Answers
Answer:
50
Step-by-step explanation:
P= 2l + 2w Formula for a perimeter
P= 184 given
l= 4x+2 given
w= 5x given
184= 2(4x+2) + 2(5x) substitution
184= 8x+4+ 10x distributive property
184= 18x+4 combine like terms
184 -4 =18x +4 -4 subtract 4 from both sides to get 18x alone
180=18x
180/18= 18x/18 divide both sides by 18 to get x alone
10= x
x=10
Side PS= 5x since it is parallel to RQ which is 5x
5(x)=5(10)=50
Related Questions
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer. Bus 14, with a median of 14 Bus 18, with a mean of 12 Bus 14, with a mean of 14 Bus 18, with a median of 12
Answers
Based on both the median and mean values, it appears that Bus 14 typically has a faster travel time compared to Bus 18.
What is the median and mean?
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.
Here,
Cοmparing the medians, we can see that Bus 14 has a higher median οf 14, while Bus 18 has a lower median οf 12. This suggests that Bus 14 may have a faster travel time οn average.
Hοwever, we alsο need tο cοnsider the means. Cοmparing the means, we can see that Bus 14 has a higher mean οf 14, while Bus 18 has a lower mean οf 12. This further supports the idea that Bus 14 may have a faster travel time οn average.
Hence, based on both the median and mean values, it appears that Bus 14 typically has a faster travel time compared to Bus 18.
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What is the slope of the line with the equation y = negative 2 x minus 1? a. -2 c. 2 b. -1 d. 1 Please select the best answer from the choices provided
Answers
The BEST answer from the choices provided is Option (A) -2.
Claudia Pragram Technologies, Inc., has narrowed its choice of outsourcing provider to two firms located in different countries. Pragram wants to decide which one of the two countries is the better choice, based on risk-avoidance criteria. She has polled her executives and established four criteria. The resulting ratings for the two countries are presented in the table below, where 1 is a lower risk and 3 is a higher risk. SELECTION CRITERION ENGLAND CANADA Price of service from outsourcer 2 3 Nearness of facilities to client 3 1 Level of technology 1 3 History of successful outsourcing 1 2 The executives have determined four criteria weightings: Price, with a weight of 0.1; Nearness, with 0.6; Technology, with 0.2; and History, with 0.1. a) Using the factor-rating method, which country would you select? b) Double each of the weights used in part (a) (to 0.2, 1.2, 0.4, and 0.2, respectively). What effect does this have on your answer? Why?
Answers
England receives a total weighted score of [tex]1.9[/tex] , while Canada receives a score of [tex]1.6[/tex].
What is an illustration of outsourcing?Instead of hiring an own accountant, a small business may choose to contract bookkeeping responsibilities to an accounting company in to cut expenses. Some companies find it advantageous to outsource HR department duties including payroll and medical coverage.
What justifies outsourcing?Outsourcing has several benefits, including better systems and service quality, access to the world's best workers, improved scheduling, avoiding personnel concerns, and many more.
a) Using the factor-rating method, we can calculate the total weighted score for each country as follows:
For England:
Total score [tex]= (2 * 0.1) + (3 * 0.6) + (1 * 0.2) + (1 * 0.1) = 1.9[/tex]
For Canada:
Total score [tex]= (3 * 0.1) + (1 * 0.6) + (3 * 0.2) + (2 * 0.1) = 1.6[/tex]
Therefore, based on the risk-avoidance criteria and weightings established by the executives, we would select Canada as the better choice.
b) If we double each of the weights used in part (a), the total weighted score for each country changes as follows:
For England:
Total score [tex]= (2 * 0.2) + (3 * 1.2) + (1 * 0.4) + (1 * 0.2) = 4.0[/tex]
For Canada:
Total score [tex]= (3 * 0.2) + (1 * 1.2) + (3 * 0.4) + (2 * 0.2) = 2.2[/tex]
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Do the cylinders shown have equivalent volumes? Explain.
Answers
The two cylinders have the exact same volume given by:
V = pi*r²*h
Do the cylinders shown have equivalent volumes?The volume of a cylinder of radius r and height h is given by:
V = pi*r²*h
Where pi = 3.14
While the volume for a slanted cylinder, like the one in the image, is computed in the same way, as long as the height h is measured with a line normal from the bases (like in the image).
