also a positive number.
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The graph of a linear function is shown on the grid.
#6. Find the slope:
#7. Find the y-intercept:
#8. Write the equation in slope-intercept form:
Answers
The slope m = -5/4 , y - intercept is 5 and the equation in slope - intercept form is y = (-5/4)x + 5 .
Given :
The graph of a linear function is shown on the grid.
From the graph :
Take two points ( 0 , 5 ) and ( 4 , 0 )
slope m = 0 - 5 / 4 - 0
= -5 / 4
we know that ,
slope intercept form is y = mx + b
substitute m and ( 0 , 5 )
5 = -5 / 4 ( 0 ) + b
5 = 0 + b
b = 5 ( y - intercept )
substitute b and m value
y = (-5/4)x + 5
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answers
The value of x that will make the two given solids similar is: d. x = 31.
What are Similar Solids?Similar solids are solids that are scale copy of each other, that is, either of the solids can produce the other when enlarged by a scale factor to get the dimension of the other solid.
Therefore, if two solids are similar, their corresponding linear dimensions would have an equal ratio, or they would be proportional.
Applying the definition of similar solids, the equation below would be created in order to determine the value of x:
x/15.5 = 29/14.5
Cross multiply:
14.5x = 15.5 × 29
14.5x = 449.5
14.5x/14.5 = 449.5/14.5
x = 31
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give an example of a nonabelian group g with the property that every subgroup h of g is a normal subgroup.
Answers
Hamiltonian group is an example of a nonabelian group g with the property that every subgroup h of g is a normal subgroup.
To prove that h be a subgroup of g. and suppose h is the only subgroup of g of order(h) h is normal in g is that it is proven by homomorphism .
This is a small contribution, however in reaction to a remark above, you may additionally clear up this with out the use of any homomorphism properties. Assume the subgroup H has order n and select out g∈g.
Since H has order n. The above holds for all h∈H, so the subgroup gHg−1 has order n, so it's miles identical to H through assumption. Then each h∈H has a few h∈H such that ghg−1=h′, implying gh=h′g, so gH=H
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Deloitte employment survey asked sample of human resource executives how their company planned to change its workforce over the next 12 months_ categorical response variable showed three options: The company plans to hire and add to the number of employees the company plans no change in the number of emplovees_ or the company plans to lay off and reduce the number of emplovees_ Another categorical variable indicated if the company was private public Sample data for 168 companies are summarized as follows Company Employment Plan Private Public Add Employees No Change Lay Off Employees Conduct test of independence to determine if the employment plan for the next 12 months is independent of the type of company At a 05 level of significance_ Compute the value of the x? test statistic (to 2 decimals). 8.73 The p-value petween 01 and .025 What is your conclusion? Conclude the employment plan not independent of the type of company. Discuss any differences in the employment plans for private and public companies Over the next 12 months_ Private companies are more likely to add employees Public companies are more likely to lay off employees_ of private companies plan on adding employees_ 34.9 % of public companies plan on adding off employees. (to decimal)
Answers
As per the chi square test, the variable are dependent to each other.
What is meant by chi-square test?
In math, the chi square test refer a statistical test used to compare observed results with expected results.
From the table in the question; we can see the changes in employees adding, shedding, or not changing their staffing.
Converting the table to chi- squared using the relation.
Here the observed frequency is = 44 and the expected frequency is = 34.8
And the Number Change 0.1421 0.0079 0.15
=> Lay Off 4.8286 2.4083 7.2369
=> Total = 14.657
Therefore, the total chi-square = 14.657;
In order to find the value for p; we need to determine the degree of freedom
=> df = (2-1)(3-1)
Then the result to a degree of freedom of 2
Here from the chi square chart at the chi-square is 14.657 and degree of freedom is 2 ; the p value is between 0.1 and 0.005. Since this makes p-value less than 0.05.
Therefore, the variables are dependent.
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12 Express this in scientific notation: (1.33) (13 × 10³)
1.729 × 10⁰
B) 1.729 x 108
C) 17.29 x 10⁹
D) 17.29 x 108
Answers
The given expression can be written in scientific notation as 1.729 x 10⁹.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
Given is to express the given expression in scientific notation.
The given expression is -
(1.33) (13 × 10⁸)
Solving further -
1.33 x 13 x 10⁸
17.29 x 10⁸
1.729 x 10⁹
Therefore, the given expression can be written in scientific notation as 1.729 x 10⁹.