Now, notice that the first cylinder has a diameter of 2r and height h, so its radius is 2r/2 = r, and the volume is:
v = 3.14*r²*h
The second cylinder has a radius r and a height h, so its volume is
v = 3.14*r²*h
So yea, both cylinders have the same volume.
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For Sequence A, describe (in words) a way to produce each new term from the previous term. Write a definition for the nth term of Sequence B. If these sequences continue, which will be greater, A(9) or B(9)? Explain or show how you know.
Answers
Answer:
Sequence A is defined by subtracting 6 from the previous term and taking the absolute value, while Sequence B is the sum of the first n odd integers. B(9) > A(9).
For Sequence A, The first term is 19.To produce each new term from the previous term, subtract 6 from the previous term, then take the absolute value of the result. That is, if the previous term is x, then the next term is |x - 6|.
The nth term of Sequence B is defined as the sum of the first n positive odd integers. That is, B(n) = 1 + 3 + 5 + ... + (2n - 1) = n².To find A(9) and B(9), we can apply the rules we have for each sequence:
A(0) = 19
A(1) = |19 - 6| = 13
A(2) = |13 - 6| = 7
A(3) = |7 - 6| = 1
A(4) = |1 - 6| = 5
A(5) = |5 - 6| = 1
A(6) = |1 - 6| = 5
A(7) = |5 - 6| = 1
A(8) = |1 - 6| = 5
A(9) = |5 - 6| = 1
B(0) = 0 (the sum of the first 0 odd integers)
B(1) = 1
B(2) = 1 + 3 = 4
B(3) = 1 + 3 + 5 = 9
B(4) = 1 + 3 + 5 + 7 = 16
B(5) = 1 + 3 + 5 + 7 + 9 = 25
B(6) = 1 + 3 + 5 + 7 + 9 + 11 = 36
B(7) = 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
B(8) = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64
B(9) = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
Therefore, we have A(9) = 1 and B(9) = 81. Since 81 is greater than 1, we know that B(9) is greater than A(9).Need help with HW question 4
Answers
The eigen values of the first matrix is λ=4, λ=0 and λ=-3. The eigenvalues of the second matrix is 0 and 6.
What is an eigenvalue and eigenvector?If there is a scalar such that Ax = x, then a non-zero vector x is an eigenvector of A given a square matrix A. The scalar eigenvalue of the eigenvector x is known as the scalar.
To put it another way, when an eigenvector x is added to a matrix A, the outcome is a scalar multiple of x, where the scalar is the eigenvalue.
Many applications of linear algebra depend on eigenvectors and eigenvalues, such as the solution of differential equation systems, identifying the major variables in a dataset, and assessing the stability of dynamic systems.
The eigenvalues of the matrix can be found using the equation:
det(A - λI) = 0
Substituting the values we have:
[tex]\left[\begin{array}{ccc}4&2&0\\0&0&0\\1&0&-3\end{array}\right] - \lambda \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc} 4 - \lambda &0&0\\0&- \lambda & 0\\1 &0 & -3 - \lambda\end{array}\right][/tex]
Now determine the det of the matrix:
(4 - λ) (-3λ + λ² ) - 0 + 0 = (4 - λ)(λ)(-3 + λ)
Thus the eigen values are:
λ= 4, λ = 0, and λ = 3.
For the second matrix we have:
Given that B has identical rows throughout, B has a rank of 1, and B's null space has a dimension of 2. With two eigenvalues equal to zero and one eigenvalue equal to the trace of B, which is 6, B has two eigenvalues equal to zero.
Hence, the eigenvalues of B are 0 and 6.
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Question The perimeter of the base of a right square pyramid is 24 cm. The height of the pyramid is 6 cm. What is the volume of the pyramid?
Answers
Answer:1152
Step-by-step explanation:monkey
Last year, an investor purchased 120 shares of stock A at $90 per share and 35 shares of stock B at $145 per share. What is the difference in overall loss or gain between selling at the current day's high price or low price?
Answers
Therefore, the overall difference in loss or gain between selling at the current day's high price or low price would be $3460.
What is expression?An expression is a mathematical or logical statement that represents a value or a result. It can consist of numbers, variables, operators, and/or functions that are combined in a specific way to form a valid statement. Expressions can be simple, such as a single number or variable, or complex, involving multiple operations and functions. In mathematics, expressions can be used to represent mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and more.
Here,
To calculate the difference in overall loss or gain between selling at the current day's high price or low price for the stocks purchased, we need to know the current day's high and low prices for stock A and stock B. Once we have that information, we can use the following formula:
Difference = (Current day's high price - Purchase price) * Number of shares
Let's assume the current day's high price for stock A is $100 per share and the low price is $80 per share, while the high price for stock B is $150 per share and the low price is $130 per share.
For stock A:
Purchase price = $90 per share
Number of shares = 120 shares
Difference in overall loss or gain for stock A when selling at the high price:
Difference = ($100 - $90) * 120
= $1200
Difference in overall loss or gain for stock A when selling at the low price:
Difference = ($80 - $90) * 120
= -$1080
For stock B:
Purchase price = $145 per share
Number of shares = 35 shares
Difference in overall loss or gain for stock B when selling at the high price:
Difference = ($150 - $145) * 35
= $175
Difference in overall loss or gain for stock B when selling at the low price:
Difference = ($130 - $145) * 35
= -$525
So, the overall difference in loss or gain between selling at the current day's high price or low price would be the sum of the differences for stock A and stock B:
Overall difference in loss or gain = (Difference for stock A when selling at the high price + Difference for stock B when selling at the high price) - (Difference for stock A when selling at the low price + Difference for stock B when selling at the low price)
Overall difference in loss or gain = ($1200 + $175) - (-$1080 + -$525)
= $1855 + $1605
= $3460
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Cole, a caterer, is investing some money in equipment and employees to help grow his business. Recently he spent $100 on equipment and hired a server who makes $16 per hour. Cole is hoping to make up these expense at the next job that is scheduled, which pays a base of $50 in addition to $18 per hour that the server works. In theory, this event could pay enough to cancel out Cole's expenditures. How much would the job pay?
Answers
16x
In addition to the server's cost, Cole also spent $100 on equipment. So the total amount he needs to make up at the next job is:
16x + 100
Now we need to find out how much the next job will pay. We know that it pays a base of $50 plus $18 per hour that the server works. If the server works for "x" hours, the total amount the job will pay is:
50 + 18x
To break even, the amount Cole makes from the job must be equal to the amount he spent on equipment and the server. So we can set up an equation:
16x + 100 = 50 + 18x
Simplifying and solving for "x", we get:
2x = 50 - 100
2x = -50
x = -25
This doesn't make sense, since you can't have negative hours. It means that the job wouldn't pay enough to cover Cole's expenses. So there's no way for Cole to break even on this job, regardless of how many hours the server works.
Factor the following polynomials by finding a GCF.
2.) x^2 + x
Answers
Answer: Factors of a polynomial is x(x+1)
Step-by-step explanation: To find the GCF, we first seek the greatest common divisor of these two terms.
Taking common x from (x^2+x).
x(x+1)
carlo is 175 cm tall while his friend reggie is 1680mm tall. after three years carlo grew by 40mm and reggie grew by 7cm. which of the two is taller after a year? how tall in centimeters
Answers
After three years, Carlo is taller than Reggie. Carlo is 179 cm tall and Reggie is 175 cm tall.
What is metric system?A method for measuring temperature, length, volume, weight, and distance is known as the metric system. It is founded on three fundamental units that allow us to measure almost anything in the universe.
M- meter, used to measure the lengthKg- kilogram, used to measure the massS- second, used to measure timeTo compare the heights of Carlo and Reggie, we need to convert their heights to the same unit. We can convert Reggie's height from millimeters to centimeters by dividing by 10:
Reggie's height = 1680 mm ÷ 10 = 168 cm
Now we can compare their heights before and after three years:
Carlo before: 175 cmReggie before: 168 cmAfter three years:
Carlo after: 175 cm + 4 cm = 179 cm (since 40 mm = 4 cm)Reggie after: 168 cm + 7 cm = 175 cmTherefore, after three years, Carlo is taller than Reggie. Carlo is 179 cm tall and Reggie is 175 cm tall.
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Our class is the best of all of the MA 110 sections, so we average an 80 on our tests. Assuming a standard deviation of 6:
What is the z-score of a student who scores 97?
Is this student in the top 1% of performers? Explain how you arrived at your answer here.
Show all work
Answers
The z-score of a student who scores 97 is 2.83. In this case, since the z-score is greater than 1.96, the student is in the top 1% of performers.
What is z-score?It is used to indicate how many standard deviations a certain value is from the mean. It is calculated by subtracting the mean from the observed value and then dividing the result by the standard deviation.