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Carissa skis along a circular ski trail with a radius 1.3 km long. Carissa starts at the 3-o'clock position of the trail (the East-side) and travels in the CCW direction. Which of the following expressions represents Carissa's distance to the right of the center of the skitrail in km, h, in terms of the number of km that Carissa has traveled since she started skiing.d? Oh 1.3 cos(d+ 1.3) Oh = 1.3 cos(1.3. d) h = 1.3 cos d 1.3 Oh = 1.3 cos(d) OhCOS 1.3 Submit Question 16. Points possible: 4
Answers
The expressions that represents Carissa's distance to the right of the center of the skitrail, i.e, h in terms of the number of times Carissa has traveled since she started skiing,d is h = 1.3 cos( d/1.3). So, correct answer is option (c).
We have, Carissa skis along a circular ski trail. Radius of circle , r = 1.3 km
Carissa starts at the 3-o'clock position of the trail travels in the counter clockwise direction. let "d" km be total distance that Carissa has traveled since she started skiing and "h" km be Carissa's distance to the right of the center of the skitrail in km.
We have to wright an expressions for "h" in terms of d . Here, we see an sector is formed with one side length is r and arc's distance is d km . Let θ be angle formed by this sector . Using the sector formula,
θ = arc length /radius of circle
=> θ = d/r = d/1.3 --(1)
Also, ∆ formed here , h = r cos θ
=> h = 1.3 cos( d/1.3)
Hence, the required expression is h=1.3 cos( d/1.3).
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Complete question:
Carissa skis along a circular ski trail with a radius 1.3 km long. Carissa starts at the 3-o'clock position of the trail (the East-side) and travels in the CCW direction. Which of the following expressions represents Carissa's distance to the right of the center of the skitrail in km, h, in terms of the number of km that Carissa has traveled since she started skiing.d?
a)h 1.3 cos(d+ 1.3)
b) h = 1.3 cos(1.3/d)
c)h = 1.3 cos (d /1.3 )
d)h = 1.3 cos(d)
e) h = COS( 1.3 )
Submit Question 16. Points possible:
which of the variables listed above would best be displayed graphically using a bar graph? mark all that apply. group of answer choices number of minutes of exposure to secondhand smoke per day currently diagnosed with asthma race years of education gender
Answers
The two possible variables design are; "COHORT STUDY" and "CROSS-SECTIONAL STUDY".
Cohort study design is an observational study in which people who receives a particular treatment or are under a particular condition, are been observed and studied. This type of research model also allows a researcher to compare people affected by a condition to people unaffected by the same conditions.
The investigator is likely to use the cohort design because it will help in studying the children that are always exposed to smoke, and to observe the affected and unaffected children.
The CROSS-SECTIONAL design is an observational study in which a specific population are studied at a particular time. This type of research allows the researcher to study the difference in that population at a time interval.
This study design is likely to be used by the investigator, because it will help the investigator to determine the amount of secondhand smoke each child inhale at a particular time. It will also help the investigator to know the outcome of each child after 5years
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Write a congruence statement for the triangles. Then identify all pairs of congruent corresponding paris.
∠Q≅ ?
∠R≅ ?
∠P≅ ?
PQ≅ ?
QR≅ ?
Answers
The ΔPQR and ΔCBA are congruent using ( SAS , AAA , ASA) properties
If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.
According to the question,
We have to identify all the pairs of congruent
In ΔPQR and ΔCBA,
If we look the figure
(1) ∠Q ≅ ∠B
(2) ∠R ≅ ∠A
(3) ∠P ≅ ∠C
(4) PQ ≅ CB
(5) QR ≅BA
Therefore , All three angles are equal and all three sides
hence , ΔPQR ≅ ΔCBA by using AAA or ASA or SAS properties
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Is the following information a statistic or a parameter?
You have surveyed a group of 35 randomly selected peers to inquire how many cell phones they owned in their life and found that the most common answer was 4 cell phones.
Statistic
Parameter
Answers
It is based on a sample and provides information about the sample based on a survey of 35 samples, this four cell phone is a statistic, so the response is a statistic.
When looking at populations, the term "median" is a significant and frequently used statistic. Most of the time, it's used to represent a set of numbers.
We sort the population numbers to find the one in the middle to find the median. It differs from the mean and can sometimes be more useful than the mean, such as when there are outliers that could have an excessive impact on the mean. We should take the average of the two values in the middle if the number of values is even.
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differentiate of the following w.r.t.
give me this answer i mark u brainlist
Answers
Answer:
[tex]\frac{dy}{dx}=\frac{4}{3}x^{1/3}+e^x +\cos x[/tex]
Step-by-step explanation:
[tex]\frac{d}{dx} x^{4/3}=\frac{4}{3}x^{1/3} \\ \\ \frac{d}{dx} e^x=e^x \\ \\ \frac{d}{dx} \sin x=\cos x \\ \\ \therefore \frac{dy}{dx}=\frac{4}{3}x^{1/3}+e^x +\cos x[/tex]
Tipton Tile has seen an increase in tile sales over the last few weeks. They sold 4,212 square feet of tile to 36 customers last week. If they are expecting between 51 and 59 people to buy tile this week, about how many square feet of tile can they expect to sell?
Answers
Tipton Tile expected to sell between, 5967 and 6902 square feet of tiles.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given,
Tipton Tile has seen an increase in tile sales over the last few weeks.
They sold 4,212 square feet of tile to 36 customers last week.
That means,
4212 / 36 = 117 square feet of tiles per person.
If they are expecting between 51 and 59 people to buy tile this week.
To find the number of square feet of tiles:
For 51 people,
117 x 51 = 5967 square feet of tiles.
And for 59 people,
117 x 59 = 6903 square feet of tiles.
Therefore, They expected to sell between, 5967 and 6902 square feet of tiles.
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I NEED SOME CORRECT ANSWER PLEASE WITH SOLVING!!
A. You need to buy 3eggs cost 8.00, 2 hotdogs cost 10.00 and 3bread cost 5.00 each. How much money you will need to take to the sari-sari store B. Evaluate the following polynomial 4x² + 2x - 3
(i need a reaal math genius please solve it with the right answer and right solving please i'm begging you
Answers
89 is the money you will need to take to the sari-sari store and x=-1±√13/4 is the value of polynomial 4x² + 2x - 3.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that need to buy 3 eggs cost 8.00
2 hotdogs cost 10.00
3 bread cost 5.00 each.
We need to find the money you will need to take to the sari-sari store.
3(8)+2(10)+3(15)
24+20+45
89
The given polynomial is 4x² + 2x - 3=0
a=4, b=2 and c=-3
x=-b±√b²-4ac/2a
x=-2±√4-4(4)(-3)/8
x=-1±√13/4
Hence, 89 is the money you will need to take to the sari-sari store and x=-1±√13/4 is the value of polynomial 4x² + 2x - 3.
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a 13 foot ladder is leaning against the side of a house when its base starts to slide away. by the time the base is 12 feet from the house, the base is moving at a rate of 5 feet per second.
Answers
If the base of the ladder is moving at 5 ft/s , then the speed of top of the ladder is 12ft/s .
Pythagoras Theorem states that the relation between the square of the longest side is equal to the squares of the other two sides .
the length of the ladder (L) = 13 ft ;
the rate of movement of the base (dx/dt) = 5 m/s ;
By Pythagoras Theorem ,
13 = x + y ....eqn(1)
So , y = √(169 - x)
putting x = 12 , we get ;
y = √(169 - 144) = 5 ft ;
Differentiating eqn(1) , w.r.t. "x" ,
we get ;
0 = 2x(dx/dt) + 2y(dy/dt)
So , dy/dt = (-x/y)(dx/dt)
putting the values ,
we get ;
dy/dt = -12 ft/s .
Therefore , the ladder is sliding down the wall at 12 ft/s .
The given question is incomplete , the complete question is
A 13 foot ladder is leaning against the house when its base starts to slide away. By the time it is 12 feet from the house, the base is moving at the rate of 5 ft/sec.
How fast is the top of the ladder sliding down the wall at that moment ?
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researchers are testing a new diagnostic tool designed to identify a certain condition. the null hypothesis of the significance test is that the diagnostic tool is not effective in detecting the condition. for the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective. which of the following should the researchers do to avoid the more consequential error?
Answers
Based on the null hypotheses, the type of error is Decrease the significance level to decrease the probability of Type I error.
What does null hypotheses means?
In math, null hypotheses refers a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations.
Here we have give that researchers are testing a new diagnostic tool designed to identify a certain condition. the null hypothesis of the significance test is that the diagnostic tool is not effective in detecting the condition. for the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective.
And we need to find in which of the following should the researchers do to avoid the more consequential error.