This is calculated by subtracting the mean (80) from the student’s score (97) and dividing the result by the standard deviation (6).
97- 80/6
= 2.83
The z-score of 2.83 indicates that the student is in the top 1% of performers. This is because the z-score of 2.83 is greater than the z-score of 1.96, which is the z-score that is associated with the 1% percentile.
A z-score of 1.96 means that it is higher than 1% of the scores.
In this case, since the z-score is greater than 1.96, the student is in the top 1% of performers.
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Write down four decimal numbers between 1 and 1,2
Answers
Step-by-step explanation:
(1; 1,2)
Write any 4 decimal numbers that belong to this interval, for example:
1; 1,04; 1,08; 1,12; 1,16; 1,2
It takes Claudia 43 minutes to get to work every morning. Claudia
spends 47% of the time stuck in traffic on the drive. How many
minutes does Claudia spend stuck in traffic?
Answers
70 adults with gum disease were asked the number of
times per week they used to floss before their
diagnoses. The (incomplete) results are shown below:
# of
times
floss
per
week
0
1
2
3
4
5
6
7
4
11
15
11
6
7
(6 is blank)
6
Relative
Frequency
(4 is blank)
0.1571
0.1429
0.2143
0.1571
0.0857
0.1
0.1429
0.0857
Cumulative
Frequency
4
15
30
41
47
(5 is blank)
64
70
a. Complete the table (Use 4 decimal places when
applicable)
b. What is the cumulative relative frequency for
flossing 3 times per week?
%
Answers
The cumulative relative frequency for flossing 3 times per week is 58.57%.
How to solvea. Let's complete the table.
We can calculate the missing relative frequency for 0 times flossing per week by dividing the frequency (4) by the total number of people (70).
Relative Frequency for 0 times flossing = 4/70 = 0.0571 (rounded to 4 decimal places)
For 6 times flossing per week, the frequency is missing.
We can calculate it by summing up the frequencies for all other days and subtracting that from the total number of people.
Missing frequency for 6 times flossing = 70 - (4 + 11 + 15 + 11 + 6 + 7 + 6) = 70 - 60 = 10
Now, let's calculate the cumulative frequency for 5 times flossing per week.
Cumulative Frequency for 5 times flossing = Cumulative Frequency for 4 times flossing + Frequency for 5 times flossing = 47 + 7 = 54
The completed table looks like this:
of times floss per week | Frequency | Relative Frequency | Cumulative Frequency
0 | 4 | 0.0571 | 4
1 | 11 | 0.1571 | 15
2 | 15 | 0.2143 | 30
3 | 11 | 0.1571 | 41
4 | 6 | 0.0857 | 47
5 | 7 | 0.1 | 54
6 | 10 | 0.1429 | 64
7 | 6 | 0.0857 | 70
b. The cumulative relative frequency for flossing 3 times per week is the cumulative frequency for 3 times flossing divided by the total number of people (70).
Cumulative Relative Frequency for 3 times flossing = Cumulative Frequency for 3 times flossing / Total number of people = 41 / 70 = 0.5857 (rounded to 4 decimal places)
The cumulative relative frequency for flossing 3 times per week is 58.57%.
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In a survey about a change in public policy, 100 people were asked if they favor the change, oppose the change, or have no opinion about the change. Of the 100 people surveyed, 50 are male and 37 oppose the change in policy. Of the 37 who oppose the change, 25 are female. What is the probability that a randomly selected respondent to the survey is a man or opposes the change in policy? Express your answer as a percent
Answers
Answer: 75%
Step-by-step explanation:
factor the following polynomials by finding a GCF.
1.) 28c - 12
Answers
First, we can factor out a 4 from both terms, since 4 is a common factor of 28 and 12:
28c - 12 = 4(7c - 3)
Therefore, the GCF of 28c and 12 is 4, and we can write the polynomial as the product of 4 and the expression (7c - 3).
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answers to three decimal places, for example: 0.123]
Answers
The prοbabiIity οf seIecting 3 peanut M&M's at randοm, and having aII 3 be a different cοIοr, is P(aII 3 are different) = 1 * 5÷6 * 2÷3 = 0.556
What is PrοbabiIity ?The study οf randοm events οr οccurrences is the fοcus οf the mathematical field οf prοbability. It is a measurement οf the likelihοοd that an event will οccur, expressed as a number between 0 and 1, where 0 denοtes an imprοbable event and 1 denοtes a specific event.