According to the given question, the null hypothesis is that the new diagnostic tool is not effective in detecting the condition.
Here the more consequential error described is that the diagnostic tool is not effective, but the significance test indicated that it is effective. This is a type I error.
And in Hypothesis testing, a type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.
Therefore, it involves saying there is significant evidence to show that the new diagnostic tool is effective in detecting the condition when in reality, it isn't.
When the level of significance (α) of a hypothesis test directly gives the probability of a type I error. So, by setting it lower, we reduce the chances of a type I error.
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a. compute the sample mean and sample standard deviation for private and public colleges. round your answers to two decimal places.
Answers
The sample mean is = 6.98, the standard deviation is = 4.53 (2) The pint estimate difference is = 20.2 (3) The confidence interval limits are $ 15943.6 and $24456.4
a)
Private Universities
Sample median: 42,500 dollars
Mean = (Σx)/N
where N = Sample size
Σx = sum of all variables
Private colleges
Σx = (52.8+43.2+45.0+33.3+44.0+30.6+45.8+37.8+50.5+42.0) = 425
N = 10
Mean = 425/10 = 42.5 thousand dollars
Standard deviation = S1 = √[Σ(x - xbar)²/N]
Σ(x - xbar)² = (52.8-42.5)² + (43.2-42.5)²
+ (45.0-42.5)² + (33.3-42.5)²
+ (44.0-42.5)² + (30.6-42.5)² + (45.8-42.5)² + (37.8-42.5)² + (50.5-42.5)² + (42.0-42.5)² = 438.56
N = 10
Standard deviation = √[Σ(x - xbar)²/N]
Standard deviation = √(438.56/10) = 6.62 thousand dollars
S1 or the standard deviation equals $6.62k.
b)
The sample means the difference in both circumstances is 42.5 minus 22.3, or 20.2 thousand dollars.
Going to a private college often costs 20.2 thousand dollars more than going to a public institution on average.
c)
A sample distribution's 95% confidence interval for the price difference between private and public colleges is provided as
(15.0, 25.4) dollars in thousands.
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The wildlife game commission poured 5 cans of fish (each can contained approximately 100 fish) into a farmer's lake. The function N defined by 600t +500 Ne)represents the approximate number of fish in the lake as a tunction of time (n years) Which ome f he olowin N(t)0.5+1 describes how the number of fish in the lake changes over time? O The number of fish gets larger each year, but does not exceed 1200. OThe number of fish gets smaller every year but does not get smaller then 1200. O The number of fish gets arger each year, but does not exceed 600. O The number of fish gets larger each year, but does not exceed 500. O The number of fish gets smaller every year, but does not get smaller than 500.
Answers
This steady-state number of fish is ... 1200 - 1058 = 142 . . . . below the original carrying capacity
The differential equation is modified by adding a -100 fish per year constant term:
(dN)/(dt) = (0.4)/(1200)N(1200-N) -50
The steady-state value of the fish population will be when N reaches the value that makes dN/dt = 0.
(0.4/1200)(N)(1200-N) -50 = 0
N(N-1200) = -(50)(1200)/0.4) . . . . rewrite so N^2 has a positive coefficient
N^2 -1200N + 600^2 = -150,000 +600^2 . . . . complete the square
(N -600)^2 = 210,000 . . . . . simplify
N = 600 + √210,000 ≈ 1058
This steady-state number of fish is ...
1200 - 1058 = 142 . . . . below the original carrying capacity
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An electronics store receives a shipment of 30 graphing calculators, including 7 that are defective. Four of the calculators are selected to be sent to a local high school. How many of these selections will contain no defective calculators?
Answers
Based on probability, three of the four selected calculators will contain no defective.
What is the probability?Probability refers to the likelihood or chance that an expected outcome occurs in the midst of many possible outcomes or events.
Probability is zero when uncertain and one when 100% certain. Otherwise, probability lies between zero and one, which yields a fractional value denoted by decimals, percentages, or fractions.
The number of shipped graphing calculators = 30
The number of defective calculators = 7
The probability of defective calculators = 0.233 (7/30)
The probability of no defective calculators = 0.767 (1- 0.233)
The number of calculators to be sent to a high school = 4
The number of these that will contain no defective calculators = 3.068 (4 x 0.767)
= 3
Thus, the local high school will probably receive 3 non-defective units.
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to determine that a item is not in an unordered array of 100 items, how many values must linear search examine on average? a) 7 b) 10 c) 100
Answers
To determine that an item is not in an unordered array of 100 items, total numbers of values which have to linear search examine on average is 100. The correct answer is C.
What is Linear Search?Linear Search is described as a sequential search algorithm which starts at one end and goes through each element of a list until the needed element is found, otherwise the search continues till the end of the data set. This is the simplest searching algorithm.
Starting at the beginning of the data set, each item of data is examined until a match is made. Once the item is found, the search ends.
Hence, in this case, since there are 100 items, then there will be 100 numbers of values.
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Help me thank u with these questions I appreciate it
Answers
18. not a function
19. not a function
20. the left side graph is a function
18. Any relation to be a function, any x value should have only one y value
this is not a function because when x=7 , y= 9 and 12 (two y values for one x value)
19. x=-1 has two y values
and x=1 also has two y values
20. here, you can use the vertical line test.
the left graph passes the vertical line test which is a function because any vertical line drawn intersects the curve in only 1 point, but the right graph, the vertical line intersects the curve in 2 points, which is not a function.
Compared to the parent function f(x)=x², the function g(x) has been horizontally shrunk by a factor of 1/3 and then vertically stretched by a factor of 4 .
Which is g(x) ?
(A) g(x)=3(1/4x)²
(B) g(x)=3(4 x)²
(c) g(x)=4(1/3x)²
(D) g(x)=4(3 x)²
Answers
If the parent function f(x) = x² is horizontally shrunk by factor of 1/3 ad vertically stretch by factor of 4 then g(c) will be g(x) = 4(1/3x)² , the correct option is (c) .
In the question ,
it is given that ,
the parent function is ⇒ f(x) = x² ;
the graph is horizontally shrunk by a factor of 1/3 that means
the function will become (1/3x)² .
next the function is then vertically stretch by a factor of 4 ,that means
then the function becomes g(x) = 4(1/3x)².
Therefore , the correct option is g(x) = 4(1/3x)² .
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. in triangle 4abc, m is the midpoint of the side ab and n is the midpoint of the side ac. find the length of the segment mn if ab =18, bc= 10 and ac= 20
Answers
The length of the segment of the MN is 10 units, by using the midpoint formula and distance formula.
Distance FormulaThe algebraic phrase is known as the distance formula, which provides the distances between two places in terms of their coordinates (see coordinate system). The distance formulas for points in rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.
Since M is the midpoint of side AB and N is the midpoint of side AC, we can use the midpoint formula to find the coordinates of points M and N.
Midpoint Formula: (x₁ + x₂)/2, (y₁ + y₂)/2
For M:
(A x + B x)/2, (A y + B y)/2
= (18 + 0)/2, (0 + 0)/2
= 9, 0
For N:
(A x + C x)/2, (A y + C y)/2
= (18 + 20)/2, (0 + 0)/2
= 19, 0
Step 4: Now that we have the coordinates of M and N, we can use the distance formula to find the length of the segment MN.
Distance Formula: √((x₂ - x₁)² + (y₂ - y₁)²)
For MN:
√((19 - 9)² + (0 - 0)²)
= √(100)
= 10
Therefore, the length of the segment MN is 10 units.
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Please solve these equations! Ill give brainiest!
Answers
Answer:
see explanation
Step-by-step explanation:
1
[tex]\frac{bh}{2}[/tex] = A ( multiply both sides by 2 to clear the fraction )
bh = 2A ( divide both sides by h )
b = [tex]\frac{2A}{h}[/tex]
2
2l + 2w = P ( subtract 2l from both sides )
2w = P - 2l ( divide both sides by 2 )
w = [tex]\frac{P-2l}{2}[/tex]
3
C = 2πd ( isolate d by dividing both sides by 2π )
[tex]\frac{C}{2\pi }[/tex] = d
2. To help pay for college, you worked part-time at a local restaurant, earning $25,000 in
wages and tips. Using the FICA table on your formula sheet, calculate the FICA taxes for
you to pay.
FICA=
Ir part-time at a local supermarket. The job pays $8.80-
40% of his gross pay
Answers
Answer:
8584946569585889594934u
Two times the sum of a number and nine is 24. What is the number?
Answers
Answer: The number is 3
Step-by-step explanation:
2(x+9)=24
x+9=12
x=3
Consider The Following Problem: Min - X1 + X2 S.T. X1 + X3 – 2xı = 0 (X1, X2) E X Where X Is The Convex Combination Of The Points (-1,0), (0,1) (1,0), (0,-1). a. find the optimal solution graphically b. Do the frizt john or KTT condition hold the optimal solution in part (a)? if not explain in the term of the theorem 4.3.2.and 4.3.7 in the textbook.