Based οn the infοrmatiοn prοvided, we are given the fοIIοwing prοbabiIities fοr the different cοIοrs οf peanut M&M's:
P (brοwn) = 0.12
P (yeIIοw) = 0.15
P (red) = 0.12
P (bIue) = 0.23
P (οrange) = 0.23
P (green) = 0.15
We can use this infοrmatiοn tο answer variοus prοbabiIity questiοns. Fοr exampIe:
What is the prοbabiIity οf selecting a bIue οr an οrange peanut M&M?
P (bIue οr οrange) = P(bIue) + P(οrange) = 0.23 + 0.23 = 0.46
Therefοre, the prοbabiIity οf selecting a bIue οr an οrange peanut M&M is 0.46 οr apprοximateIy 0.460.
What is the prοbabiIity οf nοt selecting a green peanut M&M?
P(nοt green) = 1 - P(green) = 1 - 0.15 = 0.85
Therefοre, the prοbabiIity οf nοt selecting a green peanut M&M is 0.85 οr apprοximateIy 0.850.
If yοu seIect 3 peanut M&M's at randοm, what is the prοbabiIity that aII 3 are a different cοIοr?
The prοbabiIity οf the first M&M being any cοIοr is 1, since we have nοt seIected any M&M's yet. The prοbabiIity οf the secοnd M&M being a different cοIοr than the first is:
P(secοnd is different) = 1 - P(secοnd is same)
P(secοnd is different) = 1 - (1÷6) = ÷/6
(The prοbabiIity οf the secοnd M&M being the same cοIοr as the first is 1/6, since there are 6 cοIοrs and οnIy οne οf them is the same as the first cοIοr.)
SimiIarIy, the prοbabiIity οf the third M&M being a different cοIοr than the first twο is:
P(third is different) = 1 - P(third is same as first οr secοnd)
P(third is different) = 1 - (2÷6) = 2÷3
(The prοbabiIity οf the third M&M being the same cοIοr as the first οr secοnd is 2/6, since there are twο cοIοrs that have already been seIected.)
Therefοre, the prοbabiIity οf seIecting 3 peanut M&M's at randοm, and having aII 3 be a different cοIοr, is:
P(aII 3 are different) = 1 * 5÷6 * 2÷3 = 0.556
Therefοre, the prοbabiIity οf selecting 3 peanut M&M's at randοm, and having aII 3 be a different cοIοr, is apprοximateIy 0.556.
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You're studying different function tools and begin working with this function: y = -200 - 6(x) Use the equation to answer the question. y = -200 - 6(x) What is the y-value when x equals -12? y = -200 - 6(x) Enter the correct answer. DONE 00
Answers
Answer:
Y value is -128
Step-by-step explanation:
To find the y-value when x = -12, sub -12 for x in the equation.
y = -200 - 6(x)
y = -200 - 6(-12)
y = -200 + 72
y= -128
A souvenir shop sells t-shirts. The shop determines the price of each shirt by adding $3.75 to the price that it pays for the item. Then, that amount is doubled.
Before tax is added to the purchase, how much will a customer pay for a t-shirt that costs the souvenir shop $16.88?
Responses
A $20.63
B $36.95
C $45.35
D $41.26
The souvenir store pays $12.99 for a t-shirt. The store uses its usual price markup and adds $1.34 for sales tax., Which choice is the total amount a customer pays for the t-shirt?
Responses
A $34.82
B $23.71
C $28.40
D $14.33
Answers
First question:
The cost of the t-shirt for the souvenir shop is $16.88. The shop adds $3.75 to the cost and then doubles the amount to get the price that the customer pays. So, the price that the customer pays before tax is:
2 x (16.88 + 3.75) = 2 x 20.63 = 41.26
Therefore, the answer is (D) 41.26.
Second question:
The cost of the t-shirt for the souvenir shop is $12.99. The shop adds $3.75 to the cost to get the price of the t-shirt. Then, the shop adds sales tax of $1.34 to the price to get the total amount that the customer pays. So, the total amount that the customer pays is:
12.99 + 3.75 + 1.34 = 18.08
Therefore, the answer is (C) 28.40.
36 Grâce à sa carte "Collège Jeunes", Maël bénéfice d'une réduction de 35% sur une place à 28€ pour assister à un spectacle de patinage. Combien va-t-il payer pour assister au spectacle de patinage ?
Answers
Y varies inversely as x and y =38 when x =26 find y when x =24
Answers
In summary in axis when x = 24, y = 41.1667.
Why is it?
If y varies inversely as x, then y = k/x for some constant k. To find k, we can use the initial values given:
y = k/x
38 = k/26
k = 38×26
k = 988
Now we can use k to find y when x = 24:
y = k/x
y = 988/24
y = 41.1667 (rounded to four decimal places)
Therefore, when x = 24, y = 41.1667.
In mathematics, an axis is a straight line that defines a reference direction for a coordinate system. It is used to locate or plot points, and describe geometric shapes in a plane or in space. In a two-dimensional coordinate system, there are two axes: the x-axis, which is horizontal, and the y-axis, which is vertical.
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What is the mean of the following set? 2/3, 1/6, 1/3, 2/3, 7/9, 1/3
Answers
The mean of the set is 1/2.
What is mean?The mean is a statistical measure that represents the average value of a set of numbers. To calculate the mean, you add up all the values in the set and then divide by the total number of values in the set.
To find the mean of a set of numbers, you add up all the numbers in the set and then divide the result by the total number of numbers in the set.
In this case, the set has six numbers:
2/3, 1/6, 1/3, 2/3, 7/9, 1/3
Adding them up, we get:
(2/3) + (1/6) + (1/3) + (2/3) + (7/9) + (1/3) = 3
So the sum of the numbers in the set is 3.
To find the mean, we divide this sum by the total number of numbers in the set, which is 6:
3/6 = 1/2
Therefore, the mean of the set is 1/2.
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Please help me if you can calculate it
I can only calculate Q1 a b c
Question 1
A taxi company reveals that the daily earnings of taxi drivers in the company follows a normal distribution
with a mean of $1062.5 and standard deviation of $350.
(a) Find the probability that a taxi driver earns less than $1500 in a day.
(b) 93.7% drivers earn more than $k a day. Find the value of k.
John is a taxi driver in this company. Besides driving taxi, he has another part time online job. The daily
earnings from the part time online job follow a normal distribution with a mean of $235.5 and standard
deviation of $84.5. The daily earnings from driving taxi and part time online job are assumed to be
independent.
(c) Use T to denote the total daily earning for a day he drives taxi and works on the part time online job.
Find the mean and standard deviation of T. (Round off the mean and standard deviation to the nearest
integer.)
(d) Hence, by using $(L1, L2) to denote the middle 96.6% of the total daily earning T, find the values of L1
and L2. (Round off L1 and L2 to the nearest integer.)
Question 2
Tom is a supermarket manager. He reviewed transaction time when a customer paid by credit card. The
transaction time is normally distribution with mean of 20 seconds and standard deviation of 5 seconds.
(a) For a group of 6 customers, find the probability that 5 customers can finish the transaction within 20
seconds. (Assume that the transaction times of customers are independent.)
After discussion with the network provider, he will upgrade the network so that it is promised that each
transaction time can be reduced by 15%.
(b) Use Y to denote the transaction time after network upgrade. Find the mean and standard deviation of Y.
(c) Calculate the 97th percentile of Y. (i.e. find the value of t such that P(Y
(d) Compare with the transaction time before upgrade, is it (I) a higher proportion, (II) a lower proportion,
or (III) the same proportion of all customers can finish the transaction within 20 seconds? (Just state
your answer, no calculation is needed.)