Answers
The objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, satisfies the KKT condition.
To find the optimal solution graphically, first plot the points (-1,0), (0,1), (1,0), and (0,-1) on the coordinate plane. These points form a square. The objective function for this problem is to minimize -x1 + x2. So we need to find the point on the square that is as low as possible on the y-axis (because the y-axis represents x2).
The constraint in question is x1 + x3 - 2x1 = 0, which can be rewritten as x3 = 2x1. Since x1 and x3 are variables, this represents a line on the coordinate plane. You can draw this line by selecting two points on this line and connecting them with a line. For example, you can select points (-1, -2) and (1, 2). These points lie on the line x3 = 2x1 and the connecting lines are plotted in the coordinate plane.
We can find the best solution by finding the point on the square that is the lowest possible on the straight line of y-axis and x3 = 2x1. The point that satisfies both of these conditions is the point (0,-1). This is the best solution for your problem.
To answer the second part of the question we need to determine whether the Fritz-John condition or the KKT condition is the optimal solution. The Fritz-John condition is an optimality requirement involving an objective function and problem constraints. A KKT condition is a necessary and sufficient condition for optimality that includes an objective function, a constraint, and a multiplier associated with the constraint.
The Fritz-John condition is not considered optimal for this problem. This is because the optimal solution does not satisfy the condition x1 + x3 – 2x1 = 0. The point (0,-1) does not satisfy the condition because it is not on the line x3 = 2x1.
KKT conditions are considered to be the best solution. This is because the point (0,-1) is a legal point (it lies on the square representing the legal region) and the global minimum of the objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, which satisfies the KKT condition.
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a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week, t(t). the function t(t) can be expressed as t(t)
Answers
a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week is C(T) = $730 + $25T
R(T) = $35T
T = 193 transact
C = cost ; R = revenue ; T = number of transactions
Amount paid per transaction = $25
Cost keeping office open = $730
Amount collected on each transaction = $35
(a) Find a formula that gives C as a function of T.
C(T) = Cost of keeping office open + (cost per transaction × number of transactions)
C(T) = $730 + $25T
(b) Find a formula that gives R as a function of T.
R(T) = (Amount collected per transaction * number of transactions)
R(T) = $35T
(c) Find the number of daily transactions that are needed to make the revenue $1200 more than the cost.
R = C + 1200
Substitute the value of R and C into the equation:
35T = 730 + 25T + 1200
35T - 25T = 730 + 1200
10T = 1930
T = 1930 / 10
T = 193 transactions
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the ceo of a cable company claims that the mean wait time for callers at the company's customer service center is no more than 7 minutes. a random sample of 36 customers who called the company's customer service center produces the following data:
Answers
To test the CEO's claim about the mean wait time we need to conduct a hypothesis test.
The null hypothesis is that the mean wait time is no more than 7 minutes, which we can represent as H0: μ ≤ 7. The alternative hypothesis is that the mean wait time is greater than 7 minutes, which we can represent as Ha: μ > 7. We can use a one-tailed t-test for this situation, with a significance level of alpha = 0.05.
To perform the t-test, we need to calculate the sample mean, sample standard deviation, and the t-statistic. The sample mean is the sum of the wait times divided by the sample size, which is 36 in this case. The sample standard deviation is a measure of the dispersion of the data. The t-statistic is calculated using the sample mean, sample standard deviation, and the hypothesized mean wait time of 7 minutes.
Once we have calculated the t-statistic, we can compare it to the critical value from the t-distribution table to determine the p-value. If the p-value is less than alpha, we can reject the null hypothesis and conclude that the mean wait time is indeed greater than 7 minutes. If the p-value is greater than alpha, we cannot reject the null hypothesis and must conclude that the mean wait time is no more than 7 minutes.
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Mrs. Parker earns a 8.5% commission on her total sales. Last month, she had sales of $53,910. How much commission did Mrs. Parker earn last month
Answers
The commission earn by Mrs. Parker earn last month is $ 4,582.35
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
What is the formula's percentage?
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
Given that:
Total sales = $53,910
Commission = 8.5%
Commission in cash = 53910 * 0.085 = 4,582.35
Hence commission earn by Mrs. Parker earn last month is $ 4,582.35
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