Answers
Question 1:
(a) To find the probability that a taxi driver earns less than $1500 in a day, we need to standardize the value using the given mean and standard deviation, and then find the corresponding probability from the standard normal distribution table:
z = (1500 - 1062.5) / 350 = 1.20
Using the standard normal distribution table, the probability of a standard normal random variable being less than 1.20 is approximately 0.8849. Therefore, the probability that a taxi driver earns less than $1500 in a day is approximately:
P(X < 1500) = P(Z < 1.20) = 0.8849
(b) We need to find the value of k such that 93.7% of the drivers earn more than $k a day. This means that the probability of a driver earning less than or equal to $k a day is 1 - 0.937 = 0.063. We can standardize k using the given mean and standard deviation, and then find the corresponding z-score from the standard normal distribution table:
z = (k - 1062.5) / 350
Using the standard normal distribution table, we find that the z-score corresponding to a probability of 0.063 is approximately -1.51. Therefore:
-1.51 = (k - 1062.5) / 350
k = -1.51 * 350 + 1062.5 = $499.25 (rounded to the nearest cent)
(c) The mean of the total daily earning is:
μT = μ1 + μ2 = 1062.5 + 235.5 = 1298
The variance of the total daily earning is the sum of the variances of the two earnings, since they are assumed to be independent:
σT² = σ1² + σ2² = 350² + 84.5² ≈ 128681
Therefore, the standard deviation of the total daily earning is:
σT ≈ √128681 ≈ 358.5
(rounded to the nearest integer)
(d) To find L1 and L2, we need to find the z-scores corresponding to the lower and upper 2.2% tails of the standard normal distribution:
z1 = -1.81
z2 = 1.81
Then we can use the formula for standardizing a normal random variable to find the corresponding values of T:
z1 = (L1 - μT) / σT
z2 = (L2 - μT) / σT
Solving for L1 and L2, we get:
L1 = μT + z1σT ≈ 1298 + (-1.81) * 358.5 ≈ $645
L2 = μT + z2σT ≈ 1298 + 1.81 * 358.5 ≈ $1951
(rounded to the nearest integer)
Question 2:
(a) We can model the transaction time of a single customer as a normal random variable with mean 20 and standard deviation 5. Then the total transaction time for 6 customers can be modeled as a normal random variable with mean 6 * 20 = 120 and standard deviation √(6 * 5²) = 15. To find the probability that 5 customers can finish the transaction within 20 seconds, we need to standardize the value using this mean and standard deviation, and then find the corresponding probability from the standard normal distribution table:
z = (5 * 20 - 120) / 15 = -0.53
does thes formula for surface area of a cylinder work for right cylinders and oblique cylinders true or false
Answers
The height h, on the other hand, denotes the slant height for oblique cylinders, which is the distance between the two circular bases on a straight line.
how can you describe cylinder ?Two identical parallel spherical bases and a curving surface connecting the bases make up the three-dimensional geometric object known as a cylinder. It can be compared to a prism with rounded bases.
A line connecting the centres of the circle bases is the axis of a cylinder. The possibility that the axis is straight to the bases determines whether a cylinder is right or oblique.
Diagonal cylinders have bases that aren't perpendicular to the axis while right cylinders have bases that are perpendicular to the axis.
given
Both right and oblique cylinders can be calculated using the surface area of a cylinder formula, A = 2r2 + 2rh.
The height h, on the other hand, denotes the slant height for oblique cylinders, which is the distance between the two circular bases on a straight line.
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In a brand recognition study, 897 consumers knew of Costco, and 10 did not. Use these results to estimate the probability that a randomly selected consumer will recognize Costco.
Answers
The estimated probability that a randomly selected consumer will recognize Costco is 0.988 or approximately 98.8%.
What is Probability ?
Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
In this brand recognition study, we are given that 897 consumers knew of Costco and 10 did not.
The probability of a randomly selected consumer recognizing Costco can be estimated as the number of consumers who knew of Costco divided by the total number of consumers in the study:
P(recognizing Costco) = number of consumers who knew of Costco : total number of consumers in the study
P(recognizing Costco) = 897 : (897 + 10)
P(recognizing Costco) = 897 : 907
P(recognizing Costco) = 0.988 or approximately 98.8%
Therefore, the estimated probability that a randomly selected consumer will recognize Costco is 0.988 or approximately 98.8%.
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You spin the spinner and flip a coin. Find the probability of the compound event.
The probability of spinning an even number and flipping heads is what?
Answers
1/6
Step-by-step explanation:
the reason is because of the tail and the spinner
Pls help me
How long is the side CD? (Hint: opposite sides are equal. Put the expressions equal to each other and solve for x. Then, plug back into the expression for CD to find CD).
Answers
Answer:
the best answer would be 27
Step-by-step explanation:
Boom
D
Are the two triangles similar?
28°
R
110°
Yes
No
E
V
28°
T
42°
A
Answers
Answer:
Yes
Step-by-step explanation:
Angle RDE =angle TVA=28°
REV=TAV=42°
DRE=VTA=110°
THEREFORE TRIANGLE DER IS SIMILAR TO TRIANGLE ATV
What is the diameter of a hemisphere with a volume of
62617cm[tex]What is the diameter of a hemisphere with a volume of 62617cm3, to the nearest tenth of a centimeter[/tex]
Answers
this is answer 44rrrrrrrrrrrrrrrrrrrrfrrrrrrrrrrr